Teach | Level 1 Module 5 | Eureka Math² Florida B.E.S.T. Edition

What does this painting have to do with math?

American realist Edward Hopper painted ordinary people and places in ways that made viewers examine them more deeply. In this painting, we are in a restaurant, where a cashier and server are busily at work. What can you count here? If the server gave two of the yellow fruits to the guests at the table, how many would be left in the row? We will learn all about addition and subtraction within 10s in Units of Ten.

On the cover

Tables for Ladies, 1930

Edward Hopper, American, 1882–1967

Oil on canvas

The Metropolitan Museum of Art, New York, NY, USA

Edward Hopper (1882–1967), Tables for Ladies, 1930. Oil on canvas, H. 48 1/4, W. 60 1/4 in (122.6 x 153 cm). George A. Hearn Fund, 1931 (31.62). The Metropolitan Museum of Art. © 2020 Heirs of Josephine N. Hopper/Licensed by Artists Rights Society (ARS), NY. Photo credit: Image copyright © The Metropolitan Museum of Art. Image source: Art Resource, NY

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ISBN 978-1-63642-505-4

Module

1 2 3

Counting, Comparison, and Addition

4 5 6

Addition and Subtraction Relationships

Properties of Operations to Make Easier Problems

Comparison and Composition of Length Measurements

Place Value Concepts to Compare, Add, and Subtract

Advancing Place Value, Addition and Subtraction, and Measurement

Before This Module

Overview

Kindergarten Module 6

Students begin to develop place value understanding when they come to see that teen numbers are composed of 10 ones and some more ones. They represent the number 13, for example, with verbal expressions: 10 ones and 3 ones, 1 ten 3 ones, 10 and 3, or ten 3. Students also count to 100 by tens and by ones.

Grade

1 Module 3

Students rename groups of ten ones as units of ten. They come to see that all two-digit numbers are composed of tens and ones. They use this understanding as they begin subtracting a one-digit number from a two-digit teen number in topic E.

Grade 1 Module

4

Students use 10-centimeter sticks (tens) and centimeter cubes (ones) to measure lengths. They state total lengths in terms of tens and ones. Students also work with numbers in word form to 20.

Place Value Concepts to Compare, Add, and Subtract

Topic A

Grouping Units in Tens and Ones

Topic A builds on work with tens and ones from modules 3 and 4. Lessons develop the idea that smaller units, such as ones, compose larger units, such as tens. The following place value models, which increase in complexity, help students to internalize the equivalence of 10 ones and 1 ten and to understand that two-digit numbers represent amounts of tens and ones.

Groupable Pre-grouped Nonproportional

Physically group 10 ones to compose a new unit of ten. The size of the new unit is proportionally larger than the base unit.

Tens are composed by trading 10 ones for a new item that represents 1 ten. The new item is proportionally larger than the base unit.

10 ones are traded for a new item that represents 1 ten. However, the new item is non-proportional. Visually, it is not 10 times larger than the base unit.

Students represent two-digit totals in different ways. For example, a total of 21 may be shown as 21 ones, 1 ten 11 ones, or 2 tens 1 one. Students see that the digits used to write a numeral, such as 2 and 1 in 21, show how many tens and ones there are when the number is expressed in its “most composed” form.

Topic B

Use Place Value to Compare

Students compare two-digit numbers by using the place value structure of tens and ones rather than by using size or length. They represent comparisons with number sentences that include the symbols >, =, or < and explain why the number sentences are true. Comparing numbers such as 39 and 93 helps students focus on the value of each digit. They see that if two numbers have different digits in the tens place, then they can use those digits to compare them efficiently.

Topic C

Addition of One-Digit and Two-Digit Numbers

Students add a one-digit number to a two-digit number by using place value to make easier problems. They solve problems with the help of a variety of tools such as cubes, drawings, number bonds, and number paths, and they explain their thinking.

Students solve problems where the ones do not compose a new ten (e.g., 25 + 3 = 28) by decomposing the two-digit addend into tens and ones, combining the ones with the

one-digit addend, and then adding the tens. They also find the total when the ones do compose a ten (e.g., 25 + 5 = 30). Students decompose an addend to make the next ten, and then add the tens. Sometimes the ones compose a ten and some ones (e.g., 25 + 7 = 32).

Topic D

Addition and Subtraction of Tens

Students identify the number that is one more, one less, ten more, and ten less than a given two-digit number. As students identify the number that is 10 more and 10 less, they make connections to adding and subtracting tens. To add and subtract tens, students use the Stage 2 strategies of counting on and counting back with tens. They advance to using the Stage 3 strategy of representing an equation in unit form, or numeral word form, to find an easier one-digit fact they know. For example, rewriting 20 + 40 as 2 tens + 4 tens helps students see that they can use 2 + 4 to solve the problem. Similarly, rewriting 60 – 30 as 6 tens – 3 tens helps students see that they can use 6 – 3 to solve this problem. Then students add tens to a two-digit number by adding the tens first and recognizing that the ones-digit stays the same.

Topic E

Subtraction of One-Digit Numbers from Two-Digit Numbers

Students deepen their place value understanding as they explore how to make easier subtraction problems. Students use cubes and the number path as tools for subtraction as they take from a ten, count back to a ten, or count on to a ten. Students also explore decomposing a ten for more ones when needed. They self-select strategies and tools based on the numbers in a problem and what makes sense.

After This Module

Grade 1 Module 6 Part 2

Students count beyond 100 to 120 and begin to understand that 10 tens compose 100.

Students apply the same addition strategies they used in this module, but with addends where more than 1 or 2 new tens can be composed.

Grade 2 Module 1

Students extend their place value knowledge with larger numbers. Specifically, they learn that 10 tens make 1 hundred. They represent three-digit numbers in different ways by using place value understanding.

Grade 2 Module 2

Students continue to use place value to make easier problems when adding and subtracting within 1,000. Strategies include add or subtract like units, count on or count back with benchmark numbers, and compose or decompose units within 200. Students also extend place value thinking to make easier problems within 1,000.

Why Place Value Concepts to Compare, Add, and Subtract

How do students deepen and advance their understanding of the equal sign?

Students evaluate number sentences such as 90 – 40 = 20 + 30. They determine whether the number sentence is true or false by calculating the value of the expressions on either side of the equal sign. This provides practice with adding and subtracting tens while giving students opportunities to engage with uncommon and complex equation types.

Students also evaluate number sentences with equivalent expressions that represent different ways to make an easier problem. For example, the expression on either side of the equals sign in 10 + 10 + 2 + 6 = 12 + 10 + 6 shows one way to break up the addends in 12 + 16. Students find the expressions have the same value and conclude that the number sentence is true. This helps confirm that there are several valid ways to solve a problem.

Why is telling time included in a module on place value?

Module 5 centers on the idea that smaller units such as ones compose larger unit such as tens. Time also involves composing units. For example, minutes make up hours and half hours, and hours make up days. Work with units in various contexts (e.g., time, measurement, and shapes) develops reasoning that helps students understand numerical units such as ones, tens, and hundreds. Students revisit telling time to the half hour in module 6.

Achievement Descriptors: Overview

Place Value Concepts to Compare, Add, and Subtract

Achievement Descriptors (ADs) are standards-aligned descriptions that detail what students should know and be able to do based on the instruction. ADs are written by using portions of various standards to form a clear, concise description of the work covered in each module.

Each module has its own set of ADs, and the number of ADs varies by module. Taken together, the sets of module-level ADs describe what students should accomplish by the end of the year.

ADs and their proficiency indicators support teachers with interpreting student work on

• informal classroom observations (recording sheet provided in the module resources),

• data from other lesson-embedded formative assessments,

• Exit Tickets,

• Topic Tickets, and

• Module Assessments.

This module contains the nine ADs listed.

Read and write numbers to 100 as numerals and as expressions or equations using tens and ones. Read numbers to 100 in words.

Represent a set of up to 99 objects with a two-digit number by composing tens.

Represent two-digit numbers within 99 in multiple ways as tens and ones.

FL.1.Mod5.AD1

MA.1.NSO.1.2

FL.1.Mod5.AD2

MA.1.NSO.1.3

FL.1.Mod5.AD3

MA.1.NSO.1.3

FL.1.Mod5.AD4

Determine the values represented by the digits of a two-digit number.

FL.1.Mod5.AD5

Compare two-digit numbers by using the symbols >, =, and <.

FL.1.Mod5.AD6

Find 10 more and 10 less than a twodigit number.

MA.1.NSO.1.3

FL.1.Mod5.AD7

Add a two-digit number and a onedigit number that have a sum within 100 by using manipulatives, number lines, drawings, or models.

FL.1.Mod5.AD8

Subtract a one-digit number from a two-digit number by using manipulatives, number lines, drawings, or equations.

FL.1.Mod5.AD9

Tell time to the hour and half hour on analog and digital clocks.

The first page of each lesson identifies the ADs aligned with that lesson. Each AD may have up to three indicators, each aligned to a proficiency category (i.e., Partially Proficient, Proficient, Highly Proficient). While every AD has an indicator to describe Proficient performance, only select ADs have an indicator for Partially Proficient and/or Highly Proficient performance.

An example of one of these ADs, along with its proficiency indicators, is shown here for reference. The complete set of this module’s ADs with proficiency indicators can be found in the Achievement Descriptors: Proficiency Indicators resource.

MA.1.NSO.1.4

MA.1.NSO.2.3

MA.1.NSO.2.4

MA.1.NSO.2.5

MA.1.M.2.1

ADs have the following parts:

• AD Code: The code indicates the grade level and the module number and then lists the ADs in no particular order. For example, the first AD for grade 1 module 5 is coded as FL.1.Mod5.AD1.

• AD Language: The language is crafted from standards and concisely describes what will be assessed.

• AD Indicators: The indicators describe the precise expectations of the AD for the given proficiency category.

• Related Standard: This identifies the standard or parts of standards from the Florida Benchmarks for Excellent Student Thinking (B.E.S.T.) that the AD addresses.

FL.1.Mod5.AD3 Represent two-digit numbers within 99 in multiple ways as tens and ones.

RELATED B.E.S.T.

MA.1.NSO.1.3 Compose and decompose two-digit numbers in multiple ways using tens and ones. Demonstrate each composition or decomposition with objects, drawings and expressions or equations.

Partially Proficient Proficient

Represent two-digit numbers within 50 as tens and ones.

Show 45 using tens and ones. tens

Represent two-digit numbers within 99 in multiple ways as tens and ones.

Show ways to make 71 using tens and ones.

Highly Proficient

Represent numbers 100–120 in multiple ways as tens and ones.

Show ways to make 114 using tens and ones.

Topic A Grouping Units in Tens and Ones

Topic A builds on work with tens and ones that students completed in modules 3 and 4. At first students reason about units in the context of time. They learn through experience that smaller units can compose larger units. For example, they discover that 1 hour is made of 60 minutes and 1 half hour is made of 30 minutes.

Lessons build on the idea that smaller units can be used to compose larger units by considering the place value units of tens and ones. Students work with sets of objects to compose groups of 10 and to represent the two-digit totals in different ways. For example, 26 ones can also be represented as 1 ten 16 ones or 2 tens 6 ones. Working with numbers that have more than 9 ones prepares students for adding and subtracting with larger numbers in later grades.

Students come to understand that the digits we use to write a number, such as the 2 and the 6 in 26, show how many tens and ones there are when the number is expressed in its “most composed” form. This leads to recognition that the value of digits can be determined based on their place in the number. The value of the digit 2 in 26 can be expressed as 2 tens or 20. The value of the digit 6 in 26 can be expressed as 6 ones or simply 6. Students compose (or decompose) a total such as 26 by place value units: 20 and 6 or 2 tens 6 ones. They read the number in standard form (26) and word form (twenty-six). While students are not formally introduced to the term expanded form until grade 2, they learn to write a two-digit number as an addition number sentence that shows the value of the tens and ones, such as 20 + 6 = 26. Using different representations of the same total invites students to consider equivalence and deepens their number sense.

Several place value models that increase in complexity help students internalize the basic understanding that 10 ones are equivalent to 1 ten.

50 pennies

50 ones

5 dimes

5 tens

Groupable Pregrouped

Students group 10 ones to compose a new unit of ten. They may put 10 bears into 1 cup, link 10 cubes into a stick, or circle 10 donuts to represent a box of 10. Students can see and manipulate the individual units within the new larger unit. The size of the new unit is proportionally larger than the base unit.

Students group 10 ones and trade them for a new item that represents 1 ten. For example, given 23 centimeter cubes, students trade 10 cubes for 1 ten-centimeter stick. The new item is proportionally larger than the base unit.

Nonproportional

Students trade 10 ones for a new item that represents 1 ten, but the ten looks different from the 10 ones. An example is trading 10 pennies for 1 dime. These models are nonproportional because the new unit, in this case a dime, is not visually 10 times larger than the base unit, or penny. Nonproportional models prepare students to work with place value disks in grades 2–5.

In this topic, students also add 10 and take 10 all at once from numbers. They add to and subtract from numbers in sequence: 54 + 10 = 64, 64 + 10 = 74, and so on. From this a pattern becomes visible: the digit in the tens place changes by 1, but the digit in the ones place remains the same.

Progression of Lessons

Lesson 1

Tell time to the hour and half hour by using digital and analog clocks. 4:30

Lesson 2

Count a collection and record the total in units of tens and ones.

Lesson 3

Recognize the place value of digits in a two-digit number.

The minute hand is pointing at the 6, and the hour hand is not at 5 yet, so it is 4:30.

0 5 3

3 0 5

After we composed all the tens, there were 5 tens and 3 ones. That makes 53. We can write 53 as a number sentence that shows the value of the tens and ones. 50 + 3 = 53. Fifty-three is how we write 53 in words.

We composed tens by making groups of 10. We had 5 groups of ten and 2 extras. That is 52 bears.

Lesson 4

Represent a number in multiple ways by trading 10 ones for a ten.

Lesson 5

Reason about equivalent representations of a number.

I can trade 10 pennies for a dime and use dimes and pennies to show different ways to make 30 cents.

I would rather have 30 loose crayons so I can see all the colors, but both pictures have the same number of crayons. 30 ones is 30 and 3 tens is 30.

When I add ten, the digit in the tens place is 1 more. When I subtract ten, the digit in the tens place is 1 less.

30 crayons 3 boxes of crayons

Tell time to the hour and half hour by using digital and analog clocks.

Lesson at a Glance

Students analyze an analog clock and a digital clock that show the same time. They learn how each clock represents the hour and minutes and practice reading the time to the hour and half hour on both kinds of clocks.

Key Question

• What time is it? How do you know?

Achievement Descriptor

FL.1.Mod5.AD9 Tell time to the hour and half hour on analog and digital clocks. (MA.1.M.2.1)

Agenda Materials

Fluency 10 min

Launch 5 min

Learn 35 min

• Hours and Minutes

• Tell Time to the Hour and Half Hour

• Match: Time

• Problem Set

Land 10 min

Teacher

• Computer with internet access*

• Projection device*

• Teach book*

• 100-bead rekenrek

Students

• Dry-erase marker*

• Pencil*

• Personal whiteboard*

• Personal whiteboard eraser*

• Learn book*

• Match: Time cards removable (1 per student pair, in the student book)

* These materials are only listed in lesson 1. Ready these materials for every lesson in this module.

Lesson Preparation

• The Match: Time cards removables must be torn out of student books. Cut out the cards on the removable to make a set. Each student pair needs one set of cards.

• Prepare the digital interactive clock for the lesson.

Fluency

Whiteboard Exchange: 4 as an Addend

Students find a total and use the commutative property to write a related addition sentence to build procedural reliability for addition within 20.

After each prompt for a written response, give students time to work. When most students are ready, signal for them to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

Display 1 + 4 = .

Write the equation, and then find the total.

Display the completed addition sentence: 1 + 4 = 5.

Change the order of the addends to write a related addition sentence. (Point to the addends.)

Display the related addition sentence: 4 + 1 = 5.

Repeat the process with the following sequence:

5-Groups: 20 and Some More

Students recognize a group of dots and say the number two ways to prepare for identifying a given set with all the tens composed.

Display the 5-group cards that show 20.

How many dots? Raise your hand when you know.

Wait until most students raise their hands, and then signal for students to respond.

We can say 20 is 2 tens. On my signal, say it with me. Ready?

20 is 2 tens.

Repeat the process with the following sequence:

As students are ready, challenge them to recognize the groups of dots more quickly by showing each 5-group set for a shorter time.

Counting on the Rekenrek by Tens and Ones

Materials—T: 100-bead rekenrek

Students count to a specified number the Say Ten way, then in standard form to prepare for recording the units of tens and ones in a given set in lesson 2.

Show students the rekenrek. Start with all the beads to the right side.

Let’s count to 41 the Say Ten way.

Say how many beads there are as I slide them over.

Slide over 10 beads in each row all at once as students count to 4 ten.

1 ten, 2 ten, 3 ten, 4 ten

Slide over 1 more bead as students count to 4 ten 1.

4 ten 1

Slide all the beads back to the right side.

Let’s count to 41 the regular way.

Say how many beads there are as I slide them over.

Repeat the process as students count by tens and ones to 41. 10, 20, 30, 40, 41

Repeat the process as students count by tens and ones the Say Ten way and in standard form to the following numbers:

Language Support

Consider using strategic, flexible grouping throughout the module.

• Pair students who have different levels of mathematical proficiency.

• Pair students who have different levels of English language proficiency.

• Join pairs of students to form small groups of four.

As applicable, complement any of these groupings by pairing students who speak the same native language.

Students listen to sounds of different durations and learn that 60 minutes make an hour.

Tell students to prepare to listen carefully. Play the first sound, which lasts for 1 second.

What do you notice?

It is very short.

Play the next sound, which lasts for 10 seconds.

What do you notice this time?

It was longer this time, so I can tell it is music.

The first sound is a short part. (Show your palms facing each other, close together.) The sound we just heard is longer. (Increase the distance between your palms.)

Play the third sound, which is 60 seconds long.

Is this sound shorter (show palms close together) or longer (expand the distance between palms) than the first one?

Longer

That last sound was a minute long!

Help students recall their learning about time by asking the following questions.

Which is longer, a minute or an hour? How do you know?

An hour is longer. A minute goes by fast, but an hour takes more time.

You are right. An hour is longer because 60 minutes go together to make an hour.

Transition to the next segment by framing the work.

Today, we will look at a clock and see how minutes make an hour.

Learn Hours and Minutes

Students count minutes to see how analog and digital clocks represent the time. Show students 1 o’clock on the analog clock only.

(Point to the red hand.) The short hand is the hour hand. It tells the hour.

(Point to the blue hand.) The long hand is the minute hand. It tells the minutes.

Promoting the Mathematical Thinking and Reasoning Standards

Students complete tasks with mathematical fluency (MTR.3) when they use minutes and hours appropriately to describe lengths of time. Maintaining accuracy through the appropriate use of units begins with understanding that a minute is a short length of time and an hour is a longer length of time. It extends to discussing how larger units are made out of smaller ones.

Reasoning with units in different contexts (e.g., time, measurement, or shapes) helps students to work with numerical units (tens, hundreds, etc.) later on.

Turn on the digital clock as well.

This is a different type of clock. It shows the time using only numbers. The numbers to the left of the dots tell the hour. (Point to the 1 on the digital clock.) The numbers to the right of the dots tell the number of minutes. (Point to the 00 on the digital clock.)

Tell students that both clocks show 1 hour and 0 minutes. Help them read the time on each clock as 1 o’clock. Tell students that as time passes, the hands on the first clock (the analog clock) move, but the numbers on the second clock (the digital clock) just change.

Watch and see what happens on each clock as time passes. Let’s count minutes.

Slowly move the minute hand from 1:01 to 1:30. Have the class chorally count the minutes.

1 minute, 2 minutes, … , 29 minutes, 30 minutes

Point to the analog clock that shows 1:30.

What did the hands do on this clock as we counted?

The minute hand moved a little bit at a time. It went from the top of the clock to the bottom of it.

The hour hand only moved a little. Now it’s past the 1, but not to the 2.

Reset the clock to 1 o’clock.

As time passes, the minute hand moves forward one tick mark at a time. Each tick mark represents 1 minute. Watch the blue minute hand.

Slowly move the minute hand from 1:00 to 1:05.

The hour hand moves too. As minutes go by, the hour hand moves slowly from one number on the clock to the next. Watch the red hour hand.

Slowly move the minute hand to 1:30.

Now the hour hand is between two numbers, or hours. The minute hand points straight down to the 6. When the hands are in this position, we say the first number for the hour and read the time as one thirty.

Point to the digital clock that also shows 1:30.

What did the numbers on this clock do as we counted?

They changed. The minutes went from 00 up to 30. They went up by 1 each time.

What time does the clock show?

1:30

Both clocks started at 1 o’clock. We counted 30 minutes from 1 o’clock to 1:30. Now the clocks show 1:30.

Let’s keep counting until the minute hand moves all the way around the clock. (Point to the picture of the analog clock.)

Slowly move the minute hand from 1:30 to 2 o’clock. Have the class chorally count the minutes.

31 minutes, 32 minutes, … , 59 minutes, 60 minutes

What time do the clocks show now? How do you know?

2 o’clock

The hour hand is pointing at the 2 and the minute hand is on the 12. There is a 2 and two zeros on the clock with only numbers.

Confirm that both clocks show 2 o’clock.

(Point to the digital clock.) On this clock, after the minutes show 59, they start over at 0. It shows 1:59 and then 2:00. This happens because there are 60 minutes in 1 hour. How many minutes are in an hour?

60 minutes

(Point to the analog clock.) On the other clock, when the minute hand goes all the way around the clock, the hour hand arrives at the next number, or hour. Now the hour hand is pointing to 2.

Tell Time to the Hour and Half Hour

Students practice telling time to the hour and half hour by using an analog clock.

Have students practice telling time to the hour and half hour. Consider having students stand.

Use only the analog clock set to 2 o’clock.

What time is it?

2 o’clock

Move the minute hand to show 2:30. Provide a moment of wait time.

What time is it?

2:30

Continue to show various times to the hour and half hour (3:00 and 3:30, 11:00 and 11:30, etc.) until students say the time to the half hour with confidence.

Match: Time

Materials—S: Match: Time cards

Students match cards that use different formats of time to show time to the hour and half hour.

Demonstrate and explain how to play Match: Time by using the following directions:

• Place all of the Match: Time cards faceup.

• One partner finds two cards that match because they show the same time.

• They tell their partner how they know the cards match.

• Partners take turns finding matches until all the matches have been found.

Differentiation: Support

If needed, provide additional support for students with telling time to the half hour.

• The hour hand is between 2 and 3. When the hour hand is between two hours, or numbers, we say the first hour. The hour hand is getting closer to the next hour, but it’s not there yet.

• When the minute hand points straight down at the 6, 30 minutes of the hour have passed.

• This clock shows 2:30. The hour hand is still in the two o’clock hour and 30 minutes have passed.

Circulate as students play and ask the following questions:

• (Point to a card.) Where do you see the hour? Where do you see the minutes?

• Show me a match. What is the time on both cards?

Problem Set

Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex.

Directions may be read aloud.

Land

Debrief 5 min

Objective: Tell time to the hour and half hour by using digital and analog clocks.

Show the analog clock set to 4:30.

What time is it? How do you know?

4:30

The hour hand is a little past 4 and the minute hand points to 6.

Show 4:30 with both clocks. Have students consider, discuss, and share the similarities and differences between the two clocks.

How are the clocks the same?

Both have numbers and tell the time.

Both tell you the time is 4:30.

Both clocks show 4 hours and 30 minutes.

UDL: Engagement

Foster collaboration and help students to engage successfully in the sorting game by assigning clear roles for each partner. Review the activity goal, directions, and group norms before groups begin.

Consider embedding any socio-emotional skills students are learning in other areas of their day, such as sharing, taking turns, and disagreeing respectfully, into the activity.

How are the clocks different?

One only has numbers. It does not have hands.

One has hour and minute hands.

For 30 minutes, one has the number 30. The other one shows 30 minutes at the 6.

These clocks show the time in different ways. They both make a new hour every 60 minutes.

Exit Ticket 5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Teacher Note

Distributed practice with telling time helps students master the skill. Each day, consider pausing periodically at the hour and half hour to ask: What time is it?

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

Count a collection and record the total in units of tens and ones.

Lesson at a Glance

Students analyze a counting collection organized into groups of tens and ones and discuss the values of the digits in the total. Partners organize, count, and record their own collections. The class discusses student work and considers how groups of 10 and extra ones combine to make a total.

The term digit is introduced in this lesson.

There is no Fluency component, Exit Ticket, or Problem Set in this lesson. This allows students to spend more time completing the counting collection activity. Use student recordings to analyze their work.

Key Question

• What do the digits in a number tell us?

Achievement Descriptors

FL.1.Mod5.AD2 Represent a set of up to 99 objects with a two-digit number by composing tens. (MA.1.NSO.1.3)

FL.1.Mod5.AD4 Determine the values represented by the digits of a two-digit number. (MA.1.NSO.1.3)

Agenda Materials

Launch 15 min

Learn 40 min

• Organize, Count, and Record

• Share, Compare, Connect

Land 5 min

Teacher

• Chart paper

• Hide Zero® cards, demonstration set Students

• Counting collection (1 per student pair)

• Work mat (1 per student pair)

• Organizing tools

• Hide Zero® cards (1 set per student pair)

Lesson Preparation

• Copy or print the counting collection recording page to use for demonstration.

• Use small, everyday objects to assemble at least one counting collection per pair of students. Place each collection in a bag or box. Each collection should contain 50–100 objects. Differ the number of objects in the collections based on the needs of your students. Provide a challenge by creating collections with 101–120 objects. Save collections for future use.

• Provide tools students can choose from to organize their counting. Place them in a central location. Tools may include cups, plates, number paths, or 10-frames.

• Gather large pieces of construction paper or trays for students to use as work mats. Work mats help students keep track of and organize the objects in their collection. They can also make students’ work portable.

• Prepare an anchor chart that will be used to keep track of tens, ones, and totals in the lesson (see image in Launch).

Launch

Materials—T: Chart paper, Hide Zero cards

Students analyze the way a counting collection is organized and describe it in terms of tens and ones.

If needed, briefly review the procedure of counting a collection by using the chart from module 3 lesson 15.

Display a picture of a counting collection. Give students a quiet moment to study the image.

How

is the counting collection organized?

The cubes are in sticks of 10. There are 5 extra cubes next to the sticks.

Why do you think the collection is organized this way?

It is fast to count by tens.

There are a lot of cubes. It’s helpful to put them into groups of 10 to make them easier to count.

Organizing larger collections into tens and ones can help make counting efficient.

Have students turn and talk to estimate or make a good guess about the total. Then guide the class to chorally count by tens and ones to find the total, 75.

Show 75 by using Hide Zero cards. Then separate the cards to show 70 and 5. 70 and 5 make 75.

(Point to the 70 card.) Where do you see 70 in the collection?

The ten-sticks equal 70.

0 7 5 0 7 5

Language Note

Support students in reading two-digit numbers by using the rekenrek and the Say Ten way.

For example, show 75 on the rekenrek. Help students read the number the Say Ten way: 7 tens 5. Connect the Say Ten way to the standard form: 7 tens is 70, so we say seventy-five.

If needed, count the ten-sticks by tens to 70.

(Point to 5.) Where do you see 5 in the collection?

There are 5 extra cubes to the side of the tens.

70 and 5 is …

75

Put the cards back together to show 75.

Numbers such as 7 and 5 are called digits. When we write digits next to each other, we make another number. For example, we write the digits 7 and 5 next to each other to make 75.

In 75, the digit 7 tells us that there are 7 tens. We know that 7 tens is 70. (Separate the cards again to show 70 and 5.)

The digit 5 in 75 tells us that there are 5 ones, or 5.

Put the cards back together to show 75.

What are the digits in 75?

7 and 5

Show the counting collection recording page from the student book. Use a combination of the following questions to interactively demonstrate how to record a collection:

• What are we counting in this collection?

• What was one of our good guesses about the total number of objects?

• What can we draw to show how the counting collection is organized?

• How many groups of 10 are there? How many extra ones are there?

• What is the total number of objects in the collection?

Post a chart for keeping track of counting collection totals in terms of tens and ones. Record the sample on the chart.

Let’s keep track of all the counting collections we talk about today. In this collection there are 7 groups of 10 and 5 extra ones.

What is the total?

Transition to the next segment by framing the work.

Today, we will organize, count, and record a collection.

Learn

Organize, Count, and Record

Materials—S: Counting collection, organizing tools, Hide Zero cards, work mat Students organize, count, and record a collection of objects.

Partner students and invite them to choose a collection, organizing tools, a work mat, and a workspace. Have them open their student book to the counting collection recording page.

After you count your collection and record your work, use Hide Zero cards to represent the total. Look for the digits that show how many tens and how many ones.

Circulate as students work. Use any combination of the following questions or statements to assess and advance student thinking:

• Show me how many tens and ones are in your collection.

• What is the total? How do you know?

• What does your drawing show? How can you label it?

• How can you show the total with Hide Zero cards?

Promoting the Mathematical Thinking and Reasoning Standards

Students demonstrate their understanding by representing problems in multiple ways (MTR.2) while they record their collection. They build understanding through modeling and by using manipulatives. Using a symbol such as a line or a box to record a group of 10 shows that students are thinking abstractly and understand that you can represent 10 without drawing 10 distinct items.

Ask the following questions to promote MTR.2:

• How is what you wrote or drew the same as your collection? How is it different from your collection?

• Why is it helpful to draw groups of 10 instead of drawing every item in your collection?

• What are the digits that make your total?

• What could be a more efficient way to organize the collection?

Select student work that makes use of tens and ones to share in the next segment. The following chart shows samples. If some pairs finish early, invite them to draw number bonds or write number sentences to represent their total.

Corey and Kioko

Sakon and Violet

Teacher Note

To fully grasp place value concepts, students need ample experience with grouping, or putting together items to make a new unit.

By grouping, students see the individual units that compose the new, larger unit. For instance, one cup of 10 bears contains 10 individual bears.

Grouping also allows students to see that the size of the new unit is proportionally larger than the base unit. For example, 10 disks in a 10-frame are visually about 10 times larger than a single disk.

Consider providing distributed practice with groupable models during the remainder of the year. Invite students to group and count various collections. Have them label their collections with Hide Zero cards and represent them by using number bonds, unit form, and number sentences.

Teacher Note

Unit form expresses a number in terms of how many (as a numeral) of a certain unit (as a word) make that number (e.g., 2 tens or 14 hundreds 8 ones). The term unit form is synonymous with numeral word form and was chosen because it helps emphasize unit thinking.

Share, Compare, Connect

Materials—T: Chart, Hide Zero cards; S: Hide Zero cards

Students share and discuss recordings of counting collections. Invite two pairs to share their work. Encourage the class to use the Talking Tool to engage in discussion by asking questions, making observations, and sharing compliments.

Corey and Kioko

How did you organize and count your collection?

We put 10 disks in each line, 5 red and 5 yellow.

At first we skip-counted by fives. But then it was even quicker to count by tens since 2 fives make a ten.

Tell us about your recording.

We drew rectangles to show a group of 10.

We drew 3 circles to show our extra disks.

Draw attention to the unit form at the bottom of the recording page.

Class, where do you see 9 tens in the drawing? Where do you see 3 ones?

The 9 rectangles are 9 tens.

The 3 circles labeled with a 1 are 3 ones.

Invite students to turn and talk to their partner.

Do you agree this recording shows a total of 93? Why?

Using the recording, guide students to count chorally by tens and ones.

Show 93 by using Hide Zero cards.

What digits do you see?

9 and 3

Teacher Note

The sample student work shows common responses. Look for similar work from your students and encourage authentic classroom conversations about the key concepts.

If your students do not produce similar work, choose a student’s work to share and highlight how it shows movement toward the goal of this lesson.

Then select a provided sample that advances your class’s thinking. Consider presenting the work by saying, “This is how another student counted the collection. What do you think this student did?”

Refer back to the recording of the collection as needed to support students with answering the following questions.

What does the digit 9 tell us in the number 93?

It tells there are 9 tens.

How many is 9 tens?

90

Slide apart the cards to confirm. Then put them back together. Repeat the process for the digit 3.

9 tens is 90 and 3 ones is 3. 90 and 3 make 93. Record the pair’s work under 75 on the class chart.

This collection has 9 groups of 10 and 3 more ones.

What is the total?

93 Sakon and Violet

Invite a different pair to share their work. Then direct the class’s attention to the unit form.

Class, how is this recording different from the other group’s recording?

This one has circles instead of rectangles for the groups of 10.

They have 5 tens. Corey and Kioko had 9 tens. They have 2 ones, not 3 ones.

Invite students to think–pair–share about the second recording.

Differentiation: Challenge

At another time, invite pairs who count collections with more than 100 objects to share their work. Facilitate discussion by using the following questions:

• Do you all agree this recording shows a total of 103 cubes? Why?

• How many tens and ones do you see?

• How many is 10 tens 3 ones?

Do you agree that this recording shows a total of 52? Why?

Yes. 10, … , 50, 51, 52.

50 plus 2 equals 52.

5 tens and 2 ones is 52.

Ask partners to show 52 by using their set of Hide Zero cards.

What digits do you see?

5 and 2

In 52, what does the digit 5 tell us?

5 tens

How many is 5 tens?

50

Have students slide apart the cards to confirm and then put them back together. Repeat the process for the digit 2.

Record the pair’s work on the class chart.

In this collection there are 5 groups of 10 and 2 ones.

What is the total? 52

Allow a few minutes for cleanup. Collect students’ recordings to review as an informal assessment.

Land

Debrief 5 min

Materials—T: Chart, Hide Zero cards

Objective: Count a collection and record the total in units of tens and ones.

Gather students and display the class chart. (Point to the first row.) What was the total of this collection?

75

The digits of these numbers tell us how many tens or ones there are. In the number 75, what does the digit 7 tell us? (Point to the 7 in the tens column.)

There are 7 groups of 10.

How many is 7 tens?

70

As needed, use Hide Zero cards to support students.

In the number 75, what does the digit 5 tell us? (Point to the digit in the ones column.)

There are 5 ones.

How many is 5 ones?

5 70 and 5 is 75.

Ask a pair to share a new total and add it to the chart. Repeat the process.

Recognize the place value of digits in a two-digit number.

Lesson at a Glance

Students work with sets of objects to compose as many groups of 10 as they can. They record their work by writing the total in both standard form and as the number of tens and ones. Students also write a number sentence that shows the value of the tens and ones as a two-digit number. The terms compose, value, and place (as in place value) are introduced in this lesson.

Key Question

• What is the value of each digit in a two-digit number? How do you know?

Achievement Descriptors

FL.1.Mod5.AD1 Read and write numbers to 100 as numerals and as expressions or equations by using tens and ones. Read numbers to 100 in words. (MA.1.NSO.1.2)

FL.1.Mod5.AD2 Represent a set of up to 99 objects with a two-digit number by composing tens. (MA.1.NSO.1.3)

FL.1.Mod5.AD4 Determine the values represented by the digits of a two-digit number. (MA.1.NSO.1.3)

Circle all the groups of 10.

Show the total with a number sentence.

Agenda Materials

Fluency 5 min

Launch 5 min

Learn 40 min

• Place Value

• Tens and Ones

• Compose Tens

• Problem Set

Land 10 min

Teacher

• 100-bead rekenrek

• Hide Zero® cards, demonstration set

Students

• Tens and Ones removable (in the student book)

• Hide Zero® cards (1 set per student pair)

Lesson Preparation

The Tens and Ones removables must be torn out of student books and placed in personal whiteboards. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

Fluency

Whiteboard Exchange: 5 as an Addend

Students find a total and use the commutative property to write a related addition sentence to build procedural reliability for addition within 20.

After each prompt for a written response, give students time to work. When most students are ready, signal for them to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

Display 1 + 5 = .

Write the equation, and then find the total.

Display the completed addition sentence: 1 + 5 = 6.

Change the order of the addends to write a related addition sentence. (Point to the addends.)

Display the related addition sentence: 5 + 1 = 6.

Repeat the process with the following sequence:

Counting on the Rekenrek by Tens and Ones

Materials—T: 100-bead rekenrek

Students count to a specified number the Say Ten way, then in standard form to prepare for identifying a given set with all the tens composed.

Show students the rekenrek. Start with all the beads to the right side.

Let’s count to 52 the Say Ten way.

Say how many beads there are as I slide them over.

Slide over 10 beads in each row all at once as students count to 5 ten.

1 ten, 2 ten, 3 ten, 4 ten, 5 ten

Slide over 2 more beads, one at a time, as students count to 5 ten 2.

5 ten 1, 5 ten 2

Slide all the beads back to the right side.

Let’s count to 52 the regular way.

Say how many beads there are as I slide them over.

Repeat the process as students count by tens and ones to 52.

10, 20, 30, 40, 50, 51, 52

Repeat the process as students count by tens and ones the Say Ten way and in standard form to the following numbers:

Student View

Launch

Students see a group of items composed into tens and ones and discuss how they are composed.

Have students watch part 1 of the video, which shows a baker boxing doughnuts as they come down a conveyor belt. Invite students to discuss what they notice and wonder.

I noticed he made a box of 10 donuts. Are there 50 donuts in all?

I wonder if he will make more boxes of 10.

Play part 2, which shows the baker making progress toward boxing all the doughnuts.

The baker is making full boxes. Can he fill more boxes with the doughnuts that are left? How do you know?

He can make more. He puts 10 doughnuts in a box. There are more than 10 doughnuts left.

Play part 3, which shows 5 complete boxes and 3 leftover doughnuts.

Why do you think the baker did not put the last 3 doughnuts in a box? Because he’s making full boxes of 10 doughnuts, and 3 doughnuts won’t fill a box.

The baker composed as many boxes of 10 doughnuts as he could. To compose means to put together or group. Many of us compose groups of 10 when we count a collection.

What did the baker compose?

Groups of 10 doughnuts

Transition to the next segment by framing the work.

Today, we will find the total number of doughnuts. We will talk about how many tens and ones are in the total.

Teacher Note

To fully grasp place value concepts, students need experience with groupable pictorial models.

Although items in pictorial models cannot be physically grouped, students can still compose units. They may circle 10 items or group them in other ways to show that 10 items go together to make 1 ten. They may also rename the group by saying 1 box of doughnuts rather than 10 doughnuts, for example. They are internalizing that 10 ones are equivalent to 1 ten.

Many pictorial models are proportional: The next unit is visually ten times larger than the base unit from which it is composed.

Language Support

Support understanding of the term compose by having students make ten. Ask them to lace their fingers together and say, “I composed a ten by putting together 10 ones.”

Show other examples of composition, such as these:

• A table group is composed of 4 desks.

• Our class is composed of 24 students.

• A band is composed of many musical instruments.

• A painting can be composed of many shapes and colors.

Learn

Place Value

Materials—T: Hide Zero cards

Students analyze a two-digit number and see that it is made of tens and ones.

Display the image of the baker’s doughnuts as he first begins to box them.

First the baker composed 1 box of 10 doughnuts. He had 43 more doughnuts, or ones, to box.

Record this as 1 ten 43 ones.

Display the image of the doughnuts at the end of the video.

The baker composed as many tens as he could. How many boxes, or tens, did he compose?

5 tens

How many extra doughnuts, or ones, did he have left?

3 ones

Record this as 5 tens 3 ones.

Invite students to think–pair–share about the total number of doughnuts in the video.

What is the total number of doughnuts?

53

Support students as needed by chorally counting doughnuts by tens and ones. Show 53 using Hide Zero cards.

Teacher Note

Unit form, or numeral word form, is a way of representing numbers in terms of place value units. For example, 48 can be written as 4 tens 8 ones or 3 tens 18 ones. Unit form is helpful for these reasons:

• The unit is written to the right of the number so that students read left to right.

• Units may be presented in a different order. For example, 43 can be written as 3 ones 4 tens.

• When ones or tens are not fully grouped (e.g., 2 tens 43 ones), it may be easier for students to identify totals when they are written in unit form rather than shown on a place value chart. On a place value chart, students are more likely to mistake 2 in the tens and 43 in the ones as the number 243.

Unit form, or numeral word form, is familiar from previous modules. However, students do not need to know it by name. The place value chart is introduced in lesson 6.

1 ▸ M5 ▸ TA ▸ Lesson 3 EUREKA MATH2 Florida B.E.S.T. Edition

Numbers with two digits have two places. This is the tens place. (Point to 5.) And this is the ones place. (Point to 3.)

Tell students that the digit in the tens place tells how many tens are in the number. The digit in the ones place tells how many ones are in the number.

What are the places in a number with two digits?

The tens place and the ones place

In 53, what digit is in the tens place?

5

Language Support

(Point to the image of the doughnuts.) How many is 5 tens?

50

When 5 is in the tens place, it has a value of 50. Value tells how much something is worth.

What digit is in the ones place?

3

3 is in the ones place. What is the value of 3 ones?

3

Display the picture of Hide Zero cards for 53 that are separated.

53 is made of 50 and 3. (Draw arms to form a number bond.) That is 5 tens and 3 ones. (Point to the digits in 53.)

0 5 3 0 5 0 5 3 0 5 © Great Minds PBC 48

Tens and Ones

Materials—S: Tens and Ones removable, Hide Zero cards

Students find the value of digits in the tens and ones places and reason about their relationship to the total.

Make sure students have inserted a Tens and Ones removable in their personal whiteboards.

Display the picture of 35 doughnuts.

The baker made this many doughnuts the next day.

Invite students to think–pair–share about the number of tens shown in the picture.

How many tens did he compose? How many ones are left?

He composed 3 tens. There are 5 ones left.

Turn and whisper this number in tens and ones to a partner.

3 tens 5 ones

Record the number of tens and ones as students do the same.

Record each place value unit numerically in a single horizontal line. Consider using different-color markers to emphasize the different units.

Point to each unit as students count up chorally to 35. Pause briefly at the change in units. 10, 20, 30, 31, 32, 33, 34, 35 (Pausing after 30.)

Teacher Note

Although students are not formally introduced to the term expanded form until grade 2, here they learn to write a two-digit number as a number sentence by using their understanding of place value units (i.e., tens and ones). For example:

This sharpens students’ understanding of composition and equivalence as they progress through the grades.

Insert addition symbols to make an expression.

Invite students to think–pair–share about how the addition expression shows 35.

If you add all the tens, you get 30. If you add all the ones, you get 5.

You are adding 3 tens and 5 ones. That’s 35.

Tell students to record the total in the number bond.

What are the digits in 35?

3 and 5

What place is 3 in?

The tens place

What is the value of 3 in 35? How do you know?

30

There are 3 tens. 10, 20, 30

Tell students to record the value of the digit 3 in the number bond as shown.

What place is 5 in?

The ones place

What is the value of 5 in 35? How do you know?

5

There are 5 ones. 1, 2, 3, 4, 5

Tell students to record the value of the digit 5 in the number bond as shown.

We can write an addition number sentence that shows the value of the tens and ones: 30 + 5 = 35.

Record the equal sign and total as students record the number sentence.

Support students as needed by having them use Hide Zero cards to show the total. They can separate them to show the value of the digits.

Compose Tens

Materials—S: Tens and Ones removable

Students compose groups of 10 within a set of objects and represent the total in terms of tens and ones.

Tell students to turn to the ladybugs picture in their student book.

What is an efficient way to find the total number of ladybugs?

We could count groups of 10. We could count by fives.

Have students circle groups to compose as many groups of 10 as they can.

How do you know you composed as many tens as you can?

There are only 4 ladybugs left. I can’t make another group of 10.

Have students use their Tens and Ones removable to record their work in unit form, and to record the total number of ladybugs in the number bond.

Look at the total. What digit is in the tens place? 2

What is the value of 2 in 24? How do you know? 20

There are 2 tens. 10, 20.

What digit is in the ones place?

Teacher Note

Consider having students play Spill and Snap to provide additional practice with composing tens. Students take two big handfuls of cubes and spill them onto a surface. They snap ten cubes together to compose as many tens as possible. There are likely to be extra ones.

Students use the Tens and Ones removable to record their work. As they work, ask questions such as these:

• How do you know you composed all of the tens?

• What digit is in the tens place?

• What digit is in the ones place?

• What is the value of the digit     ? How do you know?

What is the value of 4 in 24? How do you know?

There are 4 ones. 1, 2, 3, 4.

Ask students to complete the parts of the number bond to show the value of each digit.

Now, it’s your turn to write an addition number sentence that shows the value of the tens and ones in 24.

Repeat the process for the feathers and the peanuts.

Problem Set

Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex.

Directions may be read aloud.

Land

Debrief 5 min

Objective: Recognize the place value of digits in a two-digit number.

Display the picture of candles. State and record the number of tens and ones in the picture in unit form.

Are all of the tens composed? How do you know?

No, there are 11 extra candles. We could compose another ten.

Promoting the Mathematical Thinking and Reasoning Standards

As students relate the digits in a number to a representation of that number with all of the tens composed, they use structure to help them understand and connect mathematical concepts (MTR.5).

The digits in a number always represent the number in its most composed form. Students need experience representing numbers that have different quantities of tens and ones to prepare them for adding and subtracting with larger numbers later in grade 1 and throughout grade 2.

Display the second candle image.

How many tens do you see now? How many extra ones do you see?

2 tens, 1 one (Write the number of tens and ones in unit form.)

We can write digits to represent the total as a number. When there are tens and ones, we write a digit in the tens place and a digit in the ones place.

Invite students to think–pair–share about the number that shows 2 tens 1 one.

What number can we write to represent 2 tens 1 one? 21

Record the total number of candles below the unit form.

What is the value of each digit in 21? How do you know?

The 2 means 20. We made 2 tens.

The 1 in the ones place means there was 1 extra candle.

tens ones

Draw a number bond to record 20 and 1 as parts of 21. Write a number sentence below the number bond to show the value of the tens and ones.

Exit Ticket 5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Teacher Note

Grouping amounts to make different units is whimsically portrayed in the picture book entitled One is a Snail, Ten is a Crab: A Counting by Feet Book, written by Sayre and Sayre. A wide range of critters on the beach have their feet counted in all sorts of combinations, including crabs with 10 legs. Consider using this book as a read-aloud to complement the lessons in this topic.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

3. Circle more groups of 10.

Show the total with a number sentence.

4. Draw the number with tens and ones.

Show the total with a number bond or a number sentence. Sample:

Represent a number in multiple ways by trading 10 ones for a ten.

Lesson at a Glance

This lesson advances students from grouping objects to compose a ten to trading a group of 10 objects for an object that represents the next unit. For example, students trade 10 pennies for 1 dime. As they compose groups of 10, students record their thinking in unit form and also record the total as a two-digit number. They discuss the equivalence of various ways they can represent a given total.

Key Question

• How can we represent the same number in different ways using tens and ones?

Achievement Descriptors

FL.1.Mod5.AD3 Represent two-digit numbers within 99 in multiple ways as tens and ones. (MA.1.NSO.1.3)

FL.1.Mod5.AD4 Determine the values represented by the digits of a two-digit number. (MA.1.NSO.1.3)

Show ways to make 25 using tens and ones.

Agenda Materials

Fluency 10 min

Launch 10 min

Learn 30 min

• Trade Coins

• Coin Combinations

• Problem Set

Land 10 min

Teacher

• 100-bead rekenrek

• Base 10 rod

• Centimeter cube

• Dimes (6)

• Pennies (50)

Students

• Base 10 rods (5)

• Centimeter cubes (25)

• Dimes (6 per student pair)

• Pennies (50 per student pair)

Lesson Preparation

• Consider preparing bags of coins before beginning the lesson for easy distribution. Each pair of students needs one bag of 6 dimes and 50 pennies. Save the bags of coins for use in a later lesson.

• Ready the base 10 rods (ten-sticks) and cubes from module 4. Add 5 cubes to each bag so that each student has 25 cubes.

Note: Base 10 rods are referred to as ten-sticks throughout the lesson.

Fluency

Counting on the Rekenrek by Twos

Materials—T: Rekenrek

Students count by twos to build fluency counting within 20. Show students the rekenrek. Start with 2 beads to the left side. How many beads?

2

Say how many beads there are as I slide them over. Slide over the beads in the first row, 2 at a time, as students count by twos.

2, 4, 6, 8, 10

Keep counting. Watch closely and say how many beads there are as I slide them over.

Slide the beads, 2 at a time, to the left or to the right in the following sequence as students count by twos:

Continue counting on the rekenrek by twos within 20. Change directions occasionally, emphasizing the numbers when students hesitate or count inaccurately. Invite play and promote focus by varying the pace or inserting dramatic pauses.

Student View

Whiteboard Exchange: 6 as an Addend

Students find a total and use the commutative property to write a related addition sentence to build procedural reliability for addition within 20.

After each prompt for a written response, give students time to work. When most students are ready, signal for them to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

Display 1 + 6 = .

Write the equation and then find the total.

Display the completed addition sentence: 1 + 6 = 7.

Change the order of the addends to write a related addition sentence. (Point to the addends.)

Display a related addition sentence: 6 + 1 = 7.

Repeat the process with the following sequence:

Counting on the Rekenrek by Tens and Ones

Materials—T: 100-bead rekenrek

Students count to a specified number the Say Ten way, then in standard form to prepare for work with tens and ones.

Show students the rekenrek. Start with all the beads to the right side.

Let’s count to 71 the Say Ten way.

Say how many beads there are as I slide them over.

Slide over 10 beads in each row all at once as students count to 7 ten.

1 ten, 2 ten, 3 ten, 4 ten, 5 ten, 6 ten, 7 ten

Slide over 1 more bead as students count to 7 ten 1.

7 ten 1

Slide all the beads back to the right side.

Let’s count to 71 the regular way.

Say how many beads there are as I slide them over.

Repeat the process as students count by tens and ones to 71. 10, 20, 30, 40, 50, 60, 70, 71

Repeat the process as students count by tens and ones the Say Ten way and in standard form to the following numbers:

Student View

Launch

Materials—T: Centimeter cube, base 10 rod (ten-stick); S: Centimeter cubes, base 10 rods (ten-sticks)

Students compose groups of 10 ones and trade them for 1 ten. Make sure students have ten-sticks and cubes sorted into piles. Hold up a ten and a one.

We call these tools a cube and a stick when we measure. Today, we are not going to measure. For our work today, we will call them ones and tens.

Tell partners to place 23 ones between them.

What is the total? 23

Have we composed any tens yet?

No.

Write the total as 0 tens 23 ones.

Let’s compose a ten. Group 10 ones and trade them for 1 ten. (Hold up a ten-stick.)

Guide students to group their ones and have them trade 10 ones for 1 ten, returning the 10 ones to the pile of cubes.

How many tens and ones are there now?

1 ten 13 ones

Write the total in unit form as 1 ten 13 ones.

Do we still have a total of 23? Why?

Yes, we did not change the number of cubes. We just traded 10 cubes for a ten-stick.

Can we compose another ten from the ones that are left? How can we do that?

Yes. There are more than 10 ones. We can trade another 10 ones for 1 ten.

Have students compose another ten and trade 10 ones for 1 ten-stick.

How many tens and ones are there now?

2 tens 3 ones

Write the total in unit form as 2 tens 3 ones.

Do we still have a total of 23? Why?

Yes, we did not change the number of cubes. We just traded 10 more cubes for another ten-stick.

We can make 23 using groups of tens and ones in many ways. (Gesture to the different ways of recording the total.) 23 ones, 1 ten 13 ones, and 2 tens 3 ones all represent the same number, 23.

When we have composed as many tens as we can, we write digits in the tens place and in the ones place to represent the total as a number.

Write 23.

What are the values of the digits 2 and 3 in the number 23? 20 and 3

Draw arms from 23 to make a number bond and write 20 and 3 as the parts. Have students clean up. Or if students need more practice, have them repeat the process with 18, 27, or 35.

Transition to the next segment by framing the work.

Today, we will continue to compose groups and trade 10 ones for 1 ten.

UDL: Representation

To develop students’ understanding of and flexibility with place value concepts, consider making an anchor chart to show some different ways one number, such as 23, can be represented.

Learn

Trade Coins

Materials—T/S: Dimes, pennies

Students group 10 pennies and trade them for 1 dime.

Display the picture of a penny.

What is the name of this coin?

It’s a penny!

The value of a penny is 1 cent.

Display the picture of a dime.

This is a dime. The value of a dime is 10 cents.

Display the picture of the two children. Invite students to think–pair–share about the following situation.

Senji has 10 pennies. Kioko has 1 dime. Senji wants to trade his 10 pennies for Kioko’s 1 dime. Is that fair? Why?

Yes, it is fair because 10 pennies is 10 cents and 1 dime is 10 cents.

Yes, it is like trading 10 cubes for a ten-stick.

We can trade 10 pennies for 1 dime. It is the same as composing a group of 10 ones and trading them for 1 ten.

Distribute dimes and pennies to pairs of students. Model how to group and trade 10 pennies for 1 dime as students follow along with their coins.

Teacher Note

To fully grasp place value concepts, students need experience with pregrouped models (ten-sticks and cubes) and nonproportional models (coins).

When students compose a ten using cubes and ten-sticks by trading these objects rather than physically grouping them because the sticks have already been grouped by tens, such pregrouped models are still proportional.

Coins are not groupable in the sense that 1 dime is not literally made of 10 pennies. Students trade 10 pennies for the dime. Coins are nonproportional because the new unit (dime) is not visually 10 times larger than the base unit (penny).

These types of models help students internalize the fact that 10 ones are equivalent to 1 ten, regardless of the representation. Working with nonproportional models such as coins will prepare students for work with place value disks in grade 2.

Coin Combinations

Materials—T/S: Dimes, pennies

Students find all the possible combinations of tens and ones for a given total.

Pretend you have 30 cents in your pocket. You may have just dimes, just pennies, or dimes and pennies. Use your coins to figure out which coins you could have. Have pairs of students find and then share at least one possible coin combination. If they mention other coins, validate their ideas and refocus students on pennies and dimes. Circulate and ask questions to advance students’ thinking. For example:

• A penny is 1 cent. A dime is 10 cents. How many cents do you have?

• Is there a way to make 30 cents with different coins?

Then show 30 pennies. Have partners also set out 30 pennies. Ask them to sort their remaining dimes and pennies into two piles, one pile for the dimes and one pile for the pennies.

Let’s find all the different ways we could make 30 cents. One way is 30 pennies. Count the 30 pennies and arrange them in 5-groups as pairs do the same. Write the number of pennies as 0 tens 30 ones.

Can we compose a ten? How?

We can make a group of 10 pennies and trade them for a dime. Trade 10 pennies for 1 dime as pairs do the same. Chorally count the total starting with the dime.

10, 11, … , 29, 30

How many tens and ones do you see?

1 ten 20 ones

Write the total in unit form as 1 ten 20 ones.

1 ten and 20 ones is the same as how many ones? 30

Promoting the Mathematical Thinking and Reasoning Standards

As students move to using dimes and pennies to represent numbers, they demonstrate understanding by representing problems in multiple ways (MTR.2). Dimes and pennies are nonproportional representations of tens and ones because students cannot see 10 pennies inside a dime. This requires students to think more abstractly.

Ask the following questions to promote MTR.2:

• Which coin represents a ten? Which coin represents a one? Why?

• How do you know a dime represents a 10 even though it is not made out of 10 pennies?

Have we composed all the tens we can?

No, we can still trade more groups of 10 pennies.

Repeat the process of grouping, trading, and chorally counting.

How many tens and ones are there?

2 tens 10 ones

Write the total in unit form as 2 tens 10 ones.

2 tens 10 ones is the same as 1 ten 20 ones. It is also the same as how many ones?

30

Repeat the process of grouping, trading, and chorally counting. Write the total in unit form as 3 tens 0 ones.

Have students look at the recordings of equivalent unit forms for 30.

What do you notice about these representations?

These are all the ways we made 30.

The number of tens goes up by 1 ten each time.

The number of ones goes down each time.

Which way helps us write 30 as a two-digit number?

3 tens and 0 ones

Circle 3 tens and 0 ones.

30 is 3 tens and 0 ones. (Write 3 and 0 as you say each digit.)

What is the value of the digit 3? What is the value of the digit 0?

3 is 3 tens.

0 is 0 ones.

Draw arms from 30 to make a number bond and write 30 and 0 as the parts.

As needed, provide more practice with trading ones for tens using 25, 32, or 44 pennies.

Problem Set

Differentiate the set by selecting problems for students to finish within the timeframe. Problems are organized from simple to complex.

Directions may be read aloud.

Land

Debrief 5 min

Materials—T: Dimes, pennies

Objective: Represent a number in multiple ways by trading 10 ones for a ten.

Display the picture of Senji and Kioko. Invite students to discuss the similarities and differences between the two sets of coins the children are thinking about.

What is different about Senji’s money and Kioko’s money?

Senji has 16 coins. Kioko has 7 coins.

Kioko has a dime and pennies. Senji has only pennies.

What is the same about the two sets of coins they have?

They both have 16 cents.

Kioko has a ten and some ones. Senji only has ones. How do you know they both have 16 cents?

They both have 1 ten and 6 ones, only in different coins.

Senji could trade 10 pennies for 1 dime, and then they would have the same coins. Set out 16 pennies.

Here are 16 ones. We can trade 10 ones for 1 ten. Then we have 1 ten and 6 ones.

Teacher Note

Consider having students play Take and Trade to provide additional practice with trading ones for tens. Students use a handful of cubes and 5 ten-sticks. They group and trade as many ones for tens as they can. There are likely to be extra ones.

Use pennies and dimes as a variation.

As students work, ask questions like these:

• How do you know you have traded for or composed all of the tens?

• What is the new total? How do you know?

How do we write 1 ten and 6 ones as a two-digit number?

Write 1 in the tens place and 6 in the ones place.

Record 16 and write tens and ones over the numbers as shown.

How can we represent the same number in different ways using tens and ones?

We can use all ones.

We can trade some ones for tens.

Exit Ticket 5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

3. Show ways to make 20. Use only tens, only ones, or tens and ones. Use

4. Show ways to make 38. Use only ones, or tens and ones. Use

Lesson at a Glance

Students work with different representations of the same total. Some representations show all tens composed, others show no tens composed, and still others show a mix of tens and ones. Students compare the representations and find totals to confirm the equivalence of the sets.

Key Question

• Why can different representations show the same total?

Achievement Descriptors

FL.1.Mod5.AD1 Read and write numbers to 100 as numerals and as expressions or equations by using tens and ones. Read numbers to 100 in words. (MA.1.NSO.1.2)

FL.1.Mod5.AD2 Represent a set of up to 99 objects with a two-digit number by composing tens. (MA.1.NSO.1.3)

FL.1.Mod5.AD3 Represent two-digit numbers within 99 in multiple ways as tens and ones. (MA.1.NSO.1.3)

Agenda Materials

Fluency 10 min

Launch 10 min

Learn 30 min

• Equivalent Representations

• Sort: Number Forms

• Problem Set

Land 10 min

Teacher

• 100-bead rekenrek

• Number Forms cards (digital download)

• Numbers in Word Form (digital download)

Students

• Number Forms cards

• Numbers in Word Form

Lesson Preparation

• Additional Number Forms cards are available in the teacher edition. Each set increases in complexity. Consider making copies of sequences for differentiation.

• Save the Number Forms cards and Numbers in Word Form for use in subsequent lessons.

Fluency

Counting on the Rekenrek by Twos

Materials—T: Rekenrek

Students count by twos to build fluency counting within 20. Show students the rekenrek. Start with 2 beads to the left side.

How many beads?

2

Say how many beads there are as I slide them over. Slide over the beads in the first row, 2 at a time, as students count by twos.

2, 4, 6, 8, 10

Keep counting. Watch closely and say how many beads there are as I slide them over. Slide the beads, 2 at a time, to the left or to the right in the following sequence as students count by twos:

Differentiation: Challenge

Students are only expected to master counting by twos within 20 at this time. To increase complexity, consider inviting students to extend the counting sequence in the following ways:

• Count by 2 tens the Say Ten way. (2 ten, 4 ten, 6 ten, 8 ten, 10 ten.)

• Count by 2 tens the standard way. (20, 40, 60, 80, 100)

• Count by twos from 20 within 40. (22, 24, 26, 28, …)

• Count by twos within 60, starting at a given number. (Thirty-eiiiight, 40, 42, 44, 46, …)

Continue counting on the rekenrek by twos within 20. Change directions occasionally, emphasizing the numbers when students hesitate or count inaccurately. Invite play and promote focus by varying the pace or inserting dramatic pauses.

Whiteboard Exchange: 4, 5, or 6 as an Addend

Students find a total and use the commutative property to write a related addition sentence to build procedural reliability for addition within 20.

After each prompt for a written response, give students time to work. When most students are ready, signal for them to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

Display 4 + 3 =   .

Write the equation and then find the total.

Display the completed addition sentence: 4 + 3 = 7.

Change the order of the addends to write a related addition sentence. (Point to the addends.)

Display a related addition sentence: 3 + 4 = 7.

Repeat the process with the following sequence:

Counting on the Rekenrek by Tens and Ones

Materials—T: 100-bead rekenrek

Students count to a specified number the Say Ten way, then in standard form to prepare for work with tens and ones.

Show students the rekenrek. Start with all the beads to the right side.

Let’s count to 82 the Say Ten way.

Say how many beads there are as I slide them over.

Slide over 10 beads in each row all at once as students count to 8 ten.

1 ten, 2 ten, 3 ten, 4 ten, 5 ten, 6 ten, 7 ten, 8 ten

Slide over 2 more beads, one at a time, as students count to 8 ten 2.

8 ten 1, 8 ten 2

Slide all the beads back to the right side.

Let’s count to 82 the regular way.

Say how many beads there are as I slide them over.

Repeat the process as students count by tens and ones to 82.

10, 20, 30, 40, 50, 60, 70, 80, 81, 82

Repeat the process as students count by tens and ones the Say Ten way and in standard form to the following numbers:

Student View

Launch

Students discuss the equivalence of different representations. Display the pictures of crayons.

30 crayons 3 boxes of crayons

What do you notice?

Some crayons are in a pile. Some are in boxes.

How many crayons are in a box?

10

Would you rather have 3 boxes of 10 crayons or a pile of 30 crayons? Why?

I would rather have boxes to keep them neat.

I would rather have a pile. Then I can see all the colors.

Invite students to think–pair–share about whether the pile of 30 and the 3 boxes of 10 have the same total number of crayons. Encourage partners to explain how they know.

Yes. 3 tens is 30. I counted by ten to be sure. Each crayon in the pile is 1. We can think about the pile of 30 crayons as 30 ones.

Record 30 ones under the pile. Ask students what number to write to represent 30 ones. Record 30 below the unit form.

Each box has 10 crayons. We can think about the 3 boxes of 10 crayons as 3 tens.

Record 3 tens below the boxes. Ask students what number to write to represent 3 tens. Record 30 below the unit form.

30 ones and 3 tens are both ways to write 30. 3 tens has all the tens composed, and 30 ones has no tens composed.

Promoting the Mathematical Thinking and Reasoning Standards

As students play Would You Rather, they engage in discussions that reflect on their mathematical thinking and that of others (MTR.4).

In this instance, students have the interesting task of constructing an argument that is both mathematical and nonmathematical. They may prefer one choice over the other for personal reasons while still recognizing that both representations have the same total.

30 crayons 3 boxes of crayons

Display the pennies and dimes.

50 pennies

5 dimes

Invite students to think–pair–share about which set of coins they would rather have.

Would you rather have 50 pennies or 5 dimes? Why?

I would rather have 50 pennies because that’s a lot more coins.

5 dimes is better because 50 pennies is too many to put in my pocket.

Each penny is 1 cent. We can think about the 50 pennies as 50 ones.

Record 50 ones under the pennies. Ask students what number to write to represent 50 ones. Record 50 below the unit form.

Each dime is 10 cents. We can think about the 5 dimes as 5 tens.

Record 5 tens under the dimes. Ask students what number to write to represent 5 tens. Record 50 below the unit form.

50 ones and 5 tens are both ways to make 50. 50 ones is the same as 5 tens.

Transition to the next segment by framing the work.

Today, we will compare totals when all of the tens are composed, some of the tens are composed, and none of the tens are composed.

Learn

Equivalent Representations

Students determine the equivalence of sets using place value concepts.

Display the pair of Match: Place Value cards

3 tens 2 ones

Pair students and ask them to work together, using their whiteboards as needed, to determine whether the cards represent the same amount.

Use the following questions to facilitate a class discussion. Record students’ thinking.

How many is 3 tens 2 ones? How do you know?

32. I wrote 3 in the tens place and 2 in the ones place.

I drew 3 tens and 2 ones, then I counted: 10, 20, 30, 31, 32.

How many is 2 dimes and 12 pennies? How do you know?

32. I counted: 10, 20, 21, … , 32.

2 dimes is 2 tens. 10 pennies is a ten too. 3 tens is 30. 2 more is 32.

Confirm that both cards show 32. Then point to the card showing unit form.

This card shows all the tens composed. We can easily see how many tens and ones there are. That helps us find the total.

Consider repeating the process with other pairs of cards if needed.

Sort: Number Forms

Materials—T/S: Sort: Number Forms cards, Numbers in Word Form

Students match different representations of the same total.

Direct students to remove Numbers in Word Form from their books. Give them a moment to preview the chart. Consider folding the page to hide the third column until it is needed.

Have students form pairs. Distribute a set of Number Forms cards to each student pair. Have students sort cards by using the following procedure. Consider doing a practice round.

• Lay out all the cards faceup.

Teacher Note:

There are four different sets of Number Forms cards. Each set increases with complexity and is coded with a shape for easy distribution. Consider differentiating the sets by offering opportunities to build confidence or by advancing to more challenging sets.

• Green triangle set: numbers within 20

• Orange square set: numbers within 50

• Yellow circle set: numbers within 100

• Red trapezoid set: numbers within 100 with varying compositions of tens and ones

• Sort cards that have the same total into a row.

• Continue until all cards are sorted.

Remind students to use the Numbers in Word Form removable. Circulate as students work and provide support as needed. Ask questions such as these to assess student thinking:

• What is the total of this card? How do you know?

• How do you know these totals are the same?

• What are the digits in this total?

• How much is each digit worth in this total?

Have students sort until all the cards are sorted or until time is up. Save the cards for additional practice in subsequent lessons.

Problem Set

Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex.

Directions may be read aloud. Students may select various compositions of tens and ones when they write how many two different ways. Accept a variety of responses as long as both responses match.

Land

Debrief 5 min

Objective: Reason about equivalent representations of a number. Display the picture of two students with a pair of Match: Place Value cards.

Adrien and Zoey play Match.

UDL: Representation

Consider having students use cubes or coins to represent the cards before they compare them. Students may also make drawings to find the totals.

Invite students to think–pair–share about whether the cards match.

Did they find a match?

Yes, 2 tens and 6 ones is 26. 26 ones is also 26.

Display Adrien’s drawing.

Adrien showed his card like this. What is the total? How do you know?

26. 10, 20, 21, … , 26

Write 26 to label the drawing.

Display Zoey’s drawing.

Zoey showed her card like this. What is the total? How do you know?

26. She drew dots to make 2 groups of 10, then drew 6 more. That’s the same total as Adrien’s picture.

Write 26 to label the drawing.

Adrien’s card shows all the tens composed. Zoey’s card shows no tens composed.

Invite students to think–pair–share about how to make a ten with some of the tens composed.

What is a way to make 26 with only some tens composed?

1 ten 16 ones

Why can different representations show the same total?

They may have all the tens composed, some of the tens composed, or none of the tens composed. The total is still the same.

Exit Ticket 5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

2. Write how many in two ways.

Sample: 2 tens 1 one is the same as 20 + 1 .

5. Do the cards match?

how you know. Sample: 10 10 10 10

They are a match because they both show 40. 10 10 10 10

They are not a match. One shows 28 and the other one shows 30.

6. Show ways to make 24 by using tens and ones. Sample

Lesson at a Glance

Students count forward and backward by tens. They look at recordings of the counts and notice a pattern in the digits in the tens place. They study the pattern further by using concrete materials to add 10 to a number or take 10 from the number. In one activity, students watch a video and model the actions of adding and taking 10.

There is no Problem Set in this lesson. This allows students to spend more time working with concrete manipulatives.

Key Questions

• What do you notice about the digit in the tens place when you add 10 to a number?

• What do you notice about the digit in the tens place when you take 10 from a number?

Achievement Descriptor

FL.1.Mod5.AD6 Find 10 more and 10 less than a two-digit number. (MA.1.NSO.2.3)

Agenda Materials

Fluency 10 min

Launch 10 min

Learn 25 min

• Ten More Patterns

• Ten Less Patterns

• Ko’s Coins

Land 15 min

Teacher

• 100-bead rekenrek

• Tens and Ones removable (digital download) Students

• 4, 5, or 6 as an Addend Sprint (in the student book)

• Base 10 rods (ten-sticks) (5)

• Centimeter cubes (3)

• Tens and Ones removable (in the student book)

• Bag of 50 pennies and 6 dimes (1 per student pair)

Lesson Preparation

• The 4, 5, or 6 as an Addend Sprints and the Tens and Ones removables must be torn out of student books. The Tens and Ones removables must also be placed in personal whiteboards. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

• Copy or print the Tens and Ones removable to use for demonstration.

• Ready the bags of coins that were assembled in lesson 4. Save for use in a later lesson.

Fluency

Sprint: 4, 5, or 6 as an Addend

Materials—S: 4, 5, or 6 as an Addend Sprint

Students find a part or total to build procedural reliability for addition within 20.

Have students read the instructions and complete the sample problems.

Direct students to Sprint A. Frame the task.

I do not expect you to finish. Do as many problems as you can, your personal best.

Take your mark. Get set. Think!

Time students for 1 minute on Sprint A.

Stop! Underline the last problem you did.

I’m going to read the answers. As I read the answers, call out “Yes!” and mark your answer if you got it correct.

Read the answers to Sprint A quickly and energetically.

Count the number you got correct and write the number at the top of the page. This is your personal goal for Sprint B.

Celebrate students’ effort and success.

Provide about 2 minutes to allow students to analyze and discuss patterns in Sprint A.

Lead students in one fast-paced and one slow-paced counting activity, each with a stretch or physical movement.

Teacher Note

Consider asking the following questions to discuss the patterns in Sprint A:

• What do you notice about problems 1–5? 6–10? 11–15?

• What strategy did you use to solve problem 4? For which other problems could you use the same strategy?

Point to the number you got correct on Sprint A. Remember this is your personal goal for Sprint B.

Direct students to Sprint B.

Take your mark. Get set. Improve!

Time students for 1 minute on Sprint B.

Stop! Underline the last problem you did.

I’m going to read the answers. As I read the answers, call out “Yes!” and mark your answer if you got it correct.

Read the answers to Sprint B quickly and energetically.

Count the number you got correct and write the number at the top of the page.

Stand if you got more correct on Sprint B.

Celebrate students’ improvement.

Launch

Materials—T: 100-bead rekenrek

Students count up and back by tens on a rekenrek. Show students the rekenrek. Start with all the beads to the right side.

Say how many beads there are as I slide them over.

Slide over 6 beads in the first row all at once. 6

Slide over 10 beads in the second row all at once.

Teacher Note

Count on by tens from 0 to 100 for the fastpaced counting activity.

Count back by tens from 100 to 0 for the slow-paced counting activity.

How do you know there are 16?

6 and 10 is 16.

Continue to slide over 10 beads all at once in each row until 86 beads have been moved. Have students count by tens to 86 as you move each row of beads. Display the ascending tens and ones chart.

These are the numbers we counted. The chart shows each number’s digits in the tens place and in the ones place. What do you notice?

The digit in the ones place is always 6. The digit in the tens place changes. It goes up 1 each time.

Highlight the digits in the tens place.

There is a pattern. We added 1 ten each time. What is the value of 1 ten?

10

Write + 10 next to the chart.

Suppose we add another ten. What is the new total? How do you know?

96

You can use the chart to see the next number. 9 comes after 8. 6 stays the same. Repeat the process, this time starting with 96 on the rekenrek and counting back by tens. Stop at 16. Display the descending tens and ones chart.

Ask students to identify the pattern. Label the chart – 10. Have students use the pattern to figure out the final number, 6.

Transition to the next segment by framing the work.

Let’s add 10 to or take 10 from different numbers. Today, we will think about how adding 10 or taking 10 from different numbers changes the digit in the tens place, and we will look for patterns in the number words.

Promoting the Mathematical Thinking and Reasoning Standards

Throughout this lesson, as students add and subtract 10 all at once and they recognize that the tens digit changes while the ones digit stays the same, they are using patterns and structure to help them understand and connect mathematical concepts (MTR.5).

Recognizing these patterns gives students the conceptual understanding they need to understand the standard algorithms for addition and subtraction in grade 2.

Learn

Ten More Patterns

Materials—T: Tens and Ones removable; S: Centimeter cubes, base 10 rods (ten-sticks), Tens and Ones removable

Students use ten-sticks to count forward by tens. Distribute cubes and ten-sticks and have students put them in piles at the top of their work area. Make sure students have the Tens and Ones removable inserted into a personal whiteboard.

Ask students to place one cube next to their chart.

How many tens?

How many ones?

Demonstrate writing 1 in the ones place on the chart as students do the same.

Add 10 by placing a ten-stick next to your cube.

Again, ask students how many tens and ones there are. Write 1 in the ones place and in the tens place on the chart as students do the same.

What is 1 and 10 more?

Teacher Note

Students may want to put a 0 in the tens column to complete the pattern. Explain how that is fine as 0 means none when writing the number of tens in a chart or next to the word ten but that we do not write 0 to write the numbers 1–9.

UDL: Representation

Consider supporting students by having them use a different format. Instead of using ten-sticks and cubes, have students draw lines (also called quick tens) and dots to represent the amounts and find 10 more and 10 less.

What do you think 10 more than 11 will be? Why?

We will have 2 tens and 1 one.

Repeat the process through 51. For each new total ask, 10 more than (the previous total) is …?

Display the number words and numbers chart. Invite students to think–pair–share about the patterns they see on the chart.

What patterns do you see in the numbers and number words on the chart?

The ones digit stays the same in all the numbers. It is always 1. All the number words end with the word one except for eleven. The pattern starts at 21. The tens digit goes up by 1. 1, 2, 3, 4, 5.

Why does the digit in the tens place change while the digit in the ones place stays the same?

When we add 10 all at once, we change the number of tens but the number of ones stays the same.

Which part of the number word stays the same? Which part changes?

The tens part changes. I see twenty, thirty, forty, fifty. The ones part stays the same. It’s always one, except in eleven. Eleven doesn’t match the pattern.

When we add 10 to a number, the digit in the tens place is 1 more, but the digit in the ones place stays the same.

Differentiation: Challenge

Invite students to count by tens starting at any two-digit number as far as they can, even past 100.

Ten Less Patterns

Materials—T: Tens and Ones removable; S: Centimeter cubes, base 10 rods (ten-sticks), Tens and Ones removable

Students use ten-sticks to count backward by tens. Tell students to erase their chart.

Have students show 43 by using ten-sticks and cubes. Have students place them next to their chart.

How many tens?

4

How many ones?

3

Record the digits on the tens and ones chart as students do the same.

What is the total?

43

Tell students to take ten by removing a ten-stick. Ask students how many tens and ones there are now. Record the answers as students do the same.

10 less than 43 is …?

33

What do you think 10 less than 33 is? Why?

23

We will have 2 tens and 3 ones.

Repeat the process through to 3. For each new total ask, 10 less than (the previous total) is …?

Display the number words and numbers chart. Invite students to think–pair–share about the patterns they see on the chart.

Invite students to turn and talk to their partner.

What changes in this pattern? What stays the same?

Listen for and revoice student responses that mention the following ideas:

• The ones digit, 3, stays the same.

• All the number words end with the word three except for thirteen.

• The tens digit goes down by 1: 4, 3, 2, 1, because we take 10 away each time.

• The tens change: forty, thirty, twenty. It is counting down by tens.

What is the value of the 2 in 23? (Point to the tens place.) What about the value in word form?

20. It would be the same value in word form.

What is the value of the 1 in 13? 10

What is the relationship between 23 and 13? Ten less Minus 10

When we take 10 from a number, the digit in the tens place is 1 less, but the digit in the ones place stays the same.

Have students set aside their ten-sticks and cubes until it is time for the Topic Ticket.

Ko’s Coins

Materials—S: Bag of pennies and dimes

Students use coins to add 10 and take 10 from a two-digit amount. Distribute one bag of pennies and dimes to each pair of students. Then play part 1 of the video, which shows Ko putting coins in her pocket and then finding another dime.

Ask partners to use their pennies and dimes to find how much money Ko has in her pocket now. Remind them, if needed, that she has 2 dimes and 7 pennies.

How much money does Ko have? How do you know?

2 dimes and 7 pennies. 20, 21, … , 27 cents.

1 dime and 7 pennies is 17 cents. If we add 1 dime, we have 27 cents. Play part 2 of the video, which shows Ko throwing a dime into a fountain at the park.

Ask partners to use their pennies and dimes to find how much money Ko has in her pocket now.

How many cents does Ko have now? How do you know?

17 cents. She threw the dime she found into the fountain. She just took a dime away. Now she has 1 dime and 7 pennies.

10 cents less than 27 cents is 17 cents.

Dimes are the same as ten cents. We can use dimes to show adding 10 or taking 10. Let’s do that some more.

Have partners show 54 cents with dimes and pennies.

What is 10 more than 54? How do you know?

64

You just add a dime, or 10, to 54.

UDL: Representation

Consider supporting students by having them use a different format. Rather than using dimes and pennies, have students draw circles labeled with 10 and 1 to represent the amounts.

UDL: Action & Expression

As students use dimes and pennies to practice 10 more and 10 less, consider supporting them in monitoring their own progress. Provide questions that guide self-monitoring and reflection, such as these:

• How is this problem like other problems?

• What is still confusing to me about this problem? What can I do to help myself?

• What patterns do I notice?

Display the two place value charts. Confirm that 10 more than 54 is 64.

54 is 5 tens and 4 ones. 64 is 6 tens and 4 ones.

Record 54 and 64 in the charts as shown. Draw an arrow from 5 tens to 6 tens, and label it + 10.

When we add a 10, the digit in the tens place is 1 more.

Leave the place value charts displayed but erase the recording. Have students show 42 cents with dimes and pennies.

What is 10 less than 42? How do you know?

32

It is 1 ten less than 42.

You just take away a dime.

Confirm that 10 less than 42 is 32. Record 32 and 42 in the charts as shown. Draw an arrow from 4 tens to 3 tens and label it – 10.

When we take a 10, the digit in the tens place is 1 less.

As time allows, use the following suggestions to repeat the process:

• 74 cents (show 10 less)

• 85 cents (show 10 more)

tens ones tens ones

tens ones tens ones

Land

Debrief 10 min

Objective: Add 10 or take 10 from a two-digit number.

Display 24 shown two ways.

How many does each drawing show? How do you know?

I think the lines are ten and the dots are one: 20, 21, 22, 23, 24. The circles are labeled with 10 and 1. 2 tens and 4 ones is 24. Ask students to choose one of these ways to show 24 and copy it on their whiteboard. Then partner students.

Partner A, draw to show 10 more than 24. Partner B, draw to show 10 less than 24.

Display the three place value charts. Write 24 in the place value chart in the middle.

Partner A: What is 10 more than 24? How do you know?

It’s 34. We just drew 1 more ten.

Write 34 in the place value chart on the right.

Partner B: What is 10 less than 24?

How do you know?

It’s 14. I erased 1 ten.

Write 14 in the place value chart on the left.

What do you notice about the digit in the tens place when the number is 10 more?

It is 1 more ten.

Teacher Note

Eureka Math2 refers to drawings like this that use lines for tens and dots for ones as quick tens. When students draw quick tens, they do not need to label the units because the representation is proportional. A line represents a ten-stick of cubes and the dot represents a single cube.

However, when students use nonproportional models such as circles that represent both tens and ones, they label each circle with 10 or 1 to clarify what unit the drawing represents.

Teacher Note

Consider providing distributed practice with 10 more and 10 less using a quick draw activity. In this activity, someone generates a two-digit number (teacher or student). Then students represent 10 more or 10 less than that number by drawing on a whiteboard. Students hold up their whiteboards for feedback.

What do you notice about the digit in the tens place when the number is 10 less?

It is 1 less ten.

Draw an arrow from 2 tens to 3 tens, and label it + 10. Draw another arrow from 2 tens to 1 tens, and label it – 10.

Topic Ticket 5 min

Provide up to 5 minutes for students to complete the Topic Ticket. It is possible to gather formative data even if some students do not complete every problem.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

Topic B Use Place Value to Compare

In topic B, students compare two-digit numbers by using the skills they have acquired over the course of the year. These include reading and writing comparison symbols, grouping ones to compose tens, and understanding that each digit’s value is based on its place in a number.

Previously, students compared numbers by simply knowing that one comes before the other in the count sequence or by considering the size (or length) of the totals. For example, students may have reasoned that 26 cm is greater than 17 cm because they used more cubes to make 26 cm than they did to make 17 cm, or one object is visually longer than the other object. In module 5, students look for and make use of place value structure to compare two-digit numbers. They are presented with increasingly complex comparisons to highlight the meaning of the digits in the tens and ones places.

At first, students compare the quantities of two groups of objects. They may need to compose tens first to write the total in a place value chart in a way that helps with the comparison. Students then use the chart to reason about the numbers of tens and ones to compare the totals. They represent the comparison by writing a number sentence by using the symbols >, =, or < and explain why it is true.

Students are given two digits and asked to write two different numbers, the largest number and the smallest number they can write with the digits, such as 45 and 54 with the numbers 4 and 5. Comparing these numbers helps solidify the idea that the greater number has the larger digit in the tens place.

Students compare sets of coins in a problem-solving context: How can the value of a smaller set of coins be greater than the value of a larger set of coins? After determining the coin types and total amounts, students are challenged to add coins to one set to make the sets have the same value. This prepares students to make the next ten in topic C.

Progression of Lessons

Lesson 7

Use place value reasoning to compare two quantities.

4 tens 19 ones 5 tens 6 ones

Lesson 8

Use place value reasoning to write and compare 2 two-digit numbers.

Lesson 9

Compare two quantities and make them equal.

If we add 4 pennies to 26 cents, we can trade 10 pennies for a dime. That makes 30 cents.

59 56 >

4 tens 19 ones is 59 when we compose tens. 59 and 56 both have 5 tens. 9 ones is greater than 6 ones.

I can make 39 and 93 with the digits 3 and 9. 3 tens is less than 9 tens, so 39 < 93.

Use place value reasoning to compare two quantities.

Lesson at a Glance

Students compare two quantities, either presented as pictures or written in unit form. They reason about the number of tens and ones in the totals and use that information to compare the quantities. Students represent their comparisons by writing comparison number sentences.

Key Question

• How can we compare two totals?

Achievement Descriptor

FL.1.Mod5.AD5 Compare two-digit numbers by using the symbols >, =, and <. (MA.1.NSO.1.4)

Agenda Materials

Fluency 10 min

Launch 10 min

Learn 25 min

• Compose and Compare

• Problem Set

Land 15 min

Teacher

• None Students

• Number Forms cards

• Numbers in Word Form

Lesson Preparation

• Prepare the Number Forms cards and Numbers in Word Form for use during Fluency.

Fluency

Sort: Number Forms

Materials—S: Numbers in Word Form, Number Forms cards

Students sort number cards by value to build fluency with forms of numbers.

Direct students to remove Numbers in Word Form from their books. Give them a moment to preview the chart. Consider folding the page to hide the third column until it is needed.

To get students acclimated to using the chart, write a few of the numbers in word form. Have students use the chart to locate and say the number. Use the following sequence: three, four, fourteen, six, seven, seventeen, and eleven.

Have students form pairs. Distribute a set of Number Forms cards to each student pair. Have student pairs sort cards by using the following procedure. Consider doing a practice round.

• Lay out all the cards faceup.

• Sort cards that have the same total into a row.

• Continue until all the cards are sorted.

Remind students to use the Numbers in Word Form removable. Circulate as students work and provide support to them as needed.

Teacher Note

There are four different sets of Number Forms cards. Each set increases in complexity and is coded with a shape for easy distribution. Consider differentiating the sets by offering opportunities to build confidence or by advancing to more challenging sets.

• Green triangle set: Numbers within 20

• Orange square set: Numbers within 50

• Yellow circle set: Numbers within 100

• Red trapezoid set: Numbers within 100 with varying compositions of tens and ones

Choral Response: 5-Groups to 10 with Pennies

Students recognize the value of a group of pennies and tell how many more are needed to make 10 cents to prepare for comparing coin combinations in lesson 9.

After asking each question, wait until most students raise their hands, and then signal for students to respond.

Raise your hand when you know the answer to each question. Wait for my signal to say the answer.

Display 9 pennies.

How many cents?

9 cents

How many more cents are needed to make 10 cents?

1 cent

When I give the signal, say the addition sentence starting with 9 cents.

9 cents + 1 cent = 10 cents

Display the addition sentence and the additional penny.

What can we exchange 10 pennies for?

1 dime

Display the 10 pennies exchanged for a dime.

Repeat the process with the following sequence:

Whiteboard Exchange: Compare Numbers

Students compare numbers within 30 by using symbols to prepare for comparing quantities and numerals.

Display the numbers 9 and 2.

Write a number sentence by using the greater than, equal to, or less than symbol to compare the two numbers.

Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

Display the number sentence: 9 > 2.

When I give the signal, say the number sentence starting with 9. Ready?

9 is greater than 2.

Repeat the process with the following sequence:

Teacher Note

To increase energy and engagement, consider using various voices or response styles for the last question. For example, have students whisper, shout, or tell a partner that they can exchange 10 pennies for 1 dime.

Language Support

Consider displaying sentence frames to support students with using comparison symbols and language. is greater than .

Launch

Students count and compare the totals of two sets.

Display the children and the crayons. Use the Math Chat routine to engage students in mathematical discourse.

Who has more crayons, Malik or Kioko? How do you know?

Give students quiet think time. Have students give a silent signal when they are ready. Invite them to discuss their thinking with a partner.

Display the crayons and place value charts. Facilitate a class discussion about the question. Record students’ ideas by using the pictures and the place value charts.

Kioko has more crayons. She has 32 crayons. I see 3 tens and 2 ones.

Malik only has 28 crayons. I see 2 groups of 10 and 8 ones.

The boxes of crayons are tens. How does having composed groups of 10 help you compare the two sets of crayons?

It is easier to count them.

We can see she has 3 boxes of 10. But he only has 2 groups of 10. So, she must have more.

Point to the corresponding digits in the place value charts as you ask these questions.

What is the value of the 2 in 28?

What is the value of the 3 in 32?

Differentiation: Support

If needed, students may represent the quantities shown with ten-sticks and cubes. Encourage them to trade 10 ones for 1 ten.

Malik Kioko

Malik Kioko tens ones tens ones

Which is greater, 20 or 30?

Write the total of each child’s crayons below the place value charts.

Which is greater, 28 or 32? Why?

32 is greater. It has more tens.

32 has more tens than 28, so it is greater, even though 28 has more ones.

Let’s write a number sentence to compare 28 and 32. Let’s start with 28. Is 28 less than, greater than, or equal to 32?

Less than

Draw a less than symbol between the totals and read the number sentence: 28 is less than 32.

When deciding who has more, which should you think about first—the boxes of crayons or the loose crayons? Why?

The boxes. They have 10 crayons in them. The loose crayons are just ones.

Transition to the next segment by framing the work.

Today, we will compose tens and use them to help us compare other totals.

Learn

Compose and Compare

Students use pictures to compose tens, compare totals, and explain their reasoning.

Tell students to turn to the page that shows marbles in their student book. Have students point to the picture of the jars.

How many tens?

4 tens

How many extra ones?

1 one

Ask students to write the digits in the place value chart. Then have them write the total on the blank on the left at the bottom of the page.

Have students point to the scattered marbles.

How could we make it easier to count the total marbles?

We could make tens.

Ask students to compose tens by circling groups of 10 marbles. Have them complete the place value chart and write the total on the blank on the right at the bottom of the page. They should not write a comparison symbol yet.

Which picture shows more marbles?

The picture with jars of marbles shows more.

Invite students to think–pair–share about the picture of jars of marbles.

How do you know that the picture with jars of marbles shows more marbles?

Differentiation: Support

Some students may try to write the total before they compose all the tens. Remind students that when they write a number, the digit in the tens place represents how many tens there are when all the tens are composed. To attend to precision, students should compose as many tens as possible and then write the total. Prompt students by asking the following question:

• Look at your picture again. Did you compose all the tens before you found the total?

Support student-to-student dialogue during discussion by inviting the class to agree or disagree, ask a question, share a new idea, or restate an idea in their own words.

There are 4 jars with 10. We can only make 3 groups of 10 in the other picture.

4 tens is more than 3 tens, so 41 is greater than 39. 41 comes after 39 when we count.

4 tens is 40. 3 tens is 30. So, 41 marbles is more than 39.

41 marbles is more than 39 marbles because 4 tens is more than 3 tens.

Does it matter that 39 has 9 ones and 41 only has 1 one? Why?

No, because 41 has more tens. Tens are bigger than ones.

Have students write the greater than symbol in the number sentence. Direct students to the problem presented in unit form. Have them draw the tens and ones, compose more tens if possible, and complete the place value charts. Students may draw tens and ones in a variety of ways, such as by making quick tens or labeled circles. They should not write the comparison number sentence yet.

Promoting the Mathematical Thinking and Reasoning Standards

Students make use of structure (MTR.5) when they compare two-digit numbers by using place value.

Previously, students may have compared numbers by simply knowing one was greater than the other or knowing that one comes before the other in the count sequence. Now, students can use the structure of a number to compare the digits in the tens place and then the digits in the ones place, if necessary.

We started with 4 tens and 19 ones. When we compose another ten, how many tens and ones are there?

5 tens 9 ones

What number is 4 tens and 19 ones? 59

What number is 5 tens and 6 ones?

Tell students to write a symbol between the totals at the bottom of the page to make a true number sentence. Confirm that 59 is greater than 56. Guide students to read the number sentence aloud from left to right.

When we compare numbers, we look at the tens place first because tens are bigger than ones.

59 and 56 both have 5 tens. How do you know that 59 is greater than 56? I looked at the ones place. 59 has more ones than 56.

If the tens are the same, we can compare two numbers by looking at the ones.

Invite students to work with a partner on the next two problems in the student book. Circulate, and assess and advance understanding by using the following questions and prompts:

• Which total is greater? Which total is less? How do you know?

• Read your number sentence. Is it true? Why?

When students finish, begin a class discussion by inviting a few students to share their work. Use questions to guide the discussion, such as these:

• How did you find the total? Did you compose any tens?

• Read your number sentence. Is it true? How do you know?

• What place did you look at first to compare the totals? Why?

Teacher Note

Some students may think 5 tens 6 ones is greater than 4 tens 19 ones because it shows more tens than 4 tens 19 ones. Point out that they need to compose all the tens before they use place value and compare them.

Differentiation: Support

Help students recall that the open part of the comparison symbol faces the larger number and the pointy part of the symbol faces the smaller number. Consider having students draw and label all the symbols on their whiteboard as a reference.

greater than equal to

= < less than

Problem Set

Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex.

Directions may be read aloud.

Land

Debrief 10 min

Objective: Use place value reasoning to compare two quantities.

Display Logan’s stickers.

Logan has 3 sheets of stickers. Each sheet has 10 stickers. He also has 2 rocket ship stickers. How many stickers does Logan have? How do you know? 32

3 tens and 2 ones

3 tens is 30. 30, 31, 32.

Display Violet’s stickers.

Invite students to think–pair–share about the number of stickers Violet has.

How many stickers does Violet have? How do you know? 23

We can compose 2 tens and there are 3 extra ones. The 2 groups of 10 are 20. 20, 21, 22, 23.

Display both sets of stickers.

UDL: Action & Expression

In this lesson, students use these skills acquired over the course of the year: comparing, composing, and place value understanding.

To support students in monitoring their own progress with these skills, consider providing questions such as these that guide selfmonitoring and reflection:

• How is this problem like other problems?

• How are my math skills growing?

• What is still confusing? What can I do to help myself?

Who has more stickers? Who has less? Logan has more. Violet has less.

What symbol should we write to compare their stickers?

Greater than Write >.

Let’s read the number sentence together. 32 is greater than 23. Why is the number sentence true?

3 tens is more than 2 tens.

How do we know 3 tens is greater than 2 tens?

Because 3 tens is 30 and 2 tens is 20.

Can we compose any more tens in 23? Why?

No, we need 10 ones, and we only have 3 ones.

Does it matter that 23 has more ones than 32? Why?

No, because tens are bigger than ones.

How can we compare two totals?

We see which total has more tens.

If the tens are the same, we can see which total has more ones.

Exit Ticket 5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

Use place value reasoning to write and compare 2 two-digit numbers.

Lesson at a Glance

Students write numerals in different orders to make and compare two-digit numbers. Repeated practice helps solidify the idea that the greater number has the larger digit in the tens place. When presented with the digits 0–9, students reason about the smallest and largest two-digit numbers they can make.

Key Question

• How do you know which are the smallest and which are the biggest two-digit numbers we can make?

Achievement Descriptors

FL.1.Mod5.AD4 Determine the values represented by the digits of a two-digit number. (MA.1.NSO.1.3)

FL.1.Mod5.AD5 Compare two-digit numbers by using the symbols >, =, and <. (MA.1.NSO.1.4)

Agenda Materials

Fluency 10 min

Launch 15 min

Learn 20 min

• Roll and Compare

• Problem Set

Land 15 min

Teacher

• None Students

• Double Place Value Chart removable (in the student book)

• 10-sided dice (2 per student pair)

• Number Forms cards

• Numbers in Word Form

Lesson Preparation

• The Double Place Value Chart removables must be torn out of student books and placed in personal whiteboards. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

• Prepare the Number Forms cards and Numbers in Word Form for use during Fluency.

Fluency

Sort: Number Forms

Materials—S: Numbers in Word Form, Number Forms cards

Students sort number cards by value to build fluency with forms of numbers.

Direct students to remove Numbers in Word Form from their books. Give them a moment to preview the chart. Consider folding the page to hide the third column until it is needed.

To get students acclimated to using the chart, write a few of the numbers in word form. Have students use the chart to locate and say the number. Use the following sequence: three, four, fourteen, six, seven, seventeen, and eleven.

Have students form pairs. Distribute a set of Number Forms cards to each student pair. Have student pairs sort cards by using the following procedure. Consider doing a practice round.

• Lay out all the cards faceup.

• Sort cards that have the same total into a row.

• Continue until all the cards are sorted.

Remind students to use the Numbers in Word Form removable. Circulate as students work and provide support to them as needed.

Teacher Note

There are four different sets of Number Forms cards. Each set increases in complexity and is coded with a shape for easy distribution. Consider differentiating the sets by offering opportunities to build confidence or by advancing to more challenging sets.

• Green triangle set: Numbers within 20

• Orange square set: Numbers within 50

• Yellow circle set: Numbers within 100

• Red trapezoid set: Numbers within 100 with varying compositions of tens and ones

Choral Response: 5-Groups to 20 with Pennies and Dimes

Students recognize the value of a group of coins and tell how many more are needed to make the next ten to prepare for comparing coin combinations in lesson 9.

After asking each question, wait until most students raise their hands, and then signal for students to respond.

Raise your hand when you know the answer to each question. Wait for my signal to say the answer.

Display 9 pennies.

How many cents?

9 cents

How many more cents to make the next ten?

1 cent

When I give the signal, say the addition sentence starting with 9 cents.

9 cents + 1 cent = 10 cents

Display the addition sentence and the additional penny.

What can we exchange 10 pennies for?

1 dime

Display the 10 pennies being exchanged for a dime.

Repeat the process with the following sequence:

Whiteboard Exchange: Compare Numbers

Students compare numbers within 20 in different forms by using symbols to prepare for comparing quantities and numerals.

Display the number 10 and the expression 10 + 2.

Write a number sentence by using the greater than, equal to, or less than symbol to compare. Write the total before comparing.

Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

Display the number sentences.

When I give the signal, say the number sentence starting with 10. Ready?

10 is less than 12.

Repeat the process with the following sequence:

Launch

Materials—S: Double Place Value Chart removable

Students compare two numbers that use the same digits but in a different order. Make sure students have the Double Place Value Chart removable in their whiteboards. Display the two dice.

What digits do you see?

9 and 3

Invite students to think–pair–share about the numbers they could write by using the numbers displayed on the dice.

What two numbers can we write by using 9 and 3?

39 and 93

Tell students to write each number in a place value chart and draw them by using tens and ones. Invite a few students to share their drawings. tens ones tens ones

Teacher Note

Some students may be inclined to add the numbers on the dice. Make sure students understand that for this activity, the dice show the digits they are using to write twodigit numbers.

39 and 93 are not the same number even though they have the same digits. Why aren’t they the same?

The 3 comes first in 39 and the 9 comes first in 93.

39 has 3 tens. 93 has 9 tens. The numbers have different tens, so 93 is bigger than 39. Write 93.

What is the value of the 9 in 93?

90

What is the value of the 3 in 93?

Draw a number bond for 93 with the parts 90 and 3. Write 39.

What is the value of the 3 in 39? 30

What is the value of the 9 in 39?

9

Draw a number bond for 39 with the parts 30 and 9.

Circle the 90 and the 30 in the number bonds.

Which is greater, 90 or 30?

90

Which is less, 90 or 30? 30

Does it matter that 39 has 9 ones and 93 only has 3 ones? Why?

No, it does not matter because tens are bigger than ones.

Ask students to write a number sentence comparing 39 and 93. They may write 39 < 93 or 93 > 39. Have students show thumbs-up to indicate which of the two number sentences they wrote.

Repeat the process by displaying dice that show 4 and 6.

Transition to the next segment by framing the work.

Today, we will write numbers and compare them by thinking about the value of their digits.

Learn

Roll and Compare

Materials—S: 10-sided dice, Double Place Value Chart removable

Students write and compare two different numbers made with the same two digits.

Partner students. Distribute two dice to each pair and make sure they have their Double Place Value Charts ready in their whiteboards. Give the following directions for the activity:

• Partner A rolls one die and partner B rolls the other die.

• Both partners use both digits to write the two possible numbers that can be made in the place value charts (for example, 46 and 64).

• Both partners draw tens and ones to represent each number they wrote.

• Each partner writes a comparison number sentence (for example, 46 < 64 or 64 > 46).

• Partners share and validate each other’s work.

Allow 8–10 minutes for the activity. As students work, circulate and ask the following assessing and advancing questions:

• Which place did you look at to compare the numbers? Why?

• Read your number sentence. Is it true? How do you know?

What is the value of the digit in both numbers?

After about 6–7 minutes of play, gather students to summarize the learning by asking these questions.

If we have two digits, how could we organize the digits to make the biggest number possible?

We could put the bigger digit in the tens place to make the biggest number. The more tens you have, the bigger the number is.

If we have two digits, how could we organize the digits to make the smallest number possible?

We could put the smaller digit in the tens place to make the smallest number we could.

Problem Set

Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex.

Directions may be read aloud.

Land

Debrief 10 min

Objective: Use place value reasoning to write and compare 2 two-digit numbers.

Display the digits 0–9.

UDL: Engagement

Consider allowing students to choose whether to show the numbers by drawing them or by using Hide Zero cards. Students can explain why one number is more or less than the other number based on the value of each digit, as seen when the cards are split apart.

Differentiation: Challenge

Students may not need to draw the number as tens and ones. Some may be able to use only the place value chart or a number bond to explain their reasoning.

Provide an additional challenge by having students find the difference between the two numbers being compared. Consider offering the 1–120 number path to support them.

These are all the digits. Let’s read them together.

When we write a digit in the tens place and a digit in the ones place, we make a two-digit number. In a two-digit number, the tens place can have any digit from 1 to 9.

Ask students to share different two-digit numbers they can make. Have them use their whiteboards if needed. Invite students to think–pair–share about the smallest number they can make.

What is the smallest two-digit number you can make? How did you figure it out?

10 is the smallest two-digit number. 1 is the smallest digit that can go into the tens place and 0 is the smallest digit that can go into the ones place.

Write 10.

What is the biggest two-digit number you can make? How did you figure it out?

It’s 99. Nine is the biggest digit. It makes the most tens and the most ones, so we can put it in both places.

Write 99 to the right of 10. Then draw a < symbol.

Let’s read this comparison number sentence together.

10 is less than 99.

If time allows, extend student thinking with the following discussion.

99 is the largest two-digit number because it has a 9 in the tens place and a 9 in the ones place.

Write 99 < 100 and read it aloud.

Even though 99 has 9 in both places, it is not greater than all numbers. 100 has the smallest digits, 1 and 0, but it is greater than 99. That’s because the 1 is in a place we will learn about another time: the hundreds place!

Exit Ticket 5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Promoting the Mathematical Thinking and Reasoning Standards

As students roll and compare, they engage in discussions that reflect on their mathematical thinking and that of others (MTR.4). Students have the chance to explain to each other why their comparison statement is true.

If partners disagree about how to write a true comparison number sentence, encourage them to explain their work to each other by using the place value charts and drawings. They should also be encouraged to ask each other questions.

Teacher Note

Students may try making a two-digit number by using 0 in the tens place. For example, they may suggest 01. Tell them that when there are 0 tens and some ones, we do not write 0 in the tens place. 01 is read as “one.” One is a one-digit number.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

1. Write a number sentence to compare.

2. Draw and write a number sentence to compare.

Compare two quantities and make them equal.

Lesson at a Glance

BStudents reason about how the value of a smaller set of coins can be greater than the value of a larger set of coins. Students make the value of each set equal by adding pennies to compose ten and by trading for a dime. This lesson prepares students for making the next ten in topic C.

Key Question

• How can we make a smaller total equal to a greater total?

Achievement Descriptor

FL.1.Mod5.AD5 Compare two-digit numbers by using the symbols >, =, and <. (MA.1.NSO.1.4)

Agenda Materials

Fluency 10 min

Launch 15 min

Learn 25 min

• Make it Equal

• Problem Set

Land 10 min

Teacher

• None Students

• Subtraction Expression cards (1 set per student pair, in the student book)

• Bag of 50 pennies and 6 dimes (1 per student pair)

Lesson Preparation

• The Subtraction Expression cards must be torn out of student books and cut apart. Consider whether to prepare these materials in advance, to have students prepare them during the lesson, or to use the cards from module 2. If students show proficiency within 10, consider using the cards within 20 from module 3. Consider saving these for use in lesson 17.

• Ready the bags of coins that were last used in lesson 6.

Fluency

Choral Response: 5-Groups to 30 with Pennies and Dimes

Students recognize the value of a group of coins and tell how many more to make the next ten to prepare for comparing coin combinations.

After asking each question, wait until most students raise their hands, and then signal for students to respond.

Raise your hand when you know the answer to each question. Wait for my signal to say the answer.

Display 8 pennies.

How many cents?

8 cents

How many more cents to make the next ten?

2 cents

When I give the signal, say the addition sentence starting with 8 cents.

8 cents + 2 cents = 10 cents

Display the addition sentence and the additional pennies.

What can we exchange 10 pennies for?

1 dime

Display the 10 pennies exchanged for a dime.

Repeat the process with the following sequence:

Language Support

Later in this lesson, students see circles as representations of coins without the visual cue of the actual coin. Consider supporting students by posting a coin anchor chart to reference as they work.

Match: Subtraction Expressions

Materials—S: Subtraction Expression cards

Students identify equivalent expressions to build subtraction fluency within 10.

2 - 1 2 - 2 5 - 3 8 - 4 10 - 10 9 - 0 7 - 3 8 - 6 10 - 9

Pair students. Distribute a set of cards to each student pair and have them play Match by using the following procedure. Consider doing a practice round with students.

• Lay out nine cards expression side up.

• Match two expressions that have equal differences. If there are no matches, replace a few cards with different cards from the pile.

• Turn over the cards to see if the differences are the same.

• Place the matched cards to the side and replace them with two new cards from the pile.

• Continue until no more matches can be made.

Circulate as students work and provide support as needed.

Differentiation: Challenge

Provide sets of Subtraction Expression cards within 20 from module 3 to students who demonstrate proficiency with subtraction within 10.

Launch

Materials—S: Dimes, pennies

Students find ways that fewer coins can have a higher value than a greater number of coins.

Pair students and display the bags of coins. Share the following scenario.

Kai and Lucia have coins in their purses. Kai has 8 coins. Lucia has 2 coins. Kai has more coins, but less money than Lucia. Which coins could each of them have?

Distribute the bags of dimes and pennies to partners and have students work for 2 to 3 minutes to find a solution. Circulate and look for pairs who find more than one accurate solution.

Invite a few pairs to share their solutions. If no one finds a valid solution, model the solution with coins as students follow along. Record students’ ideas. Encourage students to ask each other questions and make observations about one another’s work. Have students refer to the Talking Tool as needed.

Kai’s 8 coins are pennies. That is 8 cents. Lucia’s 2 coins are dimes. That is 20 cents. 8 is less than 20.

Kai’s 8 coins are 1 dime and 7 pennies. That is 17 cents.

Lucia’s 2 coins are 2 dimes. That is 20 cents. 17 is less than 20.

Kai’s 8 coins are 8 pennies. That is 8 cents. Lucia’s 2 coins are 1 dime and 1 penny. That is 11 cents. 8 is less than 11.

Have students set their coins aside.

Transition to the next segment by framing the work.

We found some ways to show how Lucia can have more money even though Kai has more coins. Now let’s find a way for them to have the same amount of money.

Promoting the Mathematical Thinking and Reasoning Standards

In Launch, students engage in discussions that reflect on their mathematical thinking and that of others (MTR.4) as they work together to determine how Kai can have more coins, but less money.

Because there are multiple solutions to this problem, it serves as a great opportunity for students to critique each other’s reasoning, since students need to explain why they can both be correct even though they found different solutions.

Kai Lucia

Learn

Make it Equal

Materials—S: Dimes, pennies

Students compare two quantities and add to the lesser amount to make the totals equal.

Have students turn to the word problem in their student book. Read it aloud as students follow along. Have them retell the story to a partner.

Reread the first two sentences, one at a time. After each sentence, have students draw the coins that are mentioned as tens and ones. Then help students examine their drawing.

How much money does Kai have?

17 cents

How much money does Lucia have?

20 cents

Who has more coins but less money? How do you know?

Kai; she has 8 coins that make 17 cents. Lucia’s 2 coins make 20 cents.

Reread the question. Ask students to work with a partner to add to their drawing and then answer the question. Then invite students to share their work.

We counted on from 17 to 20. Kai needs 3 cents.

Kai and Lucia both have a dime. Kai has 7 pennies, but she needs 10 cents to have the same cents as Lucia. 7 + 3 = 10, so Kai needs 3 cents.

Kai’s 17 cents plus 3 cents equals 20 cents. That’s the same amount of money Lucia has. Let’s write 17 + 3 = 20 to show that thinking.

Differentiation: Challenge

Some students may suggest trading a dime for 10 pennies and subtracting cents to make the two amounts equal. Validate this thinking and ask them to also find a way to make the money equal by adding coins.

UDL: Representation

If coins still prove difficult for some students to work with, consider providing the information in another format. Provide students with manipulatives they can use to represent the values of the dimes and pennies. Consider having students use Unifix cubes to represent dimes by stacking 10 cubes.

Guide students to complete the statement by using pennies or cents as the unit. Direct students to take out their whiteboards. Display the image of coins.

How much money does Rob have? How do you know?

28 cents

2 dimes are 20 cents and 8 pennies are 8 cents. 20 + 8 = 28.

How much money does Liv have? How do you know?

30 cents

3 dimes are 30 cents.

Who has less money? How do you know?

Rob has less money. 28 is less than 30. Have students work with their partner to make Rob’s money the same as or equal to Liv’s money. Students may show the problem by drawing the coins as tens and ones. Others may use coins to show the problem.

Write a number sentence to show your thinking. Invite a pair to share their work. Bring the class to a consensus on the solution.

When one total is less, we can add more to it to make it equal to the greater total.

As time allows, repeat the process by using one or two more sets of coins:

• Rob has 3 dimes and 5 pennies, and Liv has 4 dimes.

• Rob has 5 dimes and Liv has 4 dimes and 1 penny.

Problem Set

Differentiate the set by selecting problems for students to finish within the timeframe. Problems are organized from simple to complex.

Directions may be read aloud.

Land

Debrief 5 min

Materials—S: Dimes, pennies

Objective: Compare two quantities and make them equal.

Partner students and make sure their coins are ready. Ask partner A to put out 3 dimes and partner B to put out 2 dimes and 6 pennies.

Partner A: How much money do you have?

30 cents

Partner B: How much money do you have?

26 cents

Who has less money? How do you know?

Partner B

26 cents is less than 30 cents.

Invite partners to think–pair–share about the following prompt. Add some coins to make your money equal. Be ready to explain how you did it.

Partner B added 4 pennies to make 10 cents. Then we traded 10 pennies for a dime. Now we both have 3 dimes.

Revoice and record student thinking. 30 cents is 26 cents plus 4 cents.

How did we make a smaller total equal to a greater total?

We added more cents to the smaller amount.

Topic Ticket 5 min

Provide up to 5 minutes for students to complete the Topic Ticket. It is possible to gather formative data even if some students do not complete every problem.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

2. Read

Val has 1 dime and 2 pennies

Kit has 2 dimes

How many does Val need to have the same cents as Kit?

Kit needs 8 pennies

Topic C Addition of One-Digit and Two-Digit Numbers

In topic C, students add a two-digit number to a one-digit number. Students apply their place value understanding of tens and ones to make easier problems. They use a variety of models such as cubes, drawings, number bonds, and number paths to represent, solve, and explain their strategies.

When solving problems where the ones do not compose a new ten (e.g., 41 + 7 = 48), students use the familiar strategy of decomposing the two-digit addend into tens and ones. For example, to find 41 + 7, students think of 41 as 4 tens 1 one.

41 + 7 = 40 + 1 + 7

They use the associative property to group the 1 and 7 first and then they add the tens:

40 + 1 + 7 = 40 + 8 = 48

Students prepare for solving problems where the ones compose ten (e.g., 28 + 2 = 30) by finding an unknown addend in strings of related problems. For example, 2 is the unknown addend in the string of problems shown. The patterns that emerge help students see that they can make the next ten by looking at the digit in the ones place and finding its partner to 10. Students use the same strategy as in earlier problems: They decompose the two-digit addend into tens and ones. They combine the ones to make ten and then add the tens.

Students apply their learning to problems where the ones compose a new ten and some ones (e.g., 75 + 7 = 82). For these problems they make “the next” ten. Making the next ten requires students to use a strategy that is parallel to the make ten strategy.

• The next ten after 75 is 80.

• I need 5 more to make the next ten.

• I can get 5 by breaking up 7 into 5 and 2.

• I can add 5 from the 7 to 75 to get the next ten, 80.

• Now I have 80 and 2 more from the 7. That’s 82.

The discussions embedded in the lessons of this topic help students move toward choosing their tools and strategies thoughtfully. They study sets of problems and talk about how they can know before they add whether addends do not make ten, exactly make another ten, or make the next ten and some ones.

Although students are expected to show mastery of one- and two-digit addition at the end of this topic, they may use a variety of tools, including cubes and drawings, to help them solve problems. Expect variety in students’ recordings that show and explain their addition strategy.

Progression of Lessons

Lesson 10

Add the ones first.

Lesson 11

Add the ones to make the next ten.

Lesson 12

Decompose an addend to make the next ten.

I can add the ones first: 3 + 6 = 9. Then I can add the tens back in: 40 + 9 = 49.

I know 7 and 3 make ten. So 73 and 7 make the next ten, 80.

I can choose a tool. I will break up the addend 7 to make the next ten with 28.

Lesson 13

Reason about related problems that make the next ten.

Lesson 14

Determine which equations make the next ten.

8 needs 2 to make ten. So any addend that ends in 8 needs 2 more to make the next ten.

I can look at the ones and see what strategy will work best to find the total.

Lesson at a Glance

Students add a two-digit number to a one-digit number. They decompose the two-digit addend into tens and ones. They combine the ones with the one-digit addend. Then they add the total to the tens. Students draw models and write number sentences to show how they decompose to make an easier problem.

Key Question

• Why can it be helpful to break up a number into tens and ones to add it to another number?

Achievement Descriptor

FL.1.Mod5.AD7 Add a two-digit number and a one-digit number that have a sum within 100 by using manipulatives, number lines, drawings, or models. (MA.1.NSO.2.4)

Agenda Materials

Fluency 10 min

Launch 10 min

Learn 30 min

• Decompose to Add

• Raceway Addition Game

• Problem Set

Land 10 min

Teacher

• None

Students

• Raceway Addition Game removable (1 per student pair, in the student book)

• Counter

• 6-sided dot die (1 per student pair)

Lesson Preparation

The Raceway Addition Game removables must be torn out of student books. Consider whether to tear out one per student pair in advance or to have students tear them out during the lesson.

Fluency

Whiteboard Exchange: Relate Subtraction and Addition

Students relate subtraction and addition to build an understanding of subtraction as an unknown-addend problem.

After each prompt for a written response, give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

Display 10 – 9 = .

Write the subtraction equation.

Write a related addition sentence starting with 9 that would complete the equation.

Display the related addition sentence.

Write the answer to the subtraction equation.

Display the difference.

Repeat the process with the following sequence:

Whiteboard Exchange: Model Numbers with Quick Tens and Ones

Students model and say a two-digit number using tens and ones to prepare for adding two-digit numbers to one-digit numbers.

Display the number 11.

Draw tens and ones to show the number 11.

Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

Display the answer.

On my signal, say how many tens and how many ones. Ready?

1 ten 1 one

Display the number in unit form.

Repeat the process with the following sequence:

Teacher Note

Encourage students to draw dots in 5-group rows or columns when drawing the ones.

Teacher Note

Although drawing 1 ten and 10 ones to represent the number 20 is mathematically correct, invite students to group the extra ones into another ten whenever possible.

Launch

Students represent and add a two-digit number to a one-digit number.

Display the picture of 41 rocks in containers.

Zoey collects rocks.

Invite students to think–pair–share about Zoey’s collection of rocks.

What do you notice about her collection?

4 boxes have 10 rocks. One box has only 1 rock.

Why are there empty spots?

She has 41 rocks.

Confirm that Zoey has 41 rocks so far.

Display the picture of the collection with 7 more loose rocks.

She gets 7 more rocks. How many rocks does she have now?

Ask students to draw a picture and write a number sentence on their whiteboard to find the total. Look for a student who draws tens and ones and invite them to share.

Imani, how many rocks does she have now? How do you know?

Zoey has 48 rocks. I drew 41 as tens and a one. Then I drew 7 more ones. That made 4 tens and 8 ones.

41 + 7 = 48

Ask students to show thumbs-up if they used the same strategy.

Differentiation: Support

Instead of drawing, students can use cubes to add a two-digit number to a onedigit number.

Record 41 + 7 = .

Imani thought of 41 as 4 tens 1 one.

Write 40 + 1 + 7 = .

She added the ones first. 1 + 7 = 8.

Write a number bond by drawing arms from 1 and 7 and write the total of 8.

What is 40 + 8?

48

Write 48 as the total of 40 + 1 + 7.

So what is 41 + 7?

48

Write the total to complete the equation 41 + 7 = .

Why does adding the ones first make this problem easier?

We know 1 + 7 and we know 40 + 8.

Sometimes doing two simple problems is more efficient than doing a problem like 41 + 7.

Transition to the next segment by framing the work.

Today, we will practice adding the ones first to make other addition problems easier.

Teacher Note

When working on their own, students may show their thinking by using number bonds in different ways. See these examples:

Learn

Decompose to Add

Students decompose a two-digit addend into tens and ones and add the ones first.

Display the picture of 25 rocks in containers.

How many rocks are in this collection? How do you know?

There are 25 rocks. There are 2 tens and 5 ones.

Suppose we add 4 more rocks to this collection. How many rocks would there be then?

Pair students. Have partners find the total by drawing the problem and writing a number sentence. Then have students turn and talk to their partner to compare their work. Look for a student who draws 25 as 2 tens 5 ones and combines the ones first. Invite them to share.

5 + 4 = 9 20 + 9 = 29

You made an easier problem to find the total of 25 + 4. How?

First, I added the ones and got 9. Then I added 9 to 20.

Write 25 + 4 = and invite students to follow along on their whiteboard.

We drew 25 as 2 tens, or 20, and 5 ones. We also drew 4 more ones.

Write 20 + 5 + 4 =  .

Let’s add the ones first. What is 5 + 4?

9

Differentiation: Challenge

Use 26 + 6. Students are likely to decompose 26 as 20 and 6 and add the ones first. They may mentally add 20 and 12 or add 10 and then 2.

Write a number bond by drawing arms from 5 and 4 and write the total of 9.

What is 20 + 9? 29

Write 29 as the total of 20 + 5 + 4.

So what is 25 + 4? 29

Write the total to complete the equation 25 + 4 = . Invite students to think–pair–share about how decomposing made the problem easier.

How did we make an easier problem?

We broke 25 into 20 and 5 so we could add the ones and then the tens.

As time allows, repeat the process with 33 + 6 and 52 + 3. Release responsibility to the students as appropriate.

Raceway Addition Game

Materials—S: Raceway Addition Game removable, counter, 6-sided dot die Students practice adding a two-digit number to a one-digit number.

Gather students and give them the directions for the Raceway Addition game.

• Each partner places a counter on a car at the starting line. Students move around separate tracks, but each track has the same number of spaces.

• Students take turns rolling a die and solving the problem on the space where they land. Students may select tools to help them add, such as drawing the tens and ones or using number bonds.

• Each student must land on the last problem on their track before crossing the finish line. If they roll a number that is too high, they wait until their next turn to roll again.

Promoting the Mathematical Thinking and Reasoning Standards

As students add by decomposing the first addend into tens and ones, they use structure to help them understand and connect mathematical concepts (MTR.5). For example, in the expression 25 + 4, students use the structure of 25 as 2 tens 5 ones:

Then they use their intuitive understanding of the associative property to group the 5 and the 4 before adding in the tens, making use of the structure of a three-addend expression:

Use these questions to promote MTR.5:

• How did you represent the two-digit addend? Why was that helpful?

• What did you add together first? Why does that work? What did you do next?

Distribute the materials and have students play for 6 to 7 minutes. As they work, assist as necessary. Notice which tools students choose to help them add. For example, students could choose mental math, drawing, or number bonds.

Problem Set

Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. Directions may be read aloud.

Land

Debrief 5 min

10 10 30 10

Objective: Add the ones first.

Write 3 + 6 =     .

What is 3 + 6?

9

Write 9 to complete the equation. Write 43 + 6 =      .

What easier problem do you see in 43 + 6?

3 + 6

Circle 3 + 6.

How can knowing 3 + 6 help us with 43 + 6?

If I know 3 + 6, 43 + 6 will just be 40 more.

We can think of 43 as 40 and 3.

Write 40 + 3 + 6 = .

UDL: Representation

After drawing the number bond and finding the total, consider pausing and asking students to stop and think about how breaking up an addend makes a problem easier. Emphasize that it can be easier to add parts such as 3, 6, and 40 rather than 43 and 6.

Let’s add the ones first. What is 3 + 6?

9

Write a number bond by drawing arms from 3 and 6 and write the total of 9.

What is 40 + 9?

49

Write 49 as the total of 40 + 3 + 6.

So what is 43 + 6?

49

Write the total to complete the equation 43 + 6 = .

Why can it be helpful to break up a number into tens and ones to add it to another number?

We can add the ones first and then add the ten. Breaking up the number makes two easy problems instead of one harder problem.

Exit Ticket 5

min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

Add the ones to make the next ten.

Lesson at a Glance

Students look at two-digit numbers on the rekenrek and think about how many more ones they need to make the next ten. They study sequences of related equations and notice the usefulness of identifying partners to 10 in the ones place. They make easier problems by adding partners to 10 first.

Key Question

• How is knowing partners to 10 helpful when adding a two-digit number to a one-digit number?

Achievement Descriptor

FL.1.Mod5.AD7 Add a two-digit number and a one-digit number that have a sum within 100 by using manipulatives, number lines, drawings, or models. (MA.1.NSO.2.4)

Agenda Materials

Fluency 5 min

Launch 5 min

Learn 40 min

• Use a Basic Fact

• How Many to Make Ten?

• Make an Easier Problem

• Problem Set

Land 10 min

Teacher

• 100-bead rekenrek

• Math Past resource

Students

• Number Path to 120 (1 per student pair, in the student book)

Lesson Preparation

Make sure each student pair has a Number Path to 120 from module 3 lesson 14. If more are needed, they will need to be torn out of the student books and each section cut out. Consider whether to prepare these materials in advance or to have students prepare them during the lesson. Consider saving these for use throughout the topic.

Fluency

Whiteboard Exchange: Relate Subtraction and Addition

Students relate subtraction and addition to build an understanding of subtraction as an unknown-addend problem.

After each prompt for a written response, give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

Display 7 – 5 = .

Write the subtraction equation.

Write a related addition sentence starting with 5 that would complete the equation.

Display the related addition sentence.

Write the answer to the subtraction equation.

Display the difference.

Repeat the process with the following sequence:

Launch

Materials—T: 100-bead rekenrek, Math Past resource

Students discuss how many more they need to make the next ten by exploring the Math Past resource.

Show 14 on the rekenrek.

Say how many the Say Ten way.

1 ten 4

The Yoruba people from West Africa call this 4 past 10.

Invite students to think–pair–share about why the Yoruba people call 14 4 past 10.

Why do you think they call it 4 past 10? 14 is 10 and 4 more.

When we count, 14 is 4 more than 10.

Show 15 on the rekenrek.

Say how many the Say Ten way.

1 ten 5

The Yoruba people call this 5 before 20.

Invite students to think–pair–share about why the Yoruba people call 15 5 before 20.

Why do you think they call it 5 before 20?

15 is 5 less than 20.

15 and 5 make 20.

The Yoruba people of West Africa have deep mathematical traditions dating back centuries. They are also famous for their drumming!

Our numbers are based on ten, but Yoruba numbers, like Maya numbers, are based on 20. One distinguishing aspect of the Yoruba system is that it uses subtraction to name numbers.

Review the Math Past in the Module Resources for more information and teaching resources.

The Yoruba people are thinking about how many more they need to make the next ten, which is 20. 15 and 5 more make 20.

Show 16 on the rekenrek.

What is the next ten? 20

How many more are needed to make 20? 4

16 and 4 more make 20. The Yoruba people say 4 before 20 for 16. If time allows, repeat the process with 17, 18, and 19. Transition to the next segment by framing the work.

Today, we will look at some other two-digit numbers and see how many ones we need to make the next ten.

Learn

Use a Basic Fact

Materials—T: 100-bead rekenrek

Students use the basic fact 8 + 2 to make the next ten. Consider using choral response for the following questions.

Show 8 on the rekenrek.

How many? 8

How many more ones do we need to make ten?

Slide over 2 beads to make ten.

Say the number sentence that shows how we made the next ten.

8 + 2 = 10

Show 18 as a new starting number.

How many?

18

What is the next ten?

20

How many more ones do we need to make the next ten? 2

Slide over 2 beads to make 20.

Say the number sentence that shows how we made the next ten.

18 + 2 = 20

Repeat the process by using 28, 38, 48, 58, 68, 78, and 88 as new starting numbers. Display the list of number sentences you recorded.

These are the number sentences we showed on the rekenrek.

What do you notice?

The totals count by tens.

We added 2 every time.

The first addend always has 8 in the ones place.

8 and 2 are partners to 10. When a two-digit number has 8 ones, we can add 2 to make the next ten.

How Many to Make Ten?

Materials—S: Number Path to 120

Students find the unknown partner that makes the next ten. Pair students. Give each set of partners the six sections of the Number Path to 120 to assemble or distribute the number paths that they already assembled in module 3. Ask pairs to take their student books and move to workspaces where they have enough room to put together or lay out the number path sections (1-20, 21-40, 41-60, 61-80, 81-100).

Once the number paths are ready, ask students to turn to the string of related problems in their student book. Direct their attention to the first problem. Consider guiding students with the digital interactive number path.

What is 7’s partner to 10? 3

Have students write the unknown addend in their books. Guide them to show 7 + 3 = 10 by using their fingers to hop on the number path. Direct them to the next problem.

Find 17 on the number path. What is the next ten?

Hop to 20. How many times did you hop?

Have students write the unknown addend in their books. Use the same procedure for 27 + 3 = 30 and 37 + 3 = 40. Have students complete both the total (the next ten) and the unknown addend.

Invite students to complete the last two problems on their own (47 + 3 = 50 and 57 + 3 = 60). Some students may continue to use the number path while others make use of the pattern.

Differentiation: Support

Students may also benefit from making the next ten concretely by using Unifix Cubes.

Promoting the Mathematical Thinking and Reasoning Standards

Students look for and use structure to help them understand and connect mathematical concepts (MTR.5) when they find the unknown addend in a sequence of problems where the first addends all have the same digit in the ones place.

Students come to understand that they can use partners to 10 to figure out which addend is needed to get to the next ten. This is the first step toward extending the make ten strategy to larger numbers.

Display the list of equations with the 7s highlighted.

What do you notice?

I can count the totals by tens.

We added 3 every time.

The first addend always has 7 in the ones place.

Why did we add 3 to make the next ten every time?

7 and 3 are partners to 10. They make ten.

Invite students to think–pair–share about what the next number sentence on the list would be.

What would be the next number sentence on our list?

67 + 3 = 70

Display the list of three equations with the tens place highlighted.

What happens to the number of tens when we make the next ten?

There is 1 more ten.

Why does the number of tens grow by 1?

It happens because we made another ten with the ones.

We used the ones from both addends to compose a new ten. Have students clean up the number paths.

Make an Easier Problem

Students add the ones first to make the next ten and to make an easier problem.

Write 25 + 5 =       .

Which partners to 10 do you see in 25 + 5?

5 + 5

Differentiation: Support

Consider having students draw the problems to understand why the tens digit grows by 1 each time. For example:

We can think of 25 as 20 and 5.

Circle 5 + 5.

(Gesture to 25 + 5.) How can knowing partners to 10 help us make an easier problem?

If we make ten with 5 + 5, then we can just add 10 to 20. That is 30.

Write 20 + 5 + 5.

We can add the ones that make ten first.

Write a number bond by drawing arms from 5 and 5 to a total of 10.

What is 20 and 10?

30

So what is 25 + 5?

30

Write 21 + 9 = . Have students follow along on their whiteboard. Invite partners to find the total by using mental math or by drawing. Invite a student to share the partners to 10 that helped them to make an easier problem.

Problem Set

Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex.

Directions may be read aloud.

Students may use cubes, number paths, drawings, or number bonds to complete the problems.

Differentiation: Challenge

Write three equations: 25

Ask students to explain why they all have the same total, 30.

Consider having students write their own equations that result in a total that is the next ten. Have partners trade equations and find the totals.

Land

Debrief 5 min

Objective: Add the ones to make the next ten. Display the segment of the number path with the equation.

What is the part we know?

73 Circle 73.

What is the next ten?

80

Invite students to think–pair–share about the number of hops there will be from 73 to 80.

How many hops are there from 73 to 80? How do you know?

There are 7 hops. I know because I counted the spaces on the number path.

There are 7 hops. I know because 3 and 7 are partners to 10. So 73 and 7 make 80.

Draw an arrow from 73 to 80 and label it + 7. Complete the equation.

Which partners to 10 do you see?

3 + 7 = 10

How can finding 3 + 7 = 10 help us make it easier to figure out 73 + 7?

If we do 3 + 7 first, we get 10. Then we add 10 and 70. That’s 80.

Language Support

Support students to verbalize their ideas by providing a sentence frame that can help them describe how one number sentence can help them solve another number sentence.

+ helps me figure out +  because .

How is knowing partners to 10 helpful when you add a two-digit number to a one-digit number?

We can look for the number of ones to make the next ten.

When the ones are partners to 10, you make the next ten. Then you just add tens to tens to get the answer.

Exit Ticket 5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

Decompose an addend to make the next ten.

Lesson at a Glance

Students share a variety of ways to add 28 and 6 during a Math Chat, including making the next ten. Students make ten when combining sets and adding a two-digit number to a one-digit number. They are encouraged to show their thinking by using drawings or number bonds, but students may also self-select cubes or number paths.

Key Question

• How can we make an easier problem when adding a two-digit number to a one-digit number?

Achievement Descriptor

FL.1.Mod5.AD7 Add a two-digit number and a one-digit number that have a sum within 100 by using manipulatives, number lines, drawings, or models. (MA.1.NSO.2.4)

Agenda Materials

Fluency 10 min

Launch 10 min

Learn 30 min

• Make the Next Ten

• Break Apart an Addend

• Problem Set

Land 10 min

Teacher

• None Students

• None

Lesson Preparation

Copy or print the student work with the sets of marbles, crayons, and pencils to use for demonstration.

Fluency

Choral Response: Tell Time

Students tell time to the nearest half hour to build fluency with telling time from topic A.

Display the clock that shows 3:00.

What time does the clock show? Raise your hand when you know.

Wait until most students raise their hands, and then signal for students to respond.

3:00

Display the answer.

Repeat the process with the following sequence:

Choral Response: Subtract 4, 5, or 6

Students subtract 4, 5, or 6 to build subtraction fluency within 10.

Display 6 – 4 =   .

What is 6 – 4? Raise your hand when you know.

Wait until most students raise their hands, and then signal for students to respond.

2

Display the answer.

Repeat the process with the following sequence:

Whiteboard Exchange: Model Numbers with Quick Tens and Ones

Students find how many more to make the next ten and write a number sentence to develop fluency adding one-digit numbers to two-digit numbers.

After each prompt for a written response, give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

Display the number 18.

Draw tens and ones to show the number 18.

Display the answer.

How many more do we need to make the next ten? Raise your hand when you know.

Wait until most students raise their hands, and then signal for students to respond.

Display two additional ones.

Write an addition sentence starting with 18.

Display the addition sentence.

Repeat the process with the following sequence:

Launch

Students discuss how to find a total by decomposing an addend to make the next ten.

Display the picture of the roller coaster.

What do you notice?

10 children can fit in a car.

The last roller coaster car has two empty seats.

28 children are on the roller coaster—10, 20, 28.

6 children are in line.

Use the Math Chat routine to engage students in mathematical discourse. Give students a few minutes of silent think time to find the total number of children shown in the picture. Have students give a silent signal to indicate when they are ready.

Ask students to discuss their thinking with a partner. Circulate and listen as they talk. Identify a few students to share their ideas with the class. If possible, choose a student who finds the total by thinking of 28 and then making the next ten by adding 2 more to make 30.

(See Traun’s sample work.) If no one shares making the next ten, then demonstrate how.

Invite the selected students to share their thinking with the whole group. As students share, record their ideas. Have students use the Talking Tool to engage with one another.

How many total children are there? How did you figure it out?

Felipe: 34 children. 28 children are on the roller coaster. I counted on 6 more.

Ming: I see 10 and 10. I added 8 and 2 to make another ten. That is 30.

30 + 4 = 34.

Traun: 28 children are on the roller coaster. 28 and 2 more make 30.

30 + 4 = 34.

There are 28 students on the rollercoaster. What is the next ten?

30

Traun, how did you know that 28 and 2 make the next ten?

8 and 2 are partners to 10, so 28 and 2 make 30.

Where did the 2 come from?

You can break apart the number of children standing in line, 6, into 2 and 4.

How does breaking apart the 6 children in line make finding the total easier? We can get 2 to make a ten.

28 and 2 make 30.

We can easily add 30 and 4.

Transition to the next segment by framing the work.

Today, we will make addition problems easier by breaking apart an addend to make the next ten.

Learn

Make the Next Ten

Students combine two sets of objects by composing a ten to make the next ten. Tell students to turn to the page that shows the sets of objects. Direct their attention to the marbles.

How many marbles are in the first group?

28

What is the next ten? 30

How many more marbles do we need to make 30? Where can we get them?

We can break up the other group of 8 into 2 and 6. Invite students to circle 30 marbles.

What is the total number of marbles? How do you know? 36

There are 3 tens and 6 ones.

Show the student page and model making the next ten using a number bond. Prompt students to follow along.

Write 28 + 8 = . Point to 28.

What is the next ten? 30

How many does 28 need to make 30?

UDL: Action & Expression

Consider providing access to a Number Path to 120 to support students in identifying the next ten. In this example, they would point to 28 and identify 30 as the next ten. They can use their finger to count hops from 28 to 30.

Where can we get 2?

We can break up 8 into 2 and 6.

Draw a number bond to decompose 8 into 2 and 6.

(Circle the numbers 28 and 2.) What is 28 and 2?

30

(Write 30 + 6 = .) What is 30 and 6?

36

Write 36.

So, what is 28 + 8?

36

Write the total in the original equation.

Repeat the process with the next two sets, releasing responsibility to the students as appropriate.

Break Apart an Addend

Students find a total by decomposing an addend to make the next ten.

Have students ready their personal whiteboards. Write 35 + 6 = and ask students to do the same. Ask them to draw 35 and 6 with quick tens.

(Point to 35.) How can we make the next ten? How do you know?

We can make 40 with 5 ones from the 6 ones.

5 and 5 are partners to 10, so 35 and 5 make the next ten, 40. Prompt students to circle 40 and write the total, 41.

Promoting the Mathematical Thinking and Reasoning Standards

When students use a drawing, a number bond, or a three-addend number sentence to show how to add by making the next ten, they are demonstrating understanding by representing problems in multiple ways (MTR.2).

Students are encouraged to think about how many ones are needed to make the next ten, rather than counting on. Using these multiple ways helps students see how they can use this strategy without a countable representation.

Differentiation: Support

Allow students to use cubes or a number path to complete the problems rather than drawings or number bonds.

Then guide students to make the next ten with a number bond using the process used in the previous segment:

• Write the equation and point to the first addend.

• Determine the next ten and how many ones are needed to make it. (Encourage students to consider partners to 10.)

• Break apart the second addend with a number bond.

• Write the new, easier number sentence.

• Write the total in the original equation.

Have students erase their whiteboads and write 39 + 8 = . Ask them to find the total by making the next ten. Invite them to select the tool of their choice, such as drawings, number bonds, cubes, or a number path, to complete the problem. As students work, circulate to support and assess their thinking.

Problem Set

Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex.

Directions may be read aloud.

Students may use cubes, number paths, drawings, or number bonds to complete the problems.

A numerical representation can be shown in more than one way. For example, you may just circle the 28 and 2 to show the composition as in the sample. Or, it may be helpful to label the circled numbers as the next ten.

Some students may benefit from seeing the composition represented by a three-addend number sentence.

Take care to avoid making a procedure of any particular recording. The recording is a tool to help students show and explain their thinking.

Land

Debrief 5 min

Objective: Decompose an addend to make the next ten.

Display Felipe’s tool, a drawing.

How did Felipe use a drawing to add 75 and 7?

He drew tens and ones to show 75 and 7. Then he circled 5 ones from 75 and 5 ones from 7 to make the next ten, 80.

Display Ming’s tool, a number bond.

How did Ming use a number bond to add 75 and 7?

She broke up 7 into 5 and 2, just like Felipe. She made the next ten, 80, by circling 75 and 5.

Display Traun’s tool, the number path.

How did Traun use the number path to add 75 and 7?

He looked at 75 and thought about how many more he needed to make 80. Then he saw it was 5, so he drew an arrow with + 5. Then he had to add 2 more because 7 is 5 and 2.

We can add by breaking up one addend to make the next ten with the other addend. We can use many tools to help us make ten, like cubes, drawings, number bonds, and the number path.

Turn and talk. Which tool is most helpful to you when you make the next ten?

Exit Ticket 5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Teacher Note

Stage 3 strategies such as make the next ten require time and practice to learn. At first students directly model with a drawing or cubes. They progress to independently using number bonds and number sentences.

Expect variety in their representations. If students use cubes, encourage them to show what they did with a drawing. When working independently, it is not necessary for students to draw a picture and use number bonds; they may choose one or the other.

Some students may choose to use the number path and record their hops with arrows:

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

Reason about related problems that make the next ten.

Lesson at a Glance

Students use a number path to find totals using the make the next ten strategy. They find the totals in a string of related problems by decomposing the one-digit addend to make the next ten with the two-digit addend. Students find the totals of related problems and discuss the patterns they find.

Key Question

• How does the make the next ten strategy help us add?

Achievement Descriptor

FL.1.Mod5.AD7 Add a two-digit number and a one-digit number that have a sum within 100 by using manipulatives, number lines, drawings, or models. (MA.1.NSO.2.4)

Agenda Materials

Fluency 10 min

Launch 15 min

Learn 25 min

• Number String

• Problem Set

Land 10 min

Teacher

• None Students

• Number Path to 40 (in the student book)

• Number Path to 120 (1 per student pair, in the student book)

Lesson Preparation

• The Number Path to 40 must be torn out of student books and placed in personal whiteboards. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

• The Number Path to 120 is composed of 6 pieces. It must be torn out of student books and cut into pieces. Decide whether to prepare one set of 6 pieces per student pair in advance or to have students prepare them during the lesson.

Fluency

Choral Response: Tell Time

Students tell time to the nearest half hour to build fluency with telling time from topic A.

Display the clock that shows 2:00.

What time does the clock show? Raise your hand when you know.

Wait until most students raise their hands, and then signal for students to respond.

2:00

Display the answer.

Repeat the process with the following sequence:

Counting with Coins

Materials—None

Students identify the name and value of a nickel, and then count by fives to build fluency counting money.

After asking each question, wait until most students raise their hands, and then signal for students to respond.

Raise your hand when you know the answer to each question. Wait for my signal to say the answer.

Display the picture of the front side of a nickel.

What is the name of the coin?

Nickel

How many cents is it worth?

5 cents

Differentiation: Support

Encourage students to use what they know about counting by tens to count by fives by using the following steps:

• Display a set of 4 nickels. Circle groups of 2 nickels.

• Say, “5 cents and 5 cents make …”

• Gesture to each group of 2 nickels as students count by 10 cents.

• Remove the circles, and then count the same set by 5 cents. nickel

Let’s count by 5 cents. Start at 50 cents. Count up to 70 cents, and then back down to 50 cents. Ready?

Display each nickel, one at a time, as students count.

50 cents, 55 cents, 60 cents, 65 cents, 70 cents

70 cents, 65 cents, 60 cents, 55 cents, 50 cents

Number Path Hop: Hop to the Next Ten

Materials—S: Number Path to 40

Students represent addition within 40 on the number path by writing a number sentence to develop fluency with making the next ten when adding to a two-digit number.

Make sure students have a personal whiteboard with a Number Path to 40 removable inside.

After each prompt for a written response, give students time to work. When most students are ready, signal for them to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

Display the expression 18 + 3.

Write the expression 18 + 3.

Circle 18 on your number path.

Display the number 18 circled.

Hop to the next ten on your number path. Label your hop.

Display the labeled hop.

How many more do we need to hop to add 3 altogether?

Hop 1 more on your number path. Label your hop.

Display the labeled hop.

Write the complete number sentence.

Display the total.

Repeat the process with the following sequence:

Launch

Materials—S: Number Path to 120

Students represent addition scenarios by showing hops on a number path. Pair students. Give partners the six sections of the Number Path to 120 to assemble, or distribute the number paths they assembled in lesson 11. Have pairs move to workspaces where they have enough room to put together or lay out the number path.

Display the image of students with their science fair projects.

There are 100 science projects at the school science fair. Each project is on a table with a number. The tables are in order from 1 to 100.

Teachers ask a few students at a time to choose a science project and then to give the student who created it a compliment.

Display the image of the students talking.

The first group of students notice that all of their table numbers end in 5. They each decide to compliment the student who is 7 tables up from them. They wonder if there will be a pattern in the table numbers they will go to.

Invite students to turn and talk about the story.

Tell students to use their number paths to find the table numbers that the students go to. Consider showing their thinking on the digital interactive number path.

Nate starts at table 5. He goes to the table that is 7 up from 5 to deliver his compliment.

What table number does he go to? How do you know?

We hopped 1 space at a time and landed on 12.

We hopped 5 to 10 and then we hopped 2 more to 12. We just hopped to 12. We know 5 + 7 = 12.

Violet starts at table 15. She goes to the table that is 7 up from 15 to deliver her compliment.

What table number does she go to? How do you know?

If possible, invite a pair who makes the next ten to share their thinking. We hopped 5 to the next ten, which is 20. Then we hopped 2 more to 22.

Sam starts at table 25. He goes to the table that is 7 more than 25 to deliver his compliment.

What table number does he go to? How do you know?

It’s 32. We hopped 5 to the next ten, which is 30. Then we hopped 2 more to 32.

Liv starts at table 35. She goes to the table that is 7 more than 35 to deliver her compliment.

What table number does she go to? How do you know?

It’s 42. We hopped 5 to the next ten, which is 40. Then we hopped 2 more to 42.

Display the list of number sentences for each situation.

What do you notice?

All of the students’ first table numbers have 5 ones.

We added 7 each time.

In the new table numbers, the ones place always has a 2. The tens place goes up 1 ten.

What did we do the same every time on the number path?

We always hopped 5 to make the next ten. We always hopped 2 more.

We always hopped 5 to make the next ten. 5 ones needs 5 more to make a ten. We broke up the 7 into 5 and 2 to make ten. Then we always had 2 ones left.

So, do the table numbers the students went to have a pattern too?

Yes, they all end in 2 ones.

Have pairs set aside their number paths.

Differentiation: Challenge

Invite students to consider what the table number would be if they walked up 7 from table 65.

Transition to the next segment by framing the work.

Today, we will make ten to add and look for patterns between the problems.

Learn Number String

Students find the totals of related problems and explain the patterns they see. Have students ready their personal whiteboards.

Display each problem in the following sequence. For each problem, ask students to find the total, and provide work time. Students can signal when they are ready. The sample work shows solutions that were found by using number bonds, but students may self-select from several tools (see Teacher Note).

Display the first problem.

What is 8 + 6? How do you know?

14

I made ten. 8 and 2 is 10. 10 and 4 is 14.

Display the total and the second problem.

What is 18 + 6? How do you know?

It’s 24. I broke up 6 into 2 and 4. 18 and 2 make the next ten, 20.

18 + 6 = 24. 18 is 10 more than 8, and 8 + 6 = 14, so I just added 10 more.

Display the total and the third problem.

What is 28 + 6? How do you know?

34. I broke up 6 into 2 and 4. 28 and 2 make the next ten, 30.

It’s 34. 28 is 10 more than 18, and 18 + 6 = 24, so I just added 10 more.

Invite students to think–pair–share about what the next problem will be.

What will the next problem be? Why?

It will be 38 + 6 because the first part gets bigger by 10 each time. And we add 6 each time.

Display the total and the final problem. Before students find the total, ask the following question.

Do you see a pattern that can help us figure out 38 + 6?

The totals all have 4 ones.

The tens place in the totals are going up 1 ten every time.

The totals are counting by tens: 14, 24, 34, 44.

Have students make the next ten to confirm the total.

Display the total.

Invite students to think–pair–share about why there is always 4 in the ones place.

Why is there always 4 in the ones place?

We always broke up 6 into 2 and 4 to make ten with 8.

As time allows, continue the string with 48 + 6, and so on. Have students do the following:

• Predict the next problem,

• use the pattern to find the total, and

• confirm the total by making the next ten.

Alternatively, present a related problem from further down in the sequence, such as 68 + 6.

Have students compare it to other problems in the set.

Differentiation: Support

Consider using color to highlight the patterns in the number string.

Differentiation: Challenge

Show several addition expressions with one-digit addends. See the examples below. Invite partners to choose one expression and to use it as a starting problem to write their own number string. Partners may solve their own string or trade their string with another pair’s string.

Problem Set

Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex.

Directions may be read aloud.

Students may use cubes, number paths, drawings, or number bonds to complete the problems. Encourage students to show their thinking.

Land

Debrief 5 min

Objective: Reason about related problems that make the next ten.

Gather students with their Problem Sets. Select a problem that most students finished, such as 28 + 7 = 35. Invite students to think–pair–share about how they found the total. Consider charting the various tools students used to make the next ten.

I used the pattern 15, 25, 35. I drew quick tens and ones. I circled a ten.

I drew a number bond. I broke up 7 into 2 and 5 to make the next ten, 30.

I used the number path. I hopped 2 to 30 and then 5 to 35.

Promoting the Mathematical Thinking and Reasoning Standards

As students consider how others represented the problem, they engage in discussions that reflect on their mathematical thinking and that of others (MTR.4).

Ask the following questions to promote MTR.4:

• How did you find the total? Why did you do it that way?

• How did your partner find the total? How is that way the same or different from the way you found the total?

• What questions can you ask your partner about how they found the total?

How does the make the next ten strategy help us add?

With big numbers, it means you don’t have to count on. It’s quicker because you can look for a smaller fact you know.

It helps you because you can do a problem with big numbers just in your head.

Exit Ticket 5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Sample Solutions

Expect

Determine which equations make the next ten.

Lesson at a Glance

CStudents analyze and find the totals for related addition problems. They use repeated reasoning to help them recognize when they can make ten or make the next ten. They test the patterns they find on additional sets of problems to confirm their thinking.

Key Question

• Why can it be useful to look at the numbers in the ones place before you solve a problem?

Achievement Descriptor

FL.1.Mod5.AD7 Add a two-digit number and a one-digit number that have a sum within 100 by using manipulatives, number lines, drawings, or models. (MA.1.NSO.2.4)

Agenda Materials

Fluency 10 min

Launch 10 min

Learn 30 min

• Will it Make the Next Ten?

• Sort and Solve

• Problem Set

Land 10 min

Teacher

• Sort and Solve cards (digital download)

Students

• Subtract within 20 Sprint (in the student book)

• Sort and Solve cards (1 set per student pair, in the student book)

• Crayons (1 red crayon, 1 green crayon, 1 blue crayon per student)

Lesson Preparation

• The Subtract within 20 Sprints and the Sort and Solve cards must be torn out of student books. Each of the Sort and Solve cards must also be cut out. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

• Copy or print the Sort and Solve cards to use for demonstration.

Fluency

Sprint: Subtract Within 20

Materials—S: Subtract Within 20 Sprint

Students write the difference to build procedural reliability for subtraction within 20.

Have students read the instructions and complete the sample problems.

Teacher Note

The Sprint focuses mainly on subtraction problems students have practiced in Fluency in topics A–C. The types of problems include subtract 1, subtract 1 less, and subtract 4, 5, or 6.

Direct students to Sprint A. Frame the task.

I do not expect you to finish. Do as many problems as you can, your personal best.

Take your mark. Get set. Think!

Time students for 1 minute on Sprint A.

Stop! Underline the last problem you did.

I’m going to read the answers. As I read the answers, call out “Yes!” and mark your answer if you got it correct.

Read the answers to Sprint A quickly and energetically.

Count the number you got correct and write the number at the top of the page. This is your personal goal for Sprint B.

Celebrate students’ effort and success.

Provide about 2 minutes to allow students to analyze and discuss patterns in Sprint A.

Lead students in one fast-paced and one slow-paced counting activity, each with a stretch or physical movement.

Teacher Note

Consider asking the following questions to discuss the patterns in Sprint A:

• What do you notice about problems 1–5? About 6–10? About 11–15?

• What strategy did you use to solve problem 16?

Point to the number you got correct on Sprint A. Remember this is your personal goal for Sprint B.

Direct students to Sprint B.

Take your mark. Get set. Improve!

Time students for 1 minute on Sprint B.

Stop! Underline the last problem you did.

I’m going to read the answers. As I read the answers, call out “Yes!” and mark your answer if you got it correct.

Read the answers to Sprint B quickly and energetically.

Count the number you got correct and write the number at the top of the page.

Stand if you got more correct on Sprint B.

Celebrate students’ improvement.

Launch Materials—S: Crayons

Students find the totals of related problems and discuss their strategies for solving them.

Tell students to turn to the three-column chart of equations in their student book. Guide their attention to the blue column. Ask them to add 17 and 2 and to signal when they are ready.

What is 17 + 2? Did you make the next ten? Why? 19

I didn’t make the next ten because 7 and 2 only make 9.

Teacher Note

Have students count on by tens from 4 to 94 for the fast-paced counting activity.

Have students count back by tens from 94 to 4 for the slow-paced counting activity.

Ask students to find the total of 17 + 3 and to signal when they are ready.

What is 17 + 3? Did you make the next ten? Why?

20

I did make the next ten. 7 and 3 are partners to 10. Ask students to find the total of 17 + 4 and to signal when they are ready.

What is 17 + 4? Did you make ten to find the total? How did you do that?

21

17 needs 3 more to make 20. I broke up 4 into 3 and 1. 20 and 1 is 21.

For 17 + 4 we can make the next ten and have extra ones.

Display the completed problems. Ask students to look at them carefully. Invite students to think–pair–share about when they need to make the next ten to add.

Do we always make the next ten to add? Why?

No, there aren’t always enough ones to make ten.

Tell students to take out their red, blue, and green crayons. Have them look at their work on the problems in the blue column and guide them to do the following:

• Use a red crayon to circle the problem where the numbers do not make the next ten.

• Use a green crayon to circle the problem where the numbers do make the next ten.

• Use a blue crayon to circle the problem where the numbers make the next ten and there are extra ones.

Transition to the next segment by framing the work.

Today, we will figure out how to tell if we can make the next ten in a problem before we find the total.

Encourage students to use tools to find the totals. For example, they may draw, use a number path, or use cubes.

Will It Make the Next Ten?

Materials—S: Crayons

Students look at the numbers in the ones place to see whether they will make the next ten.

Turn students’ attention to the first problem, 28 + 1, in the green column of the threecolumn chart.

Let’s take time to make sense of this problem before we solve it. Look at the numbers in the ones place. Can we make the next ten? Why?

No, we can’t. 8 and 1 make 9. They are not partners to 10.

Have students add to confirm their idea and ask a student to share their total.

Our idea was correct. We did not make the next ten. When we put together the ones in each addend, they do not make ten. Let’s use our red crayon to circle 28 + 1.

Ask students to look at 28 + 2.

Let’s take time to make sense of this problem before we solve it. Look at the numbers in the ones place. Can we make the next ten? Why?

Yes, I think we can. 8 and 2 are partners to 10.

Have students add to confirm their idea and ask a student to share their total.

Our idea was correct. We made the next ten. When we put together the ones in each addend, they make ten. Let’s use our green crayon to circle 28 + 2.

Ask students to look at 28 + 3.

Let’s take time to make sense of this problem before we solve it. Look at the numbers in the ones place. Can we make the next ten? Why?

Yes, we can. 8 and 2 are partners to 10. And 8 and 3 make more than that. We’ll make ten and have more left.

Look at the first addend, 28. How many does it need to make the next ten?

Where can we get 2 to add to 28?

From the 3

How many extra ones will we have?

Have students add to confirm their idea and ask a student to share their total.

Our idea was correct. We made the next ten. When we put together the ones in each addend, they make more than ten. We even have extra. Let’s use our yellow crayon to circle 28 + 3.

Display the three categories and read them out loud.

Pair students and have partners find the total of the problems in the pink column. Ask students to use their crayons to circle the problems according to the categories shown. When they finish, ask students to share their work for each problem.

Display the problems students circled in red.

Look at your work. Why do all of these problems go together?

We circled them with the red crayon. They do not make the next ten.

Why can’t we make the next ten in these problems?

The ones add to less than ten.

Display the problems students circled in green.

Look at your work. Why do all of these problems go together?

We circled them in green. They make the next ten.

Why can we make the next ten in these problems?

The ones are partners to 10.

Display the problems students circled in yellow.

Look at your work. Why do all of these problems go together?

We circled them in yellow. They make the next ten and have extra ones.

Why can we make the next ten and have extra ones in these problems?

When you put together the ones, they make more than 10.

Is there a way to see if we can make the next ten before we solve the problem? How?

Yes. We can look at the ones and think about if they make partners to 10. Yes. If the ones make less than 10, then we can’t make the next ten.

Sort and Solve

Materials—T/S: Sort and Solve cards

Students play a sorting game to determine, without finding the total first, if given problems will make a new ten.

Make sure pairs have the Sort and Solve cards. Ask them to lay out the three category cards. Demonstrate the activity.

Put the problem cards in a pile. Partner A chooses a card.

Together, take time to make sense of the problem by looking at the numbers in the ones place. Sort the card by placing it into a group: Does Not Make 10, Makes Next 10, or Makes Next 10 and Extra Ones.

Partners A and B, you will find the total and check your thinking. Use your personal whiteboards. If you need to, change the group where you placed the card.

Partner B chooses the next card.

Promoting the Mathematical Thinking and Reasoning Standards

Students use patterns and structure to help them understand and connect mathematical concepts (MTR.5) when they use a sequence of problems to explain whether they can make the next ten in an addition problem. Later, they will continue to use structure to predict which problems will or will not make the next ten before finding the total.

Going forward, students can use their understanding of the structure of addition expressions to select an appropriate strategy and to reason about whether their answer makes sense.

UDL: Engagement

Foster collaboration during the game by assigning clear partner roles. Review the activity goal, directions, and group norms before pairs begin.

Consider explicitly adding into group norms the social-emotional skills that students will be practicing. These include sharing, taking turns, and respectfully disagreeing.

As students work, ask the following questions to assess and advance student thinking:

• How do you know if you can make a new ten?

• What is the next ten?

• How many more do you need to get to the next ten?

• How many extra ones will there be?

• What is the total? How do you know?

Problem Set

Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex.

Directions may be read aloud.

Land

Debrief 5 min

Objective: Determine which equations make the next ten. Display the three expressions.

Invite students to think–pair–share about which problem will make the next ten with no extra ones.

Which problem will make the next ten with no extra ones? How do you know?

It’s 25 + 5. 5 and 5 are partners to 10.

Look at 21 + 4. Will the total make the next ten? Why?

No, 1 + 4 is only 5.

Differentiation: Challenge

Invite students to make their own cards that would fit into the three categories.

Look at 29 + 6. What do you notice?

The ones make more than 10.

How would you show 29 + 6 and find the total?

We could make ten with a number bond. You’d have to break up the 6 into 1 and 5. We could draw quick tens and circle another ten, then count the tens and ones. We could hop on the number path. We would start at 29 and go 6 more.

Why can it be useful to look at the numbers in the ones place before you solve a problem?

You can tell if you can just add the ones or if you have to think about a way to break apart a number to make the next ten.

You might choose a different tool. If you see you can just add the ones, you might use your fingers. If you have to break apart a number, you might draw.

Topic Ticket 5 min

Provide up to 5 minutes for students to complete the Topic Ticket. It is possible to gather formative data even if some students do not complete every problem.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

3. Write number sentences that match the set.

Topic D Addition and Subtraction of Tens

To add and subtract tens, students extend their Stage 2 strategies of counting on and back. They represent units of ten by using rows of beads on a rekenrek, quick ten drawings, or their fingers. To add, they count on tens. To subtract, they count back tens or think about addition and count on tens from the known part to get to the total.

20, 30, 40, 50, 60, 70

Students also solve addition and subtraction problems involving multiples of ten by using a Stage 3 strategy. They represent the equation in unit form and notice an easier one-digit fact. They use the same strategy to find an unknown part in an addition or subtraction equation involving multiples of ten.

80, 70, 60, 50, 40

Optional lessons in this topic offer several opportunities for extension. For example, to practice adding and subtracting tens, students are presented with number sentences that include two addition or subtraction expressions. For example, 20 + 30 = 60 – 10 (true) or 50 + 10 = 60 – 10 (false). They determine whether the number sentences are true or false by calculating the value of each expression.

The rekenrek, drawings, and place value charts provide access to advanced work with adding tens. Students model and solve problems such as 25 + 20. At first, they may count on by tens from the first addend (e.g., 25, 35, 45). Through practice and studying patterns, they advance to using place value strategies. For example, to add 25 + 20, students think of 25 as 2 tens 5 ones and 20 as 2 tens. Students add the 2 tens in 20 to the 2 tens in 25.

Students notice that adding tens to a two-digit number causes the digit in the tens place to change, but the digit in the ones place remains the same.

To culminate topics C and D, students add one-digit numbers and multiples of ten to twodigit numbers. At first, they do this in a choral count. They count in unison while the teacher records the count. The teacher strategically pauses students and asks them to identify the number that is 1 more, 1 less, 10 more, and 10 less than a given two-digit number in the sequence. Then they add a string of numbers — one-digit numbers, two-digit numbers, and multiples of ten — to try to get to 100.

Progression of Lessons

Lesson 15

Count on and back by tens to add and subtract.

Lesson 16

Use related single-digit facts to add and subtract multiples of ten.

Lesson 17

Use tens to find an unknown part.

I can count back by tens to subtract (take away).

I can count on by tens to add.

I can use 7 + 2 = 9 to help me figure out 70 + 20.

I can use 7 – 2 = 5 to help me figure out 70 – 20.

I can use 4 + 3 = 7 to help me figure out 40 + ? = 70.

I can use 4 – 3 = 1 to help me figure out 40 – ? = 10.

Lesson 18 (Optional)

Determine if number sentences involving addition and subtraction are true or false.

Lesson 19 (Optional)

Lesson 20 (Optional)

I can find the total of the expressions on both sides of the equation. If the totals are the same, the number sentence is true.

Add tens to a two-digit number. +

tens ones tens ones

Add ones and multiples of ten to any number. I can add ones or tens to a number by using a strategy I know. I can show my thinking.

Adding 30 is adding 3 tens. When we add tens, only the tens digit in the total is more.

Count on and back by tens to add and subtract.

Lesson at a Glance

Students self-select strategies to use to solve a word problem involving subtracting more than 1 ten from a multiple of ten. They practice and discuss counting back to subtract tens and counting on to add tens by using drawings, the rekenrek, and their fingers (as units of ten).

Key Question

• What are some ways to add tens or take away tens?

Achievement Descriptor

FL.1.Mod5.AD6 Find 10 more and 10 less than a two-digit number. (MA.1.NSO.2.3)

Agenda Materials

Fluency 10 min

Launch 10 min

Learn 30 min

• Share, Compare, and Connect

• Count Back by Tens to Subtract

• Count On by Tens to Add

• Problem Set

Land 10 min

Teacher

• 100-bead rekenrek

Students

• Assorted math tools

Lesson Preparation

Gather a variety of math tools for students to choose from and have them available for use. Examples of math tools could be number paths, cubes or base 10 rods, and personal whiteboards.

Fluency

Whiteboard Exchange: Picture Graphs

Students answer questions about a picture graph to build fluency with interpreting data and representing totals with tally marks.

After each prompt for a written response, give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

Display the picture graph.

The picture graph shows the animals on a farm.

How many chickens are on the farm? Write the total. Draw the total with tallies.

Display the total: 12.

How many cows are on the farm? Write the total. Draw the total with tallies.

Display the total: 11.

How many pigs are on the farm? Write the total. Draw the total with tallies.

Display the total: 8.

Continue with the following questions.

How many more cows are on the farm than pigs? 3

How many more chickens are on the farm than pigs?

How many fewer cows are on the farm than chickens?

What is the total number of animals on the farm?

Choral Response: Subtract Within 10

Students say the difference to build subtraction fluency within 10.

Display 10 – 2 =  .

What is 10 – 2? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 8

Display the answer.

Repeat the process with the following sequence:

Beep Counting by Tens

Students complete a number sequence to build fluency with counting by tens. Invite students to participate in Beep Counting.

Listen carefully as I count by tens. I will replace one of the numbers with the word beep. I will count up, and I will count down. Raise your hand when you know the beep number. Ready?

Display the sequence 10, 20,  . 10, 20, beep.

Wait until most students raise their hands, and then signal for students to respond.

30

Display the answer.

Repeat the process with the following sequence:

10, 20, 30

50, 60, 80, 90, 30, 20, 70, 60, 100, 90, 30, , 50 20, , 0

Materials—S: Assorted math tools

Students self-select strategies and tools to use to solve a word problem.

Display the picture of the partially unrolled stickers to build context for students.

Promoting the Mathematical Thinking and Reasoning Standards

As students decide which strategy to use to solve the sticker problem, they complete tasks with mathematical fluency (MTR.3). Throughout the year, students have built up their mathematical “toolbox” of strategies, which they can now apply to this new context.

How many stickers are unrolled so far? How do you know?

There are 30 stickers unrolled. You can count the groups by ten: 10, 20, 30.

Display the word problem and read it aloud.

Miss Lin had a roll of 90 stickers.

She gave 30 stickers to students.

How many stickers are left on the roll?

Encourage students to think strategically by asking the following questions:

• Why did you choose to solve the problem that way? Did it work well?

• What other way could you use to solve the problem? Why might that way be helpful?

Have students retell the story to a partner. Ask them to engage with the problem by using the Read–Draw–Write process. Invite students to self-select strategies and tools such as base 10 rods, fingers, personal whiteboards, or number paths. Encourage all students, even those who can solve by using mental math, to justify their solutions with a representation.

Circulate and notice the variety of student work. Select two students to share their work in the next segment.

Let’s talk about the different ways you solved this problem.

Learn

Share, Compare, and Connect

Materials—T: Student work

Students discuss different ways to solve a word problem.

Invite the students whose work was selected in the previous segment to share their work. Share the most accessible strategy first. Encourage the class to use the Talking Tool to engage with one another and with the mathematics. Consider the following sample discussion.

Teacher Note

If students count on by tens (think addition) to subtract, invite them to share their thinking. Students may say they started at 30 and counted up 6 tens to 90.

30 40 50 60 70 80 90

3 0 + 6 0 = 90

Help the class compare strategies by asking, “How is counting on by tens to subtract different than counting back by tens to subtract?”

How many stickers are left on the roll?

60 stickers

Take Tens Away (Sakon’s Way)

Sakon, how did you figure out how many stickers are left?

I drew 9 tens for the 90 stickers. I crossed off 3 tens for the 30 stickers she gave away. There are 6 tens left. That means 90 – 30 = 60.

Count Back by Tens (Lucia’s Way)

Lucia, how did you figure out how many stickers are left?

I started at 90 and counted back 3 tens. I landed on 60. That’s how I knew that 90 – 30 = 60.

Invite students to think–pair–share about how the two different ways are similar.

Sakon crossed off tens. Lucia counted back by tens. What is the same about their ways of solving this problem?

They both started with 90. Then they both subtracted 30. They both got 60. It’s like when we counted back by ones to subtract, but now we’re counting 10 at a time. Transition to the next segment by framing the work. Today, we will practice counting back to subtract tens and counting on to add tens.

Count Back by Tens to Subtract

Materials—T: 100-bead rekenrek

Students count back by tens on a rekenrek and with their fingers to subtract.

Show the rekenrek with 50 beads on the left side.

How many beads?

50

Teacher Note

If most students typically count on to subtract, rather than count back, show their strategy on the rekenrek (or by using fingers).

For example, to find 80 – 40, start by showing the rekenrek with 40 beads on the left side. Consider this sample discussion:

• To think addition, or to count on to subtract, we start with the part we know, 40.

• Count on by tens with me until we get to the total, 80.

Slide a row of beads to the left all at once. Do this four times as students count. Ask this question:

• How many tens did we count?

Write 40 + 40 = 80. Ask this question:

• So, what is 80 – 40?

Help students recall as needed that when they count on to subtract, the answer is not the last number they say. Rather, it is how many tens they counted.

Let’s count back by tens to figure out 50 – 30. How many tens are in 30?

3 tens

We will start at 50 and take away 30, or 3 tens. Count back by tens with me.

Slide a row of beads to the right all at once. Do this three times as students count.

50, … , 20

What is 50 – 30?

20

Repeat the process with the rekenrek for 70 – 20 and 80 – 40.

Then ask students to show 8 fingers the math way. Tell them that each finger is a ten. Guide them to count on their fingers by tens to 80.

How many tens are in 80?

8 tens

Together, let’s count back by tens to figure out 80 – 40.

How many tens are in 40?

4 tens

Demonstrate lowering 1 finger at a time as the class counts back from 80 to 40.

What is 80 – 40? How do you know?

It’s 40. We said 40 last.

It’s 40. I know because we have 4 fingers up. That’s 4 tens.

Differentiation: Support

When counting back, students may say 80 and put a finger down. Help students to remember not to put a finger down until they take 10.

Count On by Tens to Add

Materials—T: 100-bead rekenrek

Students count on by tens on a rekenrek and with fingers to add.

Transition to adding tens. Show the rekenrek with 50 beads on the left side. Ask students to confirm the number.

Let’s count on by tens to figure out 50 + 40.

How many tens are in 40?

4 tens

We will start at 50 and add 40, or 4 tens. Count on by tens with me. Slide a row of beads to the left all at once. Do this four times as students count.

50, … , 90

What is 50 + 40?

90

Repeat the process with the rekenrek for 30 + 60. Then guide students to use their fingers to count on by tens to figure out 20 + 50.

How many tens are in 20?

2 tens

Tell students to put up 2 fingers the math way.

How many tens are in 50?

5 tens

Demonstrate raising 1 finger at a time as the class counts on from 20 to 70.

Teacher Note

If needed, consider using the rekenrek to provide distributed practice with counting on and counting back to add and subtract tens from multiples of 10. Encourage students to follow along by using their fingers.

Differentiation: Challenge

Invite students to count on by tens starting at any multiple of 10 as far as they can, even past 100. Also ask them to count back by tens starting at 100 or 120.

What is 20 + 50?

70

Problem Set

Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex.

Directions and word problems may be read aloud.

Land Debrief 5

min

Objective: Count on and back by tens to add and subtract.

Display the picture of 20 stickers.

Let’s pretend you have these 2 sheets of 10 stickers. How many stickers do you have in all?

20

Suppose you got 20 more stickers. How many stickers would you have then? How do you know?

40 stickers

I know because I counted on by tens. I started with 20 and then I counted 30, 40.

I know that 2 tens and 2 tens is 4 tens, and 4 tens is 40.

UDL: Action & Expression

Consider having students use the interactive Digital Number Path to 120 to support them in demonstrating and explaining their ideas for 20 + 20 = 40 and 40 – 30 = 10.

Display the picture of 40 stickers.

Suppose you give away 30 stickers. How many stickers would you have then? How do you know?

If you take away 3 sheets, that leaves 1. One sheet is 10 stickers.

10 stickers; I counted back by tens: 40, 30, 20, 10. I counted on: 30, 40. That’s 1 sheet so 10 stickers.

What are some ways to add tens or take away tens?

We can count on to add tens. And we can count on to take away too.

We can count back to take away tens.

Exit Ticket 5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

1. Ms. Mack picks 20 berries. Then she picks 30 more. How many berries does she have now?

+ 30 = 50 She has 50 berries.

2. There are 50 pillows in the store. 40 of them are sold. How many pillows are in the store now? 50

40 = 10

There are 10 pillows in the store.

Use related single-digit facts to add and subtract multiples of ten.

Lesson at a Glance

Students solve addition and subtraction equations involving multiples of ten by representing them in unit form (number of tens and ones) and noticing the easier, related one-digit facts they know. They play a game to practice mentally adding and subtracting multiples of ten.

Key Question

• How can facts we know help us add and subtract multiples of ten?

Achievement Descriptor

FL.1.Mod5.AD6 Find 10 more and 10 less than a two-digit number. (MA.1.NSO.2.3)

Agenda Materials

Fluency 10 min

Launch 5 min

Learn 35 min

• Add Multiples of Ten

• Subtract Multiples of Ten

• Numbers Up!

• Problem Set

Land 10 min

Teacher

• Add or Subtract Tens removable (digital download)

Students

• Base 10 rods (10 per student pair)

• Add or Subtract Tens removable (in the student book)

• Numbers Up! cards (1 set per group of 3 students, in the student book)

Lesson Preparation

• The Add or Subtract Tens removables must be torn out of student books and placed in personal whiteboards. The Numbers Up! cards must be torn out of student books and cut apart. Consider whether to prepare these materials in advance or to have students prepare them during the lesson. Consider saving the Add or Subtract Tens removables for use in lesson 17.

• Copy or print the Add or Subtract Tens removable to use for demonstration. Consider saving this for use in lesson 17.

Note: Base 10 rods are referred to as ten-sticks throughout the lesson.

Fluency

Whiteboard Exchange: Picture Graphs

Students answer questions about a picture graph to build fluency with interpreting data and representing totals with tally marks.

After each prompt for a written response, give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

Display the picture graph.

The picture graph shows students’ lunch choices.

How many students chose a taco? Write the total. Draw the total with tallies.

Display the total: 7.

How many students chose a cheeseburger? Write the total. Draw the total with tallies.

Display the total: 12.

How many students chose a sandwich? Write the total. Draw the total with tallies.

Display the total: 2.

Continue with the following questions.

How many more students chose a cheeseburger than chose a sandwich? 10

How many more students chose a cheeseburger than chose a taco? 5

How many fewer students chose a sandwich than chose a taco? 5

How many total students chose a lunch?

21

Choral Response: Subtract Within 10

Students say the difference to build subtraction fluency within 10.

Display 5 – 2 =  .

What is 5 – 2? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 3

Display the answer.

Repeat the process with the following sequence:

Beep Counting by Tens

Students complete a number sequence to build fluency with counting by tens. Invite students to participate in Beep Counting.

Listen carefully as I count by tens. I will replace one of the numbers with the word beep. Raise your hand when you know the beep number. Ready?

Display the sequence 40, 50,  .

40, 50, beep.

Wait until most students raise their hands, and then signal for students to respond.

60 Display the answer.

Repeat the process with the following sequence:

Students use their hands to represent units of ten and to add.

Tell students to show 10 with their fingers the math way.

Wiggle your fingers. How many fingers? 10

Today, our fingers are ones. Make a group of ten with your fingers by clasping your hands together. (Demonstrate clasping hands.)

We can think of all of our fingers as 10 ones or 1 ten.

Have students unclasp their hands. Invite two volunteers to come forward. Tell them to show ten by clasping their hands together. Gesture to both volunteers and ask this question.

40, 50, 60

How many fingers? How do you know?

20 fingers. I counted by tens: 10, 20.

2 tens is 20.

Invite two more volunteers to come forward. Tell them to also show ten with their hands clasped together. Gesture to all four volunteers and ask this question.

How many fingers? How do you know?

40 fingers. I counted by tens: 10, … , 40. I counted on by tens from 20: 20, 30, 40.

4 tens is 40.

Have the volunteers return to their seats.

We can write a number sentence to show our friends’ hands by writing the number of fingers, or ones, like this.

Write 20 + 20 = 40.

Or we can make the problem easier by thinking about the number of clasped hands, or tens, and write it like this.

Write 2 tens + 2 tens = 4 tens.

Turn and talk: What is the same about these number sentences? What is different about them?

Highlight the 2s and 4s in the number sentences, as shown. What addition fact do you see in both number sentences?

2 + 2 = 4

2 + 2 = 4 is an easier problem than 20 + 20 = 40. We can use that to make the problem easier by thinking, 2 tens plus 2 tens equals 4 tens. 4 tens is 40.

Transition to the next segment by framing the work.

Today, we will find and use facts we know to help us add and subtract efficiently.

UDL: Action & Expression

As students add and subtract by thinking about facts they know as numbers in unit form (e.g., 3 tens), help them monitor their own progress by providing these questions that guide self-monitoring and reflection:

• How is this problem like other problems I have solved?

• How is thinking of this part as groups of ten helping me?

Learn

Add Multiples of Ten

Materials—T: Add or Subtract Tens removable; S: Base 10 rods, Add or Subtract Tens removable

Students add multiples of ten by relating problems to basic facts within 10.

Pair students and assign each partner as either partner A or partner B. Distribute ten-sticks to each student pair.

Write 30 + 30 = .

Let’s find the total by making an easier problem.

Ask partner A to show the first addend and partner B to show the second addend with ten-sticks.

Partner A, how many tens do you have?

3 tens

Partner B, how many tens do you have?

3 tens

Partners, how many total tens do you have?

6 tens

How many is 6 tens?

60

So, what is 30 + 30?

60

Write 60 to complete the equation.

Repeat the process with 30 + 20 or 40 + 50.

Make sure that each student has the Add or Subtract Tens removable inside their whiteboard. Write 50 + 40 at the top of the addition section. Have students follow along.

How many tens are in 50?

5 tens

Write 5 in the equation.

How many tens are in 40?

4 tens

Write 4 in the equation.

What is 5 tens + 4 tens? How do you know?

It’s 9 tens. 5 + 4 = 9.

Write 9 to complete the equation.

So, what is 50 + 40?

90

Write = 90 to complete the original problem.

What addition fact do you see that helped us figure out 50 + 40 = 90?

5 + 4 = 9

Repeat the process with 20 + 70. Release responsibility to the students as appropriate. Then have students put aside their removable.

Subtract Multiples of Ten

Materials—T: Add or Subtract Tens removable; S: Base 10 rods, Add or Subtract

Tens removable

Students subtract multiples of ten by relating problems to basic facts within 10.

Write 60 – 20 =  .

Let’s find the total by making an easier problem.

Differentiation: Challenge

Change the addends so that the total crosses 100. For example, use 80 + 40 = 120 (8 tens + 4 tens = 12 tens).

Students may write 120 as 12 tens, 120, or 1 hundred 2 tens.

Differentiation: Support

If students do not know facts within 10 from memory, they may use their fingers to count on or count back by ones or tens. They may also continue to use ten-sticks.

Ask partners to show the total, 60, with ten-sticks.

How many tens do we have?

6 tens

We need to subtract 20. How many tens are in 20?

2 tens

Have partners subtract 2 tens.

Partners, how many tens are left?

4 tens

How many is 4 tens?

40

So, what is 60 – 20?

40

Write 40 to complete the equation.

Repeat the process with 90 – 40 or 80 – 20.

Ask students to pick up their whiteboards and look at the Add or Subtract Tens removable.

Write 50 – 40 at the top of the subtraction portion. Have students follow along.

How many tens are in 50?

5 tens

Write 5 in the equation at the bottom of the page.

How many tens are in 40?

4 tens

Write 4 tens in the equation.

What is 5 tens – 4 tens? How do you know?

It’s 1 ten. 5 – 4 = 1.

Write 1 to complete the equation.

So, what is 50 – 40?

Write = 10 to complete the original problem.

What subtraction fact do you see that helped us figure out 50 – 40 = 10?

5 – 4 = 1

Repeat the process with 70 – 40 or 80 – 50. Release responsibility to the students as appropriate.

Numbers Up!

Materials—S: Numbers Up! cards

Students find the unknown total or part when given two multiples of ten.

Form groups of three students and assign each player as player A, player B, or player C.

Display the picture of three players. Give students these directions for the Numbers Up! game:

• Place the pile of cards number side down. Players B and C each take a card. They hold their cards against their foreheads so they can’t see their own number, but the other players can.

• Player A looks at both cards and says the total of the two numbers.

UDL: Engagement

Depending on students’ needs, consider a variation or an alternative to Numbers Up!

As a variation, partners may use the cards to add or subtract two multiples of ten. They may use the Add or Subtract Tens removable to write the equations in two ways.

As an alternative to Numbers Up!, have partners use the Add or Subtract removable to play Roll and Add by doing the following:

• Roll two 10-sided dice.

• Record their roll as an addition expression by using numbers of tens (e.g., 4 tens + 5 tens).

• Add and write the total number of tens.

• Write a corresponding number sentence in standard form (e.g., 40 + 50 = 90).

To play Roll and Subtract, partners write the larger number shown on the dice first and the smaller number second.

• Players B and C figure out the number on their own cards by using the total and the other player’s part.

• Players B and C look at their cards to confirm their answers.

• Players may switch roles for the next round.

Distribute sets of cards to each group and have them play for 5 to 6 minutes. Provide support as needed.

Problem Set

Differentiate the set by selecting problems for students to finish independently within the shorter timeframe. Problems are organized from simple to complex.

Directions and word problems may be read aloud.

Land

Debrief 5 min

Objective: Use related single-digit facts to add and subtract multiples of ten.

Display the 3 buses.

Each bus carries 10 students. How many students are in all 3 buses? How do you know?

30 students

3 tens is 30.

Display the 6 buses.

Three more buses pull up. Each of these buses carries 10 students, too. How many students are there now? How do you know?

60 students. 3 tens and 3 tens is 6 tens. 6 tens is 60.

Promoting the Mathematical Thinking and Reasoning Standards

Students apply mathematics to real-world contexts (MTR.7) when they solve the bus problem by thinking in terms of tens.

This problem requires students to decontextualize on two levels to solve. First, they need to understand that, even though they cannot see the students inside the buses, they can count the buses to determine how many students there are. Next, they need to decontextualize each bus as a ten and reason about units to solve. They then recontextualize by converting tens to buses and buses to students.

Write 30 + 30 = 60.

How can facts we know help us add and subtract multiples of ten?

For example, how did using 3 + 3 = 6 make this problem easier?

You don’t have to worry about counting all those big numbers. You can just use the easier fact.

I know 3 + 3, so it’s faster than counting on by tens. Leave the 6 buses displayed and pose a second problem.

Suppose 4 buses drive away. How many students are in the buses that are left?

20 students

I know because 6 – 4 = 2. 2 buses is 2 tens, and that’s 20.

Cross off 4 buses and write 60 – 40 = 20.

What fact that we know helped us figure out 60 – 40 = 20? How did it help us?

6 – 4 = 2

I know 6 – 4, so it is easier than counting back by tens.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

1. Add or subtract

2. Read

4 packs of 10 crayons are on the desk.

4 packs of 10 crayons are in the desk.

How many crayons are there in all?

3. Read

Max has 9 bags of 10 nuts. He gives away 5 bags.

How many nuts does he have left?

There are 80 crayons.

Use tens to find an unknown part.

Lesson at a Glance

DStudents engage in a Math Chat routine and share ways to find an unknown addend. Then they practice finding unknown addends and subtrahends by using two strategies: by counting on or back by tens and by thinking of an easier, known fact.

Key Question

• What strategies can we use to find an unknown part?

Achievement Descriptor

FL.1.Mod5.AD6 Find 10 more and 10 less than a two-digit number. (MA.1.NSO.2.3)

Agenda Materials

Fluency 10 min

Launch 10 min

Learn 30 min

• Find an Unknown Addend

• Find an Unknown Subtrahend

• Problem Set

Land 10 min

Teacher

• Add or Subtract Tens removable (digital download)

Students

• Subtraction Expression cards (1 set per student pair)

• Add or Subtract Tens removable (in the student book)

• Assorted math tools

Lesson Preparation

• Prepare sets of Subtraction Expression cards from lesson 9 for each student pair.

• The Add or Subtract Tens removables must be torn out of student books and placed in personal whiteboards. Consider whether to prepare these materials in advance, to have students assemble them during the lesson, or to use the ones prepared in lesson 16.

• Copy or print the Add or Subtract Tens removable to use for demonstration, or use the one prepared in lesson 16.

• Make assorted math tools available for students to choose from and use in the lesson. Consider providing students with base 10 rods and a number path.

Fluency

Match: Subtraction Expressions

Materials—S: Subtraction Expression cards

Students identify equivalent expressions to build subtraction fluency within 10. Have students form pairs. Distribute a set of cards to each student pair and have them play according to the following procedure. Consider doing a practice round with students.

Differentiation: Challenge

Provide sets of Subtraction Expression cards within 20 from module 3 to students who demonstrate proficiency with subtraction within 10.

• Lay out nine cards, expression-side up.

• Match two equal expressions. If there are no matches, replace a few cards with different cards from the pile.

• Turn over the cards to check that the expressions are equal.

• Place the matched cards to the side and replace them with two new cards from the pile.

• Continue until no more matches can be made.

Circulate as students work and provide support as needed.

Beep Counting: 10 More, 10 Less

Students complete a number sequence to build fluency with mentally finding 10 more or 10 less than a number.

Invite students to participate in Beep Counting.

Listen carefully as I count on or count back by tens. I will replace one number with the word beep. Raise your hand when you know the beep number. Ready?

Display the sequence 21, 31,  . 21, 31, beep.

Wait until most students raise their hands, and then signal for students to respond.

41

Display the answer.

Repeat the process with the following sequence:

Launch

Materials—T: Add or Subtract Tens removable; S: Add or Subtract Tens removable, assorted math tools

Students share and discuss different ways to find the unknown part in an equation.

Make sure students have the Add or Subtract Tens removable inside a personal whiteboard.

Write 20 + = 70 at the top of the addition portion. Have students do the same. Use the Math Chat routine to engage students in mathematical discourse.

What is the unknown part? How do you know?

Give students 1 to 2 minutes of silent think time. Students may choose to use mental math, a basic fact, a drawing, base 10 rods, or a number path to solve the problem.

Then invite students to discuss their ideas with a partner. Listen for students who find the unknown part by

• thinking of the easier related fact, 2 + 5 = 7, or

• counting on by tens from 20, 5 times (20, … , 70).

Facilitate a class discussion by inviting one or two students to show their work and share their thinking. If needed, demonstrate the strategies mentioned above. Support student-to-student dialogue by having students refer to the Talking Tool. Encourage students to agree or disagree, ask a question, give a compliment, or restate an idea in their own words.

How did you find the unknown part?

I drew 2 tens and I counted on to 7 tens. I added 5 more tens. That is 50.

What is another way to find the unknown part?

I know 2 + 5 = 7, so 2 tens + 5 tens = 7 tens. 5 tens is 50.

So, 20 plus what number equals 70?

50

20 + 50 = 70

te ns + te ns = te n s

Complete the equation by writing the unknown part.

If we think of a fact we know, we can use it to find an unknown part. If we do not think of a fact, we can count on by tens. Transition to the next segment by framing the work.

Today, we will find unknown parts in equations.

Learn

Find an Unknown Addend

Materials—T/S: Add or Subtract Tens removable

Students connect counting on by tens to the Stage 3 strategy of using a related fact to solve.

On the Add or Subtract Tens removable, write 40 + = 80 at the top of the addition portion. Have students follow along.

Tell students to draw quick tens to represent 40.

Let’s draw more tens to count on to 80.

Draw tens one at a time as students follow along. Have them chorally count by tens from 40 to 80.

Circle the tens that we added.

te ns + te ns = te n s

Differentiation: Challenge

Present the equations as word problems with coins, as in this example:

Corey has 40 cents. He needs 80 cents to buy a ball. How much more money does he need?

Encourage students to use dimes or to draw labeled circles to help them solve the problem.

Teacher Note

Some students may be able to use their fingers to count on and count back, rather than drawing the tens. Help them recall that they can think of each finger as a unit of 10.

Other students may benefit from the concrete support of using base 10 rods.

How many tens did we count on?

4 tens

How many is 4 tens?

40

Guide students to record each known number of tens (4 and 8) in the correct spaces, leaving the unknown number of tens space blank. Point to the blank space.

What is the unknown number of tens? How do you know?

4

We counted on 4 tens.

Have students write 4 in the blank. Point to the blank space for the unknown in the original equation.

What is this unknown part? How do you know?

40

4 tens is the same as 40.

Ask students to write 40 in the blank in the original equation.

Turn and talk. Which way is more helpful to you: finding an unknown part by counting on by tens, or thinking about the number of tens as an easier, related fact?

Have students erase their whiteboard. Provide more practice by engaging them in a Whiteboard Exchange routine to solve 30 + = 80 and 70 + = 90. They may solve these problems by thinking of the number of tens or by counting on.

• Tell students to turn their boards over so the red side is up when they are ready. Say, “Red when ready!”

• When most students are ready, tell students to hold up their whiteboard to show you their work.

• Give quick individual feedback, such as “Yes!” or “Check your count.” For each correction, return to validate the corrected work.

How did you use tens to find an unknown part?

I counted on by tens.

I thought about the number of tens as a fact I know.

UDL: Representation

Consider creating a chart and highlighting the easier, related fact in each problem throughout the lesson as the class shares their thinking.

Promoting the Mathematical Thinking and Reasoning Standards

Students use structure to help them understand and connect mathematical concepts (MTR.7) when they think of a problem in unit form (e.g., 3 tens + = 8 tens) and use a basic fact (e.g., 3 + = 8) to find the unknown part, because they notice the similarity in structure between the two number sentences.

As students move toward using the standard algorithms to add and subtract in grade 2, this understanding will allow them to make sense of their work, rather than simply memorizing the steps.

Find an Unknown Subtrahend

Materials—T/S: Add or Subtract Tens removable

Students connect counting back by tens to the Stage 3 strategy of using a related fact to solve a problem.

On the Add or Subtract Tens removable, write 70 – = 50 at the top of the subtraction portion. Have students follow along.

Tell students to draw quick tens to represent 70.

Let’s cross off tens and count back to 50.

Cross off tens one at a time as students follow along. Have them chorally count back by tens from 70 to 50.

Point to the tens that were crossed off.

How many tens did we cross off?

2 tens

How many is 2 tens?

20

Guide students to record each known number of tens (7 and 5) in the correct spaces, leaving the unknown number of tens space blank. Point to the blank space.

What is the unknown number of tens? How do you know? 2

We counted back 2 tens.

Have students write 2 in the blank. Point to the blank space for the unknown value in the original equation.

What is this unknown part? How do you know?

20

2 tens is the same as 20.

Ask students to write 20 in the blank in the original equation.

Differentiation: Challenge

Present the equations as word problems with coins. For example:

Corey has 70 cents. He buys a ball. He has 50 cents left. How much money does he spend?

Encourage students to use dimes or draw labeled circles to help them solve the problem.

Teacher Note

If students use counting on to subtract, demonstrate their strategy as well. The following sample shows a way to find the unknown part in 70 – = 50.

Tell students that to count on to subtract, we start with the part we know, 50.

Draw quick tens.

Tell students that we start at 50 and count on by tens until we get to the total, 70.

Ask students how many tens they counted.

Write 50 + 20 = 70.

Ask students what the unknown part is in 70 – = 50.

Students may also solve by thinking about addition by using the number of tens. They may say that they know 5 tens + 2 tens = 7 tens, so, 7 tens – 2 tens = 5 tens, and 2 tens is 20.

Turn and talk. Which way is more helpful to you, finding an unknown part by counting back by tens, or thinking about the number of tens as a fact you know?

Have students erase their whiteboards. Provide more practice by engaging them in a Whiteboard Exchange routine to solve 90 – = 60, and 80 – = 40. They may solve these problems by thinking of the number of tens or by counting back.

• Tell students to turn their boards over so the red side is up when they are ready. Say, “Red when ready!”

• When most are ready, tell students to hold up their whiteboard to show you their work.

• Give quick individual feedback, such as “Yes!” or “Check your total.” For each correction, return to validate the corrected work.

How did you use tens to find an unknown part?

I counted back by tens.

I thought about the number of tens as a fact I know.

Problem Set

Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex.

Directions and word problems may be read aloud.

Land

Debrief 5 min

Objective: Use tens to find an unknown part.

Gather students and display the hand and 2 dimes.

Baz has these dimes, and he also has some dimes hidden under his hand. He has 60 cents altogether.

Invite students to think–pair–share about how much money is under Baz’s hand.

How much money is under his hand? How do you know?

40 cents

I know because 20 cents is showing, and I counted back from 60 to 20. I put up 4 fingers. (Shows 4 fingers.)

40 cents; I know because I started at 20 and counted on 4 tens to 60.

40 cents; I know that 2 + 4 = 6, so 20 + 40 = 60.

40 cents; 2 dimes + 4 dimes = 6 dimes.

Display 6 dimes to confirm students’ thinking.

Display the two number bonds. Discuss the part–whole relationship.

Some of you thought about 20 and 40 as the parts and 60 as the total. Others thought about 2 tens and 4 tens as the parts and 6 tens as the total.

What strategies can we use to find an unknown part?

We can count on or back by tens.

I can use the number of tens to think of an easier fact I know.

Topic Ticket 5 min

Provide up to 5 minutes for students to complete the Topic Ticket. It is possible to gather formative data even if some students do not complete every problem.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

1. Find the unknown part.

3 tens + 3 tens = 6 tens 30 + 30 = 60

5 tens – 3 tens = 2 tens 50 – 30 = 20

6 tens + 3 tens = 9 tens 60 + 30 = 90

7 tens – 3 tens = 4 tens 70 – 30 = 40

2. Read Max has 30 flies in a jar. He gets more flies

Now he has 80 flies.

How many more flies did Max get?

4. Read

Zan has these dimes:

Zan finds some dimes.

Now he has 9 dimes.

How much money did Zan find?

5. Read Dan has these dimes: Dan loses some dimes.

Now he has 3 dimes.

How much money did Dan lose?

Determine if number sentences involving addition and subtraction are true or false. (Optional)

Lesson at a Glance

Students determine whether number sentences are true or false and discuss their reasoning. They calculate the addition or subtraction expression on either side of the equal sign to find whether both sides represent the same amount.

Key Question

• How can we tell if a number sentence is true or false?

Achievement Descriptor

This lesson supports MA.1.AR.2.2, determining and explaining if addition and subtraction number sentences are true or false. It builds from the work in module 1 and uses students’ growing knowledge of tens. Lesson content is intended to serve as a formative assessment and is therefore not included on summative assessments in this module.

Agenda Materials

Fluency 10 min

Launch 15 min

Learn 25 min

• True or False?

• Match: Addition and Subtraction

Expressions

• Problem Set

Land 10 min

Teacher

• None Students

• Count by Tens Sprint (in the student book)

• Match: Addition and Subtraction Expressions cards (1 set per student pair, in the student book)

Lesson Preparation

• The Count by Tens Sprint must be torn out of student books. Consider whether to prepare these materials in advance or to have students tear them out during the lesson.

• Some students may choose to use cubes or the number path to confirm their thinking about why number sentences are true or false. Consider making these tools available as needed.

• The Match cards must be torn out of student books and cut apart. Consider whether to prepare the cards in advance or to have students prepare them during the lesson.

Fluency

Sprint: Count by Tens

Materials—S: Count by Tens Sprint

Students complete a number sequence to build fluency with counting by tens.

Have students read the instructions and complete the sample problems.

Direct students to Sprint A. Frame the task.

I do not expect you to finish. Do as many problems as you can, your personal best.

Take your mark. Get set. Think!

Time students for 1 minute on Sprint A.

Stop! Underline the last problem you did.

I’m going to read the answers. As I read the answers, call out “Yes!” and mark your answer if you got it correct.

Read the answers to Sprint A quickly and energetically.

Count the number you got correct and write the number at the top of the page. This is your personal goal for Sprint B.

Celebrate students’ effort and success.

Provide about 2 minutes to allow students to analyze and discuss patterns in Sprint A.

Lead students in one fast-paced and one slow-paced counting activity, each with a stretch or physical movement.

Point to the number you got correct on Sprint A. Remember this is your personal goal for Sprint B.

Teacher Note

Consider asking the following questions to discuss the patterns in Sprint A:

• What do you notice about problems 1–6? About problems 7–12?

• What strategy did you use to solve problem 13? What strategy did you use to solve problem 19?

Teacher Note

Count on by tens from 0 to 120 for the fast-paced counting activity.

Count back by tens from 120 to 0 for the slow-paced counting activity.

Direct students to Sprint B.

Take your mark. Get set. Improve!

Time students for 1 minute on Sprint B.

Stop! Underline the last problem you did.

I’m going to read the answers. As I read the answers, call out “Yes!” and mark your answer if you got it correct.

Read the answers to Sprint B quickly and energetically.

Count the number you got correct and write the number at the top of the page.

Stand if you got more correct on Sprint B.

Celebrate students’ improvement.

Launch

Students discuss whether number sentences are true or false. Display the story and read it aloud.

Turn and talk. What number bond could we draw to represent this story?

Use the following questions to generate and record a number bond.

What is the total in this story? How do you know?

50; it says there are 50 grapes in the bowl.

What are the parts in this story? How do you know?

30 and 20; they are the two colors or groups of grapes.

There are 50 grapes in a bowl.

30 grapes are green.

20 grapes are red.

Pair students. Ask partners to write addition and subtraction number sentences to represent the story and the number bond. They do not need to write all of the possibilities. Share a few different number sentences and ask students to explain their reasoning.

Display the list of number sentences. Point to the first one. Here are some number sentences I wrote. Show thumbs-up if you agree that this number sentence matches the story.

Show thumbs-up if you think this number sentence is true.

Call on a student to share their reasoning. They may use the story or the total to justify why it is true. Emphasize that it is true because both sides of the equal sign show the same amount: 50.

Repeat the process with the next three number sentences. Emphasize that true number sentences can have addition or subtraction on either side of the equal sign as long as the amounts on either side of the equal sign are the same.

Read the last number sentence. Have students turn and talk about whether this number sentence matches the story.

Is this number sentence true or false? Why?

It’s false. 30 take away 50 doesn’t make 20.

If we start with 30 grapes there aren’t enough to take away 50.

Yes, this number sentence is false. We have 20 on one side of the equal sign. For this number sentence to be true, the other side has to make 20, too.

On the other side we have 30 – 50. If there are only 30 grapes, then there are not enough grapes to take away 50 because 50 is more than 30. Draw an X on the number sentence.

Transition to the next segment by framing the work.

Today, we will talk about more number sentences to see if they are true or false.

Teacher Note

30 – 50 = 20 is students’ first time seeing a number sentence that is false, but it cannot be shown to be false by calculating because finding 30 – 50 requires working with negative numbers.

Help students make sense of why this number sentence is false by focusing on the part-total relationships, rather than the amount each side represents. 50 is the total, and 30 is a part. To subtract, we take a part from the total. If we start with a part, there are not enough to take away the total.

Number sentences such as these help students see that while they can write the addends of an addition expression in any order without changing the total, the same is not true of subtraction expressions, where the order matters.

Differentiation: Challenge

Provide a number bond with different numbers of tens and have students write a math story and as many matching number sentences as they can with them.

Learn

True or False?

Students calculate to determine whether number sentences are true or false. Display the false number sentence.

20 + 30 50 + 10 =

Let’s figure out if this number sentence is true or false.

What is 20 + 30?

50

Write 50 below 20 + 30.

What is 50 + 10?

60 Write 60 below 50 + 10.

The total for each expression on either side of the equal sign is not the same. This number sentence is false.

Draw an X on the number sentence.

A number sentence is true when the expressions on both sides of the equal sign represent the same amount.

UDL: Representation

Activate prior knowledge by helping students recall how to determine if a number sentence containing two expressions is true or false. Ask the following questions:

• What is a true number sentence?

• What is a false number sentence?

• What can we do with the expressions on either side of the equal sign to figure out if the number sentence is true or false?

Teacher Note

If time allows, encourage students to revise false number sentences to make them true. For example:

• False: 20 + 30 = 50 + 10

• True: 30 + 30 = 50 + 10

Display the following number sentences one at a time. Engage students in a Whiteboard Exchange routine to determine whether each of the following number sentences is true or false. Have students complete the work. Have students show their thinking, including drawing an X on false number sentences. Consider having students stand. Encourage them to notice the symbols for addition and subtraction.

• Tell students to turn their whiteboards over so the red side is up when they are ready.  Say, “Red when ready!”

• When most are ready, tell students to hold up their whiteboard to show you their work.

• Give quick individual feedback, such as “Yes!” or “Check your total.” For each correction, return to validate the corrected work.

After each number sentence, ask the following question. How do you know this number sentence is true or false?

Match: Addition and Subtraction Expressions

Materials—S: Match: Addition and Subtraction Expressions cards

Students match expressions that are equal.

Demonstrate the following variation on the Match card game:

• Partners work together. They get out six cards from their set. The rest of the cards go in a pile to the side.

Teacher Note

Students may use varied reasoning to determine if the number sentences are true or false. They may simply calculate the total on either side of the equation, use relational thinking about parts on either side of the equal sign, or a combination of both.

• Partners find two expression cards that are equal because they represent the same amount. They use their whiteboards to show how the cards match. Students may use tools such as cubes or the number path as needed.

• Partners set aside the cards that match, draw two new cards from the pile to replace them, and repeat the process.

• Partners play until they have found all the matches. Distribute the Match cards to partners. As students play, circulate and ask them to explain why two cards are a match.

Problem Set

Differentiate the set by selecting problems for students to finish independently within the shorter timeframe. Problems are organized from simple to complex.

Directions may be read aloud.

Land

Debrief 5 min

Objective: Determine if number sentences involving addition and subtraction are true or false.

Let’s play Convince Me. I’ll go first to try and convince you. Display the false number sentence, which invites discussion about a common misconception.

Differentiation: Challenge

Students can find cards that do not match and use them to write comparison number sentences with the greater than and less than symbols.

Individual students may also write their own true and false number sentences and then trade them with their partner’s sentences.

Promoting the Mathematical Thinking and Reasoning Standards

Students engage in discussions that reflect on their mathematical thinking and that of others (MTR.7) when they play Convince Me. This requires students to consider the teacher’s position critically and construct a precise argument to communicate and explain why the teacher is wrong.

If students have trouble critiquing the teacher’s position, or they have difficulty understanding one another’s explanations, encourage them to ask questions or express what they don’t understand about someone else’s reasoning.

I think this number sentence is true because both expressions have 50 and 10. Ask students to show thumbs-up if they agree the number sentence is true.

I can tell that some of you are not convinced. You did not show thumbs-up. Why do you disagree?

This number sentence is false, not true. One expression is minus and the other is plus. 50 – 10 = 40 and 50 + 10 = 60. The sides show different amounts. You convinced me! The number sentence is false because 40 is not equal to 60. Draw an X on the false number sentence.

How can we tell if a number sentence is true or false?

We can see if the expressions on both sides of the equal sign make the same amount.

Exit Ticket 5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

2. Make a true number sentence.

1. Circle the number sentence if it is true. Draw an X on the number sentence if it is false.

3. Write your own true number sentence. Circle Sample: 70 + 10 = 80

4. Write your own false number sentence. Draw an X. Sample: 70 – 50 = 30

Add tens to a two-digit number. (Optional)

Lesson at a Glance

Students use the rekenrek and drawings to show adding tens to two-digit numbers. They represent the addends and the total by using place value charts, and they discuss how the digits in the tens place change but the digits in the ones place stay the same.

Key Question

• What happens to the digits when you add tens to a number?

Achievement Descriptor

FL.1.Mod5.AD6 Find 10 more and 10 less than a two-digit number. (MA.1.NSO.2.3)

Agenda Materials

Fluency 10 min

Launch 10 min

Learn 30 min

• Add Tens to Two-Digit Numbers

• More Coins for Ko

• Problem Set

Land 10 min

Teacher

• 100-bead rekenrek

• Double Place Value Chart removable (digital download)

Students

• Double Place Value Chart removable (in the student book)

Lesson Preparation

• The Double Place Value Chart removables must be torn out of student books and placed in personal whiteboards. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

• Copy or print the Double Place Value Chart removable to use for demonstration.

Fluency

Beep Counting: 10 More, 10 Less

Students complete a number sequence to build fluency with mentally finding 10 more or 10 less than a number.

Invite students to participate in Beep Counting.

Listen carefully as I count on or count back by tens. I will replace one of the numbers with the word beep. Raise your hand when you know the beep number. Ready?

Display the sequence 59, 69,  . 59, 69, beep.

Wait until most students raise their hands, and then signal for students to respond.

79

Display the answer.

Repeat the process with the following sequence:

59, 69, 79

Choral Response: True or False?

Students determine whether number sentences are equal (true) or not equal (false).

Display the number sentence 5 = 5.

Is the number sentence true or false? Raise your hand when you know.

Wait until most students raise their hands, and then signal for students to respond.

Teacher Note

Display the answer.

Repeat the process with the following sequence:

Choral Response: Add or Subtract in Unit and Standard Form

Students add or subtract units of ones or tens to develop place value understanding.

Display 2 ones + 1 one =  .

What is 2 ones + 1 one? Raise your hand when you know.

Wait until most students raise their hands, and then signal for students to respond.

3 ones

Display the answer: 3 ones.

On my signal, read the number sentence. Ready? (Point to each addend and the total as students say the equation with the numbers in unit form.)

2 ones + 1 one = 3 ones

Consider asking students to determine the value of each expression in the number sentence to confirm whether it is true or false.

Differentiation: Support

When the expression 13 – 3 precedes 13 – 4, it is common for students to think that 13 minus 4 equals 11. Consider using a tool such as a number bond or a number path to model how taking away 1 more decreases the difference by 1.

Display the equation with the numbers in standard form.

When I give the signal, read the number sentence. Ready? (Point to each addend and the total as students say the equation with the numbers in standard form.)

2 + 1 = 3

Continue with 2 tens + 1 ten = .

Repeat the process with the following sequence:

Launch

Materials—T: 100-bead rekenrek

Students add tens on the rekenrek and use the place value chart to represent them.

Show the rekenrek with 17 beads on the left side.

How many beads? 17

Starting on the third row, slide 3 rows of beads to the left. Slide each row all at once.

How many beads? How do you know?

47 beads; I counted on by tens: 17, 27, 37, 47.

There was 1 ten and you added 3 more. That makes 4 tens 7 ones, or 47.

Display the double place value chart.

We started at 17. (Write 17.) And we ended up at 47.

(Write 47.)

What do you notice about the digits in 17 and 47?

The digit in the ones place is the same. The digit in the tens place changed. It is 3 more.

The digit in the tens place is 3 more than in 17 because we added 3 tens.

(Point to 47.) What is the value of 3 tens?

30

Write + 30.

tens ones tens ones

Present a new problem. Show the rekenrek with 25 beads on the left side.

How many beads? 25

Starting on the fourth row, slide over 5 rows of beads to the left. Slide each row all at once.

How many beads? How do you know?

75 beads; I counted on by tens: 25, 35, 45, 55, 65, 75.

There were 2 tens and you added 5 more. That makes 7 tens 5 ones, 75.

Display the place value chart.

We started at 25. (Write 25.) And we ended up at 75. (Write 75.)

What do you notice about the digits in 25 and 75?

The digit in the ones place is the same. The digit in the tens place changed. It is 5 more.

The digit in the tens place is 5 more than in 25 because we added 5 tens. (Point to 75.) What is the value of 5 tens? 50

Write + 50.

Transition to the next segment by framing the work.

Today, we will notice how the digit in the tens place changes when we add tens to two-digit numbers.

Learn Add Tens to Two-Digit Numbers

Materials—T/S: Double Place Value Chart removable

Students add and represent their work by using place value charts.

Make sure that students have the Double Place Value Chart removable inserted into a whiteboard. Show the removable and have students follow along as you write the following into the chart:

• 41 + 30 =  , in the rectangle at the top

• 41, in the place value chart on the left

• 30, below the arrow, next to the plus sign

Tell students to draw quick tens to represent 41. Demonstrate drawing 4 tens and 1 one. Point to the equation and ask students whether it is addition or subtraction.

Should we represent 30 by crossing off tens or drawing more tens?

Drawing more tens

Ask students to draw 3 more tens to represent 30.

Let’s count on by tens from 41.

41, 51, 61, 71

Write 71 in the place value chart on the right.

How many tens are in the first addend?

4 tens

How many more tens did we add?

3 tens

How many tens are in the total?

7 tens

Point to the corresponding digits on the place value charts as you revoice the numbers of tens as an addition problem.

4 tens + 3 tens = 7 tens

Why did the digit in the ones place stay the same in both places?

The ones stayed the same because we only added tens.

We only added tens, so the digit in the ones place stayed the same. The digit in the tens place changes because we added tens.

Write 71 to complete the original equation.

Ask students to erase. Write 54 + 40 = in the rectangle at the top of the removable.

Promoting the Mathematical Thinking and Reasoning Standards

Students use patterns and structure to help them understand and connect mathematical concepts (MTR.5) when they notice that adding tens to a two-digit number causes the digit in the tens place to change, but the digit in the ones place remains the same.

Recognizing this pattern can help students make sense of strategies such as combining like units or making the next ten.

Ask students to write 54 in the place value chart on the left and 40 below the arrow next to the plus sign. Have students think–pair–share to find the total. They may draw tens and ones, count on by tens, or just add tens by using the place value charts. Ask students to write the total in the place value chart on the right and in the equation.

Ask one or two students to share their work and bring the class to a consensus on the answer.

If time allows, repeat the process with 36 + 60.

More Coins for Ko

Students add tens to two-digit numbers and discuss what they notice about the digits.

Play part 1 of the video, which shows Ko putting coins that total 17 cents in her pocket and then finding 3 dimes.

Display the equation 17 + 30 =   . Have students think–pair–share to answer the following questions. They may choose to use their Double Place Value Chart removable to record their thinking.

How much money does Ko have? How do you know?

47 cents; she started with 17 cents, and then she found 3 dimes. We can count on by tens. 17, 27, 37, 47.

47 cents; 3 dimes is 3 tens. 1 ten + 3 tens = 4 tens. The 7 ones stay the same.

Write 47 to answer the equation.

Play part 2 of the video, which shows Ko finding more dimes and throwing all her coins into the fountain.

Display the equation 47 + 20 =  . Have students think–pair–share to answer the following question. They may use their Double Place Value Chart removable to record their thinking.

UDL: Representation

Consider recoding and highlighting the digit in the ones place in the first addend and in the total of the equation. Record each equation to help students recognize the pattern of the digit in the ones place staying the same in the addend and the total.

How much money did Ko throw into the fountain? How do you know?

67 cents; she found 2 dimes. We can count on by tens. 47, 57, 67.

67 cents. 2 dimes is 2 tens. She had 4 tens and 7 ones.

4 tens + 2 tens = 6 tens. The ones stay the same, 7. Write 67 to answer the equation.

What happens to the digits when we add tens to a number?

47

+ 20 =

The digit in the tens place gets bigger but the ones place stays the same.

Problem Set

Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex.

Directions and word problems may be read aloud.

Students may use the Double Place Value Chart removable as they complete the problems.

Land

Debrief 5 min

Objective: Add tens to a two-digit number. Display the three equations.

Direct students’ attention to 35 + 20 = . Have students think–pair–share to find the total by using mental math or fingers.

How did you find the total?

I saw 3 tens and 2 tens. That is 5 tens. There are 5 ones. 5 tens 5 is 55.

I counted on. 35, 45, 55.

I know 30 + 20 = 50 and 5 more is 55.

Write the total.

Direct students’ attention to 20 + 35 =  . Have students think–pair–share to find the total.

How did you find the total?

This problem is the same as 35 + 20. The parts are just in a different order.

I saw 2 tens and 3 tens. That is 5 tens. There are 5 ones. 5 tens 5 is 55.

I counted on from the second addend because it’s bigger. 35, 45, 55.

Write the total.

These last two problems show us that we can add in any order.

Look at all three number sentences. What happens to the digits when we add tens to a number?

The digit in the tens place changes. It gets bigger. But the digit in the ones place stays the same.

Exit Ticket 5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

1. Read Kit has 3 boxes of crayons and 4 more. She gets 2 more boxes. How many crayons does she have now?

2. Read Baz has 35 berries. He picks 20 more berries. How many berries does he have now?

Baz has 55 berries.

Add ones and multiples of ten to any number. (Optional)

Lesson at a Glance

Students engage in choral counting and notice patterns in the tens and ones places. Then they add a string of numbers, two at a time, to get to 100 (or more). Students self-select strategies to use in a variety of problems, including adding ones to a multiple of ten and adding ones or a multiple of ten to a two-digit number.

Key Question

• How does looking at the digits in the tens and ones places help you to add?

Achievement Descriptor

FL.1.Mod5.AD6 Find 10 more and 10 less than a two-digit number. (MA.1.NSO.2.3)

Agenda Materials

Fluency 10 min

Launch 10 min

Learn 30 min

• Get to 100

• Add to 100

• Problem Set

Land 10 min

Teacher

• Chart paper (3 pieces)

• Marker

• Add to 100 cards (digital download)

Students

• Add to 100 cards (1 set per student pair, in the student book)

• Chart paper (1 piece per student pair)

• Marker

Lesson Preparation

• The Add to 100 cards must be torn out of student books, cut apart, and shuffled. Each pair of students needs one set of cards. Consider whether to prepare these materials in advance or to have students tear out, cut, and shuffle them during the lesson.

• Copy or print the Add to 100 cards to use for demonstration.

Fluency

Counting with Coins

Students identify the name and value of a dime and then count by tens to build fluency with counting money.

After asking each question, wait until most students raise their hands, and then signal for students to respond.

Raise your hand when you know the answer to each question. Wait for my signal to say the answer.

Display the picture of the front side of a dime.

What is the name of the coin?

Dime

How many cents is it worth?

10 cents

Let’s count by 10 cents up to 100 cents and then back down to 0 cents. Ready?

Display each dime, one at a time, as students count.

10 cents, 20 cents, 30 cents, … , 100 cents

100 cents, 90 cents, 80 cents, ... , 0 cents

Choral Response: True or False?

Students determine whether number sentences are equal (true) or not equal (false).

Display the number sentence 10 – 9 = 1.

Is the number sentence true or false? Raise your hand when you know.

Wait until most students raise their hands, and then signal for students to respond.

True Display the answer.

Repeat the process with the following sequence:

Choral Response: Add or Subtract in Unit and Standard Form

Students add or subtract units of ones or tens to develop place value understanding.

Display 2 ones + 2 ones =  .

What is 2 ones + 2 ones? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond.

4 ones

Display the answer.

On my signal, read the number sentence. Ready? (Point to each addend and the total as students say the equation with the numbers in unit form.)

2 ones + 2 ones = 4 ones

Display the equation with the numbers in standard form.

When I give the signal, read the number sentence. Ready? (Point to each addend and the total as students say the equation with the numbers in standard form.)

2 + 2 = 4

Continue with 2 tens + 2 tens =  .

Repeat the process with the following sequence:

Launch

Materials—T: Chart paper, marker Students choral count by tens and notice patterns.

Gather the class and show them the chart paper in landscape orientation.

Begin a first column by writing 50 in the top left corner of the paper.

Take a moment to think about what the next few numbers would be if we count by ones. Show thumbs-up when you are ready.

Invite students to chorally count by ones starting at 50. Record the count in rows. Start a new row with the next ten. Ask students to watch the marker carefully so the recording guides their pace and lets the class sound like one unified voice. Leave ample space around each number to record patterns that students may notice later. Count and record up to 69.

Under 60, draw a line to start the third row. Do not write 70 yet.

What number comes next? How do you know?

70; it comes after 69. 50, 60, 70. It is counting by tens as you go down.

Write 70 on the line. Continue to count and record up to 85. Draw three lines and circle the third line (where 88 belongs).

What number goes here? How do you know?

88. I counted on 3.

88. I see a pattern counting by tens: 58, 68, 78, 88.

Teacher Note

Recording choral counts on chart paper allows students to notice patterns. They may also revisit previous counts to look for additional patterns, confirm how to write certain numbers, or simply enjoy recounting.

Write 86, 87, and 88 on the three lines. Continue to count and record up to 99. Draw a line where 100 belongs.

What number goes here? How do you know?

99, 100. I counted on.

I see a pattern with tens: 50, 60, 70, 80, 90. The next ten is 100. Write 100 on the line. Circle the first column and label it tens. Guide students to count by tens the math way from 10 to 100 to help students see that 10 tens make 100.

100 is 10 tens.

As time allows, invite students to share other patterns they see. The following are possible observations:

• As you move down the columns, the numbers increase by 10.

• As you move up the columns, the numbers decrease by 10.

• In the columns, the tens digits change but the ones digits stay the same.

• In the rows, the ones digits change but the tens digits stay the same. Label or highlight observations directly on the chart. Consider using a different color for each pattern students notice. Encourage place value language by reminding students to use the words tens and ones as they share their ideas. Consider asking students to revoice other students’ patterns in their own words, e.g., “She saw a pattern of adding 10.”

Transition to the next segment by framing the work.

Today, we will add ones and tens and try to get to 100.

Teacher Note

Students do not need to master the concept that 10 tens make 100 in grade 1.

Learn

Get to 100

Materials—T: Chart paper, marker

Students add a string of ones and tens to get to 100 as a class.

Show students chart paper in landscape orientation. Begin a row by writing 6 and then 30 in the top left corner of the paper. Draw a box around each number. Ask students to find the total of 6 and 30 by using mental math or on their personal whiteboard. Students may use a number path or cubes if needed. Have them give a silent signal when they are ready.

What is the total? How do you know?

36; there are 3 tens and 6 ones.

30 and 6 is 36.

Draw to represent each number and record the addition the arrow way below your drawing.

Next to 30, write the number 40 and draw a box around it. Ask students to add 36 and 40. Have them give a silent signal when they are ready. After they share the total, draw to represent 40 and record the addition the arrow way.

Next to 40, write the number 4 and draw a box around it. Repeat the process of having students add the numbers and share the total. Draw and record the process on the chart.

We are at 80. Have we gotten to 100 yet? How do you know?

No, 80 comes before 100.

We are not yet at 100. 8 tens make 80, and 10 tens make 100. Let’s add another number.

Turn and talk: Which number should we add to make 100?

UDL: Action & Expression

Help students recall that mathematicians take time to plan and make sense of the addends before deciding on a strategy. Consider guiding students’ thinking aloud decision making by providing sentence frames such as this one:

If I had a problem that was tens plus ones, such as , then I would choose strategy because I know    .

Provide sentence frames to help with think-aloud strategies for other combinations, such as:

• Tens + tens

• Two-digit numbers + ones

• Two-digit numbers + tens

After they work, ask students how they solved the problem and how well their strategy worked for them. Ask them if they would use the same strategy next time or try another one.

Teacher Note

The picture book Let’s Count to 100! by Masayuki Sebe may complement this lesson. It features 100 unique objects that invite children to search and count.

Masayuki Sebe has authored many books featuring 100. Students may also enjoy 100 People, 100 Things, 100 Animals on Parade, and 100 Hungry Monkeys.

Next to 4, write the number 20 and draw a box around it. Repeat the process of having students add the numbers and share the total. Draw and record the process on the chart.

Add to 100

Materials—T: Add to 100 cards, chart paper; S: Add to 100 cards, chart paper, marker Students practice adding tens and ones to get to 100.

Ask a volunteer to be your partner to demonstrate the activity. Use the following procedure:

• Place the cards in a pile, facedown.

• Each partner chooses a card. Partners place their cards side by side at the top of the chart paper.

• Partners find the total and record their thinking directly below the cards. They can show their work in any way they choose. They do not need to use the arrow way or drawings from the previous segment.

• After the first round, partners take turns choosing one card and placing it in the row of numbers at the top of the chart paper.

• With each new card, partners work together to add the amount on the new card to the previous total.

• Partners play until they reach or pass 100, or until time is up. Partner students and distribute a piece of chart paper and a set of cards to each pair. As partners play, advance and assess their thinking by asking the following questions.

What is the total now? How did you find it?

How can you show your thinking?

Differentiation: Challenge

Vary the activity by having students lay out all the cards faceup. Ask them to strategically choose cards to get as close to 100 as they can without going over 100.

Teacher Note

Consider saving the Add to 100 cards for students to practice with at other times of the day. Partners could do the same activity again or they could do the challenge variation. Alternatively, they could each choose two cards and find the total. Then partners can compare their totals to see which is greater (or less).

Differentiation: Support

Draw quick tens to represent the addends in each expression.

Problem Set

Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex.

Directions and word problems may be read aloud.

Land Debrief 5 min

Objective: Add ones and multiples of ten to any number.

Display the expressions. Engage students in the Take a Stand routine.

Look at these two problems. Turn and talk: Do they have the same total? How do you know?

Ask students to stand if they think the problems have the same total, and then have them sit down.

Ask students to stand if they think the problems do not have the same total, and then have them sit down.

Invite students from each group to share their reasoning. Record their thinking. They have the same total.

In both problems there are 5 tens and 3 tens. They’re just in a different order. But we can add in any order, so there are 8 tens in both problems.

In both problems there are only 7 ones. Write an equal sign between the expressions.

Promoting the Mathematical Thinking and Reasoning Standards

Students use structure to help them understand and connect mathematical concepts (MTR.5) when they use place value reasoning to show that 50 + 37 and 57 + 30 have the same total.

This Land allows students to expand their intuitive understanding of the commutative property of addition. Students already know that they can add in any order, and here they reason that they can decompose the numbers into tens and ones and add those parts in any order without changing the total.

Even though the addends aren’t the same, the totals are the same. In both problems there are 5 tens, 3 tens, 7 ones, and 0 ones.

How does looking at the digits in the tens and ones places help you to add?

We can just add the tens or ones. We do not need to count on. We can use easy facts to help us add the tens and then the ones. Then we can put it all together.

Exit Ticket 5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

Topic E Subtraction of One-Digit Numbers from Two-Digit Numbers

In module 3, students made easier problems so they could subtract within 20. Students leaned on the structure of ten to take from ten, count on by using ten, and count back by using ten. In module 5, students use these familiar strategies to subtract one-digit numbers from two-digit numbers, this time with larger minuends.

As students explore subtraction, they choose strategies that make sense to them based on the given numbers. Whenever appropriate, students are guided toward more efficient strategies such as the following:

• Count Back to Get to a Ten: Students subtract by breaking apart the subtrahend (the number being subtracted). For 36 − 7, they count or hop back one part to get to a ten; for example, 36 − 6 = 30. Then students count or hop back the remaining part to find the difference: 30 − 1 = 29.

• Count On to Get to a Ten: Students connect subtraction to the strategy of counting on to find an unknown part. For 30 − 8, they take the part they know, 8, and make a cube stick of 8 cubes in one color. Students then count on by using cubes of a different color. While students use cubes, the teacher models on the number path.

• Take from the Ten or Take from the Ones: Students deepen their understanding of place value as they explore whether to take all or a part from a ten and add the remaining ones, whether there are enough ones to simply take only from the ones, or whether to take from the ones and then decompose a ten into ones to take the rest. Developing the habit of deciding whether to take from the tens or take from the ones is a crucial part of regrouping in grade 2.

Take from Ones

Take from Tens

Take from Ones and Tens

The last lesson of this topic offers students the opportunity to self-select from the strategies they have learned to solve a series of subtraction problems. The numbers in each problem, along with personal preference, inform their decision about which strategy to use. Though mastering every strategy is not necessary, knowing more than one way to solve a problem gives students a choice and helps them become flexible thinkers.

Progression of Lessons

Lesson 21

Count back to subtract from a two-digit number.

Lesson 22

Count on to subtract from a two-digit number.

Lesson 23

Take from the ten or take from the ones, part 1.

I can count on to find the unknown part. I start with the part I know, 8, and hop to 10. Then I hop by tens until I get to 30.

I can get to a ten by counting back 3. I know that 3 and 5 is 8. So I need to count back 5 more. That is 45.

I can break up 34 into 30 and 4. I take 9 from 30 and then add what is left. 21 and 4 is 25.

Lesson 24

Take from the ten or take from the ones, part 2.

Lesson 25

Choose a strategy to make an easier problem.

I can’t take 8 from the 5 ones in 45. So I break apart a ten to make 15 ones. 15 take away 8 is 7. Now, I add what is left. 30 and 7 is 37.

Taking 9 ones from the ten is easier. I can choose the strategy that is the most helpful to me.

Count back to subtract from a two-digit number.

Lesson at a Glance

Students subtract by breaking the subtrahend into two parts. They count back by the amount of the first part to get to a ten, and then they count back by the amount of the second part. Students represent their thinking with cubes or by using a number path.

Key Question

• How can we count back efficiently to subtract?

Achievement Descriptor

FL.1.Mod5.AD8 Subtract a one-digit number from a two-digit number by using manipulatives, number lines, drawings, or equations. (MA.1.NSO.2.5)

Agenda Materials

Fluency 10 min

Launch 5 min

Learn 35 min

• Decompose a Part

• Count Back to Get to a Ten

• Problem Set

Land 10 min

Teacher

• Unifix® Cubes (50)

• Number Path removable Students

• Number Path to 120 (in the student book)

• Unifix® Cubes (50 per student pair)

• Number Path removable (in the student book)

Lesson Preparation

• Assemble sticks of 10 Unifix Cubes and gather some single cubes. Use a single color of cubes for each stick. Each student pair needs four sticks and 10 single cubes. Save them for use in subsequent lessons.

• The Number Path to 120 may have been torn out of student books and assembled earlier in the module. Consider whether to use specific segments of the Number Path, which can be slid into personal whiteboards, or to use the Number Path to 120 previously prepared.

Fluency

Number Path Hop: Get to a Ten

Materials—S: Number Path to 120

Students use the number path to find the previous ten to prepare for relating addition and subtraction.

Have students fold their number paths in half so that numbers 1−60 are showing.

Show the number 31 circled.

Let’s count by tens and ones to get to 31. Use your finger to keep track. 10, 20, 30, 31

Find the ten that comes before. 30

Repeat the process with the following sequence:

Green Light, Red Light

Students count by ones from a given number to build fluency counting within 120.

Display the green and red dots with the numbers 97 and 100.

On my signal, start counting by ones with the green light number. Stop at the red light number.

Look at the numbers.

Think. Ready? Green light!

97 100

Teacher Note

Consider having students slide the Number Path to 120 (segment 1–60) into their personal whiteboards. Then students can show and label hops with a dry-erase marker.

Teacher Note

If more movement is desired, consider having students run in place, hop, or engage in another physical exercise while counting.

97, 98, 99, 100

Repeat the process with the following sequence:

Launch

Students consider the efficiency and accuracy of counting back as a strategy for subtraction.

Display the picture of 41 rocks in containers.

Zoey collects rocks.

How many rocks does she have? 41

She gives away 3 rocks.

Ask students to write a number sentence on their whiteboard to find how many rocks are left.

Record 41 − 3 =  .

When most students have finished, signal for students to show their answers.

What is 41 − 3? 38

How do you know?

I counted back: 41 … 40, 39, 38. (Puts up 3 fingers.)

I counted what was left: 10, 20, 30, and 8 more. 30 and 8 is 38.

Write the difference to complete the equation 41 − 3 = .

Let’s try another problem. This time Zoey gives away 7 rocks.

Teacher Note

Anticipate that students will use the picture when finding the difference. Students may do the following:

• Cross off rocks with their finger in the air.

• Hide 3 with their hand and then count the remaining rocks.

Ask students to write a number sentence on their whiteboard to find how many rocks are left.

Record 41 − 7 =  .

When most students have finished, signal for students to show their answers. Anticipate a few answers.

I see 33, 48, 34, 46 …

Why do you think there are so many different answers? I counted back and lost track.

Maybe we subtracted the wrong amount. We had to take away 7.

If students do not show a variety of answers, highlight the difference between the two problems and why counting back by ones was not an efficient strategy for both number sentences.

Why did counting back seem like an efficient strategy for 41 − 3 but not for 41 − 7?

It was easy for me to keep track of counting back 3, but it was hard to keep track of counting back 7.

Counting back may be a strategy we use when subtracting smaller numbers such as 2 or 3. But we need a more efficient strategy when subtracting larger numbers.

Transition to the next segment by framing the work.

Today, we will show how we can count back to get to a ten to subtract more efficiently.

Learn

Decompose a Part

Materials—T/S: Unifix® Cubes

Students count back to get to a ten with Unifix Cubes.

Write 36 − 2. Form student pairs and have each student pair show the total with cubes.

Say 36 the Say Ten way. 3 ten 6

What is 36 − 2? How do you know?

34. I took away 2 cubes, and there are 34 left.

I counted back on my fingers: 36 … 35, 34. (Puts up 2 fingers.)

I know that 6 take away 2 is 4, and there are 3 tens. 3 tens 4 ones is 34.

Show taking away 2 cubes as students do the same.

Write 36 − 6. Have each student pair show the total again.

What is 36 − 6? How do you know?

It’s 30. You just take away all the ones. There are 3 tens left.

6 − 6 = 0, so the answer is 30.

Show taking away 6 cubes as students do the same.

Write 36 − 7.

This time we are subtracting 7. Let’s use 36 − 6 to help us solve.

How much did we subtract from 36 to get to 30? 6

We’ve already subtracted or taken away 6, so now what do we need to do?

Take away 1 more from a ten. We need to take away 1 because we need to take away 7 in all. Show snapping off 1 cube (from a ten) as students do the same.

How many do we have left? 29

How did we take 7 in two parts?

We took 6 first and then 1 more.

Record 7 as 6 and 1 with a number bond. Write 36 − 6 = 30 and then 30 − 1 = 29.

Have students think–pair–share about why they broke 7 into two parts.

We took away 6 ones to get to 30. It’s easier to take away 1 from 30. We wanted to get to a ten. After we took away 6 ones, we could just count back 1 to 29.

Invite students to work with a partner to practice taking away in parts by using cubes. As students work, direct them to the Share Your Thinking section of the Talking Tool to explain how they used a ten to help them find the answer efficiently. Consider using the following expressions for student practice:

• 45 − 6

• 23 − 8

• 34 − 7

Differentiation: Support

To support the concept of taking away in parts to get to a ten, provide an entry point to the problem. For example, have students find 45 − 5 before finding 45 − 6.

Count Back to Get to a Ten

Materials—T/S: Number Path removable

Students count back to get to a ten with the Number Path.

Have students insert the removable in their personal whiteboards. Return to the problem 36 − 7.

We can also count back or hop back to get to a ten by using the number path. Where should we start? 36

Circle 36 on your number path. Let’s count back to get to a ten. How should we label that hop? − 6

Hop to 30 and label the hop − 6.

We only hopped back 6 so far. (Point to the labeled hop for − 6.) But we need to subtract 7.

Direct students to the number bond under 7 from the previous segment.

What is 6’s partner to 7? 1

Have students make a number bond under 7 with parts 6 and 1.

Let’s hop back 1 more. Draw a hop and label it − 1.

Where did we land? What is 36 − 7? 29

Repeat the process with 32 − 5 and 34 − 8, reducing guidance as appropriate. Then invite students to explain how to count back by using a ten.

How would you explain to a new student how we count back by using a ten on the number path when we subtract?

Start at the total. Hop back to a ten. Then hop the rest of the part you know. The number you land on is the answer.

UDL: Representation

The interactive Number Path to 120 supports the understanding of counting back to solve subtraction problems. It also helps students connect the number path with the strategy of getting to a ten by decomposing the subtrahend.

Consider allowing students to experiment with the tool independently or demonstrating the activity for the whole class.

After you hop back to a ten, how do you know where to hop next?

You have to look at the number you broke apart and see what part is left. You already hopped back part of the number you know. Now, you need to hop the other part.

Problem Set

Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex.

Directions may be read aloud.

Land

Debrief 5 min

10 5 35 10

Objective: Count back to subtract from a two-digit number.

Gather students for discussion.

Write 53 − 8 =  .

Kai counted back by ones to figure out 53 − 8.

Model counting back by ones on fingers, skipping from 51 to 49.

52, 51 (pause), 49, 48, 47, 46, 45, 44. Kai’s answer was 44. (Hold up 8 fingers.)

Is Kai correct? How do you know?

No, she skipped over 50 when she counted back.

She forgot what comes next when you count back. It goes 51, then 50, then 49.

Promoting the Mathematical Thinking and Reasoning Standards

As students explain to the class how to solve the problem by counting back to ten, they engage in discussions that reflect their mathematical thinking (MTR.4).

Ask the following questions to promote MTR.4:

• Why was this strategy more efficient than counting back by the amount of all the second part?

• How does this strategy help keep you from making errors?

Display a segment of the number path (41−60).

How could Kai count back efficiently to subtract?

Kai could break apart 8 and take away 8 in two parts.

Kai could get to 50 first and then hop back the rest on the number path. Record taking away in parts with a number bond as shown.

Why do we use a ten to count back to subtract?

I think it’s easier to make a mistake if we count back by ones. I like taking away smaller parts. I don’t get lost.

Exit Ticket 5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

LESSON 22 Count on to subtract from a two-digit number.

Lesson at a Glance

Students represent a word problem and see the part–part–total relationship between addition and subtraction. This relationship highlights subtraction as an unknown addend problem. Students get to a ten to count on efficiently from the known part to the total. They represent their thinking with cubes or on a number path.

Key Question

• How can we count on efficiently to subtract?

Achievement Descriptor

FL.1.Mod5.AD8 Subtract a one-digit number from a two-digit number by using manipulatives, number lines, drawings, or equations. (MA.1.NSO.2.5)

Agenda

Fluency 5 min

Launch 10 min

Learn 35 min

• Connect Subtraction to Counting On

• Count On to Get to a Ten

• Problem Set

Land 10 min

Materials Teacher

• Unifix® Cubes (30)

• Number Path to 120 Students

• Unifix® Cubes (50 per student pair)

• Number Path to 120

Lesson Preparation

• Assemble sticks of 10 Unifix Cubes and gather some single cubes. Use a single color of cube for each stick. Each student pair needs four sticks and 10 single cubes.

• Have tools available (e.g., Unifix Cubes, the Number Path to 120) for students to self-select as they solve.

• The Number Path to 120 may have been torn out of student books and assembled earlier in the module. If more are needed, they will need to be torn out of the student books, cut, and assembled.

Fluency

Whiteboard Exchange: Relate Subtraction and Addition

Students relate subtraction and addition to build an understanding of subtraction as an unknown addend problem.

After each prompt for a written response, give students time to work. When most students are ready, signal for them to show their personal whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

Display 10 − 9 =  .

Write the subtraction equation.

Write a related addition sentence starting with 9 that would complete the subtraction equation.

Display the related addition sentence.

Write the answer to the subtraction equation.

Display the difference.

Repeat the process with the following sequence:

Launch

Materials—T: 20 Unifix Cubes

Students represent a word problem and discuss the relationship between addition and subtraction.

Gather students with their personal whiteboards. Display the following problem. Read it aloud.

I have 20 shells. 9 shells are smooth. The rest are bumpy. How many shells are bumpy?

Have students draw a number bond to match the story.

How did you show the total and parts with a number bond?

I have 20 shells. 9 shells are smooth. The rest are bumpy.

How many shells are bumpy?

20 is the total. 9 is one of the parts. We need to find the other part.

Have students write a number sentence to match the problem without solving. Have students make a blank line to represent the unknown value. Encourage them to think of more than one way to model the situation with numbers and symbols.

What number sentence did you write to match the story?

I wrote 20 − 9 =  .

I wrote 9 + = 20.

Write the two number sentences with the unknowns. Model 20 − 9 with cubes by taking away 9 from a ten as shown.

I have 2 tens. I can take away 9. That is the part I know.

(Break off 9.)

Which part was unknown? How do you know?

11; there is 1 ten and 1 one left.

When we subtract, we look for an unknown part. 11 is our unknown part. (Write 11 in the number sentence and number bond. Draw a box around 11.)

Draw students’ attention to 9 + = 20. Have students think–pair–share about how this number sentence is related to 20 − 9 = .

What is the same and what is different about these number sentences?

They both have an unknown part.

You can use the same number bond for both of them.

In the subtraction number sentence, you are taking away the part you know. In the addition number sentence, you are adding on to the part you know.

We know we can also add, or count on, to find an unknown part.

Transition to the next segment by framing the work.

Today, we will use counting on to help us solve subtraction problems.

Learn Connect Subtraction to Counting On

Students count on to get to a ten as they think addition to subtract.

Ask students to turn to the classwork in their student book. Ask them to look at the cubes representing 20 − 9 = 11 and point to the total and each of the parts.

Why did we have 11 left?

We took 9 away from a ten. There is 1 left from the ten and then another ten.

Guide students to write the expression 10 + 1 under the cubes.

Let’s show our thinking on the number path.

As students follow along, demonstrate drawing a line to cross out spaces 1−9.

Promoting the Mathematical Thinking and Reasoning Standards

Students demonstrate understanding by representing problems in multiple ways (MTR.2). Their work with modeling subtraction problems by using cubes and the number path helps them connect the components of a subtraction problem with its representation by using the unknown addend strategy.

Ask the following questions to promote MTR.2:

• How do we know where to start on the number path to count on from?

• Where is the total for the unknown addend problem on the number path?

• Was it easier to get to the next ten instead of counting by ones on the number path?

Should we count on by ones to get to 20?

No, that would take too long. Get to ten!

Just make 1 little hop to get to ten first.

Draw 1 hop to count on from 9 to 10. Label the hop + 1 as students do the same.

Guide students to see that the 1 space in the first hop represents the same 1 as the 1 cube that is left after taking 9 from a ten.

Have students think–pair–share about the next step.

What do you think the next step will be?

You can just make 1 big hop from 10 to 20.

The answer is 11, and we already hopped 1. Now we have to hop 10 more.

Draw a second hop to count on from 10 to the total, 20. Label the hop + 10. Guide students to relate the spaces in this hop to the stick of 10 cubes.

Ask students the following questions and represent the number path work with a number sentence as students do the same.

Where did we start on the number path? 9

Write 9.

Look at our hops. How many did we add to 9 to get to 20? 11

Write + 11 = 20 next to the 9.

Guide students to draw a box around 11, the answer, in both the addition and subtraction number sentences.

The answer to a subtraction problem is an unknown part. We can also find an unknown part by counting on from the part we know to the total. We can get to a ten to help us count on.

Count On to Get to a Ten

Materials—T/S: Number Path to 120; S: Unifix Cubes

Students get to a ten to count on as they think addition to subtract.

Display 30 − 8 = and a segment of the Number Path to 120 (1–30).

Model counting on from the known part with the number path as students model with cubes.

What is the total? 30

What part do we know? 8

Have pairs of students make a stick of 8 cubes (all of one color).

Circle 8 on the number path as shown.

How many more cubes to get to ten? 2

Have pairs add 2 cubes of a different color to make a 10-stick.

Hop to 10 on the number path.

How should I label my hop? + 2

Have I hopped to my total yet? No.

Have students think–pair–share about how they can use a ten to help them count on.

How can you use a ten to help you count on?

You could add 2 more tens. Then you have 30.

You could hop to 20 and then to 30.

Hop to 20 and then 30 on the number path.

UDL: Representation

The interactive Number Path to 120 supports students’ understanding of counting on to solve subtraction problems. It also highlights subtraction as an unknown addend problem by connecting the hops on the number path to finding an unknown part.

Consider allowing students to experiment with the tool independently or demonstrating the activity for the whole class.

Teacher Note

Students may use the following terms interchangeably to describe their strategy: hop to a ten, count on to a ten, get to a ten.

How many did we count on in all? How do you know?

We counted on 22. I know because 2 + 10 + 10 = 22.

2 tens and 2 ones is 22.

What addition number sentence can we write starting with the known part?

8 + 22 = 30

If 8 + 22 = 30, then what is 30 − 8? 22

Complete the equation: 30 − 8 = 22.

Invite students to work with a partner to practice counting on to subtract. Have cubes and the Number Path to 120 available for students to self-select a tool. As students work, direct them to the Share Your Thinking section of the Talking Tool to explain how they used a ten to help find the answer efficiently. Consider using the following expressions for student practice:

• 40 − 8

• 50 − 9

• 41 − 7

Problem Set

Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex.

Students are encouraged to pick a tool to help them solve. Have Number Paths to 120 and cubes available for students to self-select.

Directions and word problems may be read aloud.

UDL: Engagement

As students explore getting to a ten on their own, offer feedback that focuses attention on their effort and use of the strategy rather than on their proficiency. Examples of feedback include the following:

• You are noticing that it would take a long time to count on by ones.

• You are using tens to help you find the unknown part.

• Now that you have hopped to a ten, I bet you can hop to another ten, and another one, and another one, until you reach the total.

Land

Debrief 5 min

Objective: Count on to subtract from a two-digit number.

Materials—T: Number Path to 120, Unifix Cubes

Write 30 − 7. Engage students in the Take a Stand routine.

Look carefully at this problem. Turn and talk: Which strategy would you use to solve this problem, counting back or counting on?

Ask students to stand if they would solve this problem by counting back, and then have them sit down.

Ask students to stand if they would solve this problem by counting on, and then have them sit down.

Invite students from each group to share their reasoning. Show or record their thinking.

I would count back 7 on a number path.

I would make 3 tens with cubes and just take away 7 from a ten.

I like adding, so I would start at 7 and hop to ten, and then count on more tens until I get to 30.

You have to count on a lot, so I would rather just count back.

Emphasize that using tens to count back or count on are two efficient strategies we can use to solve a subtraction problem.

Exit Ticket 5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Teacher Note

It is not necessary for students to solve the problem. Rather, they should reason about the strategy that makes sense to them based on the given numbers in the problem.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

3. Read

Kit has 40 stickers. She gives away 8 stickers. How many stickers does she have now? Draw Sample:

Kit has 32 stickers.

Take from the ten or take from the ones, part 1.

Lesson at a Glance

Students use place value concepts to subtract a one-digit number from a two-digit number. As in similar work with addition, students decompose the two-digit number into tens and some ones. They subtract the one-digit subtrahend from the ones and then add the tens and remaining ones to find the difference.

Key Question

• How does breaking apart a number make it easier to subtract?

Achievement Descriptor

FL.1.Mod5.AD8 Subtract a one-digit number from a two-digit number by using manipulatives, number lines, drawings, or equations. (MA.1.NSO.2.5)

Agenda

Fluency 5 min

Launch 10 min

Learn 35 min

• Take from the Ones

• Take from the Ten

• Problem Set

Land 10 min

Materials Teacher

• Unifix® Cubes (75)

Students

• Unifix® Cubes (75 per pair)

Lesson Preparation

• Assemble sticks of 10 Unifix Cubes and gather some single cubes. Use a single color of cube for each stick. Each student pair needs 7 sticks, each a different color, and 5 single cubes.

• Save the Unifix Cube sticks to use again in subsequent lessons.

Fluency

Whiteboard Exchange: Take Out 10

Students use a number bond to decompose a number into 10 and another addend to prepare for subtracting from multiples of ten.

After each prompt for a written response, give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

Display the number 16.

Write this number on your whiteboard.

Let’s take out 10.

Display the number bond with 10 as a part.

Find the unknown part.

Display the completed number bond.

Repeat the process with the following sequence:

Differentiation: Support

Offer a visual for students by modeling each decomposition with the dot side of the Hide Zero cards as you record the number bond.

Differentiation: Challenge

Provide a series of related problems to students who demonstrate proficiency with the given sequence. Give three totals, such as 6, 26, and 96, at once. Some students may notice place value connections and appreciate how the work is relevant to larger numbers.

Take Away All at Once

Students model related subtraction sentences with their fingers to develop familiarity with the take from the ones subtraction strategy and to build procedural reliability for subtraction within 20.

Show me 5.

Take away 2 all at once.

Show me 5.

When I give the signal, say the subtraction sentence starting with 5. Ready?

5 − 2 = 3

With your partner, show me 15 as 1 ten 5 ones.

Take away 2 all at once.

Show me 15 as 1 ten 5 ones.

When I give the signal, say the subtraction sentence starting with 15. Ready?

15 − 2 = 13

Repeat the process with the following sequence, with partners taking turns showing the ten:

Launch

Students consider whether to take from the tens or take from the ones. Display Lucia’s pennies.

Lucia has some pennies in her pockets and some pennies in her hand.

How many pennies are in her hand? 2

How many pennies are in her pockets? 20

How many pennies does Lucia have? 22 pennies

She wants to buy an eraser that costs 9 cents. What are some ways to pay for it?

As students share, annotate the picture to record their thinking.

She can use the 2 pennies in her hand. Then she can count on from 2 to get the rest from a pocket: Twoooo, 3, 4, 5, 6, 7, 8, 9.

She can think of 9 pennies as two parts: 2 and 7. Take 2 from her hand, 7 more from a pocket.

She could take out all 10 pennies from one of the pockets, and then put one back. 10 − 9 = 1

Invite students to think–pair–share about how many pennies Lucia has left.

How many pennies does Lucia have left?

She has 13 pennies left because there is 1 pocket with 10 pennies and another pocket with 3 pennies. 10 and 3 make 13.

I got 13 pennies, too, but I used the other picture and counted a different way: 10 and 1 more is 11. Then 2 more in her hand makes 13.

Transition to the next segment by framing the work.

Today, we will make easier problems to subtract by taking from the ones or taking from groups of 10.

Learn

Take from the Ones

Materials—T/S: Unifix Cubes

Students represent taking from the ones place.

Organize Unifix Cubes into 3 tens and 4 ones and ask student pairs to do the same.

Write 34 − 3. Model decomposing the 34 into tens and ones to take from the ones first. Ask students to follow along.

How many tens and ones are in 34?

3 tens 4 ones

What number do we write to show 3 tens? 30

What number do we write to show 4 ones?

Point to the 3 ten-sticks and 4 ones to confirm that 34 is composed of 3 tens 4 ones. Then draw number bond arms under 34 and write 30 and 4 as the parts.

Let’s take from the ones. What is 4 − 3?

Take away 3 cubes from the ones and set them aside as students do the same.

Write 4 − 3 = 1.

Now we have 30 and 1. What is 30 + 1?

(Write 30 + 1.) 31

So, what is 34 − 3? 31

Write = 31 next to 30 + 1.

Repeat the process by using the expressions 59 − 4 and 35 − 5.

Take from the Ten Materials—T/S: Unifix Cubes

Students represent taking from multiples of ten.

Organize the cubes as 3 tens as student pairs do the same.

Write 30 − 9.

How can we take 9 away from 30?

We can count back 9 from 30. Thiiiirty, 29, 28, 27, 26, 25, 24, 23, 22, 21.

We can take 9 cubes away from one of the ten sticks.

Language Support

Clarify the relationship between the manipulatives and the written recording with a show-me exercise. Invite students to point to their cubes as you point to the corresponding part of the written recording.

• Show me how we broke apart the total.

• Show me the part we took away.

• Show me the parts that are left.

Break 9 cubes off from a ten-stick all at once.

Show snapping off 9 cubes and setting them aside as students do the same.

How many cubes are left? How do you know? 21 cubes.

I counted the cubes by tens and ones: 10, 20, 21.

I see 2 tens and 1 one. 20 and 1 is 21.

How did we subtract 9 from 30?

We took 9 from a ten then we saw how many were left.

We made 30 − 9 an easier problem by breaking 30 into two parts.

Draw number bond arms to show 30 decomposed as 20 and 10.

We subtracted 9 from a ten first.

What is 10 − 9? 1

Write 10 − 9 = 1.

Then we added 20 and 1.

Write 20 + 1.

What is 20 + 1? 21

Write = 21 next to 20 + 1.

How do the cubes match the recording?

30 is broken into 20 and 10. 10 − 9 = 1. I see 1 cube left from the 10.

So, what is 30 − 9? 21

Write = 21 next to 30 − 9 to complete the equation.

Teacher Note

Promote flexible thinking by inviting students to solve another way. Refer to counting back and counting on to take away in parts to get to a ten.

Organize the cubes into 3 tens and 4 ones as student pairs do the same. Write 34 − 9.

How many tens and ones in 34?

3 tens 4 ones

Are there enough ones to take all 9 from the ones?

No, there are only 4 ones.

You would have to take the rest from the tens.

(Point to the tens.) Let’s take 9 all at once from a ten.

Show snapping off 9 cubes from a ten and setting them aside as students do the same.

How many cubes are left? 25 cubes

Students may take from ten but then forget to add the remaining ones. Highlight adding the ones that are left by pointing to the cubes.

We have 21 left after taking 9 from the tens. We also have the 4 ones. 21 + 4 = 25

How did we take from the tens?

First, we took 9 away from the tens.

Then we added what was left from the tens and the ones.

We made 34 − 9 an easier problem by breaking 34 into two parts.

Draw number bond arms to show decomposing 34 and write 30 as one part.

(Point to the tens.) We subtracted 9 from the tens first.

What is 30 − 9? 21

Write 30 − 9 = 21.

Then we counted what was left from the tens and ones.

Write 21 + 4.

What is 21 + 4? 25

Write = 25 next to 21 + 4.

How do the cubes match the written recording?

34 is broken into 30 and 4. I see 34 cubes as 3 sticks and 4 ones.

9 is taken from the 3 tens, which leaves 21. Then we add the 4 ones.

So, what is 34 − 9? 25

Write = 25 next to 34 − 9.

Repeat the process by using the expressions 70 − 5 and 45 − 8.

Problem Set

Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex.

Students are encouraged to pick a tool to help them solve. Have Number Paths to 120 and cubes readily available for students to self-select.

Directions and word problems may be read aloud.

Promoting the Mathematical Thinking and Reasoning Standards

Students demonstrate understanding by representing problems in multiple ways (MTR.2). Their work with modeling subtraction problems, using the cubes and the number bonds, helps them to connect the take from the ten strategy to the take from the one strategy.

Ask the following questions to promote MTR.2:

• When is it easier to take from a ten?

• How does breaking apart a number make subtraction easier?

Land

Debrief 5 min

Objective: Take from the ten or take from the ones.

Gather students and display Malik’s cubes. Invite students to think–pair–share to analyze the work sample.

Look at Malik’s cubes. He says 35 − 7 = 28. Is he correct? How do you know?

I notice he took away 5 ones and 2 more from a ten: that’s 7.

Now he has 2 ten sticks and 8 extras. 20 + 8 = 28

How did breaking apart a number make it easier for Malik to subtract?

Malik broke 7 into 2 and 5.

He took the 5 ones and 2 more from a ten to make 7. 35 − 5 and 30 − 2 is easier than 35 − 7.

How can we find 35 − 7 another way?

We can count on or count back to a ten.

We can take 7 away from a ten.

Exit Ticket 5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

3. Read

Baz picks 31 flowers. He gives away 7 flowers

How many flowers does he have now?

Draw Sample: Write 31 – 7 = 24

Baz has 24 flowers

Take from the ten or take from the ones, part 2.

Lesson at a Glance

Students continue to deepen their understanding of place value as they explore different ways to subtract. Students see that they may take all from a ten and add the remaining ones to find the difference. Students also explore decomposing a ten and regrouping ones when needed.

Key Question

• How does breaking apart a number make it easier to subtract?

Achievement Descriptor

FL.1.Mod5.AD8 Subtract a one-digit number from a two-digit number by using manipulatives, number lines, drawings, or equations. (MA.1.NSO.2.5)

Agenda Materials

Fluency 5 min

Launch 10 min

Learn 35 min

• Two Ways to Take from Ten

• Raceway Subtraction Game

• Problem Set

Land 10 min

Teacher

• Unifix® Cubes (75)

Students

• Unifix® Cubes (75 per student pair)

• Raceway Subtraction Game (1 per student pair, in the student book)

• Number Path to 120 (in the student book)

• Counter

• 6-sided dot die (1 per student pair)

Lesson Preparation

• Gather and distribute the 7 sticks of 10 Unifix Cubes and 5 single cubes.

• Consider tearing out the Raceway Subtraction Game boards in advance or have students tear them out during the lesson.

• The Number Path to 120 may have been torn out of student books and assembled earlier in the module. If more number paths are needed, they will need to be torn out of the student books, cut, and assembled.

Fluency

Take Away All at Once

Students model subtraction sentences with their fingers to build familiarity with the take from the ones and take from ten subtraction strategies.

With your partner, show me 15 as 1 ten 5 ones.

Take away 4 all at once.

Show me 15 as 1 ten 5 ones.

When I give the signal, say the subtraction stentence starting with 15. Ready?

15 – 4 = 11

Repeat the process with 15 – 5.

With your partner, show me 15 as 1 ten 5 ones.

Let’s take away 6 all at once. Will we take from the ten or the 5 ones? Raise your hand when you know.

The ten

Let’s break up the ten into 10 ones. Show me 15 as 10 ones and 5 ones.

Take away 6 all at once.

Show me 15 as 10 ones and 5 ones.

When I give the signal, say the subtraction sentence starting with 15. Ready?

15 – 6 = 9

Repeat the process with the following sequence, with partners taking turns showing the ten:

Launch

Students compare and discuss two ways to subtract, in parts or all at once.

Partner students and display the pictures of the crayons. Invite student pairs to think–pair–share to discuss how the pictures are similar and different.

How are the crayon pictures the same?

Both pictures have some crayons in boxes and some that are not.

Both have 24 total crayons.

Both pictures show 8 crayons marked out.

How are the crayon pictures different?

One picture shows 8 crayons marked out in a line.

The other picture has 4 crayons outside the box crossed off and 4 crayons inside the box crossed off.

That one has 2 boxes of 10 crayons, and the other only has 1 box of 10 crayons.

Point to the crayons organized as 2 tens 4 ones.

This picture shows the crayons organized in 2 boxes of ten with 4 extra ones.

Say 24 the Say Ten way. 2 ten 4

Write 24.

Point to the unboxed crayons in the picture showing 1 ten and 14 ones.

What do you notice about the loose crayons in this picture?

There are 10 crayons on top and 4 on the bottom.

We can still see 2 tens.

Both pictures show the same total number of crayons, with 8 being taken away.

This picture shows 8 crayons taken away from a ten, or all at once. (Gesture to highlight the crayons in a row.)

This one shows 8 crayons taken away in two parts, first from the 4 ones on the side and then 4 more from a box of ten. (Gesture to highlight the crayons outside and inside the box.)

What is 24 – 8? How do you know?

I can count the crayons that are left: Tennnn, 11, 12, 13, 14, 15, 16. There are 16 crayons.

There are 10 crayons in the box and 6 more to the side. 10 and 6 is 16. Transition to the next segment by framing the work.

Today, we will pay close attention to how we can subtract in two different ways, all at once or in parts.

Learn

Two Ways to Take from Ten

Materials: T/S—Unifix Cubes

Students practice taking from the ten or the ones.

Organize the Unifix Cubes as 4 tens 5 ones and ask student pairs to do the same.

Write 45 – 8. Review taking away from the tens. Use a number bond and equations to record.

Let’s take 8 all at once from a ten. (Point to the tens.)

Snap off 8 cubes from a ten and set them aside as students do the same.

How many cubes are left? 37 cubes

We have 32 left after taking 8 from the tens. We also have the 5 ones.

32 + 5 = 37

How did we take from the tens?

First, we took 8 away from the tens.

Then we added what was left from the tens and ones.

Draw number bond arms to show decomposing 45 and write 40 and 5 as the parts.

We subtracted 8 from the tens first. (Point to the tens.)

What is 40 – 8? 32

Write 40 – 8 = 32.

Then we counted what was left from the tens and ones.

Write 32 + 5.

What is 32 + 5? 37

Write = 37 to complete 32 + 5 and 45 – 8.

Organize the cubes again as 4 tens 5 ones while students follow along.

Let’s try breaking apart 45 another way.

Break apart 1 stick of 10 as students follow along.

Promoting the Mathematical Thinking and Reasoning Standards

Students complete tasks with mathematical fluency (MTR.3) as they correctly break apart, subtract, and add the various parts involved when applying the take from ten strategy.

Ask the following questions to promote MTR.3:

• How are you using benchmark numbers in your work?

• When you use the take from ten strategy, how do you know whether to break up the first number?

Differentiation: Challenge

While students are in pairs, invite one student to model subtraction by using the cubes while the other student records abstractly with a number bond and equations. Encourage partners to take turns to provide each partner with an opportunity to show their thinking both ways.

Do we still have 45 cubes? How do you know?

Yes, the number of cubes didn’t change. I can still think of the ten we broke up as a group of ten.

Yes, there are 3 ten sticks and 15 ones. 30 + 15 = 45

Write 45 – 8. Draw number bond arms to show decomposing 45. Write 30 and 15 as the parts. Point to the 15 ones.

Instead of taking 8 away from a ten, let’s take away from the 15 ones.

Show taking away 8 cubes as students do the same.

How many ones are left? 7 ones

Write 15 – 8 = 7.

Are we done? How do you know?

No, we still have 3 tens. We need to find out how many are left.

Write 30 + 7.

What is 30 + 7? 37

Write = 37 to complete both 30 + 7 and 45 – 8.

How did we take away 8 this time?

We broke apart 45 another way: 3 tens 15 ones. Then we took 8 from the ones.

How do the cubes match the recording?

I see 3 tens and 15 ones. That’s 30 and 15.

We subtracted 8. I see 8 ones moved to the side.

There are 3 tens and 7 ones left. 30 and 7 make 37.

Repeat the process for both strategies by using the expressions 73 – 8 and 54 – 6.

Teacher Note

Consider inviting students to solve by using a math drawing. Expect a variety of responses.

Raceway Subtraction Game

Materials: T/S—Raceway Subtraction Game, counter, 6-sided dot die

Students practice making subtraction problems easier by playing a game. Gather students and demonstrate the Raceway Subtraction Game.

• Partners each place a counter on a car at the starting line. Students will move around separate tracks, but each track has the same number of spaces.

• Students take turns rolling the die, landing on a problem, and solving the problem by using any strategy they choose.

• Each student must land on and solve the last problem to cross the finish line. If they roll a number that is too high, they wait until their next turn to roll again.

Allow students to play for 8 to 9 minutes. As they work, circulate and assist as necessary. Ask some of the following questions to assess their thinking:

• How did you make an easier problem?

• How did you break up the first number? The total? Why did you do that?

• Where did you take from first? What did you do next?

Problem Set

Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex.

Students are encouraged to pick a tool to help them solve. Have students’ Number Path to 120 and cubes readily available for them to self-select.

Directions and word problems may be read aloud.

Teacher Note

Ready additional tools such as cubes, rekenreks, and students’ Number Path to 120.

Land

Debrief 5 min

Objective: Take from the tens or take from the ones.

Gather students and display Adrien’s cubes. Write 35 – 7 and invite students to think–pair–share to analyze the work sample.

How did Adrien break apart a number to make it easier to subtract?

He broke apart 35 into 2 tens and 15 ones. He broke it into 20 and 15.

Is Adrien done? No.

What should Adrien do next?

He should take away 7 ones.

Advance to the next slide to show Adrien’s subtraction and confirm student thinking.

What is 35 – 7? 28

Is there another way to solve?

Yes, we can solve by taking 7 from a ten all at once instead of breaking up a ten to make more ones. We can count on or count back to a ten.

Exit Ticket 5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

3. Read

Liv has 52 cars. She gives 4 cars away. How many cars does she have now?

Draw Sample:

Lesson at a Glance

Students discuss a series of subtraction problems, strategically selecting strategies and tools, such as cubes or number paths, for solving each problem. When students cannot take only from the ones to solve, they self-select a strategy to make an easier problem, such as take from a ten, count back to a ten, or count on to a ten.

Key Question

• What strategies can we use to make subtraction problems easier?

Achievement Descriptor

FL.1.Mod5.AD8 Subtract a one-digit number from a two-digit number by using manipulatives, number lines, drawings, or equations. (MA.1.NSO.2.5)

Agenda

Fluency 10 min

Launch 10 min

Learn 30 min

• Three Ways

• 3 in a Row

• Problem Set

Land 10 min

Materials

Teacher

• Chart paper (1 sheet)

Students

• Number Path to 120 (in the student book)

• 3 in a Row (in the student book)

• Unifix® Cubes

• Counters (9 per student pair)

Lesson Preparation

• Have math tools available (Unifix Cubes, Number Path to 120) for students to self-select as they solve.

• Consider placing large containers of Unifix Cubes on tables for students to share.

• The Number Path to 120 may have been torn out of student books and assembled earlier in the module. If more number paths are needed, they will need to be torn out of the student books, cut, and assembled.

Fluency

Whiteboard Exchange: Subtract Within 20

Students select a strategy and find the difference to build procedural reliability for subtraction within 20.

Display 11 − 9 =  .

Write the equation and find the answer. Show how you know.

Give students time to work. When most students are ready, signal for students to show their personal whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

Display the answer.

Repeat the process with the following sequence:

Number Path Hop: Get to a Ten

Materials: S—Number Path to 120

Students use the Number Path to 120 get to a ten to prepare for subtracting in parts to make an easier problem.

Display a segment of the Number Path to 120.

Point to 55 on your number path.

Show the number 55 circled.

Teacher Note

You may see a variety of strategies in students’ work, including but not limited to take from ten, count on to ten, or count back to ten. Consider asking students to use a specific strategy for certain problems or consider using this fluency activity as a formative assessment to see which strategies students use.

Hop to 50 in one big hop.

Show the hop to 50.

How many spaces did you hop? Raise your hand when you know.

Wait until most students raise their hands, and then signal for students to respond.

5

Show the labeled hop.

Write the subtraction sentence starting with 55.

Give students time to work. When most students are ready, signal for them to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

Show the subtraction sentence.

Repeat the process with the following sequence:

Students reason about subtraction strategies and discuss how to use a ten to count back efficiently.

Write 55 – 3. Tell students to figure out the problem mentally and to give a silent signal when they are ready.

What is 55 – 3? How do you know?

52. You can just subtract the ones. 5 minus 3 is 2. The tens stay the same. I counted back 3. 55 … 54, 53, 52.

Record responses by using a number bond. Then write 55 – 7.

Let’s take time to make sense of this problem before we think about ways to solve it. What do you notice about 55 – 7?

This problem isn’t as simple as the first one.

We can’t just take from the ones first. We could take 7 from a ten and then add the rest.

We could break up 7 too, but it’s harder to do in my head.

Display Ren’s work and Tam’s work.

Invite partners to think–pair–share about what is the same about Ren’s strategy and Tam’s strategy to find 55 – 7. Highlight responses that describe how they used a ten to subtract efficiently.

They both took away 5 ones to get to 50.

They both got to a ten, 50.

I think they both took away 5 and then 2 more.

Display the number bond and equations.

Invite students to think–pair–share about how subtracting by getting to a ten relates to the equations and number bond.

Tam showed 55 – 7 = 48 on the number line by making a hop and labeling it – 5. I see 55 – 5 = 50 written under the number bond. Ren took away 5 cubes to get to 50 and then took away 2 more to get to 48.

Tam subtracted 5 on the number path and then subtracted 2. The number bond shows 7 decomposed into 5 and 2.

Transition to the next segment by framing the work.

Today, we will make easier problems by using one of our strategies: take from a ten, break apart and count back to get to a ten, or count on to get to a ten.

Learn

Three Ways

Materials: T—Chart paper; S—Math tools (Unifix Cubes, Number Path to 120) Students self-select strategies and tools to subtract and discuss their work. Write 36 – 9. Ask students to turn to the page titled Make Easier Subtraction Problems in their books and to look at the different strategies. Then have students think–pair–share about the following questions.

Some students used these tools and strategies to figure out a similar problem. Which strategy will you use to make 36 – 9 easier? What tool will you use to show your thinking?

I will take from ten and show my thinking with cubes.

I will break apart 9 to get to a ten first. Then I’ll show my thinking by counting back on the number path and by using my whiteboard. I like to add, so I will start with 9 cubes. I’ll count on until I get to 36.

Invite students to find the difference on their own. Encourage the use of tools, such as whiteboards, cubes, and number paths. Have such tools readily available for students to use.

As the class works, identify two or three students who use different strategies.

Teacher Note

Some students may use the Stage 1 strategy of counting and removing Unifix Cubes one at a time. Other students may use a Stage 2 strategy, such as counting on or counting back by ones. While these two approaches are valid strategies, this topic advances students toward making an easier problem by using a ten.

It is not critical for students to use any particular tool or strategy to find the solution. It is more important that they can choose a strategy that makes sense based on the numbers in the problem and explain why it works.

As students finish, gather the class. Invite the selected students to share their thinking. Chart their reasoning. Ask questions to help students share their strategies and encourage students to use the Talking Tool to ask questions about their peers’ work.

Corey, how did you subtract 9 from 36?

I made 36 with cubes. I took 9 from a ten and got 1. I had 2 tens and 7 ones left. That’s 27.

Did anyone find the difference another way?

I used cubes too, but I took from the ones first to get to a ten. I took away 6 to get to 30. Then I took away 3 more to get 27.

I used the number path to count on. Since 9 is close to ten, I hopped to 10 first. Then I hopped 10 more and 10 more and 6 more and landed on 36. I added all my hops and got 27.

Leave the chart of subtraction strategies posted.

What is the same about all these strategies?

They all use a ten.

They all show a way to find the other part.

We are either trying to take away from a ten or get to a ten.

These strategies are ways we can make a problem easier when we cannot take from just the ones.

Teacher Note

Students may name tools—such as number paths, cubes, or fingers—as well as strategies. Strategies are ways to think about a problem, whereas tools are the materials or drawings used to represent a problem.

If a student says, “My strategy was using cubes,” affirm their use of tools and probe for clarification such as, “You chose cubes to help you show the problem. How did you use them to solve?”

3 in a Row

Materials: S—3 in a Row removable, 9 counters, math tools (Unifix Cubes, Number Path to 120)

Students practice subtraction strategies by playing a cooperative game. Pair students. Make sure partners have one 3 in a Row removable as their game board and 9 counters.

Explain the game directions.

• Partners take a minute to study the game board. Then they select three problems in a row that they would like to solve together.

• Partner A selects the first problem. Each partner solves the problem on their whiteboard, self-selecting tools as needed.

• Partner A shares their strategy and solution. If Partner B agrees with the answer, they place a counter on the space.

• Partner B takes a turn and selects the next problem.

• If partners get three in a row, they may select another three problems in a row or see whether they can fill up the game board, as time allows.

As students play, assess and advance their thinking by asking questions.

• Could you make this problem easier? How?

• What strategy did you use to solve this problem?

• Can you tell me more about why you broke apart this number?

• I see you wrote [number sentence]. How does that match your work?

Have students clean up their materials. Consider using the game for centers or during other parts of the day.

Promoting the Mathematical Thinking and Reasoning Standards

As students decide which strategy to use to solve the problem, they complete tasks with mathematical fluency (MTR.3). Throughout the year, students have built up their mathematical “toolbox” of strategies, which they can now apply to this new context.

Encourage students to think strategically by asking the following questions:

• Why did you choose to solve the problem that way? Did it work well?

• What other way could you use to solve the problem? Why might that way be helpful?

Problem Set

Differentiate the set by selecting problems for students to finish within the timeframe. Students may continue to work in pairs as needed.

Students are encouraged to pick a tool to help them solve. Have Number Paths to 120 and cubes readily available for students to self-select.

Directions may be read aloud.

Land

Objective: Choose a strategy to make an easier problem.

Display the expressions 54 – 2 and 54 – 8. Remind students that these problems were part of the Problem Set. Ask students to take time to make sense of the problems.

What is the same about these expressions?

They both have 54 as the total. They are both subtracting.

What is different about these expressions?

One is subtracting 2, and one is subtracting 8.

For which problem can we just take from the ones? Why?

You can only take from the ones for 54 – 2 because 2 is less than 4.

54 only has 4 ones in the ones place. So you can’t take away 8 of them.

Refer to the chart made in the first segment of Learn. Consider showing student strategies with a number bond or arrow notation as needed.

Think about the strategy you used to find 54 – 8. How did you make the problem easier?

I took from a ten, and there were 2 cubes left. Then I added them to 44. 44 + 2 = 46. You can break apart the 8 into 4 and 4 to get to a ten. 54 - 4 = 50. 50 - 4 = 46.

I started at 8 and added 2 more to make a ten. Then I added another ten; that’s 20. Then another ten is 30, another ten is 40, another ten is 50, and 4 more is 54. 2 + 10 + 10 + 10 + 10 + 4 = 46.

What tools can help us show our thinking?

We can use cubes, number bonds, number paths, or drawings.

Mathematicians look carefully at problems before they find the answer. They think about which strategies and tools could be helpful.

Topic Ticket 5 min

Provide up to 5 minutes for students to complete the Topic Ticket. It is possible to gather formative data even if some students do not complete every problem.

UDL: Action & Expression

Consider reserving time for students to self-reflect on their overall experience of making easier subtraction problems.

• Which strategies work well for me?

• Which strategy do I want to try next time?

• How am I growing as a mathematician?

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

1. Circle tens. Write how many tens and ones. Fill in the number bond.

What is 10 less than 76?

What is 10 more than 43? 2. 3. Subtract . Pick a tool to help you. 45 − 8 =

+ 10 =

Standards

B.E.S.T. Standards

Extend counting sequences and understand the place value of two-digit numbers.

MA.1.NSO.1.2 Read numbers from 0 to 100 written in standard form, expanded form and word form. Write numbers from 0 to 100 using standard form and expanded form.

MA.1.NSO.1.3 Compose and decompose two-digit numbers in multiple ways using tens and ones. Demonstrate each composition or decomposition with objects, drawings and expressions or equations.

MA.1.NSO.1.4 Plot, order and compare whole numbers up to 100.

Develop an understanding of addition and subtraction operations with one- and two-digit numbers.

MA.1.NSO.2.3 Identify the number that is one more, one less, ten more and ten less than a given two-digit number.

MA.1.NSO.2.4 Explore the addition of a two-digit number and a one-digit number with sums to 100.

MA.1.NSO.2.5 Explore subtraction of a one-digit number from a two-digit number.

Tell time and identify the value of coins and combinations of coins and dollar bills.

MA.1.M.2.1 Using analog and digital clocks, tell and write time in hours and half-hours.

Mathematical Thinking and Reasoning Standards

MA.K12.MTR.1.1 Actively participate in effortful learning both individually and collectively.

MA.K12.MTR.2.1 Demonstrate understanding by representing problems in multiple ways.

MA.K12.MTR.3.1 Complete tasks with mathematical fluency.

MA.K12.MTR.4.1 Engage in discussions that reflect on the mathematical thinking of self and others.

MA.K12.MTR.5.1 Use patterns and structure to help understand and connect mathematical concepts.

MA.K12.MTR.6.1 Assess the reasonableness of solutions.

MA.K12.MTR.7.1 Apply mathematics to real-world contexts.

ELA Expectations

ELA.K12.EE.1.1 Cite evidence to explain and justify reasoning.

ELA.K12.EE.2.1 Read and comprehend grade-level complex texts proficiently.

ELA.K12.EE.3.1 Make inferences to support comprehension.

ELA.K12.EE.4.1 Use appropriate collaborative techniques and active listening skills when engaging in discussions in a variety of situations.

ELA.K12.EE.5.1 Use the accepted rules governing a specific format to create quality work.

ELA.K12.EE.6.1 Use appropriate voice and tone when speaking or writing.

Achievement Descriptors: Proficiency Indicators

FL.1.Mod5.AD1 Read and write numbers to 100 as numerals and as expressions or equations by using tens and ones. Read numbers to 100 in words.

RELATED B.E.S.T.

MA.1.NSO.1.2 Read numbers from 0 to 100 written in standard form, expanded form and word form. Write numbers from 0 to 100 using standard form and expanded form.

Partially Proficient Proficient

Read numbers to 100 as numerals and as expressions or equations by using tens and ones. Write numbers to 100 as numerals.

Write 80 + 6 as a number.

Read and write numbers to 100 as numerals and as expressions or equations by using tens and ones. Read numbers to 100 in words.

Write 86 with a number sentence by using tens and ones.

Highly Proficient

Write sixty-one as a number.

FL.1.Mod5.AD2 Represent a set of up to 99 objects with a two-digit number by composing tens.

RELATED B.E.S.T.

MA.1.NSO.1.3 Compose and decompose two-digit numbers in multiple ways using tens and ones. Demonstrate each composition or decomposition with objects, drawings and expressions or equations.

Partially Proficient Proficient

Represent a set of up to 50 objects with a two-digit number by composing tens.

Circle all the groups of 10.

Represent a set of up to 99 objects with a two-digit number by composing tens.

Circle all the groups of 10.

Highly Proficient

Represent a set of 100–120 objects with a written numeral by composing tens.

Circle all the groups of 10.

Total

tens ones

Total

tens ones

Total

tens ones

FL.1.Mod5.AD3 Represent two-digit numbers within 99 in multiple ways as tens and ones.

RELATED

MA.1.NSO.1.3 Compose and decompose two-digit numbers in multiple ways using tens and ones. Demonstrate each composition or decomposition with objects, drawings and expressions or equations.

Partially Proficient Proficient

Represent two-digit numbers within 50 as tens and ones.

Show 45 using tens and ones.

Represent two-digit numbers within 99 in multiple ways as tens and ones.

Show ways to make 71 using tens and ones.

Highly Proficient

Represent numbers 100–120 in multiple ways as tens and ones.

Show ways to make 114 using tens and ones.

FL.1.Mod5.AD4 Determine the values represented by the digits of a two-digit number.

RELATED B.E.S.T.

MA.1.NSO.1.3 Compose and decompose two-digit numbers in multiple ways using tens and ones. Demonstrate each composition or decomposition with objects, drawings and expressions or equations.

Partially Proficient Proficient

Determine the number represented by given amounts of tens and ones.

Write the total.

6 tens and 3 ones is   .

Determine the values represented by the digits of a two-digit number.

Fill in the number bond.

Highly Proficient

FL.1.Mod5.AD5 Compare two-digit numbers by using the symbols >, =, and <.

RELATED B.E.S.T.

MA.1.NSO.1.4 Plot, order and compare whole numbers up to 100.

Partially Proficient Proficient

Compare two-digit numbers by using the symbols >, =, and < when the numbers have the same digit in the tens place.

Write >, =, or <. 45 48

Compare two-digit numbers by using the symbols >, =, and < when the numbers have the same digit in the ones place or none of the digits in either place are the same.

Highly Proficient

Compare numbers to 120 by using the symbols >, =, and <.

FL.1.Mod5.AD6 Find 10 more and 10 less than a two-digit number.

RELATED B.E.S.T.

MA.1.NSO.2.3 Identify the number that is one more, one less, ten more and ten less than a given two-digit number.

Partially Proficient Proficient

Find 10 more and 10 less than a two-digit number by using drawings, manipulatives, or other tools.

Use cubes or draw to show 35.

What is 10 more than 35?

Find 10 more and 10 less than a two-digit number by using place value understanding.

What is 10 more than 67?

What is 10 less than 45?

Highly Proficient

FL.1.Mod5.AD7 Add a two-digit number and a one-digit number that have a sum within 100 by using manipulatives, number lines, drawings, or models.

RELATED B.E.S.T.

MA.1.NSO.2.4 Explore the addition of a two-digit number and a one-digit number with sums to 100.

Partially Proficient Proficient Highly Proficient

Add a two-digit number and a one-digit number that have a sum within 100 when composing a ten is not required.

Add.

Add a two-digit number and a one-digit number that have a sum within 100 when composing a ten is required.

Add. Show how you know.

27 + 5 = 32 2 3 30

I broke up 5 to make the next ten with 27 30 and 2 is 32

Explain multiple strategies for adding a two-digit number and a one-digit number.

Add. Show how you know.

27 + 5 = 32

2 3 30

I broke up 5 to make the next ten with 27. 30 and 2 is 32.

Show another way to add.

27 + 5 = 32

7 20

7 + 5 = 12

20 + 12 = 32

I added the ones first. 7 and 5 is 12. 20 and 12 is 32

FL.1.Mod5.AD8 Subtract a one-digit number from a two-digit number by using manipulatives, number lines, drawings, or equations.

RELATED B.E.S.T.

MA.1.NSO.2.5 Explore subtraction of a one-digit number from a two-digit number.

Partially Proficient Proficient Highly Proficient

Subtract a one-digit number from a two-digit number by counting back when crossing a ten is not required.

Subtract.

27 – 5 = 22

Subtract a one-digit number from a two-digit number by counting on or counting back.

Subtract. Show how you know.

55 – 7 = 48

I counted back 5 to 50, then counted back 2 more to 48.

Explain multiple strategies for subtracting a one-digit number from a two-digit number.

Subtract. Show how you know.

25 – 8 = 17

I counted back 5 to 20, then counted back 3 more to 17.

Show another way to subtract.

25 – 8 = 17

I counted on from 8 to 25

FL.1.Mod5.AD9 Tell time to the hour and half hour on analog and digital clocks.

RELATED B.E.S.T.

MA.1.M.2.1 Using analog and digital clocks, tell and write time in hours and half-hours.

Partially Proficient Proficient

Tell time to the hour on analog and digital clocks.

Tell time to the half hour on analog and digital clocks.

Highly Proficient

Observational Assessment Recording Sheet

Grade 1 Module 5

Place Value Concepts to Compare, Add, and Subtract

Achievement

Descriptors

FL.1.Mod5.AD1 Read and write numbers to 100 as numerals and as expressions or equations using tens and ones. Read numbers to 100 in words.

FL.1.Mod5.AD2 Represent a set of up to 99 objects with a two-digit number by composing tens.

FL.1.Mod5.AD3 Represent two-digit numbers within 99 in multiple ways as tens and ones.

FL.1.Mod5.AD4 Determine the values represented by the digits of a two-digit number.

FL.1.Mod5.AD5 Compare two-digit numbers by using the symbols >, =, and <.

FL.1.Mod5.AD6 Find 10 more and 10 less than a two-digit number.

FL.1.Mod5.AD7 Add a two-digit number and a one-digit number that have a sum within 100 by using manipulatives, number lines, drawings, or models.

FL.1.Mod5.AD8 Subtract a one-digit number from a two-digit number by using manipulatives, number lines, drawings, or equations.

FL.1.Mod5.AD9 Tell time to the hour and half hour on analog and digital clocks.

Notes

Student Name

Dates and Details of Observations

PP Partially Proficient P Proficient HP Highly Proficient

Module Achievement Descriptors and B.E.S.T. Standards by Lesson

Sample Solutions

Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

2.

1. Circle tens. Write how many tens and ones. Fill in the number bond.

What is 10 more than 43? 53

What is 10 less than 76? 66

82 + 10 = 92 82 – 10 = 72

3. Subtract Pick a tool to help you. 45 − 8 = 37

Terminology

The following terms are critical to the work of grade 1 module 5. This resource groups terms into categories called New, Familiar, and Academic Verbs. The lessons in this module incorporate terminology with the expectation that students work toward applying it during discussions and in writing.

Items in the New category are discipline-specific words that are introduced to students in this module. These items include the definition, description, or illustration as it is presented to students. At times, this resource also includes italicized language for teachers that expands on the wording used with students.

Items in the Familiar category are discipline-specific words introduced in prior modules or in previous grade levels.

Items in the Academic Verbs category are high-utility terms that are used across disciplines. These terms come from a list of academic verbs that the curriculum strategically introduces at this grade level.

A digit’s place is its position in a number. Numbers with two digits have two places: the tens place and the ones place. (Lesson 3)

Value is how much something is worth. For example, in the number 53, the 5 is in the tens place, so it has a value of 50. (Lesson 3)

To compose means to be put together, or group. (Lesson 3)

Numbers like 7 and 5 are called digits. When we write digits next to each other, we make another number. For example, we write the digits 7 and 5 next to each other to make 75. (Lesson 2)

one(s) part partners represent subtract take away ten(s) total true unit

Academic Verbs

Module 5 does not introduce any academic verbs from the grade 1 list.

Math Past

Yoruba Counting Words

Where do number words come from? Do other people use different words to represent numbers? What do other people’s number words mean?

Write the word nineteen and ask students why they think we use that word to mean 1 ten and 9 ones. It may help to add space between nine and teen, or to underline the two parts of the word as you read it. Students should point out that the word nine is in nineteen. Some may notice that teen kind of looks and sounds like ten.

In the first four modules, students learned how different people have represented and written numbers throughout history. The ways we write numbers can affect our number sense and the kinds of calculations we can perform. For example, adding and subtracting with Roman numerals is notoriously difficult!

The words we use for numbers are also connected to our number sense. The connection between words and number sense is deep. We learn the words for numbers before we learn to write them, and words for numbers developed earlier in human history than written numerals, since spoken language developed first.

Tell the class you met someone who says that where they grew up, they say “5 before 20” to describe a number. Ask students what number they think this person is describing. A number path can be used to help students answer this question.

Tell the class that this is how the Yoruba people of western Africa describe the number 15. The Yoruba people form a large ethnic group, and the Yoruba language is the native language of between 30 and 40 million people! In addition to having deep mathematical traditions dating back centuries, they are also famous for their music, which features advanced drumming techniques.

Unlike our decimal or base-10 system, the Yoruba number system is a vigesimal, or base-20 system. Many people in different regions of western Africa use base-20 systems, and they are used in the Americas too. For example, the Maya system, which we saw in modules 3 and 4, is also a base-20 system. The different and interesting aspect of the Yoruba system is its reliance on subtraction.

Remind students how we use tens to make our numbers, making as many groups of 10 as we can, and then saying how many ones are left. Ask students why they think we use 10 this way. Hint: What do most people have 10 of that you can use to count? Fingers!

When counting from 10 to 20 in Yoruba, the number words start out with a similar meaning to ours. They also describe 10 and some ones, which can be roughly translated as follows. 11

Then, at 15, the numbers start to be described differently.

Ask students if they can think of a reason the Yoruba people use 20 this way. Hint: Just like most people have 10 fingers, most people also have 10 toes. Put them together and that’s 20. Things get more complex as you move past 20. For example, the word for 35 translates roughly to five before two twenties, and the word for 45 is described as five from ten from three twenties or three twenties minus ten minus five. This goes beyond first grade learning but could be a good challenge for advanced students with the aid of the 1–120 number path.

Remember, between 30 and 40 million people describe their numbers this way! Children who grow up learning to count this way can use these numbers fluidly. They learn the numbers through hands-on activities that use objects like pebbles or beans, and through traditional games like Ayo, or Oware, a version of Mancala seen here.

How did the Yoruba people come to count this way? One theory is that this number pattern was developed so that if the multiple of 10 is understood, you can count on one hand.

For example, knowing that you’re counting from 20 to 30, you can put up fingers one at a time to count 21, 22, 23, and 24. When you put the fifth finger up, the understanding is that now you mean 5 before 30, or 25. To get from 25 to 30, you put fingers down one at a time, counting 4 before 30 (26), 3 before 30 (27), 2 before 30 (28), 1 before 30 (29), and finally when all fingers are down, you have reached 30.

Use one hand to count from 20 to 30 the Yoruba way as a class.

Ways of describing numbers that differ from our own can seem counterintuitive at first. In a sense, to understand the Yoruba number words, you need to understand the basics of addition and subtraction. However, each of the words tells you what it means.

Consider the English number words twelve and fifty. Neither of these words is descriptive of the number it represents. Fifty derives from the Old English words for five (fif) and group of ten (tig). Similarly, twelve comes from the Old English word twelf, which means two left, as in two left after 10. Since we no longer speak Old English, these descriptions are lost on us and on our students!

In fact, research shows that this lack of descriptiveness hinders young learners’ number sense. In many other languages, number words are more descriptive. For example, in Mandarin Chinese, thirteen is said “ten-three.” Understanding the limits of our point of view and incorporating other cultures’ perspectives into our thinking can only make us stronger as we work with math!

Materials

The following materials are needed to implement this module. The suggested quantities are based on a class of 24 students and one teacher.

1 10-sided dice, set of 24

1 100-bead demonstration rekenrek

3 Base 10 rods, plastic, set of 50

1 Centimeter cubes, set of 500

18 Chart paper sheets

1 Computer with internet access

24 Counters

12 Counting collections

24 Crayons (1 red crayon, 1 green crayon, 1 yellow crayon per student)

78 Dimes

1 Dot dice, set of 12

24 Dry-erase markers

1 Eureka Math2TM Hide Zero® cards, basic student set of 12

Visit http://eurmath.link/materials to learn more.

1 Eureka Math2TM Hide Zero® cards, demonstration set

1 Eureka Math2TM Hide Zero® cards, student extension set of 12

24 Learn books

25 Markers 24 Pencils

650 Pennies

24 Personal whiteboards

24 Personal whiteboard erasers

1 Projection device

12 Scissors

1 Teach book

1 Unifix® Cubes, set of 1,000

12 Work mats

Please see lesson 2 for a list of organizational tools (cups, plates, number paths, etc.) suggested for the counting collection.

Works Cited

Carpenter, Thomas P., Megan L. Franke, and Linda Levi. Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School. Portsmouth, NH: Heinemann, 2003.

Carpenter, Thomas P., Megan L. Franke, Nicholas C. Johnson, Angela C. Turrou, and Anita A. Wager. Young Children’s Mathematics: Cognitively Guided Instruction in Early Childhood Education. Portsmouth, NH: Heinemann, 2017.

CAST. Universal Design for Learning Guidelines version 2.2. Retrieved from http://udlguidelines.cast.org, 2018.

Clements, Douglas H. and Julie Sarama. Learning and Teaching Early Math: The Learning Trajectories Approach. New York: Routledge, 2014.

Danielson, Christopher. How Many?: A Counting Book: Teacher’s Guide. Portland, ME: Stenhouse, 2018.

Danielson, Christopher. Which One Doesn’t Belong?: A Teacher’s Guide. Portland, ME: Stenhouse, 2016.

Empson, Susan B. and Linda Levi. Extending Children’s Mathematics: Fractions and Decimals. Portsmouth, NH: Heinemann, 2011.

Florida Department of Education. Florida’s B.E.S.T. Standards: Mathematics. Tallahassee, FL: Florida Department of Education, 2019.

Flynn, Mike. Beyond Answers: Exploring Mathematical Practices with Young Children. Portsmouth, NH: Stenhouse, 2017.

Fosnot, Catherine Twomey, and Maarten Dolk. Young Mathematicians at Work: Constructing Number

Sense, Addition, and Subtraction. Portsmouth, NH: Heinemann, 2001.

Franke, Megan L., Elham Kazemi, and Angela Chan Turrou. Choral Counting and Counting Collections: Transforming the PreK-5 Math Classroom. Portsmouth, NH: Stenhouse, 2018.

Hattie, John, Douglas Fisher, and Nancy Frey. Visible Learning for Mathematics: What Works Best to Optimize Student Learning. Thousand Oaks, CA: Corwin Mathematics, 2017.

Huinker, DeAnn and Victoria Bill. Taking Action: Implementing Effective Mathematics Teaching Practices. Kindergarten–Grade 5, edited by Margaret Smith. Reston, VA: National Council of Teachers of Mathematics, 2017.

Kelemanik, Grace, Amy Lucenta, Susan Janssen Creighton, and Magdalene Lampert. Routines for Reasoning: Fostering the Mathematical Practices in All Students. Portsmouth, NH: Heinemann, 2016.

Kilpatrick, J., J. Swafford, and B. Findell, eds. Adding It Up: Helping Children Learn Mathematics. Washington, DC: The National Academies Press, 2001.

Ma, Liping. Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States. New York: Routledge, 2010.

Online Etymology Dictionary, s.v. “fifteen,” accessed July 1, 2020, https://www.etymonline.com/search?q=fifteen.

Online Etymology Dictionary, s.v. “fifty,” accessed July 1, 2020, https://www.etymonline.com/search?q=fifty.

Online Etymology Dictionary, s.v. “twelve,” accessed July 1, 2020, https://www.etymonline.com/search?q=twelve.

Parker, Thomas and Scott Baldridge. Elementary Mathematics for Teachers. Okemos, MI: Sefton-Ash, 2004.

Shumway, Jessica F. Number Sense Routines: Building Mathematical Understanding Every Day in Grades 3–5. Portland, ME: Stenhouse Publishing, 2018.

Smith, Margaret S. and Mary K. Stein. 5 Practices for Orchestrating Productive Mathematics Discussions, 2nd ed. Reston, VA: National Council of Teachers of Mathematics, 2018.

Smith, Margaret S., Victoria Bill, and Miriam Gamoran Sherin. The 5 Practices in Practice: Successfully Orchestrating Mathematics Discussions in Your Elementary Classroom, 2nd ed. Thousand Oaks, CA: Corwin Mathematics; Reston, VA: National Council of Teachers of Mathematics, 2020.

Van de Walle, John A. Elementary and Middle School Mathematics: Teaching Developmentally. New York: Pearson, 2004.

Van de Walle, John A., Karen S. Karp, LouAnn H. Lovin, and Jennifer M. Bay-Williams. Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3–5, 3rd ed. New York: Pearson, 2018.

Zaslavsky, Claudia. Africa Counts: Number and Pattern in African Cultures. Chicago: Chicago Review Press, 1999.

Zwiers, Jeff, Jack Dieckmann, Sara Rutherford-Quach, Vinci Daro, Renae Skarin, Steven Weiss, and James Malamut. Principles for the Design of Mathematics Curricula: Promoting Language and Content Development. Retrieved from Stanford University, UL/SCALE website: http://ell .stanford.edu/content/mathematics-resources-additional -resources, 2017.

Credits

Great Minds® has made every effort to obtain permission for the reprinting of all copyrighted material. If any owner of copyrighted material is not acknowledged herein, please contact Great Minds for proper acknowledgment in all future editions and reprints of this module.

All United States currency images Courtesy the United States Mint and the National Numismatic Collection, National Museum of American History.

For a complete list of credits, visit http://eurmath.link/media-credits.

Cover, Edward Hopper (1882–1967), Tables for Ladies, 1930. Oil on canvas, H. 48-1/4, W. 60-1/4 in. (122.6 x 153 cm.).

George A. Hearn Fund, 1931 (31.62). The Metropolitan Museum of Art. © 2020 Heirs of Josephine N. Hopper/Licensed by Artists

Rights Society (ARS), NY. Photo Credit: Image copyright © The Metropolitan Museum of Art. Image source: Art Resource, NY; page 51, Leonid Iastremskyi/Pixel-shot/Alamy Stock Photo; pages 52, 53, tarmofoto/Shutterstock; page 70, Pornsngar Potibut/Shutterstock; page 76, (left) elbud/Shutterstock; page 82, (composite image) cynoclub/Shutterstock, Kuznetsov Alexey/Shutterstock; page 83, Nynke van Holten/Shutterstock; pages 136, 137, mejorana/Shutterstock; pages 185, 406, (right) Robert Burch/Alamy Stock Photo; page 244, lattesmile/ Shutterstock; pages 249, 250, Direnko Kateryna/Shutterstock; page 251, Nataliya Nazarova/Shutterstock; page 406, (left) GagliardiPhotography/Shutterstock; page 407, (top) i_am_zews/ Shutterstock, (bottom) photka/Shutterstock; All other images are the property of Great Minds.

Acknowledgments

Kelly Alsup, Leslie S. Arceneaux, Melissa Brown, Dawn Burns, Jasmine Calin, Mary Christensen-Cooper, Hazel Coltharp, Cheri DeBusk, Stephanie DeGiulio, Jill Diniz, Brittany duPont, Melissa Elias, Lacy Endo-Peery, Scott Farrar, Ryan Galloway, Krysta Gibbs, Danielle Goedel, Melanie Gutierrez, Jodi Hale, Karen Hall, Eddie Hampton, Tiffany Hill, Robert Hollister, Christine Hopkinson, Rachel Hylton, Travis Jones, Kelly Kagamas Tomkies, Jennifer Koepp Neeley, Liz Krisher, Marie Libassi-Behr, Ben McCarty, Maureen McNamara Jones, Cristina Metcalf, Ashley Meyer, Melissa Mink, Richard Monke, Bruce Myers, Marya Myers, Andrea Neophytou Hart, Kelley Padilla, Shelley Petre, Kim L. Pettig, Marlene Pineda, Jay Powers, Elizabeth Re, John Reynolds, Meri Robie-Craven, Jessica Sims, Robyn Sorenson, Lori Sponenburgh, Marianne Strayton, James Tanton, Julia Tessler, Philippa Walker, Lisa Watts Lawton, MaryJo Wieland, Jackie Wolford, Leslie Zuckerman

Trevor Barnes, Brianna Bemel, Adam Cardais, Christina Cooper, Natasha Curtis, Jessica Dahl, Brandon Dawley, Delsena Draper, Sandy Engelman, Tamara Estrada, Soudea Forbes, Jen Forbus, Reba Frederics, Liz Gabbard, Diana Ghazzawi, Lisa Giddens-White, Laurie Gonsoulin, Nathan Hall, Cassie Hart, Marcela Hernandez, Rachel Hirsh, Abbi Hoerst, Libby Howard, Amy Kanjuka, Ashley Kelley, Lisa King, Sarah Kopec, Drew Krepp, Crystal Love, Maya Márquez, Siena Mazero, Cindy Medici, Ivonne Mercado, Sandra Mercado, Brian Methe, Patricia Mickelberry, Mary-Lise Nazaire, Corinne Newbegin, Max Oosterbaan, Tamara Otto, Christine Palmtag, Andy Peterson, Lizette Porras, Karen Rollhauser, Neela Roy, Gina Schenck, Amy Schoon, Aaron Shields, Leigh Sterten, Mary Sudul, Lisa Sweeney, Samuel Weyand, Dave White, Charmaine Whitman, Nicole Williams, Glenda Wisenburn-Burke, Howard Yaffe

Exponentially Better

Knowledge2 In our tradition of supporting teachers with everything they need to build student knowledge of mathematics deeply and coherently, Eureka Math2 provides tailored collections of videos and recommendations to serve new and experienced teachers alike.

Digital2 With a seamlessly integrated digital experience, Eureka Math2 includes hundreds of clever illustrations, compelling videos, and digital interactives to spark discourse and wonder in your classroom.

Accessible2 Created with all readers in mind, Eureka Math2 has been carefully designed to ensure struggling readers can access lessons, word problems, and more.

Joy2 Together with your students, you will fall in love with math all over again—or for the first time—with Eureka Math2.

Module 1

Counting, Comparison, and Addition

Module 2

Addition and Subtraction Relationships

Module 3

Properties of Operations to Make Easier Problems

Module 4

Comparison and Composition of Length Measurements

Module 5

Place Value Concepts to Compare, Add, and Subtract

Module 6

Attributes of Shapes • Advancing Place Value, Addition and Subtraction, and Measurement

What does this painting have to do with math?

American realist Edward Hopper painted ordinary people and places in ways that made viewers examine them more deeply. In this painting, we are in a restaurant, where a cashier and server are busily at work. What can you count here? If the server gave two of the yellow fruits to the guests at the table, how many would be left in the row? We will learn all about addition and subtraction within 10s in Units of Ten

On the cover Tables for Ladies, 1930

Edward Hopper, American, 1882–1967

Oil on canvas

The Metropolitan Museum of Art, New York, NY, USA

ISBN 978-1-63642-505-4

Edward Hopper (1882–1967), Tables for Ladies, 1930. Oil on canvas, H. 48 1/4, W. 60 1/4 in (122.6 x 153 cm). George A. Hearn Fund, 1931 (31.62). The Metropolitan Museum of Art. © 2020 Heirs of Josephine N. Hopper/Licensed by Artists Rights Society (ARS), NY.

Photo credit: Image copyright © The Metropolitan Museum of Art.

Image source: Art Resource, NY