4_SM_EM2_Teach_K-5_Grade4Module1 by Great Minds

Teach Effective Instruction with Eureka Math2, K–5 A Story of Units® Supplemental Materials

Supplemental Materials

Teach: Effective Instruction with Eureka Math2; Grades K–5 CONTENTS Module Study ................................................................................................................................................ 3 Grade 4 Module 1 ..................................................................................................................................... 3 Overview ................................................................................................................................................... 4 Contents .................................................................................................................................................... 6 Why ........................................................................................................................................................... 8 Achievement Descriptors: Overview ...................................................................................................... 11 Achievement Descriptors: Proficiency Indicators ................................................................................... 14 Topic Study.................................................................................................................................................. 15 Topic D Overview .................................................................................................................................... 15 Topic D Progression of Lessons ............................................................................................................... 17 Topic D Lesson Overviews ....................................................................................................................... 20 Lesson Study ............................................................................................................................................... 27 Lesson 19................................................................................................................................................. 27 Credits ......................................................................................................................................................... 39

Before This Module

Overview

Grade 3 Module 1

Place Value Concepts for Addition and Subtraction

In grade 3 module 1, students build a conceptual understanding of multiplication as a number of equal groups (e.g., 4 x 3

= 12

Topic A

can be interpreted as 4 groups of 3 is 12).

Multiplication as Multiplicative Comparison

Grade 3 Module 2

Students identify, represent, 4 � and interpret multiplicative 28 is 7 times as many as 4. 28=7X4 comparisons in patterns, I I I I I I I I tape diagrams, multiplication 28 equations, measurements, and units of money. They describe the relationship between quantities as times as much as or use other language as applicable to a given context (e.g., times as many as, times as long as, and times as heavy as). Students use multiplication or division to find an unknown quantity in a comparison.

In grade 3 module 2, students compose and decompose metric measurement units and relate them to place value units up to 1 thousand. They use place value understanding and the vertical number line to round two- and three-digit numbers. Grade 3 students also add and subtract two- and three-digit numbers by using a variety of strategies, including the standard algorithm.

□

Topic B Place Value and Comparison Within 1,000,000 Students name the place value units of 56,348 ten thousand, hundred thousand, and million. They recognize the multiplicative 50,000 + 6,000 + 300 + 40 + 8 relationship between place value fifty-six thousand, three hundred forty-eight units-the value of a digit in one place 56 thousands 3 hundreds 4 tens 8 ones is ten times as much as the value of the same digit in the place to its right. Students write and compare numbers with up to 6 digits in standard, expanded, word, and unit forms.

EUREKA MATH 2

Topic C Rounding Multi-Digit Whole Numbers Students name multi-digit numbers in unit form in different ways by using smaller units (e.g., 245,000 as 24 ten thousands 5 thousands or 245 thousands}, and they find 1 more or 1 less of a given unit in preparation for rounding on a vertical number line. Students round four-digit, five-digit, and six-digit numbers to the nearest thousand, ten thousand, and hundred thousand. They determine an appropriate rounding strategy to make useful estimates for a given context.

After This Module Grade 5 Modules 1 and 4

7001000 • 7 hundred thousands

In grade 5 modules 1 and 4, students extend 6501000 • 6 hundred thousands 5 ten thousands

the work of grade 4 by adding, subtracting,

634,243

rounding, and comparing multi-digit numbers with digits to the thousandths place. Students

6001000 = 6 hundred thousands

recognize that the value of a digit in one place is ..!. of what it represents in the place 10

634,243 ,. 600,000

Topic D Multi-Digit Whole Number Addition and Subtraction

to its left.

Students build fluency with addition and subtraction 800,000 -500,000 300,000 of numbers of up to 6 digits by using the standard 1.3 algorithm. They add and subtract to solve two-step 7 10 2 :S, II 4<o1,97.3 8.�:S,�lS and multi-step word problems. The Read-Draw-Write -4<o1,97.3 +.341,442 process is used to help students make sense of the 803, 415 341,442 problem and find a solution path. Throughout the topic, students round to estimate the sum or difference and check the reasonableness of their answers.

Topic E Metric Measurement Conversion Tables Students use multiplicative comparisons I kilometer is 1,000 times as long as I meter. to describe the relative sizes of metric units of length (kilometers, meters, centimeters), 1 km= 1,000 x 1 m mass (kilograms, grams), and liquid volume (liters, milliliters). They express larger units 1 kilometer= 1,000 meters in terms of smaller units and complete conversion tables. Students add and subtract mixed unit measurements. Copyright© Great Minds PBC

Contents Place Value Concepts for Addition and Subtraction Why ...................................................... 6 Achievement Descriptors: Overview.................... 10 Topic A .................................................. 13

Multiplication as Multiplicative Comparison Lesson 1 ................................................... 16 Interpret multiplication as multiplicative comparison. Lesson 2 ................................................... 40 Solve multiplicative comparison problems with unknowns in various positions. Lesson 3 ................................................... 58 Describe relationships between measurements by using multiplicative comparison. Lesson 4 ................................................... 76 Represent the composition of larger units of money by using multiplicative comparison. Topic B .................................................. 95

Place Value and Comparison Within 1,000,000 Lesson 5 ................................................... 98 Organize, count, and represent a collection of objects. Lesson 6 .................................................. 140 Demonstrate that a digit represents 10 times the value of what it represents in the place to its right.

Lesson 7 .................................................. 160 Write numbers to 1,000,000 in unit form and expanded form by using place value structure. Lesson 8 .................................................. 180 Write numbers to 1,000,000 in standard form and word form. Lesson 9 .................................................. 200 Compare numbers within 1,000,000 by using>, = , and<. Topic C ................................................. 219

Rounding Multi-Digit Whole Numbers Lesson 10 ................................................. 222 Name numbers by using place value understanding. Lesson 11.................................................. 256 Find 1, 10, and 100 thousand more than and less than a given number. Lesson 12 ................................................. 278 Round to the nearest thousand. Lesson 13 ................................................. 294 Round to the nearest ten thousand and hundred thousand. Lesson 14 ................................................. 310 Round multi-digit numbers to any place. Lesson 15 ................................................. 324 Apply estimation to real-world situations by using rounding.

EUREKA MATH 2

Topic D ................................................. 340

Topic E .................................................. 465

Multi-Digit Whole Number Addition and Subtraction

Metric Measurement Conversion Tables

Lesson 16 ................................................. 346 Add by using the standard algorithm.

Lesson 23 ................................................. 468 Express metric measurements of length in terms of smaller units.

Lesson 17 ................................................. 364 Solve multi-step addition word problems by using the standard algorithm.

Lesson 24 ................................................. 488 Express metric measurements of mass and liquid volume in terms of smaller units.

Lesson 18 ................................................. 380 Subtract by using the standard algorithm, decomposing larger units once. Lesson 19 ................................................. 398 Subtract by using the standard algorithm, decomposing larger units up to 3 times.

Resources Standards ................................................ 506 Achievement Descriptors: Proficiency Indicators .............. 508 Terminology .............................................. 520

Lesson 20 ................................................. 414 Subtract by using the standard algorithm, decomposing larger units multiple times.

Math Past ................................................ 522

Lesson 21 ................................................. 430 Solve two-step word problems by using addition and subtraction.

Works Cited .............................................. 528

Lesson 22 ................................................. 448 Solve multi-step word problems by using addition and subtraction.

Materials ................................................. 526

Credits ................................................... 530 Acknowledgments ......................................... 531

Why Place Value Concepts for Addition and Subtraction Why does the place value module begin with a topic on multiplicative comparisons? Beginning with multiplicative comparison enables students to build on their prior knowledge of multiplication from grade 3 and provides a foundation upon which students can explore the relationships between numbers and place value units. This placement also activates grade 3 knowledge of multiplication and division facts within 100 and provides students with opportunities to continue building fluency with the facts in preparation for multiplication and division in modules 2 and 3.

FigureA

FigureB

FigureC

FigureD

■ ■ ■ ■■ ■■ ■■ ■■■ ■■■ ■■■ ■■■■ ■■■■ ■■■■

• •• •••• ••••••••

FigureL •

FigureM ••

FigureN ••••

FigureO ••••••••

Students are familiar with additive comparison-relating numbers in terms of how many more or how many less. Multiplicative comparison-relating numbers as times as many-is a new way to compare numbers. Students use multiplicative comparison throughout the year to relate measurement units, whole numbers, and fractions. This important relationship between factors, where one factor tells how much larger the product is compared to the other factor, is foundational to ratios and proportional relationships in later grades. Taking time to develop this understanding across the grade 4 modules sets students up for success with interpreting multiplication as scaling in grade 5 and applying or finding a scale factor in scale drawings, dilations, and similar figures.

EUREKA MATH 2

Why is the vertical number line used for rounding numbers? The vertical number line is used to help support conceptual understanding of rounding. In grade 3, students first see the vertical number line as an extension of reading a vertical measurement scale. Using the context of temperature, students identify the tens (i.e., benchmarks) between which a temperature falls, the halfway mark between the benchmark temperatures, and the benchmark temperature the actual temperature is closer to. Students then generalize to round numbers to the nearest ten and hundred.

740,000 = 740 thousands

739,625 739,500 = 739 thousands 5 hundreds

739,000 = 739 thousands

In grade 4, students round numbers with up to 739,625 z 740,000 6 digits to any place. They continue to use the vertical number line as a supportive model. Labeling the benchmark numbers and halfway tick mark in both standard form and unit form helps emphasize the unit to which a number is being rounded. This way, the place values line up vertically, helping students see the relationship between the numbers. The pictorial support of the vertical number line when rounding is eventually removed, but the conceptual understanding of place value remains as students round mentally. These experiences with the vertical number line prepare students for representing ratios with vertical double number lines and graphing pairs of values in the coordinate plane.

EUREKA MATH 2

Why are metric units of measurement addressed in this module? When are customary units of measurement addressed? Work with metric units of length, mass, and liquid volume in topic E provides an opportunity for students to apply their place value understanding to a measurement context. Students convert metric units that have relationships involving hundreds (e.g., meters to centimeters) and thousands (e.g., kilograms to grams). They apply multi-digit addition and subtraction strategies, including the standard algorithm, to add and subtract mixed-unit measurements. Introducing metric units in module 1 also provides the opportunity to use the units in word problem contexts throughout the rest of the year.

Kilograms

Grams

1,000

2,000

5,000

12,000

583

583,000

Customary units are included within modules 2 and 3 because the relative sizes of customary units of measurement do not align with the place value unit structure. Customary units of length are addressed in module 2 when students work with two-digit multiplication, area, and perimeter. Additionally, units of time and customary units of weight and liquid volume are addressed in module 3 alongside multiplication and problem solving.

Achievement Descriptors: Overview Place Value Concepts for Addition and Subtraction 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, • data from other lesson-embedded formative assessments, • Exit Tickets, • Topic Quizzes, and • Module Assessments. This module contains the twelve ADs listed.

1 11

EUREKA MATH 2

4.Mod1.AD1

4.Mod1.AD2

4.Mod1.AD3

4.Mod1.AD4

Create two comparison statements, given a multiplication equation.

Write multiplicative comparison statements as multiplication equations.

Solve word problems involving multiplicative comparison by using multiplication or division within 100.

Assess reasonableness of estimates when using rounding as an estimation strategy.

4.0A.A.1

4.0A.A.3

4.0A.A.2

4.Modl.ADS

4.Mod1.AD6

4.Mod1.AD7

4.Mod1.AD8

Solve multi-step word problems by using addition and subtraction, represent these problems by using equations, and assess the reasonableness of the answers.

Explain the relationship between a digit in a multi-digit whole number and the same digit in the place to the right.

Read and write multi-digit whole numbers in unit, standard, word, and expanded form.

Compare two whole numbers by using>, = , or<.

4.NBT.A.2

4.NBT.A.1

4.0A.A.3

4.NBT.A.2

4.Mod1.AD9

4.Mod1.AD10

4.Mod1.AD11

4.Mod1.AD12

Round multi-digit whole numbers.

Add and subtract multi-digit whole numbers by using the standard algorithm.

Express larger units in terms of a smaller unit within the metric system in a table.

Solve addition and subtraction word problems that require expressing measurements of larger units in terms of given smaller units.

4.NBT.A.3

4.NBT.B.4

4.MD.A.1

4.MD.A.2

EUREKA MATH 2

4 ► M1

4.Mod1.AD10 Add and subtract multi-digit whole numbers by using the standard algorithm. RELATED CCSSM

4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Proficient

Partially Proficient

Highly Proficient

Add and subtract multi-digit whole numbers by using the standard algorithm without regrouping.

Add and subtract multi-digit whole numbers by using the standard algorithm with regrouping.

Analyze errors in the use of the algorithm for addition or subtraction.

Add.

James found 5,678 his mistake.

126,521 51,137

Subtract.

346,547 56,678

122,052 26,137

Subtract.

895,359 42,137

3,429. His work is shown. Explain 6 9

5,6i8. - 3,429 2,240

Topic D Multi-Digit Whole Number Addition and Subtraction In topic D, students build fluency with addition and subtraction of multi-digit numbers by using the standard algorithm, and they solve multi-step word problems. Use of the standard algorithm for addition and subtraction is familiar to students from their work with two-digit and three-digit numbers in grades 2 and 3. Topic D extends that learning as students generalize and build fluency with the algorithm to add and subtract numbers within 1,000,000. The topic begins with addition. Students build conceptual understanding by using concrete place value disks and pictorial representations of numbers on a place value chart to add like units, regrouping as necessary. Students use vertical form to record the algorithm. They add like units, rename groups of 10 as larger units, and indicate the renamed units by writing them below the addends. Students estimate sums before adding by rounding each addend and finding their totals. They use their estimates to check their final answers for reasonableness. Students add to solve two-step and multi-step word problems. Concrete place value disks and pictorial representations of numbers on a place value chart are also used to build conceptual understanding of subtraction. Students begin by subtracting multi-digit numbers that require just one renaming of units and then build to problems that require more than one renaming. Students use vertical form to record the algorithm. They rename units across the number, as necessary, to get the total ready to subtract and then subtract like units. Students continue to use rounding to estimate and check the reasonableness of their answers. Students also use addition to check their answers, providing another opportunity to see the relationship between addition and subtraction and to practice using the standard algorithm.

EUREKA MATH 2

The Read-Draw-Write process is used throughout the topic. Students solve two-step and multi-step word problems by using addition and subtraction. They draw tape diagrams to help them interpret and make sense of the problems and to determine what operation or operations to use. They write equations with a letter for the unknown, make an estimate, then solve and check their answer. In topic E, students use their place value understanding to convert metric measurement units from larger units to smaller units and to add and subtract measurements of length, mass, and liquid volume.

EUREKA MATH 2

Progression of Lessons

Lesson 16 Add by using the standard algorithm. millions

!��

•

tho!::nds

thousands hundreds

••••••••• •

• 200,000 + 50,000 250,000

tens

ones

Lesson 17

53,lo70

Men's

B3,9/o0

Kids'

'----v--'

23/o,089

I can add numbers with up to six digits by using the standard algorithm for addition. Tools such as place value disks and the place value chart can help me to understand how numbers are added. I add like units in vertical form and rename 10 of a smaller unit as 1 of the next larger unit. Rounding to estimate the sum before I add helps me determine whether my answer is reasonable.

i::1

218,050

Women's 182 ,'l 19

Subtract by using the standard algorithm, decomposing larger units once.

Solve multi-step addition word problems by using the standard algorithm.

••••• ••••

74,30B

T he Read-Draw-Write process can help me find the solution path for word problems, including problems with 2 or 3 steps. I can draw a tape diagram to make sense about what is known and unknown in the problem. I write equations with a letter for the unknown, estimate the sum, then check the reasonableness of my answer.

Lesson 18

t1to!:nds

thousands

hundreds

tens

.300,000 - 200,000 100,000 210

3�4, <o 3 7 - 182, 4 2 3 1 2 2, 2 1 4

182, 42.3 + 122, 214 .304, Co.37

I can subtract numbers with up to 6 digits by using the standard algorithm for subtraction. Before I subtract, I make an estimate. Then I make sure that I am ready to subtract in each place. I look across the number and rename 1 of a larger unit for 10 of a smaller unit. T hen I subtract. I compare my answer to my estimate and check my answer with addition. Tools such as place value disks and the place value chart can help me to understand how to regroup and subtract.

EUREKA MATH 2

I Lesson 19 Subtract by using the standard

Lesson 20 Subtract by using the standard

algorithm, decomposing larger units up

algorithm, decomposing larger units

to 3 times.

multiple times.

N0,000 - 70,000 = 70,000

l'i.G, !U, 7 t, OB3

71,0B3 + t.'l,243

t.'l, 243

140,32<.

Sometimes I have to rename more than 1 unit to get ready to subtract. I can still use the standard algorithm, and the place value chart can help me make sense of how I rename when using vertical form. Checking my answer by comparing it to my estimate and by using addition is a helpful way for me to tell if I renamed and subtracted correctly.

Lesson 21 Solve two-step word problems by using addition and subtraction.

50,000

1,000,000 - '700,000 ,. 300,000

0)10 212

0999 9910

1,000,oolS!

'723,418

2'76,582

2 117�,�� 1,000,000

When I subtract, the standard algorithm works for any numbers. I repeat the process and rename units as many times as I need. There is more than one way to show the renaming when I subtract across zeros. I can choose the way that is most efficient for me.

1 18

Uo,714

1'1,247

Sometimes I use more than one operation to solve word problems. Representing two-step word problems with a tape diagram can help me to see which part to solve first and what operations to use. I write equations with a letter for the unknown, estimate and find the answer, and then check the reasonableness of my answer.

EUREKA MATH 2

f Lesson 22 Solve multi-step word problems by using addition and subtraction. 10,loSO

eilue

fled

w ._____ y_____.,__..--'

3,780

Green '---�v---'--v--'

l,'!YS

There is more than one way to solve a word problem. When I draw tape diagrams to represent word problems, I can look at the sizes of the tapes and use the relationships to more efficiently solve the problems. I might find a way to solve the problem that I wouldn't see if I didn't draw the tape diagram. I estimate the unknown and then decide what operations to use and find the answer. My estimate helps me check my answer.

EUREKA MATH 2

Lesson 19

Agenda

Materials

Lesson Preparation

Fluency 1s min

Teacher

• Consider tearing out the Sprint pages in advance of the lesson.

Launch s min Learn

30min

• Subtract by Using Place Value Drawings and the Standard Algorithm • Subtract by Using the Standard Algorithm • Solve a Subtraction Word Problem

• Place Value Chart to Hundred Thousands (in the teacher edition)

Students • Add in Standard Form Sprint (in the student book) • Place Value Chart to Hundred Thousands (in the student book)

• Problem Set

Land

lOmin

• Consider whether to remove Place Value Chart to Hundred Thousands from the student books and place inside whiteboards in advance or to have students prepare them during the lesson.

EUREKA MATH 2

Lesson 19

Sprint: Add in Standard Form Materials-S: Add in Standard Form Sprint

Students add numbers within 1,000,000 in standard form to develop fluency with adding multi-digit whole numbers by using the standard algorithm. Have students read the instructions and complete the sample problems.

Write the sum. 1.

300 + 500

800

30,000 + 20,000

50,000

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!" if you got it correct. If you made a mistake, circle the answer.

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.

Teacher Note Consider asking the following questions to discuss the patterns in Sprint A: • What do you notice about problems 1-12?

Provide about 2 minutes to allow students to complete more problems or to analyze and discuss patterns in Sprint A. If students are provided time to complete more problems on Sprint A, reread the answers but do not have them alter their personal goals. 29

• Draw a box around problems 3, 7, 11, 15, and 20. How do these problems compare?

EUREKA MATH 2

Lead students in one fast-paced and one slow-paced counting activity, each with a stretch or physica I movement. Point to the number you got correct on Sprint A. Remember this is your personal goal for Sprint B. Direct students to Sprint B.

Lesson 19

Teacher Note Count forward by ten thousands from 50,000 to 150,000 for the fast-paced counting activity. Count backward by thousands from 15,000 to

Take your mark. Get set. Improve!

5,000 for the slow-paced counting activity.

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!" if you got it correct. If you made a mistake, circle the answer. 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. Determine your improvement score and write the number at the top of the page. Celebrate students' improvement.

Students determine how the process used to subtract three-digit numbers can be applied to subtracting with larger numbers. Write 612 - 437 horizontally. Invite students to work with a partner to use vertical form to subtract. Invite one or two students to share their work.

5 � 12

b. '1 i -437

What units did you rename to get ready to subtract?

175

We renamed 1 ten as 10 ones and 1 hundred as 10 tens.

EUREKA MATH 2

Lesson 19

Display the picture of the sequence of subtraction problems. How do you see our original problem, 612 - 437, in each new problem?

6,128 -4,375

61,289 -43,756

612,894 -437,560

The same digits are in each problem, but they represent different units. Invite students to think-pair-share about which units need to be renamed in problems A-C to get ready to subtract. In problem A, 1 hundred needs to be renamed as 10 tens and 1 thousand needs to be renamed as 10 hundreds. In problem B, 1 thousand needs to be renamed as 10 hundreds and 1 ten thousand needs to be renamed as 10 thousands. In problem C, 1 ten thousand needs to be renamed as 10 thousands and 1 hundred thousand needs to be renamed as 10 ten thousands. Draw a box around the renaming of 612 as 5 hundreds 10 tens 12 ones in the original problem.

10 5 & 12

Look at how we recorded the renaming in 612 - 437. How would the recording of the renaming look in problems A through C?

&'11 -437 175

It would look similar because you are renaming 1 of a larger unit for 10 of a smaller unit.

It would look similar because they are the same digits, but it would represent different units. Display the picture of problems A, B, and C with the renaming boxed. We can use what we know about renaming more than once with smaller numbers to help us rename more than once with larger numbers.

5 '& 12

'6.,1"X8 -4,375

5 Q 12

'6.1,"X89 -43,756

5 Q 12

'6.1"X, 94 -437,560

Transition to the next segment by framing the work. Today, we will rename more than once when we subtract and use vertical form to record our thinking. 31

EUREKA MATH 2

Lesson 19

.,,

Subtract by Using Place Value Drawings and the Standard Algorithm Materials-T/S: Place Value Chart to Hundred Thousands

Students make a drawing to represent disks on the place value chart and record the subtraction with vertical form.

Teacher Note

Write 8,267 - 5,481 horizontally.

The Subtraction on the Place Value Chart

Direct students to remove Place Value Chart to Hundred Thousands from their books and place it in their whiteboards.

interactive allows students to represent

hundred thousands

Invite students to write the problem in vertical form and estimate the difference.

ten thousands

••••• ••• •• thousands

hundreds

••••• • •••••• • tens

ones

subtraction on the place value chart alongside the vertical form. Consider allowing students to experiment with the tool individually or demonstrate by using the tool to model subtraction on the place value chart instead of drawing the disks.

8,000 - 5,000

= 3,000

Let's draw dots on a place

UDL: Action & Expression

value chart to represent Consider printing the place value chart

place value disks. What

on grid paper. The squares can support

number do we need to

students as they draw dots to represent place

represent on the place

value disks.

value chart?

Invite students to draw dots to represent 8,267 on their place value charts. Consider using the following sequence to guide students in regrouping and renaming all necessary units before subtracting. Direct students to complete the work on their place value charts as you model. Are we ready to subtract in the ones place?

ten thousands

7 "'"' �l't.7 - 5,'18 I 2,7 8/o

Are we ready to subtract in the tens place? How can we rename for more tens?

hundred thousands

thousands

hundreds

. ·-

•••••••••• tens

8,000 - 5,000 = 3,000 5,'1 8 I +2, 78/o k,i1o7

EUREKA MATH 2

Lesson 19

Demonstrate regrouping 1 hundred into 10 tens on the place value chart by crossing off 1 hundred, drawing an arrow from the hundreds to the tens column, and drawing 10 tens.

hundred thousands

How many hundreds do we have now? Tens?

Model writing the renaming in vertical form. Are we ready to subtract in the hundreds place?

ten thousands

How many thousands do we have now? Hundreds?

Model writing the renaming in vertical form.

••••• •••

hundreds

8,000 - 5,000

tens

••••• •• ones

= 3,000

I l(o

?,l'&i7 - 5,4 8 t

How can we rename for more hundreds?

Demonstrate regrouping 1 thousand into 10 hundreds on the place value chart by crossing off 1 thousand, drawing an arrow from the thousands to the hundreds column, and drawing 10 hundreds.

thousands

hundred thousands

ten thousands

•• . ..•''\ ••••• �..••••• .... thousands

•••••

hundreds

tens

ones

••••• ••••• ••

•••••

8,000 - 5,000

= 3,000

II 7\�

?,l'&i7 - 5,4 8 t

Are we ready to subtract in the thousands place? Now we are ready to subtract.

EUREKA MATH 2

Demonstrate subtracting 1 one by crossing it off on the place value chart. Confirm that 7 ones - 1 one = 6 ones in vertical form matches the remaining ones on the place value chart. Continue the process for subtracting 8 tens, 4 hundreds, and 5 thousands. Use unit form to support student understanding of the standard algorithm and its relationship to place value.

4 hundred thousands

ten thousands

..•"' .....

••••• •• •••••• ••••• •• ••••• ••••• ••••• thousands

hundreds

tens

·�

8,000 - 5,000 ll 7 \ llo

ones

�

= 3,000 5,4 8 1 + 2, 7 8 lo lo 7

?,i � 7 -5,4 8 1 2, 7 8 lo

J,i

Then compare the difference to the estimate to assess reasonableness.

.... .... -�..•••••.... •.....••••

Direct students to check their work with addition. Use a similar sequence to find 62,409 - 7,362. Invite students to turn and talk about how the place value chart and vertical form show that they renamed more than once.

hundred thousands

ten thousands

thousands

••••• ••

hundreds

512 3 10

�

55,047 + 7 I 3 lo2 lo2 I 4 09

ones

•••••

lo0,000 -10,000 = 50,000

�i,\f.�9 7,.3lo2 55,047

tens

Lesson 19

EUREKA MATH 2

Lesson 19

Subtract by Using the Standard Algorithm Students use vertical form to represent renaming 3 times when subtracting with the standard algorithm. 800,000 - 500,000 = 300,000 Write 803,415 - 461,973 horizontally. Invite students to write the problem in vertical form and estimate the difference. Consider using the following sequence to guide students in renaming all necessary units before subtracting. Are we ready to subtract in the ones place? Are we ready to subtract in the tens place? How can we rename for more tens?

13 2 3.11

803,�5 - 4<o1,973

Demonstrate renaming 4 hundreds 1 ten as 3 hundreds 11 tens. How many hundreds do we have now? Tens?

Differentiation: Support

Consider providing the place value chart for students so they can draw dots to model the subtraction. The goal is for students to become fluent with using the standard

algorithm, but students must first develop a conceptual understanding of regrouping units

to subtract. As students draw dots on the place value chart to subtract, support them in making the connection between the pictorial representation and the vertical form.

Language Support

Are we ready to subtract in the hundreds place? How can we rename for more hundreds?

Demonstrate renaming 3 thousands 3 hundreds as 2 thousands 13 hundreds.

• Am I ready to subtract in the

Repeat the process for the remaining place value units.

lace? ___ p

• Where can I rename for more

Now we are ready to subtract.

Direct students to complete the subtraction problem, use their estimates to assess the reasonableness of their answers, and use addition to check their work. Invite one or two students to share their work.

Consider displaying the following questions to guide students as they use vertical form to record the standard algorithm:

___

• How many

7 10 2

do I have now? ___ Direct students to repeat this sequence of

:3, II

8�1,�1_.5 461,9'73 3 41,442

461,9'73 + 341,442 803,41.5

questions for each place value unit as they get ready to subtract with vertical form.

As time allows, use a similar sequence to find 265,034 - 37,819 and 643,205 - 210,867.

Teacher Note

Invite students to turn and talk about all the renaming that is done before subtracting.

Students are familiar with renaming across a zero from grade 3. Students rename across multiple zeros in lesson 20.

EUREKA MATH 2

Lesson 19

Solve a Subtraction Word Problem Students draw a tape diagram and use the standard algorithm to solve a subtraction word problem.

Promoting the Standards for Mathematical Practice

Present the problem: Adam logs 140,326 steps in two weeks. He logs 71,083 steps the first week. How many steps does he log the second week? Direct students to work with a partner to use the Read-Draw-Write process to solve the problem.

As students solve subtraction word problems, estimate to assess the reasonableness of their answers, and use addition to check their work, they are making sense of problems and persevering in solving them (MPl).

Use the following questions to advance student thinking:

Ask the following questions to promote MPl:

• Can you draw something to represent this problem? What can you draw? • What else can you draw? • What part of the tape diagram represents the unknown? What letter can you use to represent the unknown? • What operation will you use to find the solution? Why? • What is a reasonable estimate for the difference?

_.l 140,326 - ,1,oa3

w_ ....___,_1_i0_a_3__........__

"'w

0\10 212

1�'6>,�'26 '71, 083 69,243

'71, 08 3 + 69,2 43 11 1 1 40, 3 2 6

Adam log, 9 6 ,243 ,tep, in the ,econd wee�.

• Are you ready to subtract? Do you need to rename? Where? • What does the number 140,326 represent in the problem? 71,083? 69,243? • What solution statement can you write? • Is the actual difference you found reasonable based on your estimate? • How can you check your solution with addition? Invite one or two students to share their work.

• What are some things you can do to start finding how many steps Adam logged the second week?

• Does your answer make sense? Why?

EUREKA MATH 2

Lesson 19

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

■ w ■ ,o -

Debrief

5 min

Objective: Subtract by using the standard algorithm, decomposing larger units up to 3 times. Use the following prompts to guide a discussion about using place value and the standard algorithm to rename units more than once when subtracting. Display a problem from today's lesson and the vertical form of one problem from the previous lesson. Look at the two problems. How is the process of subtracting similar? How is it different?

We can rename units when we do not have enough to subtract in both problems.

3 1'2

3Ais

-1/263 '2,162

13 710'2 'S-11

a� 3-A 1.s -461,973 341,44'2

When we rename units, we rename 1 of a larger unit for 10 of a smaller unit. We need to do this once in one problem and three times in the other problem. Why can we use what we know about subtracting with smaller numbers to help us subtract with larger numbers?

The process is the same; it is just the units that change. We rename units in the same way. A larger unit is the same amount as 10 of a smaller unit.

EUREKA MATH 2

How is recording in vertical form useful?

It helps me to keep track of renaming units. I can see which units need to be renamed, and then I can see how many of each unit I have. It helps me to see if I am ready to subtract. I can picture what the problem would look like on the place value chart. Recording in vertical form is a similar process. Using digits is more efficient than drawing dots.

Exit Ticket s 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.

3 38

Lesson 19

Supplemental Materials

Teach: Effective Instruction with Eureka Math2; Grades K–5

Credits Great Minds. 2021. Eureka Math2®. Washington, DC: Great Minds. https://greatminds.org/math 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 acknowledgement in all future editions and reprints of this handout.