Supplemental Materials: Assess Embedded Opportunities to Inform Instruction K-2

Supplemental Materials

Assess Embedded Opportunities to Inform Instruction, K–2

A Story of Units ®

Supplemental Materials

Assess: Embedded Opportunities to Inform Instruction, K–2

Contents Connect Assessment to Instruction ............................................................................................................. 3 Grade 1 Module 2 Overview .................................................................................................................... 3 Collect Data from Multiple Perspectives ...................................................................................................... 6 Grade 1 Module 2 Observational Assessment Recording Sheet .............................................................. 6 Proficiency Indicators for 1.Mod2.AD1 .................................................................................................... 8 Grade 1 Module 2 Lesson 11 .................................................................................................................... 9 Measure Progress Over Time ..................................................................................................................... 21 Lesson 8 .................................................................................................................................................. 21 Lesson 9 .................................................................................................................................................. 22 Lesson 10 ................................................................................................................................................ 23 Lesson 11 ................................................................................................................................................ 24 Lesson 12 ................................................................................................................................................ 25 Lesson 13 ................................................................................................................................................ 26 Kindergarten Module 5 Assessment .......................................................................................................... 28 Kindergarten Module 5 Achievement Descriptors ..................................................................................... 31 Kindergarten Sample Student OARS .......................................................................................................... 35 Grade 1 Module 2 Assessment Student Work ........................................................................................... 36 Grade 2 Module 2 Assessment Student Work ........................................................................................... 40 Putting it all Together: Supporting Artifacts .............................................................................................. 45 Shared Practice: Aby – 1.Mod2.AD1 ...................................................................................................... 45 Apply it!: Carter – K.Mod5.AD3 .............................................................................................................. 49 Apply it!: Violet – 1.Mod2.AD4 .............................................................................................................. 52 Apply it!: Lucas – 2.Mod2.AD3 ............................................................................................................... 55 Common Addition and Subtraction Problem Types ................................................................................... 58 Credits ........................................................................................................................................................ 59 Works Cited ................................................................................................................................................ 59

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Before This Module

Overview

Kindergarten

Addition and Subtraction Relationships

Kindergarten students learn to represent take from story problems by using objects, drawings, and number sentences. They solve problems such as 5 – 3 = ___ both concretely and pictorially.

Grade 1 Module 1 Counting on to find totals provides a foundation for counting on or counting back to find an unknown part.

Reasoning about the meaning of the equal sign and determining whether number sentences are true or false helps prepare students to write true number sentences and find unknowns in various equations.

Systematic study of partners to 6 through partners to 10 supports understanding subtraction equations as unknown addend problems.

Topic A Reason About Take From Situations To bridge from addition to the various types of subtraction situations, students solve result unknown stories about a school bus. They notice what happens when they add to and take from the total number of people on the bus.

School Bus Stories

School Bus Stories

5+3=8

8-2=6

As they solve sets of related take from problems that include subtract 0, subtract all, subtract 1 less than the total, and subtract 1, they notice patterns and formulate conjectures to solve similar problems efficiently.

This topic also includes subtraction by using the familiar unit of five. Students subtract 5 by taking away 5 fingers all at once. With 5 as a point of reference, they take away 4 and 6 fingers all at once too. Taking away a part all at once is foundational to the Level 3 subtraction strategy known as take from ten that is introduced in module 3.

8-5=3

While interpreting graphs, students compare categories by using greater than, less than, and equal to language.

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EUREKA MATH2 1 ▸ M2

Topic B Relate and Distinguish Addition and Subtraction Students learn the Read–Draw–Write problemsolving process to make sense of, represent, and solve related add to and take from word problems. Students read and reread problems to draw models and solve. Then they represent their solutions by writing a number sentence.

6+3=9

9-3=6 6+3=9

In addition to drawing, students use number 1 2 3 4 paths and number bonds to represent related addition and subtraction problems. The number path allows them to see subtraction as undoing addition by reversing the action. Number bonds help students discover that related addition and subtraction problems have the same parts and total, but what the unknown represents will change. See these examples:

5 6 7 8 9 10 11 12 13 14 15

9-3=6

• When you have a total and subtract a part, the unknown represents the other part.

• When you add parts together, the unknown represents the total.

Topic C Find an Unknown Part in Change Unknown Problems Students solve add to with change unknown and take from with change unknown word problems. They may • use a labeled drawing to identify the total, the known part, and the unknown part;

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Drawing

Fingers

Number Path

9 11 12 13 10

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1

2 3 4 5 6 7 8 9 10 11 12 13 14 15

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EUREKA MATH2

1 ▸ M2

• count on from the known part to the total, noting how many they counted; or • count back from the total to the known part, noting how many they counted.

When situations imply an add to action, students are likely to represent their thinking with addition. When a take from action is implied, students are likely to represent their thinking with subtraction.

They use Level 2 strategies when working with equations: counting on to find an unknown addend (9 + = 14) and counting back to find an unknown subtrahend (14 – = 9).

Topic D Find an Unknown Part by Using Addition and Subtraction Put together and take apart situations have no implied action, so students are equally likely to find the unknown part with either addition or subtraction. Students come to understand that the answer to a subtraction problem is an unknown part. To find the answer, they can count on, count back, or simply think about the parts they know that make the total. They determine that counting back is efficient when the known part is small compared to the total. To find the value of various unknowns in equations, they use known part–whole relationships and related facts.

After This Module Grade 1 Module 3 Students continue to solve result unknown and part unknown word problems and find unknown parts and totals in equations.

However, instead of using Level 2 counting strategies to solve, students use Level 3 strategies that involve forming easier yet equivalent problems.

Grade 1 Module 4 Students solve the following comparison situations involving length: difference unknown (how much longer and shorter), longer length unknown, and shorter length unknown.

Topic E Represent and Solve Comparison Problems Students move toward work with comparison word problems first by making groups equal.

They learn the strategies to figure out how many more are in one group than in another: take away the extra amount in one group or add the extra amount to one group. They record the action as a true addition or subtraction number sentence.

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Observational Assessment Recording Sheet Student Name

Grade 1 Module 2

Addition and Subtraction Relationships Achievement Descriptors

Dates and Details of Observations

1.Mod2.AD1

Represent and solve word problems within 20 involving grades K and 1 addition and subtraction problem types.

1.Mod2.AD2

Represent by using drawings and a number sentence and solve how many more word problems within 20.

1.Mod2.AD3

Subtract by using think addition strategies.

1.Mod2.AD4

Subtract within 20 by using strategies such as counting on or back.

1.Mod2.AD5

Subtract fluently within 10.

1.Mod2.AD6

Add or subtract to make groups equal and write a true number sentence to match.

1.Mod2.AD7

Find the unknown in an addition or subtraction equation.

1.Mod2.AD8

Answer questions about a graph.

PP Partially Proficient

Notes

370

This page may be reproduced for classroom use only.

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P Proficient

HP Highly Proficient

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EUREKA MATH2 1 ▸ M2 ▸ Observational Assessment Recording Sheet

Module Achievement Descriptors and Content Standards by Lesson ● Focus content ○ Supplemental content Lesson Topic A

Topic B

Achievement Descriptor

Aligned CCSSM

1.Mod2.AD1

1.OA.A.1

1.Mod2.AD2

1.OA.A.1

1.Mod2.AD3

1.OA.B.4

1.Mod2.AD4

1.OA.C.5 1.OA.C.6

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1.Mod2.AD5

1.OA.C.6

● ● ●

1.Mod2.AD6

1.OA.D.7

1.Mod2.AD7

1.OA.D.8

1.Mod2.AD8

1.MD.C.4

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Topic C 8

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Topic D 12

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Topic E 18

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○

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This page may be reproduced for classroom use only.

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Achievement Descriptors: Proficiency Indicators 1.Mod2.AD1 Represent and solve word problems within 20 involving grades K and 1 addition and subtraction

problem types.

RELATED CCSSM

1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.2 See [CCSSM] Glossary, Table 1.

2

Partially Proficient Represent word problems by using drawings or objects and solve word problems within 10 involving add to with result unknown, take from with result unknown, and put together and take apart with total unknown problem types.

Draw or use cubes to show the story.

8 bugs are on a flower.

3 bugs fly away.

How many bugs are on the flower now?

There are

bugs on the flower now.

Proficient

Highly Proficient

Represent word problems by using drawings and a number sentence and solve word problems within 20 involving add to with result unknown, take from with result unknown, put together and take apart with total unknown, add to with change unknown, take from with change unknown, and put together and take apart with addend unknown.

Read 12 bugs are on a flower.

Some bugs fly away.

Now there are 9 bugs on the flower.

How many bugs flew away?

Draw

Write

bugs flew away.

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LESSON 11

Represent and solve take from with change unknown problems.

EUREKA MATH2

1 ▸ M2 ▸ TC ▸ Lesson 11

11

Name

Read 10 frogs are on a log.

Lesson at a Glance Students connect to previous learning by comparing an add to with change unknown word problem with a take from with change unknown word problem. They concretely represent and solve a take from with change unknown problem and then draw to solve similar problems. Students discuss the meaning of the unknown, which is a subtrahend, for the first time.

Some frogs go into the pond.

Key Question

Now 3 frogs are on the log.

• What are some ways to find a part that was taken away?

How many frogs went into the pond?

Achievement Descriptor 1.Mod2.AD1 Represent and solve word problems within 20 involving

Draw

grades K and 1 addition and subtraction problem types. (1.OA.A.1)

Write

10 - 7 = 3 7

frogs went into the pond.

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EUREKA MATH2 1 ▸ M2 ▸ TC ▸ Lesson 11

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• Number Bond Dash: Make 8 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.

Launch Learn

10 min 10 min

30 min

• Act It Out • Draw It • Problem Set

Land

• None

Students • Number Bond Dash: Make 8 (in the student book) • Craft sticks (10)

• Prepare a bag of 10 craft sticks for each student.

10 min

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EUREKA MATH2

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Fluency

10 10

Choral Response: Disappearing Dots with Totals of 8 Students take away30from 8 and say a subtraction sentence to maintain fluency with decompositions within 10.

10

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 image of 8 dots.

How many dots?

8 Display 4 dots disappearing.

How many dots went away?

4 How many dots are there now?

4 Display all 8 dots again.

On my signal, say the subtraction sentence starting with 8.

8–4=4 Repeat the process with the following sequence:

8-2=6 174

8-4=4

8-6=2 11

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EUREKA MATH2 1 ▸ M2 ▸ TC ▸ Lesson 11

Number Bond Dash: Make 8 Materials—S: Number Bond Dash: Make 8

Students complete number bonds with totals of 8 to build fluency with decompositions within 10.

Teacher Note

Direct students to the Number Bond Dash. Read aloud the directions. Invite students to use their finger to practice completing a number bond on their paper.

Students who prefer to solve by counting on may wish to make tick marks in the unknown part of the number bond to track the count.

Tell students that if they finish early, they should count from 8 to the highest number they can and record their count on the back of the paper.

EUREKA MATH2

Give a signal to begin.

1 ▸ M2 ▸ TC ▸ Lesson 11 ▸ Number Bond Dash: Make 8

Number Bond Dash: Make 8 Fill in the number bonds.

Let students work for 60 seconds or until about 80% of the class nears completion of the page. Do not extend beyond 2 minutes of written work.

8

8

8 0 7 1

Call time. Have students put down their pencils. Read the number bonds aloud as students correct their own papers. When you have finished reading all problems, tell students to write the number they got correct in the star at the top of the page. Celebrate student success.

Happy Counting by Ones Within 20 Students visualize a number line while counting aloud to relate counting to addition and subtraction, and to build fluency counting within 120.

8

8

8

6 2

7 1

6 2

8

8

8

8

8

3 5

2 6

3 5

4 4

5 3

8

8

8

8

8

4 4

5 3

3 5

4 4

3 5

8

8

8

8

8

2 6

6 2

2 6

8 0

7 1

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Invite students to participate in Happy Counting.

When I give this signal, count up. (Demonstrate.) When I give this signal, count down.

(Demonstrate.)

Let’s count by ones. The first number you say is 10. Ready?

Signal up or down accordingly for each count.

10

11

12

13

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19

20

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EUREKA MATH2

1 ▸ M2 ▸ TC ▸ Lesson 11

Continue counting by ones within 20. Change directions occasionally, emphasizing crossing over 10, 15, and where students hesitate or count inaccurately.

10

Launch

10 30

Students solve and compare related addition and subtraction problems.

Gather students and 10 present the following situation.

There are 7 pencils on my desk. (Display the picture of 7 pencils.)

UDL: Engagement The pencil context is one option for presenting the situations in this lesson. If desired, use a context that is more relevant or engaging to your students. Be sure that it works for the actions of both adding to and taking away.

I put some more pencils on my desk. (Display the picture of 9 pencils.)

Now there are 9 pencils on my desk.

How many pencils did I put on my desk? How do you know?

Have students think–pair–share to determine how many pencils were put on the desk. Invite students to explain their thinking.

If possible, include someone who counted on to find the unknown part.

2 pencils. We counted on: Sevennnn, 8, 9.

2 pencils. We know 7 + 2 = 9.

Ask students to write a number sentence that corresponds to the story and to box the unknown. Have the class discuss how the number sentence represents the story, including the idea that the unknown represents the added part, or the pencils put on the desk.

7+ 2 =9 Continue to display the picture of 9 pencils.

Whisper how many pencils are on my desk.

9

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EUREKA MATH2 1 ▸ M2 ▸ TC ▸ Lesson 11

Oops! Some pencils fell off. (Display 7 pencils.)

Whisper how many pencils are on my desk now.

7 How many pencils fell off? How do you know?

Have students think–pair–share to determine how many pencils fell off. Invite students to explain their thinking. If possible, include someone who counted back. If needed, model counting back.

2 pencils. We put up 9 fingers. We put 7 down and had 2 left.

2 pencils. We counted back: Niiiine, 8, 7.

2 pencils. We drew 9 lines and crossed off 2.

Confirm students’ thinking by revoicing the solved problem.

There were 9 pencils. 2 pencils fell off. There are 7 left.

Ask students to write a number sentence that corresponds to the story and to box the unknown, modeling if needed. Have the class discuss how the number sentence represents the story, including the idea that the unknown represents the subtracted part, or the pencils that fell off the desk.

Display the number sentences for each situation.

7+ 2 =9

9- 2 =7

How are the two pencil stories different?

One story starts with 7 pencils. The other starts with 9.

Teacher Note Although take from with change unknown problems lend themselves to counting back, some students may count up from 7 or “just know” the related addition fact and use it to solve the subtraction situation.

In the first story, 2 pencils are added.

In the second story, 2 pencils fell off.

In both stories, the unknown is a part. In the first story, the unknown part is added. In the second story, the unknown part is subtracted.

Transition to the next segment by framing the work.

Today, we will show some ways to find an unknown part that was subtracted.

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10 EUREKA MATH2

1 ▸ M2 ▸ TC ▸ Lesson 11 10

Learn Act It Out

30 10

Teacher Note

Materials—S: Craft sticks

Students concretely model to solve a take from with change unknown problem.

Ensure each student has a personal whiteboard and a bag of craft sticks. Tell the students that the craft sticks represent pencils. Display the word problem and read it aloud.

I put 9 pencils on the desk.

Some fell off.

Take from with change unknown situations are particularly challenging since students cannot visualize the action. Instead, they must reason about how many are being taken away.

As they represent the situations with numbers and symbols, students recognize that sometimes the unknown is also in the middle of a subtraction equation.

Now there are 3 pencils.

How many pencils fell off the desk?

Differentiation: Challenge

Let’s use our craft sticks to show this problem. 9 pencils are on the desk at first.

Remove the scaffold of the craft sticks and encourage students to use Read–Draw–Write (RDW) on their personal whiteboards.

Ask students to organize their sticks in a 5-group row or array but not as tallies.

If the numbers presented in the lesson are known facts, adapt the problem to begin with a larger total, such as 17 or 19.

Some fall off. Now there are 3 pencils. How can we show that?

We can move 3 sticks to their own group.

We can take sticks off until there are 3 left.

Students may also write their own word problems for the same type of situation, take from with change unknown, but with a different context:

Give students a moment to model with their sticks.

How many pencils fell off the desk? How do you know?

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6 pencils. I took off one at a time until 3 were left. I took off 6 sticks.

• 8 kids were playing tag. Some left. Now there are 5.

6. I put 3 in one group. There are 6 in the other group.

• My teacher had 10 stickers. She gave some to us. Now she has 2.

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EUREKA MATH2 1 ▸ M2 ▸ TC ▸ Lesson 11

Let’s write a number sentence to match the problem. What should we write first? Why?

Promoting the Standards for Mathematical Practice

We should write 9 first because there are 9 pencils on the desk in the beginning.

Record as students follow along on their personal whiteboards.

What should we write next? Why?

When students independently choose to model or draw and then write the corresponding number sentence, they model 1 ▸ M2 ▸ TC ▸ Lesson 11 with mathematics (MP4).

Write minus 6. That is how many pencils fall off.

EUREKA MATH2

What should we write last? Why?

11

Write equals 3. There are 3 pencils left on the desk.

The guided instruction in Learn prepares students to self-select and use models that help them make sense of the problem.

Name

What were we trying to figure out?

How many pencils fell off the desk

Read

Draw a box around 6, the unknown.

I put 6 pencils on a desk.

The part that fell off the desk, or gets subtracted, is the unknown.

Point to each component of the number sentence to summarize the problem.

There were 9 total pencils. 6 fell off, and now there are 3 pencils.

When students are working independently on the Problem Set, ask the following questions are on a desk.

I put 8 pencils to promote MP4: Read

Some pencils fell off.

• How can you show the problem?

Some pencils fell off.

• How does your number sentence match

Now 2 pencils are on the desk.

your sticks or drawing?

Now 5 pencils are on the desk.

How many pencils fell off?

How many pencils fell off?

Draw

Draw

Have students clean up their craft sticks.

Draw It

D

If students are ready for more independence with the RDW process, reduce guidance for the first in this segment by using the D problem F following prompts after students read and reread the problem:

F

Students draw to solve take from with change unknown problems.

Ask students to open their student books to the pencil problem. Read the problem aloud as students follow along.

Write

Some pencils fell off.

Now 2 pencils are on the desk.

How many pencils fell off?

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Write

4

pencils fell off.

• Can you draw something? What can you draw?

• What does your drawing show? (Encourage labeling.)

6-4=2

I put 6 pencils on a desk.

Differentiation: Challenge

8-3=5

3

• What do you need to figure out? pencilsnumber fell off. sentence can you write?

• What

• What sentence answers the question?

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EUREKA MATH2

1 ▸ M2 ▸ TC ▸ Lesson 11

Reread the first line: I put 6 pencils on a desk.

Let’s ask ourselves two questions. Can we draw something? What can we draw?

Ask students to follow along in their books as you model. Draw 6 dots in a 5-group row.

Reread the next two lines: Some pencils fell off. Now 2 pencils are on the desk.

Let’s ask ourselves the two questions again. Can we draw something? What can we draw?

Differentiation: Support As needed, allow students to continue to model with craft sticks. Encourage them to draw a picture of how they used the sticks to solve the problem.

One at a time, cross off 4 dots until 2 dots are left.

Teacher Note

How can we label our drawing?

We can label the 2 dots with D for desk. Those are still on the desk.

We can label the 4 dots we crossed off with F for fell. Those are on the floor.

What does our drawing show?

We started with 6 pencils.

Although students may cross off (or circle) any of the 6 dots to show 2 left, the lesson models “taking” from the right for two reasons: • To align with counting back from 6 (6, 5, 4, 3, 2)

4 fell off.

• To model the problem as an unknown addend problem: 2 + ? = 6

2 are on the desk.

Reread the question: How many pencils fell off?

What were we trying to figure out?

Teacher Note

How many pencils fell Where is that in our drawing? Show your partner.

Invite students to work with a partner to write a number sentence and box the unknown.

Invite a student to share an accurate number sentence (or, if needed, model).

What number represents the unknown? How do you know?

4. We didn’t know how many pencils fell.

Yes, 4 was unknown because we did not know the part that was taken away.

Then ask students to answer the question by using a complete sentence.

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Although a take from with change unknown situation lends itself to a subtraction equation with an unknown subtrahend, some students may write an addition equation to represent how they solved the problem (possibly by counting up). Ask them to explain their thinking and help them see that they still found the unknown part that was taken away.

6–2=4

17

4+2=6

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EUREKA MATH2 1 ▸ M2 ▸ TC ▸ Lesson 11

If time allows, direct students to the second problem. Read it aloud and have partners use EUREKA MATH 1 ▸ M2 ▸ TC ▸ Lesson 11 the RDW process to solve.

2

11

I put 8 pencils on a desk.

Some pencils fell off.

Name

Now 5 pencils are on theRead desk.

Read

I put 6 pencils on a desk.

How many pencils fell off?

As needed, use the following prompts to guide Some pencils fell off. students through the RDW process after reading and rereading the problem: Now 2 pencils are on the desk.

• Can you draw something?

How many pencils fell off?

• What can you draw? (Encourage labeling.)

Draw

I put 8 pencils are on a desk.

Some pencils fell off.

−4

Now 5 pencils are on the desk.

2 3 4 5 6 +4

How many pencils fell off?

2 3 4 5 6 Other students may not want to draw at all.

Although they may not need to draw to solve, ask these students to show how they know their number sentence is true by drawing.

• What do you need to figure out?

D • What number sentence can you write?

F

D

• What sentence answers the question?

Circulate and look for student work to share. Consider selecting both accurate work and work that represents an error you commonly observe. Write Display student work and invite students to explain their thinking. Use questions such as the following to guide the discussion: • How did your drawing help you solve the problem?

4

pencils fell off.

• Can anyone explain how this student’s number sentence matches the drawing?

F

A goal in this lesson is for students to practice the RDW process with simple problems so that they know it well and can use it when they encounter more complex situations.

Write

6-4=2

Expect variety in students’ drawings. They might draw pictures, lines, or dots. Encourage simple yet accurate representations of the problem.

Students who count on or count back by using fingers or a number path might make different drawings to record these strategies.

Draw

• What does the drawing show?

Teacher Note

8-3=5 3

pencils fell off.

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• Class, why do you think this student put a box around the 3 in the number sentence?

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Consider engaging the class by asking additional questions such as the following: EM2_0102TE_C_L11_classwork_studentwork.indd 123

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• Who can say what this student did in their own words?

• Does anyone have questions for this student?

• Did anyone solve this problem differently?

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EUREKA MATH2

1 ▸ M2 ▸ TC ▸ Lesson 11

Problem Set

Teacher Note

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

10

If students need more practice finding an unknown change that has been taken away, allow them to act out more pencil problems.

Pair students and give each student 10 craft sticks. Share directions for the game.

Directions and word problems may be read aloud.

10

30

Land Debrief

10

5 min

Objective: Represent and solve take from with change unknown problems.

Gather students with their Problem Sets. Have them turn and talk about how they solved the third problem.

Display the provided sample work and guide students to make connections between the word problem, the drawing, and the number sentence.

Where do you see the 8 frogs on a log in this drawing?

• Partner A, put some craft sticks onto your whiteboard. Partner B, put the EUREKA MATH2 same number of craft sticks onto your whiteboard.

1 ▸ M2 ▸ TC ▸ Lesson 11

Read

Read

• Partner B, close your eyes and don’t peek!

• Partner A, take some craft sticks away and

8 frogs are on a log.

a log.

12 turtles are on hide them behind your back.

Some frogs go into the pond.

Some turtles go into the pond.

Now 3 frogs are on the log.

Now 8 turtles are on the log.

How many frogs went into the pond?

How many turtles went into the pond?

• Partner B, open your eyes. Use your craft sticks to figure out how many were taken away.

• Together, write a number sentence and draw a box around the unknown.

Draw

Draw

Write

Write

To extend student thinking, have students use 10–20 craft sticks to act out the story.

They are the 8 dots.

Where do you see the frogs that went into the pond?

It is the 5 dots that are crossed off.

What could help us see the parts of the problem in the drawing?

We could label them.

8-5=3

Where do you see the frogs that are still on the log?

The 3 circled dots

5 126

182

frogs went into the pond.

PROBLEM SET

19

12 - 4 = 8 4

turtles went into the pond.

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EUREKA MATH2 1 ▸ M2 ▸ TC ▸ Lesson 11

Focus students’ attention on the number sentence.

Why do you think this student wrote a subtraction number sentence?

The frogs went into the pond.

What number was unknown in the problem? How do you know?

5. It was how many frogs went into the pond.

Yes, it was the part taken away.

Exit Ticket

Differentiation: Support Some students benefit from visual support.

Consider displaying these images while reading the word problem before looking at the student work.

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.

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8

LESSON 8

Interpret and find an unknown change.

EUREKA MATH2

1 ▸ M2 ▸ TC ▸ Lesson 8

8

Name

Count on and fill in the sentence.

Write a number sentence.

Lesson at a Glance Students count on to solve problems in which the unknown, for the first time in grade 1, is a part rather than the total. They use concrete tools and an everyday context that represents the known addend (I have) and the total (I want) to find an unknown addend (I need).

Students start with the known part, count on until they get to the total, and then identify how many they counted on. The class writes an addition number sentence to match.

You have 8 pennies.

Key Question

You want 10 pennies.

• What is different about counting on to find a total and counting on to find an unknown part?

Achievement Descriptor 1.Mod2.AD1 Represent and solve word problems within 20 involving

grades K and 1 addition and subtraction problem types. (1.OA.A.1)

8 + 2 = 10 You need

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2

pennies.

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9

LESSON 9

Represent and solve add to with change unknown problems.

EUREKA MATH2

1 ▸ M2 ▸ TC ▸ Lesson 9

9

Name

Read Val has 6 books.

She gets some more.

Lesson at a Glance Students analyze an add to with change unknown situation and recognize that the unknown is a part that represents a change in quantity. They self-select tools to help them solve for the unknown, and then they share various solution strategies. Students study a sample drawing that represents the problem and discuss the value of using labels. They add labels to their own drawings and write number sentences and statements to complete their work.

Now she has 9 books.

Key Question

How many books did Val get?

• What are some ways to find an unknown part that was added?

Draw

Achievement Descriptor 1.Mod2.AD1 Represent and solve word problems within 20 involving

grades K and 1 addition and subtraction problem types. (1.OA.A.1)

Write

6+3=9 Val got

3

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books.

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LESSON 10

Represent and find an unknown addend in equations.

EUREKA MATH2

1 ▸ M2 ▸ TC ▸ Lesson 10

10

Name

1.

2. Fill in the part.

Read Val has 6 books.

Show how you know.

She gets some more.

Lesson at a Glance For the first time, students find the unknown in an equation. The equations are presented without the support of word problem contexts. Students use the count on strategy, which is familiar from work with word problems, to find unknown addends. The term equation is introduced in this lesson.

Key Questions

Now she has 9 books.

8+

6

• What is the same about counting on with different tools?

= 14

• Which tool is most helpful for you when you count on, and why?

How many books did Val get?

Draw

Achievement Descriptor 1.Mod2.AD7 Find the unknown in an addition or subtraction equation.

(1.OA.D.8)

Write

6+3=9 Val got

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more books.

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LESSON 11

Represent and solve take from with change unknown problems.

EUREKA MATH2

1 ▸ M2 ▸ TC ▸ Lesson 11

11

Name

Read 10 frogs are on a log.

Lesson at a Glance Students connect to previous learning by comparing an add to with change unknown word problem with a take from with change unknown word problem. They concretely represent and solve a take from with change unknown problem and then draw to solve similar problems. Students discuss the meaning of the unknown, which is a subtrahend, for the first time.

Some frogs go into the pond.

Key Question

Now 3 frogs are on the log.

• What are some ways to find a part that was taken away?

How many frogs went into the pond?

Achievement Descriptor 1.Mod2.AD1 Represent and solve word problems within 20 involving

Draw

grades K and 1 addition and subtraction problem types. (1.OA.A.1)

Write

10 - 7 = 3 7

frogs went into the pond.

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24

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LESSON 12

Represent and find an unknown subtrahend in equations.

EUREKA MATH2

1 ▸ M2 ▸ TC ▸ Lesson 12

12

Name

Fill in the part.

Show how you know.

Lesson at a Glance Students reason about take from with change unknown situations and discuss different ways to represent these problems. They work with equations to find unknown subtrahends, counting back from the total to the known part. They use their fingers as well as the number path to keep track of the count and find the answer.

Key Question

10 –

2

• What are some ways to find the unknown part? Which way is most efficient for you?

=8

Achievement Descriptor

-2

1.Mod2.AD7 Find the unknown in an addition or subtraction equation.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

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(1.OA.D.8)

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LESSON 13

Represent and solve add to and take from with change unknown problems.

EUREKA MATH2

C

Name

1.

EUREKA MATH2

1 ▸ M2 ▸ TC

1 ▸ M2 ▸ TC

2. Fill in the part.

Show how you know.

Read Peg had 13 carrots.

7+

Her dog ate some.

2

=9

Now she has 9 carrots.

+2

How many carrots did her dog eat?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Draw

Sample:

Write

13 - 9 = 4 The dog ate

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4

carrots.

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26

TO P I C T I C K E T

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EUREKA MATH2 1 ▸ M2 ▸ TC ▸ Lesson 13

Lesson at a Glance Students watch videos and read word problems that depict add to and take from changes.

Partners represent each situation with an addition or subtraction equation. They use a box to show the unknown in the equation and then solve. A game provides hands-on mixed practice with add to and take from situations.

Key Question • Should we write an addition or subtraction equation to represent the story? How do you know?

Achievement Descriptors 1.Mod2.AD1 Represent and solve word problems within 20 involving grades K and

1 addition and subtraction problem types. (1.OA.A.1) 1.Mod2.AD7 Find the unknown in an addition or subtraction equation. (1.OA.D.8)

Agenda

Materials

Lesson Preparation

Fluency

Teacher

None

Launch Learn

10 min 10 min

30 min

• Hide Zero® cards, demonstration set

Students

• Add To or Take From?

• Craft sticks (20 per student pair)

• Carrots Game

• Centimeter number path (1 per student pair)

• Problem Set

Land

10 min

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201

Module Assessment Grade K Module 5

Addition and Subtraction Only administer this assessment to students whose observational assessments show inconsistent proficiency throughout the module.

Use the suggested language or support students in their native language to better ascertain their understanding of math content.

If a student is unable to answer the first few questions, end the assessment and retry after more instruction.

Materials • Dot image in a whiteboard • Unifix® Cubes (stick of 7 connected cubes and 10 loose cubes) • Plain white paper or a personal whiteboard and dry-erase marker • Addition and subtraction equation sheet

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EUREKA MATH2 K ▸ M5

(K.OA.A.1)

K.Mod5.AD6 Add and subtract within 10 by using objects, drawings, or other math tools.

Circle parts that make ___ . (Say the student-provided total.)

Write a number sentence that tells about all the dots.

Erase the parts the student circled.

Show another two parts to make ___.

(Say the student-provided total.)

Teacher note: Students may write an addition number sentence with the total at the beginning or end of the number sentence.

Both representations are correct.

Erase marks and the number sentence on the dot card.

This page may be reproduced for classroom use only.

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339

K.Mod5.AD3 Represent subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

How many dots?

K ▸ M5 ▸ Module Assessment

(K.OA.A.1)

1. Place the dot card in a whiteboard in front of the student.

Dot Configuration

K.Mod5.AD2 Represent addition with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

Assessment Question

EUREKA MATH2

Achievement Descriptors and Standards

How many dots?

Cross out some dots.

Write a number sentence that tells about the dots.

(K.OA.A.2)

K.Mod5.AD6 Add and subtract within 10 by using objects, drawings, or other math tools.

(K.OA.A.2)

K.Mod5.AD8 Find the partner to 10 for any number 1–9. (K.OA.A.4)

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2. Give the student a stick of 7 connected cubes with a color change to show the 5-group as shown. Have loose cubes available for students to use if desired.

How many more to make 10?

Teacher note: Students may say “three” or add 3 cubes to the stick. Both responses are acceptable.

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EUREKA MATH2

K ▸ M5

Achievement Descriptors and Standards K.Mod5.AD3 Represent subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

(K.OA.A.1)

K.Mod5.AD4 Solve add to, take from, put together, and take apart with result unknown story problems within 10 by using addition and subtraction. (K.OA.A.2)

Assessment Question 3. Place a plain piece of paper in front of the student.

Listen to my story.

There are 9 children playing after school. 4 children go home. How many children are still playing?

Prompt the student to write a number sentence to show their thinking. Have math tools (such as cubes) available for students to use if desired. Point to different parts in their representation and use the following questions to check for understanding.

What does this number tell about in the story?

Where is the total in your number sentence? Where are the parts?

Which cubes show the children that are still playing?

Teacher note: If the student provides an answer without using a number sentence or any math tools, ask them to use a number sentence or drawing to explain their thinking.

K.Mod5.AD9 Add fluently within 5. (K.OA.A.5) K.Mod5.AD10 Subtract fluently within 5. (K.OA.A.5)

4. Hand out the addition and subtraction equation sheet. This part of the assessment may be administered to students in small groups.

Add and subtract to fill in the blanks.

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This page may be reproduced for classroom use only.

Teacher note: Note whether students use fingers, objects, or drawings. These supports are acceptable and encouraged when students are challenged with new math concepts or higher numbers. For sums and differences within 5, kindergarten students should know the answer without supports most of the time.

338

EUREKA MATH2

K ▸ M5 ▸ Module Assessment

+

=

+

=

-

=

-

=

340

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Achievement Descriptors: Proficiency Indicators K.Mod5.AD1 Count forward from a number other than 1.

RELATED CCSSM

K.CC.A.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

Partially Proficient Count forward from a number other than 1 with the help of a visual aid.

Count the carrots. Start at 6.

Proficient

Highly Proficient

Count forward from a number other than 1.

Count to 10 starting at 3.

6

K.Mod5.AD2 Represent addition with objects, fingers, mental images, drawings, sounds, acting out situations, verbal

explanations, expressions, or equations.

RELATED CCSSM

K.OA.A.1 Represent addition and subtraction with objects, fingers, mental images, drawings2, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

2

Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)

Partially Proficient

Proficient

Highly Proficient

Represent addition within 5 with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

Represent addition within 10 with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

Represent addition within 10 in more than one way.

Make a math drawing, write a number bond, or write an addition sentence that tells about the frogs.

Make a math drawing, write a number bond, or write an addition sentence that tells about the frogs.

344

31

Write a number bond and an addition sentence that tell about the frogs.

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EUREKA MATH2

K ▸ M5

K.Mod5.AD3 Represent subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal

explanations, expressions, or equations.

RELATED CCSSM

K.OA.A.1 Represent addition and subtraction with objects, fingers, mental images, drawings2, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

2

Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)

Partially Proficient

Proficient

Represent subtraction within 5 with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

Represent subtraction within 10 with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.

Cross out a part. Make a drawing, write a number bond, or write a subtraction sentence to tell about the crackers.

Cross out a part. Make a drawing, write a number bond, or write a subtraction sentence to tell about the crackers.

Highly Proficient Represent subtraction within 10 in more than one way.

Cross out a part. Write a number bond and a subtraction sentence to tell about the crackers.

K.Mod5.AD4 Solve add to, take from, put together, and take apart with result unknown story problems within 10 by using

addition and subtraction.

RELATED CCSSM

K.OA.A.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Partially Proficient

Proficient

Highly Proficient

Solve add to, take from, put together, and take apart with result unknown story problems within 10 by using addition and subtraction.

There are 2 frogs in the pond.

5 more frogs hop into the pond.

How many frogs are in the pond?

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345

EUREKA MATH2

K ▸ M5

K.Mod5.AD5 Record solutions to story situations in which both addends are unknown with an addition sentence.

RELATED CCSSM

K.OA.A.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Partially Proficient

Proficient

Record solutions to story situations in which both addends are unknown with objects, drawings, or number bonds.

Record solutions to story situations in which both addends are unknown with an addition number sentence.

There are 9 cookies on a pan.

There are 9 cookies on a pan.

Some are sugar cookies, and some are chocolate chip.

Some are sugar cookies, and some are chocolate chip.

How many of each cookie might there be? Fill in the number bond.

How many of each cookie might there be? Write an addition sentence.

Highly Proficient

K.Mod5.AD6 Add and subtract within 10 by using objects, drawings, or other math tools.

RELATED CCSSM

K.OA.A.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Partially Proficient

Proficient

Add and subtract within 5 by using objects, drawings, or other math tools.

Add and subtract within 10 by using objects, drawings, or other tools.

Add. You can use a drawing, a number path, your fingers, or any other tool to help.

Add. You can use a drawing, a number path, your fingers, or any other tool to help.

+ = 346

Highly Proficient

+ = 33

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EUREKA MATH2

K ▸ M5

K.Mod5.AD8 Find the partner to 10 for any number 1–9.

RELATED CCSSM

K.OA.A.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.

Partially Proficient

Proficient

Decompose 10 into two parts by using objects, drawings, or other tools.

Find the partner to 10 for any number 1–9 by using objects, drawings, or other tools.

Look at the apples. Fill in the number bond to match.

Look at the apples. How many more to make 10?

Highly Proficient

K.Mod5.AD9 Add fluently within 5.

RELATED CCSSM

K.OA.A.5 Fluently add and subtract within 5.

Partially Proficient

Proficient

Highly Proficient

Add fluently within 5.

Fill in the number sentence.

+ = 348

34

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36

37

38

39

40

41

42

43

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Supplemental Materials

Assess: Embedded Opportunities to Inform Instruction, K–2

Putting it all Together: Supporting Artifacts Shared Practice: Aby – 1.Mod2.AD1 Card 1 Topic Ticket A

Lesson 5 Problem Set Item

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Supplemental Materials

Assess: Embedded Opportunities to Inform Instruction, K–2

Card 2 Topic Ticket B

Share-Compare-Connect Problem Prompt Lesson 12 I have 8 pennies. (Open your hand and show the pennies) See? Close your eyes. (Put 6 pennies in a location that is out of students’ sight). Open your eyes. (Show the 2 pennies in your hand.)

What happened? I hid some pennies. Let’s figure out how many I hid. Remember I had 8 pennies. I hid some. I have 2 pennies left.

Have students work independently to solve. Aby’s strategy was drawing.

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Supplemental Materials

Assess: Embedded Opportunities to Inform Instruction, K–2

Card 3 Topic Ticket C

Lesson 21 Classwork

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Supplemental Materials

Assess: Embedded Opportunities to Inform Instruction, K–2 Module Assessment

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Supplemental Materials

Assess: Embedded Opportunities to Inform Instruction, K–2

Apply it!: Carter – K.Mod5.AD3 Card 1 Observational Assessment Lesson 8

Observational Assessment Lesson 13

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Supplemental Materials

Assess: Embedded Opportunities to Inform Instruction, K–2

Card 2 Observational Assessment Lesson 19

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Assess: Embedded Opportunities to Inform Instruction, K–2 Observational Assessment Lesson 26

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Assess: Embedded Opportunities to Inform Instruction, K–2

Card 3 Module Assessment

Apply it!: Violet – 1.Mod2.AD4 Card 1 Lesson 3 Exit Ticket

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Supplemental Materials

Assess: Embedded Opportunities to Inform Instruction, K–2 Topic Ticket A

Card 2 Lesson 7 Classwork

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Assess: Embedded Opportunities to Inform Instruction, K–2 Topic Ticket B

Card 3 Lesson 16 Problem Set

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Assess: Embedded Opportunities to Inform Instruction, K–2 Module Assessment

Apply it!: Lucas – 2.Mod2.AD3 Card 1 Lesson 5

Topic Ticket A

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Assess: Embedded Opportunities to Inform Instruction, K–2

Card 2 Lesson 10

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Supplemental Materials

Assess: Embedded Opportunities to Inform Instruction, K–2 Topic Ticket B

Card 3 Lesson 26

Module Assessment

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Assess: Embedded Opportunities to Inform Instruction, K–2

Common Addition and Subtraction Problem Types1

ADD TO

RESULT UNKNOWN

CHANGE UNKNOWN

START UNKNOWN

Two bunnies sat on the grass.

Three more bunnies hopped there. How many bunnies are on the grass now?

Two bunnies were sitting on the grass. Some more bunnies hopped there. Then there were five bunnies. How many bunnies hopped over to the first two?

Some bunnies were sitting on the grass. Three more bunnies hopped there. Then there were five bunnies. How many bunnies were on the grass before?

𝟐 + ?= 𝟓

? +𝟑=𝟓

Five apples were on the table.

I ate some. Then there were three apples. How many apples did I eat?

Some apples were on the table. I ate two apples. Then there were three apples. How many apples were on the table before?

𝟐+𝟑=?

TAKE FROM

Five apples were on the table. I ate two apples. How many apples are on the table now? 𝟓−𝟐=?

𝟓 − ?= 𝟑

? −𝟐=𝟑

PUT TOGETHER / TAKE APART3

COMPARE4

TOTAL UNKNOWN

ADDEND UNKNOWN

BOTH ADDENDS UNKNOWN2

Three red apples and two green apples are on the table.

How many apples are on the table?

Five apples are on the table.

Three are red and the rest are green. How many apples are green?

Grandma has five flowers. How many can she put in the red vase and how many in her blue vase?

𝟑+𝟐=?

𝟑 + ? = 𝟓, 𝟓 − 𝟑 = ?

𝟓 = 𝟎 + 𝟓, 𝟓 = 𝟓 + 𝟎, 𝟓 = 𝟏 + 𝟒, 𝟓 = 𝟒 + 𝟏, 𝟓 = 𝟐 + 𝟑, 𝟓=𝟑+𝟐

DIFFERENCE UNKNOWN

BIGGER UNKNOWN

SMALLER UNKNOWN

(“How many more?” version): Lucy has two apples. Julie has five apples. How many more apples does Julie have than Lucy?

(Version with “more”):

(Version with “more”):

(“How many fewer?” version): Lucy has two apples. Julie has five apples. How many fewer apples does Lucy have than Julie?

Julie has three more apples than Lucy. Lucy has two apples.

How many apples does Julie have?

Julie has three more apples than Lucy. Julie has five apples.

How many apples does Lucy have?

(Version with “fewer”):

(Version with “fewer”):

Lucy has three fewer apples than Julie. Lucy has two apples.

How many apples does Julie have?

Lucy has three fewer apples than Julie. Julie has five apples.

How many apples does Lucy have?

𝟐 + 𝟑 = ?, 𝟑 + 𝟐 = ?

𝟓 − 𝟑 = ?, ? + 𝟑 = 𝟓

𝟐 + ? = 𝟓, 𝟓 − 𝟐 = ?

Pink shading indicates the four Kindergarten problem types. Grade 1 and 2 students work with all types and variants. Blue shading indicates the four difficult problem types that students should work with in grade 1 but need not master until grade 2.

1

Adapted from Box 2–4 of Mathematics Learning in Early Childhood, National Research Council (2009, pp. 32, 33).

These take apart situations can be used to show all the decompositions of a given number. The Associated equations, which have the total on the left of the equal sign, help children understand that the = sign does not always mean makes or results in but always does mean is the same number as.

3 Either addend can be unknown, so there are three variations of these problem situations. Both Addends Unknown is a productive extension of the basic situation, especially for small numbers less than or equal to 10.

4 For the Bigger Unknown or Smaller Unknown situations, one version directs the correct operation (the version using more for the bigger unknown and using less for the smaller unknown. The other versions are more difficult.

2

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Supplemental Materials

Assess: Embedded Opportunities to Inform Instruction, K–2

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 acknowledgement in all future editions and reprints of this handout.

Works Cited Great Minds. Eureka Math2TM. Washington, DC: Great Minds, 2021. https://greatminds.org/math.

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