Assess EM2, 3-5 Supplemental Materials

Supplemental Materials

Assess

Embedded Opportunities to Inform Instruction, 3–5

A Story of Units ®

Supplemental Materials

Assess: Embedded Opportunities to Inform Instruction, 3–5

Contents Connect Assessment to Instruction .............................................................................................................. 3 Grade 3 Module 2 Overview ..................................................................................................................... 3 Grade 3 Module 2 Topic C Overview ........................................................................................................ 5 Grade 3 Module 2 Topic C Progression of Lessons ................................................................................... 6 Grade 3 Module 2 Lesson 19 Overview .................................................................................................... 9 Collect Data from Multiple Perspectives .................................................................................................... 10 Proficiency Indicators for 3.Mod2.AD2 ................................................................................................... 10 Measure Progress Over Time...................................................................................................................... 11 Lesson 14................................................................................................................................................. 11 Lesson 17................................................................................................................................................. 12 Lesson 18................................................................................................................................................. 13 Lesson 19................................................................................................................................................. 14 Grade 3 Module 2 Topic C Quiz Scoring Guide ........................................................................................... 15 Scored Sample Topic Quiz ....................................................................................................................... 16 Grade 3 Module 2 Topic D .......................................................................................................................... 20 Topic Overview........................................................................................................................................ 20 Progression of Lessons ............................................................................................................................ 22 Credits ......................................................................................................................................................... 24 Works Cited ................................................................................................................................................. 24

© Great Minds PBC

2

Before This Module

Overview

Grade 2 Modules 1 and 2

Place Value Concepts Through Metric Measurement

In grade 2, students describe and apply place value concepts to two- and three-digit numbers. They count and bundle ones, tens, and hundreds up to 1,000. Students read and write numbers in standard, unit, and expanded forms and apply place value understanding to add and subtract two- and three-digit numbers by using a variety of strategies. Simplifying strategies consist of composing and decomposing tens and hundreds to make problems easier to compute mentally and developing various written methods to record student thinking.

Topic A Understanding Place Value Concepts Through Metric Measurement Students estimate and measure weight and liquid volume by using grams, kilograms, liters, and milliliters. Familiar concepts, such as composing and decomposing place value units, are applied to the relationship between the smaller unit (gram or milliliter) and the unit that represents 1,000 (kilogram or liter). The number line is applied as a familiar model for understanding how to read circular and vertical measurement scales. Students solve one-step word problems that have measurement contexts.

Students also estimate and measure length by using a variety of tools and units in the customary and metric systems of measurement.

Grade 3 uses familiar place value concepts to expand student understanding of metric measurement of weight and liquid volume and to develop fluency in addition and subtraction within 1,000.

Topic B Rounding to the Nearest Ten and Hundred Reading temperatures on a thermometer provides an initial context for students to round to the nearest ten or hundred. To round a number, students determine the two consecutive tens or hundreds that the number is between and then determine which ten or hundred is closer by thinking about the number in relation to the halfway mark. The number line, when presented vertically, provides a new perspective on a familiar tool and is used to help students to round numbers. Students then apply their rounding skills to estimate sums and differences.

2

EM2_0302TE_MO.indd 2

80 = 8 tens

75 = 7 tens 5 ones 73 = 7 tens 3 ones 70 = 7 tens

Copyright © Great Minds PBC

8/28/2021 12:03:34 PM

EUREKA MATH2 3 ▸ M2

Topic C

After This Module

Simplifying Strategies to Find Sums and Differences Students apply their knowledge of the vertical number line to the scale on a scaled bar graph. They represent data in a scaled bar graph and solve addition and subtraction problems related to scaled bar graphs. They explore a variety of addition and subtraction strategies based on place value, the properties of operations, and the relationship between addition and subtraction. The strategies include adding and subtracting like units, making the next ten or hundred, taking from a ten or hundred, and using compensation. Emphasis is placed on thinking flexibly and building toward the use of mental math. Throughout the topic, students share and critique solution strategies for addition and subtraction problems and explain how their choice in strategy helps them to add or subtract efficiently.

800 1

17 + 98 = 15 + 100 = 115

800 - 258 = 542 -1 -1

1 257

15 2 15 + ((22 + 98 98))

799

258

7 9 9 - 257 = 542

Grade 4 Module 1 In grade 4, students apply their understanding of measurement units to convert weight, liquid volume, and length measurements from larger units to smaller units.

Students generalize place value and rounding concepts and relationships to larger, multi-digit numbers. They add and subtract multi-digit numbers by using the standard algorithms for addition and subtraction.

378,642 + 52 7 , 1 6 9 1 1

1 1

9 0 5, 8 1 1

?

Topic D Two- and Three-Digit Measurement Addition and Subtraction Students use concrete and pictorial place 100s 10s 1s value models alongside vertical form 9 to represent and record the work of the 7 1013 standard algorithm for addition and the 803 standard algorithm for subtraction. They _ 58 7 compose and decompose units as needed 216 and estimate to assess the reasonableness of their answers. Students apply their computation skills to select an appropriate strategy and solve one- and two-step word problems involving measurement contexts and units.

Copyright © Great Minds PBC

EM2_0302TE_MO.indd 3

3

8/28/2021 12:03:34 PM

Topic C Simplifying Strategies to Find Sums and Differences Topic C explores a variety of familiar addition and subtraction strategies based on place value, the properties of addition, and the relationship between operations. Each strategy is familiar from grade 2. Topic C also extends grade 2 work with data to include scaled bar graphs.

Experience from topic B with scales that have intervals other than 1 transfers to scaled bar graphs. Students relate the scales on scaled bar graphs to the scales used on measurement tools and the vertical number line they used for rounding. Answering how many more and how many less questions about the data helps students move from reading and creating graphs to finding sums and differences.

Students use place value understanding to demonstrate properties when they add and subtract like units, make or take from a benchmark number (i.e., a ten or hundred), and use compensation. Familiar models and recording methods, including number bonds, the arrow way, and tape diagrams, are used to represent student thinking. Emphasis is placed on developing flexibility and fluency in finding sums and differences and building toward the use of mental math. Students evaluate the types of problems that are well-suited to each strategy. Students are not expected to name and master every strategy; rather, they are expected to purposefully approach problems in ways that make each problem easier for them, even if it is a different approach than one selected by someone else. Strategy work from grade 2 is advanced by the use of parentheses to record the decompositions shown in number bonds.

In topic D, students use place value models and the standard algorithms for addition and subtraction. They continue to be encouraged to use strategies that make sense to them by evaluating problems to determine when a simplifying strategy is a more efficient approach than a place value chart and the standard algorithm. Students use addition and subtraction strategies to solve problems involving measurement contexts and measurement units.

206

EM2_0302TE_C_TO.indd 206

Copyright © Great Minds PBC

8/28/2021 11:55:00 AM

EUREKA MATH2 3 ▸ M2 ▸ TC

Progression of Lessons Lesson 13

Lesson 14

Lesson 15

Collect and represent data in a scaled bar graph and solve related problems.

Use place value understanding to add and subtract like units.

Use the associative property to make the next ten to add.

Colors of Cars in the School Parking Lot on Tuesday 60

27 + 22 = 49

17 + 98 = 15 + 100 = 115

20 7 20 2

15 2

20 + 20 = 40

40

7+2=9

Number of Cars 20

0

White

Black

Red

Blue

Color

Scaled bar graphs use a scale other than 1 to show data containing large quantities. Scaled bar graphs help represent the data so that we can see similarities and differences and answer questions about the data.

Copyright © Great Minds PBC

EM2_0302TE_C_TO.indd 207

Breaking apart numbers into tens and ones helps me add and subtract in my head. I add tens to tens and ones to ones. There are many ways I can represent my thinking.

15 + ((22 + 98 98)) When one addend is close to a benchmark number, I can compute in my head by breaking apart the other addend and making a ten or hundred.

207

8/28/2021 11:55:00 AM

EUREKA MATH2

3 ▸ M2 ▸ TC

Lesson 16

Lesson 17

Lesson 18

Use compensation to add.

Use place value understanding to subtract efficiently using take from a ten.

Use place value understanding to subtract efficiently using take from a hundred.

98 + 56 = 154 56 + 100 156 - 2 154 When one addend is close to a benchmark number, I can use compensation to compute in my head by adding the benchmark number and then subtracting the extra that I added.

208

EM2_0302TE_C_TO.indd 208

50 - 17 = 33 3 30 20 20 - 17 = 3 30 + 3 = 33

230 - 96 = 134 4 130 100 100 - 96 = 4 130 + 4 = 134

When the number I subtract is close to a ten, I can break apart the total into two parts to make one of the parts a ten so I can subtract in my head.

After I subtract from the ten, I add the answer to the other part to find the difference in the original problem.

230 - 96 = 130 + (100 - 96) = 130 + 4 = 134 When the number I subtract is close to a hundred, I can break apart the total into two parts to make one of the parts a hundred so I can subtract in my head like I did when the number was close to a ten. Then I add the other part.

Copyright © Great Minds PBC

8/28/2021 11:55:01 AM

EUREKA MATH2 3 ▸ M2 ▸ TC

Lesson 19 Use compensation to subtract.

540 - 90 = ?

550 10

540

550 - 100 = 450

10 90 100

?

800

1

799

800 - 258 = 542 -1 -1

1 257 258

7 9 9 - 257 = 542 ?

In a subtraction problem, I can add the same amount to both numbers or subtract the same amount from both numbers to make a problem that is simpler to subtract in my head.

Copyright © Great Minds PBC

EM2_0302TE_C_TO.indd 209

209

8/28/2021 11:55:01 AM

19

LESSON 19

Use compensation to subtract.

EUREKA MATH2

3 ▸ M2 ▸ TC ▸ Lesson 19

19

Name

Use a simplifying strategy to subtract.

1. 500 − 276 =

224

Lesson at a Glance Students use compensation as a strategy to subtract more efficiently.

Students intentionally select a subtraction strategy and explain their reasoning.

Key Questions

Sample:

• How does compensation help make it easier to subtract mentally?

500

1

• When is compensation a useful subtraction strategy?

500 – 276 =

499

1

–1

–1

499 – 275 = 224

275

Achievement Descriptor

?

276

3.Mod2.AD2 Add and subtract within 1,000 fluently using strategies based on place value, properties of operations, or the relationship between addition and subtraction. (3.NBT.A.2) 2. 400 − 198 =

202

Sample:

400 1 1

–1

–1

399 – 197 = 202

197 198

Copyright © Great Minds PBC

400 – 198 =

399

?

179

Copyright © Great Minds PBC

EM2_0302TE_C_L19.indd 302

8/28/2021 11:55:17 AM

EUREKA MATH2

3 ▸ M2

3.Mod2.AD2 Add and subtract within 1,000 fluently using strategies based on place value, properties of operations, or the relationship between addition and subtraction.

RELATED CCSSM

3.NBT.A.2 Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Partially Proficient

Proficient

Add and subtract within 1,000 fluently with no more than one instance of regrouping using a strategy based on place value, properties of operations, or the relationship between addition and subtraction.

Add and subtract within 1,000 fluently with two instances of regrouping using a strategy based on place value, properties of operations, or the relationship between addition and subtraction.

Add or subtract.

Add or subtract.

328 + 239 =

458 − 179 =

570 − 155 =

Highly Proficient Add and subtract within 1,000 fluently using multiple strategies.

Which of these show a correct way to find the unknown number in 500 = 197 + ?

Circle the two correct answers. −1

A.

500 499 +1 −197 −198

B.

500 +197

278 + 364 =

+3

+ 300

C. 197 200 500 D. 500 − 200 − 3 E.

418

EM2_0302TE_AD.indd 418

−1

500 499 −1 −197 −196

Copyright © Great Minds PBC

8/28/2021 11:47:05 AM

14

LESSON 14

Use place value understanding to add and subtract like units.

EUREKA MATH2

3 ▸ M2 ▸ TC ▸ Lesson 14

14

Name

Add or subtract. Show your strategy.

1. 251 + 533 =

784

Sample:

• How does place value help us add and subtract?

500 30 3 251

Students use place value understanding to add and subtract mentally. Unit form is used to support composing and decomposing like units. Students record and explain their thinking with models, including number bonds and the arrow way.

Key Questions

251 + 533

+ 500

Lesson at a Glance

+ 30

751

• How are models such as the number bond and the arrow way helpful in recording and explaining our thinking?

+3

781

784

Achievement Descriptor 2. 867 - 134 =

733

3.Mod2.AD2 Add and subtract within 1,000 fluently using strategies based on place value, properties of operations, or the relationship between addition and subtraction. (3.NBT.A.2)

Sample:

867 ‒ 134 100 30 4 ‒ 100

867

Copyright © Great Minds PBC

‒ 30

767

‒4

737

733

145

Copyright © Great Minds PBC

EM2_0302TE_C_L14.indd 226

8/28/2021 11:57:58 AM

17

LESSON 17

Use place value understanding to subtract efficiently using take from a ten.

EUREKA MATH2

3 ▸ M2 ▸ TC ▸ Lesson 17

17

Name

Use a simplifying strategy to subtract.

1. 493 − 68 =

Lesson at a Glance Students use the take from a ten strategy to subtract efficiently. They apply the strategy to two- and three-digit subtraction problems.

Key Questions

425

• How might the take from a ten strategy simplify a problem?

Sample:

493 – 68

• When is the take from a ten strategy useful?

423 70 70 – 68 = 2

Achievement Descriptor

423 + 2 = 425

3.Mod2.AD2 Add and subtract within 1,000 fluently using strategies

based on place value, properties of operations, or the relationship between addition and subtraction. (3.NBT.A.2) 2. 648 − 39 =

609

Sample:

648 – 39 608 40 40 – 39 = 1 608 + 1 = 609

Copyright © Great Minds PBC

167

Copyright © Great Minds PBC

EM2_0302TE_C_L17.indd 272

8/28/2021 11:56:08 AM

18

LESSON 18

Use place value understanding to subtract efficiently using take from a hundred.

EUREKA MATH2

3 ▸ M2 ▸ TC ▸ Lesson 18

18

Name

Use a simplifying strategy to subtract.

1. 460 − 99 =

361

Sample:

Lesson at a Glance Students build on their understanding of the take from a ten strategy to take from a hundred. They apply the strategy when subtracting from three-digit numbers when the subtrahend is close to a hundred.

Students describe when the strategy is useful.

Key Questions

460 – 99 360 100

• How can the take from a hundred strategy be used when subtracting from three-digit numbers?

100 – 99 = 1 360 + 1 = 361

• How is take from a hundred a useful strategy for some subtraction problems?

Achievement Descriptor 2. 543 − 297 =

3.Mod2.AD2 Add and subtract within 1,000 fluently using strategies

246

based on place value, properties of operations, or the relationship between addition and subtraction. (3.NBT.A.2)

Sample:

543 – 297 243 300 300 – 297 = 3 243 + 3 = 246

Copyright © Great Minds PBC

173

Copyright © Great Minds PBC

EM2_0302TE_C_L18.indd 288

8/28/2021 11:55:45 AM

19

LESSON 19

Use compensation to subtract.

EUREKA MATH2

3 ▸ M2 ▸ TC ▸ Lesson 19

19

Name

Use a simplifying strategy to subtract.

1. 500 − 276 =

224

Lesson at a Glance Students use compensation as a strategy to subtract more efficiently.

Students intentionally select a subtraction strategy and explain their reasoning.

Key Questions

Sample:

• How does compensation help make it easier to subtract mentally?

500

1

• When is compensation a useful subtraction strategy?

500 – 276 =

499

1

–1

–1

499 – 275 = 224

275

Achievement Descriptor

?

276

3.Mod2.AD2 Add and subtract within 1,000 fluently using strategies based on place value, properties of operations, or the relationship between addition and subtraction. (3.NBT.A.2) 2. 400 − 198 =

202

Sample:

400 1 1

–1

–1

399 – 197 = 202

197 198

Copyright © Great Minds PBC

400 – 198 =

399

?

179

Copyright © Great Minds PBC

EM2_0302TE_C_L19.indd 302

8/28/2021 11:55:17 AM

EUREKA MATH2

3 ▸ M2 ▸ TC ▸ Scoring Guide

Module 2 Topic C Quiz This assessment has five items. If you administer this assessment on paper, use this scoring guide and the answer key from the assessment book to score and grade each student’s assessment. No partial credit is given unless otherwise indicated in the notes.

Item Number

Achievement Descriptor

Proficiency Indicator

Raw Scale Possible × = Points Factor Points

Scoring Type

1

3.Mod2.AD2

PP

1

×

3

=

3

Polytomous

1 Each correct response is worth 1— points.

2

2

3.Mod2.AD6

P

1

×

2

=

2

Polytomous

1 Each correct response is worth — point.

2

3 Part A

3.Mod2.AD7

PP

1

×

3

=

3

Dichotomous

The correct response is worth 3 points.

3 Part B

3.Mod2.AD7

P

1

×

2

=

2

Dichotomous

The correct response is worth 2 points.

4 Part A

3.Mod2.AD2

HP

1

×

1

=

1

Dichotomous

Both correct responses must be identified to earn 1 point.

4 Part B

3.Mod2.AD2

P

1

×

2

=

2

Dichotomous

The correct response is worth 2 points.

5

3.Mod2.AD2

HP

1

×

1

=

1

Polytomous

1 Each correct response is worth — point.

3

Notes

To compute the adjusted score for each student, • divide a student’s total earned points by the total possible points (i.e., 14 total possible points for this Topic Quiz), • enter that result into the adjusted score converter on the digital platform, and • use the value from the adjusted score converter to determine a grade.

© 2021 Great Minds PBC

Shawn 400 + 300 + 10 + 60 + 9 + 4 700 + 783 524

70 + 13

700 + 83 628 – 100 – 4 528 – 4 = 524

35

45 20 15

150-90

60 120-60

303

5 850

350

Topic D Two- and Three-Digit Measurement Addition and Subtraction Topic D is devoted to using place value to model the standard algorithm for addition and the standard algorithm for subtraction with numbers within 1,000. Students use vertical form in conjunction with a place value model to allow them to better recognize like units and the value of numbers when they are not on the place value chart. Representations move from concrete to pictorial to abstract, and they serve to solidify the understanding of the composition and decomposition of units. Students learn that although standard algorithms work for all problems, there might be a more efficient strategy to use depending on the numbers being added or subtracted. Students apply learning from topic C to analyze addition and subtraction problems, many with a measurement context, and determine whether to use a simplifying strategy or the place value chart and standard algorithm for each.

Students begin the topic by using the place value chart and the standard algorithm for addition. They manipulate place value disks on a chart to represent the algorithm and record their work in vertical form. The concrete place value disks are then replaced with drawings on place value charts, where dots are used to represent the addends and the sum. Students bundle once and then twice and record the composition of new units vertically in different ways.

For subtraction, students manipulate place value disks on a chart before transitioning to drawing on the place value chart. Students get ready to subtract by checking each place value and unbundling as necessary before performing any subtractions. They record their work in vertical form with one and then two decompositions. Before subtracting, students estimate the answer by rounding the minuend and subtrahend and finding their difference.

After subtracting, students use their estimate to assess the reasonableness of their answer.

Students see that they can use addition to check their subtraction.

316

EM2_0302TE_D_TO.indd 316

Copyright © Great Minds PBC

8/28/2021 12:04:10 PM

EUREKA MATH2 3 ▸ M2 ▸ TD

Within the topic, students apply their computation skills to solve one-step addition and subtraction word problems involving measurement contexts. To conclude the topic, students solve two-step word problems involving all four operations.

In future lessons, fluency activities provide ongoing practice toward developing fluency with addition and subtraction strategies and algorithms. Use of the standard algorithms for addition and subtraction extends to numbers within 1,000,000 in grade 4 module 1 and to decimals in grade 5.

Copyright © Great Minds PBC

EM2_0302TE_D_TO.indd 317

317

8/28/2021 12:04:10 PM

EUREKA MATH2

3 ▸ M2 ▸ TD

Progression of Lessons Lesson 20

Lesson 21

Lesson 22

Add measurements using the standard algorithm to compose larger units once.

Add measurements using the standard algorithm to compose larger units twice.

Subtract measurements using the standard algorithm to decompose larger units once.

10

10

1

10

10

10

1

26 + 36 1 62

10

Place value disks help to show addition and to transition to the vertical form.

The standard algorithm is a process I can use to add like units. When I need to make a new unit, I record the new group on the line.

318

EM2_0302TE_D_TO.indd 318

566 + 347 = 913

100s

10s

100

1s

566 + 347

13 1 00 + 800 913

Instead of using actual place value disks, I can draw dots on a place value chart to represent the disks. When I need to make a new unit, there are different ways I can record it. New groups below shows the renaming on the line. Totals below shows the total for each place value below the addends.

100

100

100

100

10

10

10

10

10

10

1

1

1

100

7 12

10

10

10

825 _ 132

693

693 milliliters

Place value disks help me understand how to get ready to subtract, and they help me to see how one of a larger unit can be unbundled to ten of a smaller unit. When I subtract by using the standard algorithm, I show my work in vertical form. Estimating the answer helps me decide if my answer is reasonable.

Copyright © Great Minds PBC

8/28/2021 12:04:11 PM

EUREKA MATH2 3 ▸ M2 ▸ TD

Lesson 23

Lesson 24

Lesson 25

Subtract measurements using the standard algorithm to decompose larger units twice.

Subtract measurements using the standard algorithm to decompose larger units across two place values.

Solve two-step word problems.

100s

10s

1s

10 30 17

41 7 _ 228

189

Representing a subtraction problem by using dots on the place value chart helps me to see how to get ready to subtract. Sometimes I need to unbundle twice to be ready to subtract. I can see this on the place value chart and in vertical form. For some problems, another subtraction strategy is a better choice. After I subtract, I can check my answer by using addition.

Copyright © Great Minds PBC

EM2_0302TE_D_TO.indd 319

100s

10s

Apples

670 g ?

1s 9

7 1013

803 _ 58 7 216

When I need more ones and there are 0 tens, I need to unbundle twice to get enough ones. I can show that on the place value chart and in vertical form.

Cherries

?

434 g

670 – 434 = 669 – 433 = 236

Eva’s cherries weigh 236 grams.

670 + 236 = 906 30 206 670 + 30 = 700

700 + 206 = 906

Eva’s cherries and apples weigh a total of 906 grams.

There are many ways to show my thinking and solve two-step word problems. I choose the way that makes sense to me. I can draw tape diagrams to represent the problems.

They help me see what operations I should use to solve the problems. It is important to check each step to see if my answer is reasonable as I work.

319

8/28/2021 12:04:12 PM

Supplemental Materials

Assess: Embedded Opportunities to Inform Instruction, 3–5

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.

© Great Minds PBC

20