Change Number Stories - Everyday Math - Login and Solving Change Number Stories Math Journal 1, p....

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Lesson 2�5 123

Advance Preparation

Teacher’s Reference Manual, Grades 1–3 pp. 84–89

Key Concepts and Skills• Use basic facts to solve extended fact

problems.

[Operations and Computation Goal 1]

• Use and explain strategies to solve

addition and subtraction number stories.


• Solve change-to-more and change-to-less

multidigit addition and subtraction number

stories using change diagrams.


• Write number models for addition and

subtraction number stories.

[Patterns, Functions, and Algebra Goal 2]

Key ActivitiesChildren review the Guide to Solving Number

Stories and use change diagrams to solve

change-to-more and change-to-less

number stories.

Ongoing Assessment: Informing Instruction See page 127.

Key Vocabularychange diagram � change-to-more number

story � deposit � change-to-less number

story � withdraw � trade-first algorithm

MaterialsMath Journal 1, pp. 39 and 40

Home Link 2�4

Math Masters, pp. 406 and 409

transparency of Math Masters, p. 409

(optional) � Number-Grid Poster or Class

Number Line � calculator (optional)

Playing Number-Grid Difference Student Reference Book, p. 301


per partnership: 4 each of number

cards 0–9 (from the Everything

Math Deck, if available), calculator,

counters

Children practice finding differences

on the number grid.

Math Boxes 2�5Math Journal 1, p. 41

Children practice and maintain skills

through Math Box problems.

Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 3. [Number and Numeration Goal 1]

Home Link 2�5Math Masters, p. 46

Children practice and maintain skills

through Home Link activities.

READINESS

Changing the Calculator DisplayMath Masters, pp. 21, 45, and 47

transparency of Math Masters, p. 45

(optional) � calculator

Children complete calculator puzzles.

ENRICHMENTWriting and Solving Change Number StoriesMath Journal 1, p. 40


Student Reference Book, pp. 212 and 213

Children make up and solve change

number stories.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

Change Number StoriesObjective To guide children as they use change diagrams to

help solve change number stories.

��

eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

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124 Unit 2 Adding and Subtracting Whole Numbers

1 Teaching the Lesson

� Math Message Follow-Up WHOLE-CLASSDISCUSSION

Have children tell which label they put in the unit box. dollars or $ Invite them to share the strategies they used to solve the Math Message problem.

� Solving a Change-to-More WHOLE-CLASSDISCUSSION

Number Story(Math Masters, pp. 406 and 409)

Algebraic Thinking Refer to the Guide for Solving Number Stories as you work through the steps in the problem-solving process for the Math Message story. Be sure that children know the meaning of deposit.

1. What do you understand from the Math Message story?

● Think. What do you want to find out? The new amount of money in Madeline’s account

● What do you know from reading the story? Madeline had $38 in her bank account and she deposited $15 more.

2. What will you do?

● What do you have to do to find the new amount of money in Madeline’s account? Add 38 and 15

● What kind of number story is this? If no one mentions it, remind children about change-to-more number stories from second grade. Display a change diagram. To support English language learners, consider creating a change diagram poster similar to the parts-and-total diagram poster in the Part 3 activity in Lesson 2-4.

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Getting Started

Math Message Madeline had $38 in her bank

account. She deposited another

$15. How much money was in her

account then? $53

Home Link 2�4 Follow-Up Review the answers. Have children discuss the strategies they used to solve the parts-and-total number stories.

Mental Math and ReflexesPose questions like the following. Consider demonstrating the answers on the Number-Grid Poster or Class Number Line.

Is 18 closer to 10 or 20? 20

Is 21 closer to 20 or 30? 20

Is 188 closer to 180 or 190? 190

Is 105 closer to 100 or 110? Same distance away

Is 450 closer to 400 or 500? Same distance away

Is 2,777 closer to 2,770 or 2,780? 2,780

Change Diagrams

Name Date Time

Start EndChange

Start EndChange

Start EndChange

Math Masters, p. 409

Teaching Aid Master

StartChange

End

38 +15 ?

Unit

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● Write a question mark in the End box to represent what you want to find out. Point out that the total amount of money in Madeline’s bank account changed to more. Write 38 in the Start box and +15 on the Change line.

● Have volunteers write number models for the story on the board (See margin.)

3. Answer the question. Madeline now has $53 in her account. Have children share their solution strategies. Some children may have used mental computation to find the sum.

Possible Solution Strategies

� First add the tens: 30 + 10 = 40. Then add the ones: 8 + 5 = 13. Finally, add the two parts: 40 + 13 = 53.

� Add the second addend to the first addend in parts (tens and ones): 38 + 10 = 48; 48 + 5 = 53.

� Add the first addend to the second addend in parts (tens and ones): 15 + 30 = 45; 45 + 8 = 53.

� Take 2 from 15, leaving 13. Add the 2 to the 38 to get 40. 40 is an easy number to work with. Add 13 to 40: 40 + 13 = 53.

4. Check. Does your answer make sense? How do you know?

● Go back to the question in the number story. Have you answered it? yes How do you know your answer is reasonable? The total amount of money should be more because Madeline added money to her account.

● Does your answer make the number model true? yes Write a summary number model on the board: 38 + 15 = 53.

� Solving a Change-to-Less WHOLE-CLASS ACTIVITY

Number Story

Algebraic Thinking Pose the following number story: José had $76 in his bank account. He withdrew $29. How much money was in his bank account then? Be sure children know the meaning of the words withdraw and withdrew. Write the words on the board to support English language learners.

Guide children through the problem-solving steps:

1. What do you understand from the story?

● What do you want to find out? The new amount of money in Jose’s bank account

● What do you know from listening to the story? Jose had $76 in his bank account. He withdrew $29.


● What could you do to find out how much money Jose has in the bank? Sample answer: Subtract 29 from 76.

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Lesson 2�5 125

StartChange

End

76 -29 ?

NOTE Lesson commentaries often include

examples of solution strategies. This does not

mean that children must be comfortable with

all the strategies. Children benefit from

hearing strategies that others have used.

Help children choose a strategy that works

for them.

Possible number models:38 + 15 = ? 3815 + 38 = ? + 15 ?



● What kind of a number story is this? change-to-lessnumber story Display a change diagram. Write a question mark in the End box to represent what we want to find out. Point out that the total amount of money in José’s bank account changed to less. Write 76 in the Start box and –29 on the Change line.

● Have volunteers write number models for the story on the board.

Possible number models

76 - 29 = ? 76 29

29 + ? = 76 - 29 + ? ? 76

3. Answer the question. $47 is now in the bank account. Have children share their solution strategies.


� Some children may remember and use the trade-first algorithm from second grade. They may ask themselves: “Are there enough tens and ones in 76 so that I can subtract 2 tens and 9 ones? No, there aren’t enough ones, so I need to trade a ten for more ones.”

� Other children may try counting up: “What number added to 29 will give me 76? If I add 1 to 29, I’m at 30, which is an easy number to work with. 30 + 46 = 76, and 1 + 46 = 47.”

� Others may try counting up and then backing out the extra. For example, “I’ll try adding 50 to 29 because 50 is an easy number to work with. 50 + 29 = 79. 79 is 3 more than 76, so 50 is 3 more than I should have added. 50 - 3 = 47.”

4. Check. Does your answer make sense? How do you know?

� Go back to the question in the number story. Have you answered it reasonably? yes How do you know? The amount of money at the end should be less than the original amount because money was taken out.

� Does your answer make the number model true? yes Write a summary number model on the board: 76 - 29 = 47.

� Solving Change PARTNER ACTIVITY

Number Stories(Math Journal 1, pp. 39 and 40)

Algebraic Thinking Partners work on the two journal pages. Ask guiding questions like the ones modeled in the previous sections. Because English language learners may not be familiar with the piggy bank context, clarify what a piggy bank is. Then bring the class together and share solution strategies. As children share ideas, fill in the change diagram that you have displayed.

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Date Time

For each number story, write ? in the change diagram for the number

you want to find. Then write the numbers you know in the diagram. Next,

write a number model. Finally, solve the problem and write the answer.

1. Ahmed had $22 in his bank account. For his

birthday, his grandmother deposited $25 for him.

How much money is in his bank account now?

Number model: 22 + 25 = ?

Answer the question: $47

Check: How do you know your answer makes sense?

Sample answer: The end number has to be greater

2. Omar had $53 in his piggy bank. He used $16

to take his sister to the movies and buy treats.

How much money is left in his piggy bank?

Number model: 53 − 16 = ?



Sample answer: The answer has to be less than $53.

3. Cleo had $37 in her purse. Then Jillian returned

$9 that she borrowed. How much money does

Cleo have now?

Number model: 37 + 9 = ?



Sample answer: It’s more than $37, since $9 was added.

Start EndChange

?+2522

Number Stories: Change-to-More and Change-to-LessLESSON

2�5

Start EndChange

?53 −16

Start EndChange

?+937

than the start and change numbers.

Unit

254 255

dollars

or 16 + ? = 53

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Math Journal 1, p. 39

Student Page

Links to the FutureThe counting-up and trade-first methods for

subtraction will be reviewed in Lesson 2-8.

LESSON

2�5

Date Time

40

4. Audrey had $61 in her bank account. She

withdrew $48 to take on vacation. How much

is left in her account?


Answer the question: $13 Check: How do you know your answer makes sense?

Sample answer: Audrey has $13 left from $61

5. Trung had $15 in his piggy bank. After his

birthday, he had $60 in his bank. How much

money did Trung get as birthday presents?

Number model: 15 + ? = 60


Sample answer: The answer has to be more than 15

6. Nikhil had $40 in his wallet when he went to the

carnival. When he got home, he had $18. How

much did he spend at the carnival?



Sample answer: Nikhil spent a little more than

1

_ 2

of

Start EndChange

?

Number Stories continued

−4861

Start EndChange

60?15

Start EndChange

? 1840

because she withdrew $48.

and less than 60.

his money. $22 is about right.

Try This

or 48 + ? = 61

or 60 − 15 = ?

or 18 + ? = 40

EM3MJ1_G3_U02_30-54.indd 40 12/29/10 4:35 PM


Student Page

NOTE Some children may need to act out

their solution strategies. Make sure the

Number-Grid Poster or Class Number Line is

available to them.

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Lesson 2�5 127

t


Problem 1: Use partial sums.

Problem 2: Take 10 away from 53 to get 43. Then count back 6 more to get 37.

Problem 3: Use complements of 10. Think of 9 as 3 + 6. Add 3 to 37. 37 + 3 = 40. Then add the rest. 40 + 6 = 46.

Problem 4: Use the counting-up method. Count up from 48 to 61.

For each Try This problem, the Start and End amounts are known; the Change is not known. Children may find it helpful to ask themselves, “Did the Start amount go up or down? If it changed to more, something was added. If it changed to less, something was subtracted.”

Problem 5: Which number, added to 15, will give me 60?

Problem 6: Counting up from 18 takes how much to get to 40? From 18 to 20 is 2. Then from 20 to 40 is 20. 20 + 2 = 22.

2 Ongoing Learning & Practice

� Playing Number-Grid Difference PARTNER ACTIVITY

(Student Reference Book, p. 301;

Math Masters, pp. 21 and 452)

Children practice finding differences on the number grid by playing Number-Grid Difference. For detailed instructions, see Lesson 1-8 or page 301 in the Student Reference Book. Children may record several rounds on Math Masters, page 452 or on a half-sheet of paper.

� Math Boxes 2�5 INDEPENDENTACTIVITY

(Math Journal 1, p. 41)

Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons 2-7 and 2-9. The skill in Problem 6 previews Unit 3 content.

Ongoing Assessment: Math Boxes

Problem 3 �Recognizing Student Achievement

Use Math Boxes, Problem 3 to assess children’s ability to express the value of

digits in a given number. Children are making adequate progress if they are able

to complete the problem correctly. Some children may be able to identify the

value of digits in larger numbers.

[Number and Numeration Goal 1]

Date Time

5. Lily had 33 rings in one box and 29in another. How many did she havein all?

rings62

3. 2,345

the 2 means

the 3 means

the 4 means

the 5 means 540300

2,000

2. “What’s My Rule?”

4. Write 5 names in the 120-box.

6. How many squares are shaded?Fill in the oval for the best answer.

12 7 9 5

1. Use addition or subtraction tocomplete these problems on yourcalculator.Enter Change to How?

366 66

894 2,894

3,775 3,175

27,581 28,581 �1,000�600�2,000�300

18, 19,264 203 204

256 257

Rule

out

in

Add 4

14 1518 19

?

33 29

Math BoxesLESSON

2�5

in out

10 1421 2532 3656 60

Answers vary.

Sample answers:60 � 60 1,120 � 1,000125 � 5 10 � 12one hundred twenty

120�


Student Page

Ongoing Assessment: Informing Instruction

Watch for children who are having difficulty

solving the Try This problems. Remind

them of the calculator problems they solved

in Lesson 2-2. For example, think of

$15 + = $60 as follows: Enter 15 into

the calculator. Add or subtract a number so

the calculator displays 60. What will you

do? Add 45.

NOTE There is not necessarily one kind of

diagram that goes with a given problem. The

best diagram for a child to use depends on

the way the child thinks about the problem.

Initially, diagrams are provided to expose

children to the different ways of modeling a

problem so that they will begin to develop

resources to use for solving problems.



� Home Link 2�5 INDEPENDENTACTIVITY

(Math Masters, p. 46)

Home Connection Children use change diagrams to solve change-to-more and change-to-less number stories. Because change diagrams might not be familiar to

parents, you may want to send home the Student Reference Book.

3 Differentiation Options

READINESS PARTNER ACTIVITY

� Changing the Calculator Display 5–15 Min

(Math Masters, pp. 21, 45, and 47)

Algebraic Thinking To explore number stories involving a change to more or a change to less, have children complete the calculator puzzles on Math Masters, page 47. Children use a number grid to help them figure out the answers. They should check their answers on calculators. When children have finished the page, briefly discuss how they solved the problems.

If you have children do this activity prior to the lesson, consider making a transparency of Math Masters, page 45 and using the number sentences from Math Masters, page 47 to demonstrate a change diagram. (See the example for Problem 1 in the margin.)

ENRICHMENT PARTNER ACTIVITY

� Writing and Solving Change 15–30 Min

Number Stories(Math Journal 1, p. 40; Math Masters, pp. 45 and 407;

Student Reference Book, pp. 212 and 213)

Algebraic Thinking To apply children’s understanding of change-to-more and change-to-less number stories, have them write their own number stories in which the Start and End numbers are known, but the Change is not given. (See Problems 5 and 6 on journal page 40 for sample problems.) Children can use information from the Vending Machine Posters on pages 212 and 213 in the Student Reference Book. You may wish to compile the number stories into a class book.

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2�5

Name Date Time

Changing the Calculator Display

Solve the calculator problems. Use a number grid to help. Check youranswers on a calculator. Write a number model to show what you did.

Example:

How can you change 24 to 35?

Number model:

1. How can you change 18 to 38?

Number model:


Number model:


Number model:


Number model:


Number model: 100 � 38 � 62

Subtract 3897 � 52 � 45

Subtract 5221 � 42 � 63

Add 4230 � 50 � 80

Add 5018 � 20 � 38

Add 2024 � 11 � 35

Add 11

Math Masters, p. 47

Teaching Master


you want to find. Write the numbers you know in the diagram. Then,

write a number model and the answer. Finally, write how you know that

each answer makes sense.

1. Marcus had $25 in his wallet. He spent

$16 at the store. How much money was in

Marcus’s wallet then?

Number model: 25 - 16 = ?

Answer the question: $9 (unit)


2. Jasmine had $35. She earned $14 helping

her neighbors. How much money did she

have then?

Number model:

Answer the question: $49 (unit)


than $35 since Jasmine earned $14 more.Sample answer: The answer has to be more

35 + 14 = ?

Name Date Time

Change Number StoriesHOME LINK

2�5

Today your child learned about another diagram that helps organize the information in a number story. It is called a change diagram. For more information, see pages 254 and 255 in the Student Reference Book.

Please return this Home Link to school tomorrow.

Family Note

254 255

Start EndChange

25 -16 ?

Sample answer: Marcus spent $16 so the answer has to be less than $25.

Start EndChange

35 +14 ?

or 16 + ? = 25

EM3MM_G3_U02_036-063.indd 46 11/9/10 9:37 AM

Math Masters, p. 46

Home Link Master

StartChange

End

18 +20 38



you want to find. Write the numbers you know in the diagram. Then,

write a number model and the answer. Finally, write how you know that

each answer makes sense.

1. Marcus had $25 in his wallet. He spent

$16 at the store. How much money was in

Marcus’s wallet then?

Number model:

Answer the question: (unit)


2. Jasmine had $35. She earned $14 helping

her neighbors. How much money did she

have then?

Number model:

Answer the question: (unit)


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Name Date Time

Change Number StoriesHOME LINK

2�5

Today your child learned about another diagram that helps organize the information in a number story. It is called a change diagram. For more information, see pages 254 and 255 in the Student Reference Book.

Please return this Home Link to school tomorrow.

Family Note

254 255

46

Start EndChange

Start EndChange

EM3MM_G3_U02_036-063.indd 46EM3MM_G3_U02_036-063.indd 46 11/9/10 9:37 AM11/9/10 9:37 AM

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406

Guide to Solving Number Stories

Name Date Time

1. What do you understand from the story?

� Read the story. What do you want to find out?

� What do you know?


� Add?

� Subtract?

� Multiply?

� Divide?

� Draw a picture?

� Make tallies?

� Use counters or base-10 blocks?

� Use a number grid or number line?

� Make a table?

� Draw a diagram?

� Write a number model?

3. Answer the question.

� Solve the problem. Record your work.

� Write the answer with the units.

4. Check.

� Does your answer make sense? How do you know?

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Change Number Stories - Everyday Math - Login and Solving Change Number Stories Math Journal 1, p....

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Transcript of Change Number Stories - Everyday Math - Login and Solving Change Number Stories Math Journal 1, p....