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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.
[Operations and Computation Goal 2]
• Solve change-to-more and change-to-less
multidigit addition and subtraction number
stories using change diagrams.
[Operations and Computation Goal 6]
• 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
Math Masters, pp. 21 and 452
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
Math Masters, pp. 45 and 407
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.
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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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ELL
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.
2. What will you do?
● 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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ELL
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 ?
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126 Unit 2 Adding and Subtracting Whole Numbers
● 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.
Possible 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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ELL
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 = ?
Answer the question: $37
Check: How do you know your answer makes sense?
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 = ?
Answer the question: $46
Check: How do you know your answer makes sense?
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
EM3MJ1_G3_U02_30-54.indd 39 12/29/10 4:35 PM
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?
Number model: 61 − 48 = ?
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
Answer the question: $45 Check: How do you know your answer makes sense?
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?
Number model: 40 − 18 = ?
Answer the question: $22 Check: How do you know your answer makes sense?
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
Math Journal 1, p. 40
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
Possible Solution Strategies
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�
Math Journal 1, p. 41
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.
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128 Unit 2 Adding and Subtracting Whole Numbers
� 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:
2. How can you change 30 to 80?
Number model:
3. How can you change 21 to 63?
Number model:
4. How can you change 97 to 45?
Number model:
5. How can you change 100 to 62?
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
For each number story, write ? in the change diagram for the number
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)
Check: How do you know your answer makes sense?
2. Jasmine had $35. She earned $14 helping
her neighbors. How much money did she
have then?
Number model:
Answer the question: $49 (unit)
Check: How do you know your answer makes sense?
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
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For each number story, write ? in the change diagram for the number
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)
Check: How do you know your answer makes sense?
2. Jasmine had $35. She earned $14 helping
her neighbors. How much money did she
have then?
Number model:
Answer the question: (unit)
Check: How do you know your answer makes sense?
Copyrig
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Wrig
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raw
-Hill
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
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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?
2. What will you do?
� 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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