Subtraction Strategies...Math Masters, pp. 418 and 463 My Reference Book, pp. 140 and 141 per...

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Interactive Teacher’s

Lesson Guide

CurriculumFocal Points

Family Letters

EM Facts Workshop Game™

Algorithms Practice

eToolkitePresentations AssessmentManagement

Common Core State Standards

Lesson 6�5 401

Advance Preparation

Teacher’s Reference Manual, Grades 1–3 p. 106

�� Subtraction StrategiesObjective To review solution strategies for subtraction of

multidigit numbers.

Key Concepts and Skills• Count up and back by 1s and 10s.

[Number and Numeration Goal 1]

• Model multidigit numbers using base-10

blocks.

[Number and Numeration Goal 2]

• Develop counting up and back strategies

for subtraction.

[Operations and Computation Goal 2]

• Use and explain strategies for solving

multidigit subtraction problems.

[Operations and Computation Goal 2]

Key ActivitiesChildren solve multidigit subtraction problems

using a variety of strategies.

Ongoing Assessment: Informing Instruction See page 402.

Key Vocabularytrade (a base-10 long for 10 cubes)

MaterialsMath Journal 1, p. 144

Home Link 6�4

base-10 blocks per partnership: 6 longs,

30 cubes � overhead base-10 blocks

(optional): 6 longs and 18 cubes � number

grid � pennies or other counters (optional) �

play money (optional)

Playing the Number-Grid Difference GameMath Masters, pp. 418 and 463

My Reference Book, pp. 140 and 141

per partnership: 4 each of number

cards 0–9 (from the Everything Math

Deck, if available), number grid,

calculator, 2 pennies or counters

Children use the number grid to find

the difference between 2-digit numbers.

Math Boxes 6�5Math Journal 1, p. 145

Children practice and maintain skills

through Math Box problems.

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

Home Link 6�5Math Masters, pp. 169 and 170

Children practice and maintain skills

through Home Link activities.

READINESS

Playing the Base-10 Trading GameMath Masters, p. 427

base-10 blocks (2 flats, 20 longs,

40 cubes) � 2 dice

Children practice subtraction using a

concrete model.

ENRICHMENTAnalyzing a Subtraction StrategyMath Masters, p. 171

Children apply their understanding of

subtraction by analyzing and explaining a

subtraction strategy.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

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402 Unit 6 Whole-Number Operations and Number Stories

1 Teaching the Lesson

Number Grid

201918171615141211

1 2 3 4 5 6 7 8 9 10

13

302928272625242221 23

403938373635343231 33

504948474645444241 43

605958575655545251 53

706968676665646261 63

807978777675747271 73

908988878685848281 83

1009998979695949291 93

110109108107106105104102101 103

Open Number Line

+ 2+ 10 + 10 + 10

24 34 44 54 56

� Math Message Follow-Up WHOLE-CLASS ACTIVITY

Have children share their solution strategies. For each problem, record on the board any strategies that result in the correct answer. Emphasize that there are many good ways to get correct answers to problems.

You or the children might suggest the following strategies:

Strategy 1

Counting Up: Start with the smaller number, 24. Model on a number grid or by quickly sketching an open number line on the board. (See margin.) Count up by ones, or 10s and ones. 34, 44, 54, 55, 56; 56 - 24 = 32

Ongoing Assessment: Informing Instruction

Watch for children who use the counting up strategy but include the 24 in their

counts. For example, 24 (1), 25 (2), 26 (3), 27 (4)… + 56 (33). This will yield an

almost correct answer. This situation might be used to spark a discussion: “Mahli

has 33, but Harry has 32. Who’s right? How did Mahli get 33? How did Harry get

32?” You might also provide a penny for the children to count each move or jump.

Strategy 2

Counting Back: Start with the bigger number, 56. Model on a number grid or by quickly sketching an open number line on the board. Count back to 24 by ones, or 10s and 1s. 46, 36, 26, 25, 24

Strategy 3

Money: Think of $56 dollars. Subtract $20 and then subtract $4.

Strategy 4

Manipulatives: Use manipulatives to act out the problem. Start with 56 pennies and take away 24 pennies.

Getting Started

Home Link 6�4 Follow-Up Invite several children to share their stories with the class. Collect children’s stories to use when you need a quick “sponge” or filler activity or for use during future Mental Math and Reflexes sessions.

Mental Math and Reflexes Pose subtraction problems that feature multiples of 10. Suggestions:

48 - 10 = ? 38 63 - 30 = ? 33 195 - 80 = ? 115

72 - 10 = ? 62 72 - 50 = ? 22 152 - 20 = ? 132

? = 48 - 20 28 ? = 72 - 20 52 ? = 295 - 60 235

Math Message Solve the problem. Try to find the answer in two different ways. Be ready to explain how you found the answer. 56 - 24 = ? 32

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Adjusting the Activity

Lesson 6�5 403

}

Take away

1 long and 4 cubes.

2 longs and 2 cubes

are left.

36- 14

22

If no one suggests it, point out that they may use base-10 blocks to solve 2-digit subtraction problems as well.

Use play money to illustrate Strategy 3. Put five $10 bills and six $1 bills

in one stack. Take out two $10 bills and four $1 bills.

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L

NOTE Everyday Mathematics students solve subtraction problems using many

different strategies even though they have not been introduced to a standard

algorithm. These experiences help children understand the concept and prepare

them for more formal work with subtraction algorithms in Unit 11. If children

suggest a standard paper-and-pencil algorithm, record it on the board, but do not

take the time to teach it. Formal subtraction methods are addressed in Unit 11.

� Using Base-10 Blocks to WHOLE-CLASS ACTIVITY

Model SubtractionWrite the following problem on the board:

36- 14

Ask partners to represent the top number (the minuend) with the least number of blocks. Then ask them to subtract the bottom number (the subtrahend) by removing the correct combination of blocks.

Invite children to demonstrate and explain what they did. Have the class gather around a table as children demonstrate with actual blocks. You might want to use base-10 blocks for the overhead if you have them. Refer to the longs alternately as longs and as 10s; refer to the cubes alternately as cubes and as 1s.

Example: Model 36 - 14 = ? as follows:

1. Count out three longs and six cubes to represent 36. Lay these on the table, with the longs to the left of the cubes.

2. Ask: Are there enough longs and cubes on the table so I can remove 14 (1 long and 4 cubes)? yes

3. Remove 1 long and 4 cubes.

4. Count the remaining blocks and record the answer (the difference) on the board. 22

ELL

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SubtractionLESSON

6 � 5

Date Time

Use base-10 blocks to help you subtract.

1. 2.

3. 4.

Use any strategy to solve.

5. 6.

7. 8.

Longs Cubes

1 9 - 1 7

Longs Cubes

2 5 - 1 4

Longs Cubes

4 3 - 1 8

Flats Longs Cubes

1 3 6 - 4 7

14- 16

38- 23

124- 26

164- 126

1 2

2 5 8 9

1 1

8 15

3898

EM3MJ1_G2_U06_131_158.indd 144 1/29/11 10:57 AM

Math Journal 1, p. 144

Student Page

Write the following problem on the board:

53- 38

Ask partners to represent the top number (the minuend) with the fewest blocks. Then ask them to subtract the bottom number (the subtrahend) in any way they can.

Children cannot solve these problems by simply removing some of the blocks shown. Invite them to come up with strategies. For example:

� Subtract 38 in two stages. First, remove 3 longs and 3 cubes, leaving 2 longs. Then cover up 5 cubes on one of the longs. That leaves one long (10 cubes), plus 5 cubes showing on the second long, for a total of 15.

� Trade one of the longs for 10 separate cubes so 53 is represented by 4 longs and 13 cubes. Then remove 8 cubes and 3 longs, leaving 1 long and 5 cubes, or 15. To support English language learners, discuss the everyday meaning of trade as well as its meaning in this context.

Have the class gather around a table as children demonstrate with actual blocks. You might want to use base-10 blocks for the overhead if you have them.

Show 53

Trade a long for 10 cubes.

Take 38 away.

Example: Model 53 - 38 = ? as follows:

1. Count out five 10s and three 1s to represent 53. Lay these on the table, with longs to the left of the cubes.

2. Ask: Are there enough longs and cubes on the table so I can remove exactly 38 (3 longs and 8 cubes)? No. There are only 3 cubes on the table, so it’s not possible to remove 8 cubes.

3. Trade a long for cubes: Remove one of the longs that is usedto represent 53 and replace it with 10 cubes. 53 is now represented by 4 longs and 13 cubes.

4. Remove 38 (3 longs and 8 cubes) from the table.

5. Record the answer (difference) on the board. 15

Repeat the steps as needed. Model problems that involve 2- and 3-digit numbers.

� Solving Subtraction Problems PARTNER ACTIVITY

(Math Journal 1, p. 144)

Partners work together to solve the subtraction problems.

For Problems 1–4, children are expected to continue using base-10 blocks; many will actually trade 1 long for 10 cubes. Some children might simply move one of the longs next to the pile of cubes and answer the problem without actually exchanging the long for cubes.


Lesson 6�5 405

Name Date Time

In this lesson, your child found the answers to subtraction problemsby using longs and cubes to represent tens and ones, respectively.

This will help your child understand the concept of subtractionbefore he or she learns to subtract using a step-by-step procedure,or algorithm, with paper and pencil. When you see the problemson this Home Link, you may be eager to teach your child tosubtract the way you were taught. Please wait—the introductionof a formal algorithm for subtraction will be taught later insecond grade.

Please return this Home Link to school tomorrow.

HOME LINK

6�5 Subtracting with Base-10 Blocks

Show subtraction by crossing out cubes.

Example:

How many cubes are shown as separate cubes and as part of the longs?

Cross out (subtract) 23 cubes. How many cubes are left?

Number model:� � 192342

19

42

1.

How many cubes are shown in all?


Number model: � � 411758

41

58

long cube31

FamilyNote

Math Masters, p. 169

Home Link Master

Math BoxesLESSON

6 � 5

Date Time

1. Circle the one that is likely tohappen.

It is likely that...

you will do a Math Box today.

you will fly like a bird.

an elephant will visit the classroom.

3. Kurtis scored 13 points in thefirst half of the game and a totalof 24 points by the end. Howmany points did Kurtis score inthe second half? points 11

6. Use your calculator. Count by9s. Start at 76.

76, , , ,

,

What pattern do you see?

1211121039485

2. Measure the line segment.

about in.

about cm 52

4. How many dots are in this 7-by-9 array?63

5. Which number occurs mostoften? Choose the best answer.

8, 17, 9, 8, 10

9

17

10

8

24

13 11

�

Number model:

13 � 11 � 24 or 24 � 13 � 11

the ones place goes down by one. Sample answer: The number in

Math Journal 1, p. 145

Student Page

Name Date Time

HOME LINK

6�5 Subtracting with Blocks continued

2.




8

26 How many cubes are shown in all?



18

43




7

39 How many cubes are shown in all?



14

61

3.

5.4.


Home Link Master

Ongoing Assessment: Recognizing Student Achievement

Math Boxes

Problem 1 �Use Math Boxes, Problem 1 to assess

children’s knowledge of probability language.

Children are making adequate progress if

they circle the correct answer.

[Data and Chance Goal 3]

2 Ongoing Learning & Practice

� Playing the Number-Grid PARTNER ACTIVITY

Difference Game(Math Masters, pp. 418 and 463; My Reference Book,

pp. 140 and 141)

Children practice subtraction skills by playing the Number-Grid Difference Game. Children will find directions on page 140 of My Reference Book.

� Math Boxes 6�5 INDEPENDENTACTIVITY

(Math Journal 1, p. 145)

Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons 6-1 and 6-3. The skills in Problems 5 and 6 preview Unit 7 content.

� Home Link 6�5 INDEPENDENTACTIVITY

(Math Masters, pp. 169 and 170)

Home Connection Children subtract by crossing out cubes. Before sending this Home Link with the children, go over the example and make sure they understand that each long shows 10 connected cubes.



3 Differentiation Options

READINESS

PARTNER ACTIVITY

� Playing the Base-10 15–30 Min

Trading Game(Math Masters, p. 427)

To provide experience with subtraction using a concrete model, have children play the Base-10 Trading Game.

Begin with a bank that has 20 longs and 40 cubes. Each partner begins with 1 flat on their Place-Value Mat.

Rules:

Take turns. On each turn, a player does the following:

1. Roll the dice and find the sum of the dice.

2. Return that number of cubes to the bank. (When there are not enough individual cubes, make exchanges.)

3. The player not rolling the dice checks on the accuracy of the transactions.

4. The first player to clear their Place-Value Mat wins the game.

ENRICHMENT SMALL-GROUP ACTIVITY

� Analyzing a Subtraction 15–30 Min

Strategy(Math Masters, p. 171)

To apply children’s understanding of subtraction, have them analyze a subtraction strategy. When children have figured out the strategy and applied it to solving a new problem, have volunteers share explanations of the strategy and how they figured it out. Sample answer: “I noticed a pattern—that in the first step, only the tens place changed. Then I figured out you add back the difference between your second number and a multiple of ten.”

Ask: What is easy about Meredith’s strategy? Sample answer: You always subtract a multiple of 10 and then add some back on.

Ask: What is hard about Meredith’s strategy? Sample answer: Sometimes it’s hard to remember what to add back on.

Name Date Time

Place-Value Mat

hund

reds

tens

ones


Teaching Aid Master

Meredith uses an interesting strategy for solving subtractionproblems when you have to trade. Try to figure out how it works.

42 � 27

On my first step, I get 12.

On my second step I get 15.

15 is my final answer.

34 � 19

On my first step, I get 14.

On my second step I get 15.

15 is my final answer.

71 � 36

First Step:

Second Step:

Final Answer:

93 � 48

First Step:

Second Step:

Final Step: 4545

43

3535

31

LESSON

6�5

Name Date Time

A Subtraction Strategy

Try This


Teaching Master


Subtraction Strategies...Math Masters, pp. 418 and 463 My Reference Book, pp. 140 and 141 per...

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