Subtraction Strategies
Objective To review solution strategies for subtraction of
multidigit numbers.
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Teaching the Lesson
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 Activities
Children solve multidigit subtraction problems
using a variety of strategies.
Ongoing Assessment:
Informing Instruction See page 402.
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
1 2
4 3
Playing the Number-Grid
Difference Game
Math 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 5
Math Journal 1, p. 145
Children practice and maintain skills
through Math Box problems.
Differentiation Options
READINESS
Playing the Base-10 Trading Game
Math Masters, p. 427
base-10 blocks (2 flats, 20 longs,
40 cubes) 2 dice
Children practice subtraction using a
concrete model.
ENRICHMENT
Analyzing a Subtraction Strategy
Math Masters, p. 171
Children apply their understanding of
subtraction by analyzing and explaining a
subtraction strategy.
Use Math Boxes, Problem 1. [Data and Chance Goal 3]
Home Link 6 5
trade (a base-10 long for 10 cubes)
Math Masters, pp. 169 and 170
Children practice and maintain skills
through Home Link activities.
Math Journal 1, p. 144
Home Link 64
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)
Interactive
Teacher’s
Lesson Guide
Ongoing Assessment:
Recognizing Student Achievement
Key Vocabulary
Materials
Curriculum
Focal Points
Advance Preparation
Teacher’s Reference Manual, Grades 1–3 p. 106
Lesson 6 5
401
Mathematical Practices
SMP1, SMP2, SMP3, SMP4, SMP5, SMP6
Content Standards
Getting Started
2.NBT.2, 2.NBT.5, 2.NBT.7, 2.NBT.9, 2.MD.6
Mental Math and Reflexes
Home Link 6 4 Follow-Up
Pose subtraction problems that feature multiples of 10.
Suggestions:
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.
48 - 10 = ? 38
72 - 10 = ? 62
? = 48 - 20 28
63 - 30 = ? 33
72 - 50 = ? 22
? = 72 - 20 52
195 - 80 = ? 115
152 - 20 = ? 132
? = 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
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
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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.
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34
35
36
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40
You or the children might suggest the following strategies:
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50
Strategy 1
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53
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56
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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
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Ongoing Assessment: Informing Instruction
101 102 103 104 105 106 107 108 109 110
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.
Number Grid
+ 10
24
+ 10
34
+ 10
44
Open Number Line
+2
54 56
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.
402
Unit 6 Whole-Number Operations and Number Stories
If no one suggests it, point out that they may use base-10 blocks to
solve 2-digit subtraction problems as well.
Adjusting the Activity
ELL
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
Model Subtraction
WHOLE-CLASS
ACTIVITY
PROBLEM
PR
PRO
P
RO
R
OB
BLE
BL
LE
L
LEM
EM
SO
S
SOLVING
OL
O
LV
VIN
IN
ING
Write 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.
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.
36
- 14
22
}
Example: Model 36 - 14 = ? as follows:
Take away
1 long and 4 cubes.
2 longs and 2 cubes
are left.
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
Lesson 6 5
403
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.
Student Page
Date
Time
LESSON
Subtraction
6 5
3. Trade a long for cubes: Remove one of the longs that is used
to represent 53 and replace it with 10 cubes. 53 is now
represented by 4 longs and 13 cubes.
Use base-10 blocks to help you subtract.
1. Longs Cubes
2. Longs Cubes
1
- 1
9
7
2
- 1
5
4
1
2
1
1
3. Longs Cubes
4
- 1
3
8
2
5
4. Remove 38 (3 longs and 8 cubes) from the table.
5. Record the answer (difference) on the board. 15
4. Flats Longs Cubes
1
-
3
4
6
7
8
9
Repeat the steps as needed. Model problems that involve 2- and
3-digit numbers.
Use any strategy to solve.
5.
14
- 16
6.
8
7.
Solving Subtraction Problems
38
- 23
15
124
- 26
8.
(Math Journal 1, p. 144)
164
- 126
Partners work together to solve the subtraction problems.
38
98
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.
Math Journal 1, p. 144
EM3MJ1_G2_U06_131_158.indd 144
404
PARTNER
ACTIVITY
1/29/11 10:57 AM
Unit 6 Whole-Number Operations and Number Stories
Student Page
Date
2 Ongoing Learning & Practice
Playing the Number-Grid
PARTNER
ACTIVITY
Difference Game
Time
LESSON
Math Boxes
6 5
䉬
1. Circle the one that is likely to
夹
2. Measure the line segment.
happen.
It is likely that...
about
you will do a Math Box today.
about
2
5
in.
cm
you will fly like a bird.
an elephant will visit the
classroom.
(Math Masters, pp. 418 and 463; My Reference Book,
pp. 140 and 141)
3. Kurtis scored 13 points in the
Children practice subtraction skills by playing the Number-Grid
Difference Game. Children will find directions on page 140 of
My Reference Book.
4. How many dots are in this
first half of the game and a total
of 24 points by the end. How
many points did Kurtis score in
the second half? 11 points
13 11 24
11
or 24 13 11
5. Which number occurs most
Math Boxes 6 5
63
Number model:
24
13
INDEPENDENT
ACTIVITY
7-by-9 array?
6. Use your calculator. Count by
often? Choose the best answer.
9s. Start at 76.
8, 17, 9, 8, 10
76,
85 , 94
112 , 121
9
(Math Journal 1, p. 145)
Home Link 6 5
the ones place goes down by one.
8
Math Journal 1, p. 145
Ongoing Assessment:
Recognizing Student
Achievement
(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.
Sample answer: The number in
10
INDEPENDENT
ACTIVITY
103 ,
What pattern do you see?
17
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.
,
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]
Home Link Master
Name
HOME LINK
65
䉬
Family
Note
Date
Home Link Master
Time
Name
Subtracting with Base-10 Blocks
65
䉬
In this lesson, your child found the answers to subtraction problems
by using longs and cubes to represent tens and ones, respectively.
long
cube
Example:
Number model:
26 18 1.
How many cubes
are shown in all?
26
Cross out (subtract)
18 cubes. How
many cubes are left?
Show subtraction by crossing out cubes.
Cross out (subtract)
23 cubes. How
many cubes are left?
Number model:
42 23 How many cubes
are shown in all?
42
19
Number model:
43 25 8
19
Math Masters, p. 169
18
18
5.
58
Cross out (subtract)
17 cubes. How
many cubes are left?
Number model:
58 17 43
Cross out (subtract)
25 cubes. How
many cubes are left?
8
4.
How many cubes
are shown as
separate cubes and
as part of the longs?
continued
3.
How many cubes
are shown in all?
31
Time
Subtracting with Blocks
2.
This will help your child understand the concept of subtraction
before he or she learns to subtract using a step-by-step procedure,
or algorithm, with paper and pencil. When you see the problems
on this Home Link, you may be eager to teach your child to
subtract the way you were taught. Please wait—the introduction
of a formal algorithm for subtraction will be taught later in
second grade.
Please return this Home Link to school tomorrow.
Date
HOME LINK
How many cubes
are shown in all?
41
41
Cross out (subtract)
32 cubes. How
many cubes are left?
Number model:
39 32 How many cubes
are shown in all?
39
7
7
61
Cross out (subtract)
47 cubes. How
many cubes are left?
Number model:
61 47 14
14
Math Masters, p. 170
Lesson 6 5
405
Teaching Aid Master
Name
Date
Time
3 Differentiation Options
Place-Value Mat
ones
READINESS
Playing the Base-10
PARTNER
ACTIVITY
15–30 Min
Trading Game
tens
(Math Masters, p. 427)
To provide experience with subtraction using a concrete model,
have children play the Base-10 Trading Game.
hundreds
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.
Math Masters, p. 427
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
Analyzing a Subtraction
SMALL-GROUP
ACTIVITY
15–30 Min
Strategy
(Math Masters, p. 171)
Teaching Master
Name
LESSON
65
䉬
Date
Time
A Subtraction Strategy
Meredith uses an interesting strategy for solving subtraction
problems 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
31
Second Step: 35
Final Answer: 35
First Step:
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.
Try This
93 48
First Step:
43
45
45
Second Step:
Final Step:
Math Masters, p. 171
406
Unit 6 Whole-Number Operations and Number Stories