Objectives
To review addition of positive and negative integers;
and to introduce subtraction of positive and negative integers.
1
materials
Teaching the Lesson
Key Activities
Students discuss and practice subtraction of positive and negative integers, and review
addition of such numbers, in the context of an accounting problem. Students play the
Credits/Debits Game (Advanced Version).
Key Concepts and Skills
• Compare integers.
[Number and Numeration Goal 6]
• Add and subtract signed numbers.
[Operations and Computation Goal 2]
• Describe rules for patterns and use them to solve problems.
[Patterns, Functions, and Algebra Goal 1]
Ongoing Assessment: Informing Instruction See page 881.
2
Student Reference Book, p. 239
Study Link 11 5
Game Master (Math Masters,
p. 469)
Transparency (Math Masters,
p. 321; optional)
1 penny per partnership
per partnership: deck of number
cards (from the Everything Math
Deck, if available)
slate
number line (optional)
materials
Ongoing Learning & Practice
Students summarize the Gram & Ounce Museum.
Students practice and maintain skills through Math Boxes and Study Link activities.
Math Journal 2, pp. 303 and 304
Study Link Master (Math Masters,
p. 333)
Ongoing Assessment: Recognizing Student Achievement Use journal page 304.
[Geometry Goal 3]
3
materials
Differentiation Options
READINESS
Students use a number line to subtract
positive and negative numbers.
EXTRA PRACTICE
Students practice adding and subtracting
positive and negative numbers.
Additional Information
Advance Preparation For the optional Readiness activity in Part 3, use masking tape to
create a life-size number line (–10 to 10) on the floor.
878
Unit 11 3-D Shapes, Weight, Volume, and Capacity
5-Minute Math, pp. 100 and 189
masking tape
See Advance Preparation
Technology
Assessment Management System
Math Boxes, Problem 2
See the iTLG.
Getting Started
Mental Math and Reflexes
Math Message
Pose problems involving the addition of positive and negative numbers.
Suggestions:
On a sheet of paper, list any
shortcuts that you use when
you add credits and debits
(positive and negative numbers).
7 9 2
4 (5) 1
6 (8) 2
20 (30) 10
70 (50) 20
10 (90) 80
1
1
1
() 2
4
4
1
1
2
– 3 (3) 3
2
1
2
1
() , or 8
2
8
4
Study Link 11 5
Follow-Up
Have volunteers write number
models on the board to show how they
calculated the volume of each figure.
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
Ask students to share any shortcuts they devised for adding
positive and negative numbers the last time they used credits
and debits. For example:
When two positive numbers are added, the result is
“more positive.”
When two negative numbers are added, the result is
“more negative.”
When a positive and a negative number are added, the result
is the difference of the two addends (ignoring the signs); the
sign in the answer is that of whichever addend is “bigger.”
Teaching Master
Name
LESSON
10 6
Using Credits and Debits to
WHOLE-CLASS
ACTIVITY
Date
Time
Ledger
Transaction
Start
End/Start of
Next Transaction
Change
Practice Subtraction of
Positive and Negative Numbers
(Math Masters, p. 321)
Links to the Future
Addition and subtraction of signed numbers is a Grade 5 Goal.
Tell students that in this lesson they will pretend to be
accountants, as they did in Lesson 10-6. They record what
happens as they help start a business and keep track of the
“bottom line” by posting credits and debits.
–10 – 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 –1
0
1
2
3
4
5
6
7
8
9
10
Math Masters, p. 321
Lesson 11 6
879
Student Page
Inform students that this is a new business, and there are some
kinks in the accounting system; sometimes the credits or debits
are not reported correctly. The subtraction of positive and negative
numbers can be understood as the taking away or subtracting
from the bottom line what were considered to be credits or debits.
Games
Credits/Debits Game (Advanced Version)
Materials 1 complete deck of number cards
1 penny
1 Credits/Debits Game (Advanced
Version) Record Sheet for each
player (Math Masters, p. 469)
Players
2
Skill
Addition and subtraction of positive and
negative numbers
Object of the game To have more money after
adding and subtracting credits and debits.
When a debit (negative number) is taken away or subtracted,
the result is an increase in the bottom line.
Each player uses one
Record Sheet.
Directions
1. Shuffle the deck and lay it number-side down between
the players.
When a credit (positive number) is taken away or subtracted,
the result is a decrease in the bottom line.
2. The black-numbered cards are the “credits,” and the
blue- or red-numbered cards are the “debits.”
3. The heads side of the coin tells you to add a credit or debit
to the bottom line. The tails side of the coin tells you to
subtract a credit or debit from the bottom line.
10
4. Each player begins with a bottom line of $10.
5. Players take turns. On your turn, do the following:
10
♦ Flip the coin. This tells you whether to add or subtract.
♦ Draw a card. The card tells you what amount in dollars
(positive or negative) to add or subtract from your bottom
line. Red or blue numbers are negative numbers. Black
numbers are positive numbers.
♦ Record the results in your table.
2
2
6. Scoring is the same as in the Credits/Debits Game.
Examples Max has a “Start” balance of $5. His coin lands heads up
Remind students that you are labeling credits with “” and debits
with “–” to help keep track of them as positive or negative numbers.
When credits and debits come in, the class will figure out the
bottom line as you post transactions on an overhead transparency
of Math Masters, page 321.
Following is a suggested series of transactions. Entries in black
would be reported to the class; entries in color are appropriate
student responses.
and he records in the “Addition or Subtraction” column.
He draws a red 9 and records $9 in the “Credit or Debit” column.
Max adds: $5 ($9) $4. He records $4 in the “End” balance
column and also in the “Start” column on the next line.
Beth has a “Start” balance of $20. Her coin lands tails up, which
means subtract. She draws a black 2 ($2). She subtracts:
$20 ($2) $22. Her “End” balance is $22.
Student Reference Book, p. 239
Start
Change
End, and
next start
New business.
Start at $0.
$0
$0
$0
Credit (payment)
of $8 comes in.
$0
add $8
$8
Credit of $3
$8
add $3
$11
Debit of $4
$11
add $4
$7
Credit of $3
was an error.
Adjust account.
$7
subtract $3
$4
Debit of $6
$4
add $6
–$2
Credit of $5
–$2
add $5
$3
Debit of $4
was an error.
Adjust account.
$3
subtract –$4
$7
Debit of $6
was an error.
Adjust account.
$7
subtract –$6
$13
Event
NOTE Try to consistently use the terms
positive and negative for numbers and
amounts and add or subtract for operations.
It is important to be consistent in subtracting
the credits and debits as positive and
negative numbers when there is an error.
Game Master
Name
Date
Time
Credits/Debits Game (Advanced Version) Record Sheets
1 2
4 3
Game 1
239
Start
Change
Addition or
Subtraction
Credit or Debit
End, and
next start
1
2
3
Playing the Credits/Debits Game
4
5
6
PARTNER
ACTIVITY
(Advanced Version)
7
8
9
(Student Reference Book, p. 239; Math Masters, p. 469)
10
Game 2
Start
Change
Addition or
Subtraction
Credit or Debit
Have students read the rules for the Credits/Debits Game
(Advanced Version) on page 239 of the Student Reference Book.
Play one round as a class to be sure that students understand
how the game is played. Have students record their steps on
Math Masters, page 469.
End, and
next start
1
2
3
4
5
6
7
8
9
10
469
Math Masters, p. 469
880
Unit 11 3-D Shapes, Weight, Volume, and Capacity
Student Page
ELL
Adjusting the Activity
Date
Time
LESSON
Gram and Ounce Museum
11 6
Encourage students to use a class number line to assist in subtracting
the debits and credits.
140
1. a. What was the heaviest item in the class Gram and Ounce Museum?
b. How much did it weigh?
grams
Answers vary.
ounces
2. a. What was the lightest item in the class Gram and Ounce Museum?
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
b. How much did it weigh?
grams
Answers vary.
ounces
Complete.
6,000 mg
3,000 g
7. 2.9 g 2,900 mg
96 oz
9. 6 lb 56 oz
11. 3.5 lb Ongoing Assessment: Informing Instruction
Watch for students who are beginning to devise shortcuts for finding answers.
For example, some students may notice that subtracting a negative number is
the same as adding a positive number. Do not expect students to explain these
strategies; explanations will evolve over time as students acquire experience
manipulating positive and negative numbers.
3. 6 g 4.
5. 3 kg 6.
8.
10.
12.
7 g 7,000 mg
8 kg 8,000 g
4.5 kg 4,500 g
9 lb 144 oz
8 T 16,000 lb
Use the Rules of Thumb below to solve Problems 13–15. Write number models to show
how you estimated.
Rules of Thumb
1 kilogram equals about 2.2 pounds
1 ounce equals about 30 grams
Sample answers:
13. A video camera weighs about 120 grams. About how many ounces is that?
120 30 4
Number model:
4
oz
14. A baby weighs about 3.5 kilograms at birth. About how many pounds is that?
3.5 2.2 7.7
Number model:
7.7
lb
15. An African elephant weighs 11,023 pounds. About how many kilograms is that?
Number model:
2 Ongoing Learning & Practice
Summarizing the Gram
11,000 2.2 5,000
5,000
kg
303
Math Journal 2, p. 303
PARTNER
ACTIVITY
& Ounce Museum
(Math Journal 2, p. 303)
Have partners discuss the Gram & Ounce Museum before
completing journal page 303.
Math Boxes 11 6
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 304)
Mixed Practice Math Boxes in this lesson are linked
with Math Boxes in Lessons 11-2 and 11-4. The skills
in Problems 5 and 6 preview Unit 12 content.
Student Page
Date
Time
LESSON
Math Boxes
11 6
1. The object below has the shape of a
Ongoing Assessment:
Recognizing Student Achievement
Math Boxes
Problem 2
2. Which figure below shows the original
1
figure rotated clockwise 2-turn.
geometric solid. Name the solid.
A
Original
Use Math Boxes, Problem 2 to assess students’ ability to identify an example of
a rotation. Students are making adequate progress if they are able to correctly
1
identify what the figure would look like if it were rotated clockwise 2-turn. Some
students may be able to determine the degree of rotation for each figure.
A
B
C
cone
101
3. Write a number model to estimate the
answer. Then correctly place the
decimal point.
[Geometry Goal 3]
106 107
4. Insert , , or to make a true number
sentence.
.
34
b.
89
a. 6 32.9 1 9 7 4
Number model:
6 30 180
c.
.
b. 3 2 9 98.7 3
Number model:
99 3 33
d.
e.
5. Round 8.99 to the nearest tenth. Circle the
best answer.
9
99
2.99 2.9
2
a.
1
4
18
9
1
3
1
4
6
60
6. It takes 2 cups of flour to make about
A. 8.0
20 medium-size peanut butter cookies.
How many cups of flour will you need
to make about
B. 9.0
a. 40 cookies?
C. 9.1
b. 60 cookies?
D. 8.09
c. 50 cookies?
d. 740 cookies?
4
6
5
74
cups
cups
cups
182 183
cups
47
304
Math Journal 2, p. 304
Lesson 11 6
881
Study Link Master
Name
Date
STUDY LINK
Study Link 11 6
Time
(Math Masters, p. 333)
Add or subtract.
1.
3.
5.
7.
9.
110
2.
14 (6)
4.
15
6.
12 7 40 (70) 8
14
15 (1) 70
60 (130)
8
15.
Home Connection Students add and subtract positive
and negative integers and compare and order positive and
negative numbers.
10 (5)
19
Write two addition problems with an answer of 30.
13.
6 60
18 2 (20)
Answers vary.
8.
30
6
8
7 (2)
27 (16)
26 (14)
07
8
Answers vary.
Write or to make a true number sentence.
11.
8
12 20 Write two subtraction problems with an answer of 8.
10.
INDEPENDENT
ACTIVITY
Positive and Negative Numbers
11 6
30
12.
11
14.
18 (8)
16.
9 (11)
3 Differentiation Options
13 (5)
18
0 (20)
List the numbers in order from least to greatest.
30
17. 6,
8, 14, 0.7, 5.6, 2.5
30
6
14 2.5 0.7
5.6
least
18.
8
greatest
3
24
0.02, 5, 7, 4, 0.46, 6
7
24
6
3
5
0.02 0.46
least
4
greatest
Practice
19.
21.
2,652
632 ÷ 4 34 º 78
158
20.
22.
44,114
746 / 7 Math Masters, p. 333
46 º 959
4
106 R4, or 106 7
SMALL-GROUP
ACTIVITY
READINESS
Using a Number Line to
5–15 Min
Subtract Positive and
Negative Numbers
To explore subtraction of positive and negative numbers using a
number line model, have students act out subtraction problems by
walking on a life-size number line from –10 to 10.
The first number tells students where to start.
The operation sign – means face toward the negative end
of the number line.
If the second number is negative, then walk backward.
Otherwise, walk forward.
The second number tells how many steps to walk.
The number where the student stops is the answer.
Example: 2 (3)
Start at 2.
Face toward the negative end of the number line.
Walk forward 3 steps.
You are now at 5. So 2 (3) 5.
2 (3)
Start
at 2.
Face
negative
5 4 3 2 1
882
Unit 11 3-D Shapes, Weight, Volume, and Capacity
Walk
forward
3 steps.
0
1
2
3
Example: 5 (2)
Start at 5.
Face toward the negative end of the number line.
Walk backward 2 steps.
You are now at 7. So 5 (2) 7.
5 (2)
Start
at 5.
1
0
Face
negative.
1
2
3
Walk
backward
2 steps.
4
5
6
7
Suggestions:
●
–2 – (–3) ? (Start at –2. Face in the negative direction.
Walk backward 3 steps. End up at 1.)
●
4 – (–5) ? (Start at 4. Face in the negative direction.
Walk backward 5 steps. End up at 9.)
EXTRA PRACTICE
5-Minute Math
SMALL-GROUP
ACTIVITY
5–15 Min
To offer students more experience with adding and subtracting
positive and negative numbers, see 5-Minute Math, pages 100
and 189.
Lesson 11 6
883