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Mathematical Reasoning
Lesson 9: Integers
LESSON 9: Integers Computation and Word Problems
Weekly Focus: integers
Weekly Skill: addition,
subtraction, multiplication, and
division
Lesson Summary: First, students will solve a word problem with percentages. In Activity 1, they will review
vocabulary with true/false statements. In Activity 2, they will put numbers on the number line. In Activity 3,
students will practice adding and subtracting integers. Activity 4, they will practice multiplication and division of
integers. In Activity 5, they will do word problems. For Activity 6, they will do an application problem related to
paying bills. There is an extra problem at the end. Estimated time for the lesson is two hours.
Materials Needed for Lesson 9:
 Post-it notes
 3 Worksheets with Answers (attached)
 Video (length 10 minutes) on 2 methods of adding and subtracting integers. The video is required for
teachers and recommended for students.
 Fun music video on adding and subtracting integers (length 2:30)
 Video on multiplying and dividing integers (length 7:31). Required for teacher and recommended for
students.



Exit ticket (attached; use pencils, rulers, flyswatters, etc.)
Mathematical Reasoning Test Preparation for the 2014 GED Test Student Workbook p. 10-13
Teacher Note: You may decide to have students complete only part of the worksheets in class and
assign the rest as homework or extra practice depending on students’ needs and time.
Objectives: Students will be able to:



Review vocabulary related to integers
Do computation of integers and word problems
Solve a real-life application problem
ACES Skills Addressed: N, CT, LS
CCRS Mathematical Practices Addressed: Attend to Precision, Mathematical Fluency, Use Appropriate Tools
Strategically
Levels of Knowing Math Addressed: Intuitive, Pictorial, Abstract, and Application
Notes:
You can add more examples if you feel students need them before they work. Any ideas that concretely
relates to their lives make good examples.
For more practice as a class, feel free to choose some of the easier problems from the worksheets to do
together. The “easier” problems are not necessarily at the beginning of each worksheet. Also, you may
decide to have students complete only part of the worksheets in class and assign the rest as homework or
extra practice.
The GED Math test is 115 minutes long and includes approximately 46 questions. The questions have a focus
on quantitative problem solving (45%) and algebraic problem solving (55%).
Students must be able to understand math concepts and apply them to new situations, use logical
reasoning to explain their answers, evaluate and further the reasoning of others, represent real world
problems algebraically and visually, and manipulate and solve algebraic expressions.
D. Legault, Minnesota Literacy Council, 2014
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Mathematical Reasoning
Lesson 9: Integers
This computer-based test includes questions that may be multiple-choice, fill-in-the-blank, choose from a
drop-down menu, or drag-and-drop the response from one place to another.
The purpose of the GED test is to provide students with the skills necessary to either further their education or
be ready for the demands of today’s careers.
Lesson 9 Warm-up: Solve the percent problem
Time: 10 Minutes
Write on the board: Cindy wants to save 15% of her gross monthly income for retirement.
Basic Questions:

If she saves $235.00 a month, how much will she save in a year? ($235 x12 = $2820)

At the end of two years, she had an emergency and had to spend ¼ of what she had saved.
How much did she take out of her savings? ($2820 x 2 = $5640 divided by 4 = $1410)
Extension Questions:

If $235 represents 15% of her income, how much does she make monthly? (0.15x=235.
X=235/0.15 = $1566.67)

She wants to increase her monthly savings to 17%. How much is that? (0.17 x 1566.67 =
$266.33)
Lesson 9 Activity 1: Vocabulary True or False
Time: 10 Minutes
This activity can be projected on the board and done as a whole class. (attached) Have
students volunteer to write answers. Then do some examples.
Answers:
1. True
2. False. An integer is a whole number that is either positive or negative. Zero is also an integer.
3. True
4. True
5. False. Absolute value means the distance from zero. It is expressed with a positive number or
zero and written with the symbol parallel bars symbol. Ex. l-4l = 4 and l4l = 4. Both positive and
negative 4 are four units away from 0 on the number line.
D. Legault, Minnesota Literacy Council, 2014
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Mathematical Reasoning
Lesson 9: Integers
Lesson 9 Activity 2: Place the numbers on the line
Time: 10 Minutes
1. Write a number line on the board from negative 5 to positive 5.
2. Write various positive and negative numbers on post-it notes and hand out to students.
Choose the difficulty of the numbers you write according to your students’ skill level, but
make sure to include a combination of + and – numbers as well as some easy-to-measure
fractions (1/10, 2¼, ¾, -1½ for example) and decimals (0.3, -4.7, etc.)
3. Ask them to place the post-it note at about the correct place on the line.
4. As a class discuss whether the posted numbers are in the correct locations.
5. Now talk about absolute value. How far is each number from zero? That is its absolute value.
Write a few examples, such as l-3/4 l = ¾. Have students come write more examples.
6. Don’t erase this line. Use it for the next activity to show addition and subtraction of numbers.
Activity 3: Addition and Subtraction of + and - Numbers
Time: 20-25 Minutes
Use the number line to show how addition and subtraction of integers works. Some students
prefer to see how the numbers move along the number line, whereas others prefer to know
the rules. To add, go right on the number line. To subtract, go left on the number line. Here
are examples of each:

If integers have like signs, add and keep the common sign. If integers have different signs, find
the difference. Then use the sign of the number with the greater absolute value.
D. Legault, Minnesota Literacy Council, 2014
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Mathematical Reasoning
Lesson 9: Integers
Example:

To subtract an integer, go left on the number line. Example: -5 -4 = -9

If there are two negatives next to each other, they become a positive because you start
going left on the number line, and then need to switch directions again for the second sign.
Example: -9 - -4 = -9 + 4 = -5.
Example: 18 - - 5 = 18 + 5 = 23
It is very helpful to watch the video assigned to this lesson for more explanations.
Do Worksheet 9.1. Have students volunteer to do a few problems on the number using the
number line.
D. Legault, Minnesota Literacy Council, 2014
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Mathematical Reasoning
Lesson 9: Integers
Lesson 9 Activity 1 Vocabulary: True or False
1. _____
A positive whole number is an integer.
2. _____
A positive fraction is an integer.
3. _____
Zero is an integer.
4. _____
A negative whole number is an integer.
5. _____
The absolute value of a number is always
negative.
D. Legault, Minnesota Literacy Council, 2014
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Mathematical Reasoning
Lesson 9: Integers
Kuta Software - Infinite Algebra 1
Worksheet 9.1
Name___________________________________
Adding and Subtracting Positive and Negative NumbersDate________________
Period____
Evaluate each expression.
1) (-2) + 3
2) (-14) + (-7)
3) 3 - (-8)
4) (-9) + 14
5) (-8) - (-2)
6) 5 + (-8)
7) (-27) - 24
8) (-41) + (-40)
9) 38 - (-17)
10) (-44) + (-9)
11) (-16) - (-36)
12) (-6) - 24
13) (-16) - 6 + (-5)
14) 15 - 13 + 2
15) 16 - (-13) - (-5)
16) (-7) - (-2) - 9
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D. Legault, Minnesota Literacy Council, 2014
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Worksheet by Kuta
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Mathematical Reasoning
Lesson 9: Integers
Kuta Software - Infinite Algebra 1
Worksheet 9.1 Answers
Adding
Name______________________________
and Subtracting Positive and Negative NumbersDate________________
Perio
Evaluate each expression.
1) (-2) + 3
2) (-14) + (-7)
1
-21
3) 3 - (-8)
4) (-9) + 14
11
5
5) (-8) - (-2)
6) 5 + (-8)
-6
-3
7) (-27) - 24
8) (-41) + (-40)
-51
9) 38 - (-17)
-81
10) (-44) + (-9)
55
11) (-16) - (-36)
-53
12) (-6) - 24
20
13) (-16) - 6 + (-5)
-30
14) 15 - 13 + 2
-27
15) 16 - (-13) - (-5)
4
16) (-7) - (-2) - 9
34
-14
7
D. Legault, Minnesota Literacy Council, 2014
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Works
Mathematical Reasoning
Lesson 9: Integers
Lesson 9 Activity 4: Multiplication and Division of + and - Integers
Time: 15-20 Minutes
For multiplying and dividing integers:

If the signs are the same, the answer will be positive. Example: (-2)(-6)= 12

If the signs are different, the answer will be negative. Example: -6/2 = -3
Do Worksheets 9.2 and 9.3. Choose a few problems to do on the board.
Note to teacher: It is difficult to explain why the rules are such for multiplying and dividing +
and – integers. This is one of the rare occasions it is easier just to know the rule. You can find
the explanation if you search online.
Lesson 9 Activity 5: Word Problems
Time: 25-30 Minutes
Do the word problems on pages 10-13 of the workbook. Choose a few more challenging
problems for students (or you) to do on the board.
Lesson 9 Activity 6: Application Problem
Time: 10 Minutes
Jason keeps track of his checking account every month. He uses his debit card to pay for his
expenses so they are withdrawn immediately. Here are this month’s expenses:

He started with a beginning balance of $1,000 on the first of the month

He paid his rent of $825 on the 2nd of the month

He bought groceries for $130 on the 6th of the month

He put gas in his truck twice at $55 each time the week of the 10th

He was paid $1,010 on the 15th of the month
1. How much money does he have at the end of the month?
2. Was he ever overdrawn on his account? If so, by how much?
3. Write an equation to show the changes to his account.
D. Legault, Minnesota Literacy Council, 2014
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Mathematical Reasoning
Lesson 9: Integers
4. If he gets paid twice a month, what percent of his income goes toward rent?
Lesson 9 Exit Ticket
Time: 5 Minutes
Write “Negative” and “Positive” on the board or on two pieces of paper. Give some students
pencils, rulers or flyswatters and as you write an equation, have them race to hit one of the
words to show that the solution is either negative or positive (you can divide them into teams
or call students up two at a time).

-5 + 8
(Positive)

-1 – 3
(Negative)

-10 – ( -11)
(Positive)

-41 + ( -11) + 51
(Negative)

-8 / 4
(Negative)

(-3) (-6)
(Positive)
Lesson 9 Extra Problem
Time: 3-5 Minutes
Write on the board:

The temperature this morning was -8 and now it’s +15. How much did the temperature change
from the morning until now? (23 degrees)

Yesterday the temperature went from +2 to -12. What was the change in temperature? (14
degrees)
Draw a vertical number line (thermometer) and have students use it to show how they
obtained the answer.
D. Legault, Minnesota Literacy Council, 2014
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Mathematical Reasoning
Kuta Software - Infinite Algebra 1
Name_____________________________
Lesson 9: Integers
Multiplying and Dividing Positives and Negatives
Date________________ Per
Worksheet 9.2: Find the Quotient
Find each quotient.
1)
10
5
2)
-24
12
3)
-20
-2
4)
-300
-20
5)
65
5
6)
-66
-6
7)
75
-15
8)
-56
-14
9)
102
-17
10)
-72
-4
11) 153 ¸ 17
12) 12 ¸ -3
13) 48 ¸ 6
14) -120 ¸ -20
15) 306 ¸ 18
16) -65 ¸ 13
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D. Legault, Minnesota
Literacy Council, 2014
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W
Mathematical Reasoning
Lesson 9: Integers
Name___________________________
Kuta Software - Infinite Algebra 1
Multiplying
Worksheet 9.2: Find the Quotient
Answersand
Dividing Positives and Negatives
Date________________ P
Find each quotient.
1)
10
5
2)
-2
2
3)
-20
-2
4)
65
5
6)
75
-15
8)
102
-17
-56
-14
4
-5
9)
-66
-6
11
13
7)
-300
-20
15
10
5)
-24
12
10)
-72
-4
-6
18
11) 153 ¸ 17
12) 12 ¸ -3
-4
9
13) 48 ¸ 6
14) -120 ¸ -20
6
8
15) 306 ¸ 18
16) -65 ¸ 13
17
-5
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D. Legault, Minnesota Literacy Council, 2014
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23) -8 ´ -11
24) -6 ´ 4
Mathematical Reasoning
25) -3 ´ -11
Lesson 9: Integers
26) -5 ´ -9
Worksheet 9.3: Find the Product
27) 9 ´ -7
28) -9 ´ -3
29) 12 ´ -12
30) 11 ´ -6
31) 6 ´ -5 ´ 3
32) 6 ´ -1 ´ 2
33) 8 ´ -6 ´ -3
34) -3 ´ 6 ´ -6
35) (3 )(3)(-1 )(3)
36) (-3)(3)(-3 )(-3)
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D. Legault, Minnesota Literacy Council, 2014
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Wor
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23) -8 ´ -11
24)Mathematical
-6 ´ 4
Reasoning
-24
88
Lesson 9: Integers
25) -3 ´ -11
26) -5 ´ -9
33
45
Worksheet 9.3 Answers
27) 9 ´ -7
28) -9 ´ -3
-63
27
29) 12 ´ -12
30) 11 ´ -6
-144
-66
31) 6 ´ -5 ´ 3
32) 6 ´ -1 ´ 2
-90
-12
33) 8 ´ -6 ´ -3
34) -3 ´ 6 ´ -6
144
108
35) (3 )(3)(-1 )(3 )
36) (-3 )(3)(-3 )(-3)
-27
-81
Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.co
Lesson 9 Activity 6 Application Problem Answers
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Jason keeps track of his checking account every month. He uses his debit card to pay for his
expenses so they are withdrawn immediately. Here are this month’s expenses:

A beginning balance of $1,000 on the first of the month

He paid his rent of $825 on the 2nd of the month

He bought groceries for $130 on the 6th of the month

He put gas in his truck at $55 each time twice the week of the 10th

He was paid $1,010 on the 15th of the month
1. How much money does he have at the end of the month? $945
2.
Was he ever overdrawn on his account? If so, by how much? Yes, by $65
3. Write an equation to show the changes to his account.
D. Legault, Minnesota Literacy Council, 2014
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Mathematical Reasoning
Lesson 9: Integers
$1,000 - $825 -$130- (2 x 55) + 1,010 = $945
4. If he gets paid twice a month, what percent of his income goes toward rent?
$1,010 x 2 = $2,020. $825/$2,020 = 0.408 = 40.8%
D. Legault, Minnesota Literacy Council, 2014
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