Name __________________________
L ea rn i n g Obj e cti v e
Today, we will multiply and divide integers.
CFU
What are we going to do today?
Acti va t e ( o r p r o vi de ) P ri o r K n o wl edg e
Find the product or quotient below.
 The product is the answer to a multiplication problem.
 The quotient is the answer to a division problem.
1. 4 × 5 =
2. 6 × 2 =
3. 20 ÷ 5 =
4. 12 ÷ 2 =
CFU
Students, you already know how to multiply and divide whole numbers.
Today, we are going to multiply and divide integers.
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6th Grade Number Sense 2.3 (6Q)
Solve addition, subtraction, multiplication, and division problems, including
those arising in concrete situations, that use positive and negative integers
and combinations of these operations.
Lesson to be used by EDI-trained teachers only.
Co n c e pt D ev el opm e n t
An integer is a positive whole number or negative whole number.
• Positive integers can be shown with a (+) sign or with no sign at all.
• Negative integers must be shown with a (-) sign.
Positive Integer
Negative Integer

+
3 and 3
3
The multiplication and division integer rules are determined by the signs of the
integers used.
Multiplication and Division Integer Rules
Same Sign
The product or quotient will be positive.
(Pos) × (Pos)  Pos
6÷32
(Pos) ÷ (Pos)  Pos
2×36

2 × 3  6
(Neg) × ( Neg)  Pos

(Neg) ÷ (Neg)  Pos

6 ÷ 3  2
Different Sign
The product or quotient will be negative.
(Pos) × (Neg)  Neg

2 × 3  6
(Neg) × (Pos)  Neg
2 × 3  6
(Pos) ÷ (Neg)  Neg
6 ÷ 3  2
(Neg) ÷ (Pos)  Neg

6 ÷ 6  2
CFU
On your whiteboards, write a positive integer. How do you know it is a positive integer?
On your whiteboards, write a negative integer. How do you know it is a negative integer?
Will the product of -2 × -4 be negative or positive? How do you know?
Will the product of 21 ÷ -7 be negative or positive? How do you know?
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6th Grade Number Sense 2.3 (6Q)
Solve addition, subtraction, multiplication, and division problems, including
those arising in concrete situations, that use positive and negative integers
and combinations of these operations.
Lesson to be used by EDI-trained teachers only.
Ski l l Dev el o pm en t /G u i ded P ra cti c e
The multiplication and division integer rules are
determined by the signs of the integers used.
Multiplication and Division Integer Rules
Same Sign
Different Sign
The product or quotient
will be positive.
The product or quotient
will be negative.
(Pos) × (Pos)  Pos
(Pos) × (Neg)  Neg
(Pos) ÷ (Pos)  Pos
(Pos) ÷ (Neg)  Neg
(Neg) × (Neg)  Pos
(Neg) × (Pos)  Neg
(Neg) ÷ (Neg)  Pos
(Neg) ÷ (Pos)  Neg
Step #1: Use integer rules to determine1 the sign of the product or quotient.
a. Identify2 the signs of the integers. (write)
b. Determine the sign of the product or quotient. (Hint: Use integer rules)
Step #2: Multiply or divide the values3, ignoring the signs.
Step #3: Write the product or quotient with the correct sign.
1
2
figure out
1. 4 × 6 =
Signs:
3
find
numbers
2. 5 × 3 =
×
=
Signs:
3. 18 ÷ 6 =
×
=
Signs:
×
4. 32 ÷ 8 =
=
Signs:
×
=
Product: ____
Product: ____
Quotient: ____
Quotient: ____
5. 5 × 7 =
6. 4 × 3 =
7. 54 ÷6 =
8. 30 ÷ 5 =
Signs:
×
Product: ____
=
Signs:
×
=
Product: ____
Signs:
×
=
Quotient: ____
Signs:
×
=
Quotient: ____
CFU
(#1a) How did I/you determine the sign of the product or quotient?
(#3) How did I/you write the product or quotient with the correct sign?
DataWORKS Educational Research
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©2012 All rights reserved.
Comments? feedback@dataworks-ed.com
6th Grade Number Sense 2.3 (6Q)
Solve addition, subtraction, multiplication, and division problems, including
those arising in concrete situations, that use positive and negative integers
and combinations of these operations.
Lesson to be used by EDI-trained teachers only.
Ski l l Dev el o pm en t /G u i ded P ra cti c e ( c on t i n u ed)
The multiplication and division integer rules are
determined by the signs of the integers used.
Multiplication and Division Integer Rules
Same Sign
Different Sign
The product or quotient
will be positive.
The product or quotient
will be negative.
(Pos) × (Pos)  Pos
(Pos) × (Neg)  Neg
(Pos) ÷ (Pos)  Pos
(Pos) ÷ (Neg)  Neg
(Neg) × (Neg)  Pos
(Neg) × (Pos)  Neg
(Neg) ÷ (Neg)  Pos
(Neg) ÷ (Pos)  Neg
Step #1: Use integer rules to determine the sign of the product or quotient.
a. Identify the signs of the integers. (write)
b. Determine the sign of the product or quotient. (Hint: Use integer rules)
Step #2: Multiply or divide the values, ignoring the signs.
Step #3: Write the product or quotient with the correct sign.
9. 3 × 6 =
Signs:
×
10. 5 × 8 =
=
Signs:
11. 48 ÷ 6 =
×
=
Signs:
×
12. 42 ÷ 7 =
=
Signs:
×
=
Product: ____
Product: ____
Quotient: ____
Quotient: ____
13. 9 × 5 =
14. 6 × 1 =
15. 81 ÷ 9 =
16. 60 ÷ 10 =
Signs:
×
Product: ____
=
Signs:
×
=
Product: ____
Signs:
×
=
Quotient: ____
Signs:
×
=
Quotient: ____
CFU
(#1a) How did I/you determine the sign of the product or quotient?
(#3) How did I/you write the product or quotient with the correct sign?
DataWORKS Educational Research
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©2012 All rights reserved.
Comments? feedback@dataworks-ed.com
6th Grade Number Sense 2.3 (6Q)
Solve addition, subtraction, multiplication, and division problems, including
those arising in concrete situations, that use positive and negative integers
and combinations of these operations.
Lesson to be used by EDI-trained teachers only.
Rel e van c e
The multiplication and division integer rules are determined by the signs of the
integers used.
1. Multiplying and dividing with integers will help you solve equations.

4x = 20
-4
-4
x
20 ÷ -4 = -5
= -5
2. Multiplying and dividing with integers will help you do well on tests.
CFU
Does anyone else have another reason why it is relevant to multiply and divide with integers? (pair-share)
Why is it relevant to multiply and divide with integers? You may give me one of my reasons or your own.
Which reason is more relevant to you? Why?
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6th Grade Number Sense 2.3 (6Q)
Solve addition, subtraction, multiplication, and division problems, including
those arising in concrete situations, that use positive and negative integers
and combinations of these operations.
Lesson to be used by EDI-trained teachers only.
The multiplication and division integer rules are
determined by the signs of the integers used.
Skill Closure
Multiplication and Division Integer Rules
Same Sign
Different Sign
The product or quotient
will be positive.
The product or quotient
will be negative.
(Pos) × (Pos)  Pos
(Pos) × (Neg)  Neg
(Pos) ÷ (Pos)  Pos
(Pos) ÷ (Neg)  Neg
(Neg) × (Neg)  Pos
(Neg) × (Pos)  Neg
(Neg) ÷ (Neg)  Pos
(Neg) ÷ (Pos)  Neg
Multiply and divide integers.
Step #1: Use integer rules to determine the sign of the product or quotient.
a. Identify the signs of the integers. (write)
b. Determine the sign of the product or quotient. (Hint: Use integer rules)
Step #2: Multiply or divide the values, ignoring the signs.
Step #3: Write the product or quotient with the correct sign.
1. 16 ÷ 2 =
Signs:
×
2. 7 × 4 =
=
Quotient: ____
Signs:
×
=
Product: ____
Constructed Response Closure
Dean is multiplying integers and concludes that a negative integer
times another negative integer is always negative. Explain why Dean
is incorrect and give an example proving he is incorrect.
______________________________________________________________
______________________________________________________________
Summary Closure
What did you learn today about multiplying and dividing integers?
Day 1 ___________________________________________________________________________
________________________________________________________________________________
Day 2 ___________________________________________________________________________
________________________________________________________________________________
DataWORKS Educational Research
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6th Grade Number Sense 2.3 (6Q)
Solve addition, subtraction, multiplication, and division problems, including
those arising in concrete situations, that use positive and negative integers
and combinations of these operations.
Lesson to be used by EDI-trained teachers only.
Name ______________________
In d ep en d en t P ra cti c e
The multiplication and division integer rules are
determined by the signs of the integers used.
Multiplication and Division Integer Rules
Same Sign
Different Sign
The product or quotient
will be positive.
The product or quotient
will be negative.
(Pos) × (Pos)  Pos
(Pos) × (Neg)  Neg
(Pos) ÷ (Pos)  Pos
(Neg) × (Neg)  Pos
(Neg) × (Neg)  Pos
(Neg) ÷ (Neg)  Pos
(Neg) ÷ (Neg)  Pos
(Pos) ÷ (Neg)  Neg
(Neg) × (Pos)  Neg
(Neg) × (Pos)  Neg
(Neg) ÷ (Pos)  Neg
(Neg) ÷ (Pos)  Neg
Step #1: Use integer rules to determine the sign of the product or quotient.
a. Identify the signs of the integers. (write)
b. Determine the sign of the product or quotient. (Hint: Use integer rules)
Step #2: Multiply or divide the values, ignoring the signs.
Step #3: Write the product or quotient with the correct sign.
1. 7 × 2 =
Signs:
3. 2 × 5 =
2. 36 ÷ 4 =
×
=
Signs:
×
=
Signs:
×
4. 18 ÷ 6 =
=
Signs:
×
=
Product: ____
Quotient: ____
Product: ____
Quotient: ____
5. 8 × 5 =
6. 21 ÷ 3 =
7. 5 × 6 =
8. 63 ÷ 7 =
Signs:
×
Product: ____
=
Signs:
×
=
Quotient: ____
DataWORKS Educational Research
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Comments? feedback@dataworks-ed.com
Signs:
×
Product: ____
=
Signs:
×
=
Quotient: ____
6th Grade Number Sense 2.3 (6Q)
Solve addition, subtraction, multiplication, and division problems, including
those arising in concrete situations, that use positive and negative integers
and combinations of these operations.
Lesson to be used by EDI-trained teachers only.
Name ______________________
P eri odi c R evi ew 1
The multiplication and division integer rules are
determined by the signs of the integers used.
Multiplication and Division Integer Rules
Same Sign
Different Sign
The product or quotient
will be positive.
The product or quotient
will be negative.
(Pos) × (Pos)  Pos
(Pos) × (Neg)  Neg
(Pos) ÷ (Pos)  Pos
(Neg) × (Neg)  Pos
(Neg) × (Neg)  Pos
(Neg) ÷ (Neg)  Pos
(Neg) ÷ (Neg)  Pos
(Pos) ÷ (Neg)  Neg
(Neg) × (Pos)  Neg
(Neg) × (Pos)  Neg
(Neg) ÷ (Pos)  Neg
(Neg) ÷ (Pos)  Neg
Step #1: Use integer rules to determine the sign of the product or quotient.
a. Identify the signs of the integers. (write)
b. Determine the sign of the product or quotient. (Hint: Use integer rules)
Step #2: Multiply or divide the values, ignoring the signs.
Step #3: Write the product or quotient with the correct sign.
1. 18 ÷ 9 =
Signs:
×
2. 7 × 6 =
=
Signs:
3. 9 × 6 =
×
=
Signs:
×
4. 8 ÷ 2 =
=
Signs:
×
=
Quotient: ____
Product: ____
Product: ____
Quotient: ____
5. 4 × 10 =
6. 20 ÷ 4 =
7. 3 × 9 =
8. 9 ÷ 3 =
Signs:
×
Product: ____
=
Signs:
×
=
Quotient: ____
DataWORKS Educational Research
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Comments? feedback@dataworks-ed.com
Signs:
×
Product: ____
=
Signs:
×
=
Quotient: ____
6th Grade Number Sense 2.3 (6Q)
Solve addition, subtraction, multiplication, and division problems, including
those arising in concrete situations, that use positive and negative integers
and combinations of these operations.
Lesson to be used by EDI-trained teachers only.
Name ______________________
P eri odi c R e vi ew 2
The multiplication and division integer rules are
determined by the signs of the integers used.
Multiplication and Division Integer Rules
Same Sign
Different Sign
The product or quotient
will be positive.
The product or quotient
will be negative.
(Pos) × (Pos)  Pos
(Pos) × (Neg)  Neg
(Pos) ÷ (Pos)  Pos
(Neg) × (Neg)  Pos
(Neg) × (Neg)  Pos
(Neg) ÷ (Neg)  Pos
(Neg) ÷ (Neg)  Pos
(Pos) ÷ (Neg)  Neg
(Neg) × (Pos)  Neg
(Neg) × (Pos)  Neg
(Neg) ÷ (Pos)  Neg
(Neg) ÷ (Pos)  Neg
Step #1: Use integer rules to determine the sign of the product or quotient.
a. Identify the signs of the integers. (write)
b. Determine the sign of the product or quotient. (Hint: Use integer rules)
Step #2: Multiply or divide the values, ignoring the signs.
Step #3: Write the product or quotient with the correct sign.
1. 72 ÷ 9 =
Signs:
×
2. 28 ÷ 7 =
=
Signs:
×
4. 5 7 =
3. 7 ÷ 1 =
=
Signs:
×
=
Signs:
×
Quotient: ____
Quotient: ____
Quotient: ____
Product: ____
5. 6 × 6 =
6. 50 ÷10 =
7. 7 × 9 =
8. 7 × 8 =
Signs:
×
Product: ____
=
Signs:
×
=
Quotient: ____
DataWORKS Educational Research
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Comments? feedback@dataworks-ed.com
Signs:
×
Product: ____
=
Signs:
×
=
=
Product: ____
6th Grade Number Sense 2.3 (6Q)
Solve addition, subtraction, multiplication, and division problems, including
those arising in concrete situations, that use positive and negative integers
and combinations of these operations.
Lesson to be used by EDI-trained teachers only.
Name ______________________
P eri odi c R evi ew 3
The multiplication and division integer rules are
determined by the signs of the integers used.
Multiplication and Division Integer Rules
Same Sign
Different Sign
The product or quotient
will be positive.
The product or quotient
will be negative.
(Pos) × (Pos)  Pos
(Pos) × (Neg)  Neg
(Pos) ÷ (Pos)  Pos
(Neg) × (Neg)  Pos
(Neg) × (Neg)  Pos
(Neg) ÷ (Neg)  Pos
(Neg) ÷ (Neg)  Pos
(Pos) ÷ (Neg)  Neg
(Neg) × (Pos)  Neg
(Neg) × (Pos)  Neg
(Neg) ÷ (Pos)  Neg
(Neg) ÷ (Pos)  Neg
Step #1: Use integer rules to determine the sign of the product or quotient.
a. Identify the signs of the integers. (write)
b. Determine the sign of the product or quotient. (Hint: Use integer rules)
Step #2: Multiply or divide the values, ignoring the signs.
Step #3: Write the product or quotient with the correct sign.
1. 4 × 1 =
Signs:
2. 32 ÷ 4 =
×
=
Signs:
×
3. 5 × 12 =
=
Signs:
×
4. 25 ÷ 5 =
=
Signs:
×
=
Product: ____
Quotient: ____
Product: ____
Quotient: ____
5. 2 × 6 =
6. 24 ÷ 4 =
7. 36 ÷ 4 =
8. 10 ÷ 10 =
Signs:
×
Product: ____
=
Signs:
×
=
Quotient: ____
DataWORKS Educational Research
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Comments? feedback@dataworks-ed.com
Signs:
×
=
Quotient: ____
Signs:
×
=
Quotient: ____
6th Grade Number Sense 2.3 (6Q)
Solve addition, subtraction, multiplication, and division problems, including
those arising in concrete situations, that use positive and negative integers
and combinations of these operations.
Lesson to be used by EDI-trained teachers only.