Inquiry Lab: Multiply Integers
Find the product. Show your work using drawings.
1. 2 × (–3) =
SOLUTION: Place 2 sets of 3 negative counters on the mat. Count the number of negative counters.
So, 2 × (–3) = –6.
ANSWER: –6
2. 6 × (–1) =
SOLUTION: Place 6 sets of 1 negative counters on the mat. Count the number of negative counters.
So, 6 × (–1) = –6.
ANSWER: –6
3. –2 × 4 =
SOLUTION: Place 2 sets of 4 zero pairs on the mat. Remove 2 sets of 4 positive counters. Count the number of negative
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Inquiry Lab: Multiply Integers
3. –2 × 4 =
SOLUTION: Place 2 sets of 4 zero pairs on the mat. Remove 2 sets of 4 positive counters. Count the number of negative
counters.
So, –2 × 4 = –8.
ANSWER: –8
4. –1 × 5 =
SOLUTION: Place 1 set of 5 zero pairs on the mat. Remove 1 set of 5 positive counters. Count the number of negative counters.
So, –1 × 5 = –5.
ANSWER: –5
5. –4 × 2 =
SOLUTION: Place 4 sets of 2 zero pairs on the mat. Remove 4 sets of 2 positive counters. Count the number of negative
counters.
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Inquiry Lab: Multiply Integers
5. –4 × 2 =
SOLUTION: Place 4 sets of 2 zero pairs on the mat. Remove 4 sets of 2 positive counters. Count the number of negative
counters.
So, –4 × 2 = –8.
ANSWER: –8
6. –2 × (–4) =
SOLUTION: Place 2 sets of 4 zero pairs on the mat. Remove 2 sets of 4 negative counters. Count the number of positive
counters.
So, –2 × (–4) = 8.
ANSWER: 8
7. –3 × (–1) =
SOLUTION: Place 3 sets of 1 zero pairs on the mat. Remove 3 sets of 1 negative counters. Count the number of positive
counters.
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Inquiry Lab: Multiply Integers
7. –3 × (–1) =
SOLUTION: Place 3 sets of 1 zero pairs on the mat. Remove 3 sets of 1 negative counters. Count the number of positive
counters.
So, –3 × (–1) = 3.
ANSWER: 3
8. –6 × (–2) =
SOLUTION: The expression –6 × (–2) means to remove 6 sets of 2 negative counters. Place 6 sets of 2 zero pairs on the mat.
Then remove 6 sets of 2 negative counters from the mat. There are 12 positive counters remaining. So, –6 × (–2) = 12.
ANSWER: 12
9. What do your models show about removing sets of positive counters? removing sets of negative counters?
SOLUTION: Sample answer: Removing sets of positive counters result in negative counters that are left. Removing sets of negative counters result in positive counters that are left.
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ANSWER: Sample answer: Removing sets of positive counters result in negative counters that are left. Removing sets of Page 4
Inquiry Lab: Multiply Integers
9. What do your models show about removing sets of positive counters? removing sets of negative counters?
SOLUTION: Sample answer: Removing sets of positive counters result in negative counters that are left. Removing sets of negative counters result in positive counters that are left.
ANSWER: Sample answer: Removing sets of positive counters result in negative counters that are left. Removing sets of negative counters result in positive counters that are left.
Complete the table. Use counters if needed. The first one is already done for you.
10. SOLUTION: Since the integers have different signs, the product will be negative. Multiply.
7 × 2 = 14
So, 7 × (–2) = –14.
ANSWER: 11. SOLUTION: Since both integers have the same signs, the product will be positive. Multiply.
3 × 4 = 12
So, –3 × (–4) = 12.
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Inquiry Lab: Multiply Integers
11. SOLUTION: Since both integers have the same signs, the product will be positive. Multiply.
3 × 4 = 12
So, –3 × (–4) = 12.
ANSWER: 12. SOLUTION: Since the integers have different signs, the product will be negative. Multiply.
5 × 3 = 15
So, 5 × (–3) = –15.
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Inquiry Lab: Multiply Integers
12. SOLUTION: Since the integers have different signs, the product will be negative. Multiply.
5 × 3 = 15
So, 5 × (–3) = –15.
ANSWER: 13. SOLUTION: Since both integers have the same signs, the product will be positive. Multiply.
2 × 8 = 16
So, 2 × 8 = 16.
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Inquiry Lab: Multiply Integers
13. SOLUTION: Since both integers have the same signs, the product will be positive. Multiply.
2 × 8 = 16
So, 2 × 8 = 16.
ANSWER: 14. SOLUTION: Since both integers have the same signs, the product will be positive. Multiply.
4 × 1 = 4
So, –4 × (–1) = 4.
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Inquiry Lab: Multiply Integers
14. SOLUTION: Since both integers have the same signs, the product will be positive. Multiply.
4 × 1 = 4
So, –4 × (–1) = 4.
ANSWER: 15. SOLUTION: Since the integers have different signs, the product will be negative. Multiply.
3 × 6 = 18
So, –3 × 6 = –18.
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Inquiry Lab: Multiply Integers
15. SOLUTION: Since the integers have different signs, the product will be negative. Multiply.
3 × 6 = 18
So, –3 × 6 = –18.
ANSWER: 16. SOLUTION: Since the integers have different signs, the product will be negative. Multiply.
2 × 5 = 10
So, –2 × 5 = –10.
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17. Reason Abstractly Study the pattern in the table. Write a rule you can use to find the product of two integers without using counters. Test your rule by finding 3 x (-7) using counters.
Inquiry Lab: Multiply Integers
16. SOLUTION: Since the integers have different signs, the product will be negative. Multiply.
2 × 5 = 10
So, –2 × 5 = –10.
ANSWER: 17. Reason Abstractly Study the pattern in the table. Write a rule you can use to find the product of two integers without using counters. Test your rule by finding 3 x (-7) using counters.
SOLUTION: Review each column of the table. Pay particular attention to whether or not the multiplication sentence has same
signs or different signs. Then compare each product. You will notice that the product of two factors with the same
sign is positive and that the product of two factors with different signs is negative. For 3 x (-7) you should have
three sets of seven negative counters placed on the mat which will be -21. ANSWER: Sample answer: When multiplying integers, when the signs are the same, the product is positive. When the signs are
different, the product is negative. See students' models.
18. Model with Mathematics Write a real-world problem that could be represented by the expression -5 × 4.
SOLUTION: Sample answer: Jack withdraws $5 each week for 4 weeks from his savings account. How much money does Jack
withdraw?
ANSWER: Sample answer: Jack withdraws $5 each week for 4 weeks from his savings account. How much money does Jack
withdraw?
19. WHEN is the product of two integers a positive number? WHEN is the product a negative number?
SOLUTION: The product of two integers is a positive number when both integers have the same sign. Examples:
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5 × 3 = 15 The product is positive since both integers have the same sign.
–4 × (–6) = 24 The product is positive since both integers have the same sign.
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withdraw?
ANSWER: Inquiry
Lab:
Multiply
Sample
answer:
JackIntegers
withdraws $5 each week for 4 weeks from his savings account. How much money does Jack
withdraw?
19. WHEN is the product of two integers a positive number? WHEN is the product a negative number?
SOLUTION: The product of two integers is a positive number when both integers have the same sign. Examples:
5 × 3 = 15 The product is positive since both integers have the same sign.
–4 × (–6) = 24 The product is positive since both integers have the same sign.
The product of two integers is a negative number when the integers have different signs.
Examples:
–5 × 3 = –15 The product is negative since the integers have different signs.
4 × (–6) = –24 The product is negative since the integers have different signs.
ANSWER: The product of two integers is a positive number when both integers have the same sign. The product of two integers
is a negative number when the integers have different signs.
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