Integer Multiplication Rules

Guided Practice Table (Solutions)

Student Guided Practice Check

Guided Practice Calculations (Step-by-Step)

Notice patterns between positive and negative pairings

a) 3 × 4

Same signs (+, +)
3 groups of 4 = 12

Ans:

12

b) 2 • 5

Same signs (+, +)
2 groups of 5 = 10

Ans:

10

c) 4(2)

Same signs (+, +)
Parentheses mean multiply

Ans:

8

d) 3(−4)

Diff signs (+, −)
(−4) + (−4) + (−4) = −12

Ans:

-12

e) 2 * −5

Diff signs (+, −)
2 groups of −5 = −10

Ans:

-10

f) 4 × (−2)

Diff signs (+, −)
4 groups of −2 = −8

Ans:

-8

Lesson 11: Multiplying Signed Integers • Teacher Answer Key Page 2 of 4

Part 2: Independent & Partner Work Solutions

Skill Practice & Conceptual Reasoning

Answer Key

Sign & Product Analysis (Solutions)

Checking two-digit integer multiplication

Independent Work (Solutions)

Notice signs: g-i different; j-l same

g) −3 • 4

Diff signs → neg

Ans:

-12

h) −2(5)

Diff signs → neg

Ans:

-10

i) −4 * 2

Diff signs → neg

Ans:

-8

j) (−3)(−4)

Same signs → pos

Ans:

12

k) −2 * −5

Same signs → pos

Ans:

10

l) −4 × (−2)

Same signs → pos

Ans:

8

Partner Work (Reasoning Key)

Tell whether the product is positive or negative WITHOUT multiplying. Explain your reasoning.

1)15,735(−213)

Sign of product: Positive ✓ Negative

Reasoning: The two factors have different signs (one positive and one negative). Multiplying different signs always results in a negative product.

2)−635 * (−1,250)

Sign of product: ✓ Positive Negative

Reasoning: Both factors have the same sign (both negative). Multiplying two negative numbers always yields a positive product.

3)−94 × 681,212

Sign of product: Positive ✓ Negative

Reasoning: The two factors have different signs (negative factor multiplied by positive factor), which always gives a negative product.

Lesson 11: Multiplying Signed Integers • Teacher Answer Key Page 3 of 4

Part 3: Applications & Extension Solutions

Fluency, Challenge & Real-World Problems

Answer Key

Determine the Product of Each Expression (4–7)

Fluency Solutions

4. −13(0)

Zero Property: any number × 0 = 0

Ans:

0

5. 15(−2)

Diff signs (+, −) → negative: 15 × 2 = 30

Ans:

-30

6. −6 • (−13)

Same signs (−, −) → positive: 6 × 13 = 78

Ans:

78

7. −11 * 11

Diff signs (−, +) → negative: 11 × 11 = 121

Ans:

-121

Challenge Problems! (Three or More Factors)

Odd count of negatives = negative; even count = positive

8. 6(−9)(−1)

6 × (−9) = −54

(−54) × (−1) = +54

Ans:

54

9. −7(−3)(−5)

(−7) × (−3) = +21

21 × (−5) = −105

Ans:

-105

10. 3 • (−12) • 0

3 × (−12) = −36

(−36) × 0 = 0

Ans:

0

11. 1 • (−1) • 1 • (−1)

[1 × (−1)] × [1 × (−1)]

(−1) × (−1) = +1

Ans:

1

Real-World Problem Solving (Solutions & Modeling)

Focus on contextual interpretation of negative quantities

12

You lose 5 Soar Bucks each time you are late for a day of school. Write an integer expression to represent the change in your balance if you were tardy for 3 days of school in a week!

Multiplication Expression:

3 × (−5) or (−5) × 3

Product & Meaning:

−15 (Account decreased by 15 Soar Bucks)

Work space / models:

Repeated addition: (−5) + (−5) + (−5) = −15 3 groups of −5 lost bucks = total loss of 15 bucks

13

Frank owes five people two dollars each. How much money does he owe in total?

Multiplication Expression:

5 × (−2) or 5 × 2 = 10 owed

Product & Meaning:

−10 (Frank owes a total of $10)

Work space / models:

Debt representation: 5 × (−$2) = −$10 net balance Owing $2 five separate times totals $10 in debt

14

The offense of a football team lost three yards on two consecutive plays. How many yards in total were lost?

Multiplication Expression:

2 × (−3) or (−3) × 2

Product & Meaning:

−6 (The team had a total loss of 6 yards)

Work space / models:

Field position: (−3) + (−3) = −6 yards 2 plays losing 3 yards each equals 6 total yards lost

Lesson 11: Multiplying Signed Integers • Teacher Answer Key Page 4 of 4