(7) Inquiry lab - Multiply Integers

1. WHEN is the product of two
integers a positive number?
WHEN is the product a
negative number?
The Number System
Course 2, Inquiry Lab before Lesson 3-4

2. • 7.NS.2
Apply and extend previous understandings of multiplication and division
and of fractions to multiply and divide rational numbers.
• 7.NS.3
Solve real-world and mathematical problems involving the four operations
with rational numbers.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
The Number System
Course 2, Inquiry Lab before Lesson 3-4 Common Core State Standards © Copyright 2010. National Governors Association Center
for Best Practices and Council of Chief State School Officers. All rights reserved.

3. Course 2, Inquiry Lab before Lesson 3-4
Activity 1
Continued

The Number System
The number of students who bring their lunch to Phoenix Middle
School has been decreasing at a rate of 4 students each month.
What integer represents the total change in the number of students
bringing their lunch after three months?
The integer represents a decrease of 4 students each month.
After three months, the total change will be 3 x (–4).
Add 3 sets of 4 negative
counters to the mat.

4. Course 2, Inquiry Lab before Lesson 3-4
The Number System
The number of students who bring their lunch to Phoenix Middle School
has been decreasing at a rate of 4 students each month. What integer
represents the total change in the number of students bringing their
lunch after three months?
Count the number of negative counters.
There are negative counters.
So, 3 x (–4) = . After three months, the total change in the number of
students bringing their lunch will be .
The model shows that adding sets of negative counters results in negative
counters on the mat.

5. Course 2, Inquiry Lab before Lesson 3-4
Activity 2
Continued

The Number System
Use counters to find –2 x 3.
If the first factor is negative, you need to remove counters from the mat.
There are no counters on the mat, so add two sets of three
zero pairs on the mat. The value on the mat is zero.

6. Course 2, Inquiry Lab before Lesson 3-4
The Number System
Use counters to find –2 x 3.
If the first factor is negative, you need to remove counters from the mat.
Remove two sets of three positive counters from the mat.
There are negative counters remaining.
So, –2 x 3 = .
The model shows that removing sets of positive counters results in sets of
negative counters that are left.

7. Course 2, Inquiry Lab before Lesson 3-4
Activity 3
Continued

The Number System
Use counters to find –2 x (–4).
Both factors are negative. Remove sets of negative
counters from the mat.
There are no counters on the mat, so draw two sets of
four zero pairs on the mat.

8. Course 2, Inquiry Lab before Lesson 3-4
The Number System
Use counters to find –2 x (–4).
Cross out two sets of four negative counters from the mat.
There are positive counters remaining.
So, –2 x (–4) = .
The model shows that removing sets of negative counters results in
sets of positive counters that are left.

9. Course 2, Inquiry Lab before Lesson 3-4
WHEN is the product of two
integers a positive number?
WHEN is the product a
negative number?
The Number System