(7) Inquiry Lab - Add Integers

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

2. • 7.NS.1
Apply and extend previous understandings of addition and subtraction to add
and subtract rational numbers; represent addition and subtraction on a horizontal
or vertical number line diagram.
• 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.
7 Look for and make use of structure.
The Number System
Course 2, Inquiry Lab before Lesson 3-2 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 3-2
Activity 1
Continued

The Number System
In football, forward progress is represented by a positive integer.
Losing yardage is represented by a negative integer. On the first play,
a team lost 5 yards. On the second play the team lost 2 yards. What
is the team’s total yardage on the two plays? Find out in Activity 1.
Use counters to find the total yardage.
Use negative integers to represent the yards lost on each play.
+

4. Course 2, Inquiry Lab before Lesson 3-2
Activity 1
Continued

The Number System
In football, forward progress is represented by a positive integer. Losing
yardage is represented by a negative integer. On the first play, a team
lost 5 yards. On the second play the team lost 2 yards. What is the team’s
total yardage on the two plays? Find out in Activity 1.
Use counters to find the total yardage.
Combine a set of 5
negative counters
and a set of 2
negative counters.

5. Course 2, Inquiry Lab before Lesson 3-2
The Number System
In football, forward progress is represented by a positive integer.
Losing yardage is represented by a negative integer. On the first play,
a team lost 5 yards. On the second play the team lost 2 yards. What
is the team’s total yardage on the two plays? Find out in Activity 1.
There is a total of negative counters.
The model shows that adding a negative
number to another negative number
results in a negative sum.
So, –5 + (–2) = . The team lost a total of yards on the first two plays.
Use counters to find the total yardage.

6. Course 2, Inquiry Lab before Lesson 3-2
Activity 2
Continued

The Number System
The following two properties are important when modeling operations
with integers.
• When one positive counter is paired with one negative counter,
the result is called a zero pair. The value of a zero pair is 0.
• You can add or remove zero pairs from a mat because adding or
removing zero does not change the value of the counters on the
mat.
Use counters to find –4 + 2.
Combine negative counters with positive counters.
The addends have different signs.

7. Course 2, Inquiry Lab before Lesson 3-2
Activity 2
Continued

The Number System
The following two properties are important when modeling operations with integers.
• When one positive counter is paired with one negative counter, the result is
called a zero pair. The value of a zero pair is 0.
• You can add or remove zero pairs from a mat because adding or removing
zero does not change the value of the counters on the mat.
Use counters to find –4 + 2.
Remove all zero pairs.
There are more negative counters
than positive counters.
4 > 2

8. Course 2, Inquiry Lab before Lesson 3-2
The Number System
The following two properties are important when modeling operations with integers.
• When one positive counter is paired with one negative counter, the result is
called a zero pair. The value of a zero pair is 0.
• You can add or remove zero pairs from a mat because adding or removing
zero does not change the value of the counters on the mat.
Use counters to find –4 + 2
Find the number of counters remaining.
There are negative counters remaining. So, –4 + 2 = .
How would the model and sum change if the addition expression was 4 + (–2)?
________________________________________________________________
The model shows that the sum has the same
sign as the greater number of counters.

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