Question

lesson 7 | session 2
model it: adding two negative integers
try these two problems about adding two negative integers.
the football team loses 5 yards from its starting position.
then it loses another 2 yards. the model shows - 5+( - 2).
3 a. why are there no zero pairs to circle?
b. what is the value of the chips? what does the sum mean in this
situation?
4 complete the model
to find - 5+( - 2).

• 5+( - 2)=

connect it
complete the problems below.
5 how is finding the sum 2+( - 3) using integer chips similar to finding the sum
2+( - 3) using a number line? how is it different?
6 a football team loses 6 yards on its first play. it gains 8 yards on the next play.
use a model to find the sum - 6 + 8. what does the sum mean in this situation?

Explanation:

Step1: Analyze zero - pair concept

Zero pairs are formed by one positive and one negative integer chip. In the case of \(-5+(-2)\), there are only negative integer chips, so no zero - pairs.

Step2: Determine value of chips and sum meaning

Each negative chip has a value of \(- 1\). There are \(5 + 2=7\) negative chips, so the value is \(-7\). In the football situation, it means the team has lost a total of 7 yards.

Step3: Calculate \(-5+(-2)\)

\(-5+(-2)=-7\)

Step4: Compare integer - chip and number - line methods for \(2+(-3)\)

Similarity: Both methods represent adding a positive and a negative integer. In both, we start at the position of the positive integer (2) and then account for the negative integer (-3).
Difference: With integer chips, we physically combine positive and negative chips and look for zero - pairs. On a number line, we move left (for negative) from the starting point (2).

Step5: Model \(-6 + 8\)

Using integer chips, we start with 6 negative chips and 8 positive chips. After forming 6 zero - pairs, we are left with \(8 - 6=2\) positive chips. Using a number line, we start at -6 and move 8 units to the right, ending at 2. In the football situation, it means the team has a net gain of 2 yards.

Answer:

a. There are only negative integer chips, so no zero - pairs can be formed.
b. The value of the chips is \(-7\), meaning the team has lost 7 yards in total.
\(-5+(-2)=-7\)
For \(2+(-3)\): Similarity - both represent adding a positive and negative integer starting from the positive integer's position. Difference - integer chips use physical combination and zero - pairs, number line uses movement.
For \(-6 + 8\), the sum is 2, meaning the team has a net gain of 2 yards.