Question

develop understanding of addition with negative integers
model it: adding a positive and a negative integer
try these two problems involving adding a positive and a negative integer.

1. on the first play, angels football team gains 5 yards from its starting position. on the second play, the team loses 7 yards. to find where the team is relative to its starting position, add 5 and - 7.

a. you can use integer chips to model 5+( - 7). circle all the zero - pairs.
b. what is the value of the remaining chips?
c. 5+( - 7)=
d. after the second play, where is angels team relative to its starting position?

1. you can also use a number line to find 5+( - 7).

a. draw and label arrows to show - 7 added to 5.
b. what number do you end at?
c. 5+( - 7)=

Explanation:

Step1: Understand integer addition concept

Adding a positive and a negative integer is like combining gains and losses.

Step2: Analyze integer - chip model

We have 5 positive chips and 7 negative chips. When we pair them (zero - pairs), we are left with 2 negative chips since \(7 - 5=2\). So the value of the remaining chips is - 2.

Step3: Calculate the sum

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

Step4: Interpret the result for the football team

A result of - 2 means Angel's team is 2 yards behind its starting position.

Step5: Analyze number - line model

To show \(-7\) added to 5 on a number line, we start at 5. Since we are adding a negative number, we move 7 units to the left. We end at - 2.

Answer:

1.

• b. - 2
• c. - 2
• d. 2 yards behind its starting position

2.

• a. Start at 5 on the number line. Draw an arrow 7 units long pointing to the left.
• b. - 2
• c. - 2