Question

Felicia needs to write a story problem that relates to the order in which the numbers -6 1/2 and −10 are represented on a number line. She writes the following:

"During a recent football game, our team lost yards on two consecutive downs. We lost 6 1/2 yards on the first down. During the second down, our quarterback was sacked for an additional 10-yard loss. On the number line, I represented this situation by first locating -6 1/2. I located the point by moving 6 1/2 units to the left of zero. Then, I graphed the second point by moving 10 units to the left of 0."

Determine if you agree or disagree with the representation. Then, defend your stance by citing specific details in your writing.

Answer 1

The representation of the Felicia story problem is not correct.

Explanation:

The problem is about representing the numbers -6 1/2 and -10 on a number line.

In Felicia story, the first number is well represented as the football team lost 6 1/2 yards on the first down of a game, which is a negative representation since is a lost: -6 1/2.

In the second representation, the team lost another 10 yards in the second down, that is
`(-6(1)/(2))+(-10) = -16(1)/(2)` which is an incorrect representation for the purpose of the problem.

So, instead of losing an additional 10 yards, the football team must lost 3 1/2 yards in the second down, that means the team is now at -10 yards, since
`(-6(1)/(2))+ (-3(1)/(2)) = -10`. Here you could graphic -10 moving 10 units to the left of 0.