John left a classroom and walked 35 feet down the hall before realizing he had dropped a piece of paper along the way.
He walked 12 feet back and picked it up.
Explain how to use a number line, starting at 0, to show that the distance John walked and the distance the paper fell away from the classroom are not the same distance. Then find both of these distances.
To use a number line to show that the distance John walked and the distance the paper fell away from the classroom are not the same, we can represent John's starting point as 0 on the number line and mark the distances he walked and then walked back to pick up the paper.
Let's say moving to the right on the number line represents moving forward and moving to the left represents moving backward.
1. John walked 35 feet down the hall, so we move 35 units to the right on the number line.
2. Next, he walked 12 feet back to pick up the paper, so we move 12 units to the left on the number line.
After doing this, we will see that the starting point (0) is not the same as the point where John picked up the paper. This demonstrates that the distances are not the same.
Now, let's find the distances:
- John walked 35 feet down the hall.
- John walked 12 feet back to pick up the paper.
Therefore, the distance John walked is 35 feet, and the distance the paper fell away from the classroom is 12 feet.