# Jumping Flea

Alignments to Content Standards:
6.NS.C.7

## Task

A flea is jumping around on the number line.

- If he starts at 1 and jumps 3 units to the right, then where is he on the number line? How far away from zero is he?
- If he starts at 1 and jumps 3 units to the left, then where is he on the number line? How far away from zero is he?
- If the flea starts at 0 and jumps 5 units away, where might he have landed?
- If the flea jumps 2 units and lands at zero, where might he have started?
- The absolute value of a number is the distance it is from zero. The absolute value of the fleaâ€™s location is 4 and he is to the left of zero. Where is he on the number line?

## IM Commentary

This purpose of this task is to help students understand the absolute value of a number as its distance from $0$ on the number line. The context is not realistic, nor is meant to be; it is a thought experiment to help students focus on the relative position of numbers on the number line.

## Solution

It would be a good idea to use a number line to illustrate these solutions.

- If he starts at $1$ and jumps $3$ units to the right, then the flea is at $4$. He is $4$ units away from zero.
- If he starts at $1$ and jumps $3$ units to the left, then the flea is at $-2$. He is $|-2|=2$ units away from zero.
- If the flea starts at $0$ and jumps five units away, then he is either at $-5$ or $5$.
- If the flea lands on $0$ and jumped $2$ units, then he started at either $-2$ or $2$.
- If the absolute value of the fleaâ€™s location is $4$, then he is either at $-4$ or $4$. Since he is to the left of zero, the flea is at $-4$.

## Jumping Flea

A flea is jumping around on the number line.

- If he starts at 1 and jumps 3 units to the right, then where is he on the number line? How far away from zero is he?
- If he starts at 1 and jumps 3 units to the left, then where is he on the number line? How far away from zero is he?
- If the flea starts at 0 and jumps 5 units away, where might he have landed?
- If the flea jumps 2 units and lands at zero, where might he have started?
- The absolute value of a number is the distance it is from zero. The absolute value of the fleaâ€™s location is 4 and he is to the left of zero. Where is he on the number line?