Jumping Journey
How it works
Imagine you're standing at 0 on a number line. You can only move on the line by jumping 2 or 3 to the left or right. You can make any combination of jumps of either size in either direction. Which numbers can you reach? Are there any numbers you can’t reach? What if your two jump sizes are 2 and 4 instead of 2 and 3?
In this activity, students explore a variety of different pairs of jump sizes. For each pair of jump sizes, they try to figure out whether or not they can reach every number. As they explore new jump sizes, they find that sometimes you can reach every number and sometimes you can't, and they develop rules that help them to predict whether or not it will be possible to reach every number with given pairs of jump sizes (and if not, which numbers they will be able to reach).
Why we like this activity
- It’s fun! Students enjoy trying to reach all the numbers with different pairs of jump sizes.
- It helps students develop numerical reasoning.
- It helps students develop algorithmic reasoning.
It requires students to engage in mathematical habits of mind:
Making observations / looking for patterns / making and testing predictions / understanding and explaining when trying to figure out which lily pads you'll be able to get to with different jump sizes.
Finding and using strategies to get to as many lily pads as possible when you can only visit each lily pad once.
- It has a low floor and a high ceiling: It's easy for students to start exploring by trial and error, but coming up with rules that help to predict when you will and won't be able to get to every number with a given pair of jump sizes is more challenging.