Jumping Beans
How it works
We have a row of 21 squares, labeled 0 through 20 from left to right. We have a bean that starts in square 0.
- The goal is to get the bean into square 1.
- However, we only have two legal moves: The bean can only jump 5 squares to the right or 3 squares to the left.
Is it possible to get the bean into square 1 using only these moves? If not, what is the square with the smallest number (bigger than 0) we can reach? What if the bean can only jump 6 squares to the right or 3 squares to the left? What about with other pairs of jumps?
In this activity, students explore a variety of different jump sizes. They discover that it's possible to get the bean into square 1 for some jump sizes but not for others. They develop strategies for getting the bean into square 1 when it's possible, and try to predict whether or not it will be possible to get the bean into square 1 based on the jump sizes.
Why we like this activity
- It’s fun! Students enjoy trying to solve the different puzzles and predicting whether or not it's possible to solve different puzzles.
- It helps students develop algorithmic reasoning.
- It helps students develop numerical reasoning.
It requires students to engage in mathematical habits of mind:
Using logic and finding and using strategies when trying to get the bean into square 1.
Looking for patterns, using logic, making and testing predictions, and understanding and explaining when trying to determine whether it's possible or impossible to get the bean into square 1 with a given pair of jumps.
- It has a low floor and a high ceiling: Students can get started solving puzzles by trial and error, but more complex puzzles require more careful strategizing, and there are some interesting patterns to discover!