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.

Data Recording handout 1

Data Recording handout 2

Data Recording handout 3

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!