Shake, Rattle, and Roll – A Bean Game

Suggested Grades



Students (organized in partners) will analyse a game through probability to decide whether it is a fair game or not.


  • clean empty juice boxes
  • scissors
  • 12 dried beans per student pair
  • marker


  • bean Use the marker to label the beans to match this picture. Click to view, press the ‘back’ button on your browser to return to this page.
  • Cut a hole in the top of the juice box small enough so that only one bean can go through it at a time.
  • bean graph Click for a printable bean graph, press ‘back’ in your browser to return to this page. Or, ask each student pair to draw a bean graph like the example provided.
  • Put 12 beans in the box. Shake the box until two beans come out. Add the numbers on the beans together. Mark an X on the graph above the total of the two beans
  • Put the two beans back in the box. Shake two more out, and mark their total on the graph. Repeat this until you have 10 X’s on the graph. Take a look at the graph. Is there a pattern in the numbers? Do any of them appear more than once?
  • Now shake out and total beans until you have 20 X’s on the graph. What does the graph look like now?
  • Shake and total beans until you have 30 X’s on the graph. Then compare the graph with others’ in the class.
  • Ask students to respond to these questions:
    • Do the graphs look alike or different?
    • Which numbers seem to appear most often?
    • Which numbers seem to appear least often?
    • Why might this be so?
    • What might the graphs look like with 50 X’s? Try it.
    • Do you think the bean game is fair or unfair? Why do you think so?