Tricky Sticks
How it works
Pick any whole number from 1 to 15. Which of the four cards shown above contain your number?
By knowing only which cards on which a number appears, you can determine which number someone chose. Performing the trick is only the beginning, however: The real magic lies in figuring out how the cards were designed!
In this activity, students start by having an instructor perform the magic trick on them. Next, they explore a challenge: Each student is given one 1-unit stick, one 2-unit stick, one 4-unit stick, and one 8-unit stick, and their goal is to figure out how to combine these sticks to make composite sticks of different lengths. (For example, you can combine a 1-unit stick, a 4-unit stick, and an 8-unit stick to make a 13-unit composite stick.) They then connect the adding sticks to the mind-reading trick.
Why we like this activity:
It’s fun! Students enjoy seeing the magic trick, performing it, and figuring out how it works.
It helps to develop numerical reasoning and connects numerical reasoning with physical intuition.
It requires students to engage in mathematical habits of mind:
Making observations / finding similarities and differences / looking for patterns / finding and using strategies / understanding and explaining when exploring how to use the adding sticks to make different numbers.
Understanding and explaining the connection between the adding sticks and the mind reading trick.
It has a low floor and a high ceiling: It’s possible to start using the adding sticks to make different numbers by trial and error, but it’s possible to strategize to do this more efficiently, and it’s also possible to explore adding sticks with different lengths.
To find out more about our approach to math and math education, click here.