It can be a challenge to teach change of base in middle school or high school. After explaining the concept most students will look at me in confusion and have difficulty converting between different numeral systems. Introducing the binary numbers is a great first step and can provide tie ins with many other math concepts. In this blog I want to introduce a wonderful “math-e-magic” trick that you can perform to get your students excited about binary numbers.

**Instructions:**

Begin by asking one volunteer to pick a secret number between 1 and 31 (or perhaps the day of the month in their birthday). Then ask them to accurately point out all of the cards that contain their secret number. To guess their secret number total the upper left hand numbers from each of the selected cards (see image). I recommend using some showmanship at this point, for example you might want to tell the students you need to clear your mind first in order to pick up the psychic signals.

**The Math Behind the Magic:**

_{2}.

You can check and see that 19 belongs to exactly three of the cards, the cards chosen correspond to the 1’s in the binary representation and those not chosen correspond to the 0’s.

It is worthwhile to ask the students to look for patterns in the cards before giving away the trick. For example the first card consists of only oddnumbers, and the second consists of numbers with remainder 2 and 3 when divided by four. This corresponds to having a one in the “1’s place” and “2’s place” in the binary representation respectively.

**Conclusion and Beyond:**

My roommate and I built this app and we really appreciate your support. We recommend hooking it up to an external display and performing the trick on a group of students. If you have any questions or feedback please leave us some comments below!