Mathemagic and Arithemetricks: Connecting Math Patterns to Magic

One way to engage students in math problem solving is to “perform” some math magic, then have students try to figure out the number patterns that make the tricks possible. Many books, videos, and lesson plans incorporate “mathemagic,” and there are many university studies promoting its effectiveness in the classroom. It’s the presentation that makes this valuable in GT instruction. Here are two “arithmetricks” I’ve used with my third-grade gifted students, along with some presentation tips.

Trick #1 Mind-Reader

Begin by telling the students you’re going to perform a math trick. Say, “I’m going to read your minds.” Have a student volunteer come to the board and turn your back so that you are facing the class and not looking at the board. Say to the student, “I want you to write a 3-digit number in which all 3 digits are different. For example, you can write 852, but not 858 or 555 o 221.” Ask the students watching to raise their hands when the student at the board has followed that direction (this way your class is double-checking that the number written meets the criteria).

Next, say, “Now I want you to write that 3-digit number in reverse. For example, if you wrote 652, you would then write 256, or if you wrote 389, your second number would be 983.” Again, have the students in the “audience” verify by raising their hands when the second number has been correctly written.

Finally, tell the student to find the difference between the two numbers. You may have to give further cues (to find the difference means to subtract the lesser number from the greater). When the audience verifies (perhaps using calculators) that the difference is correct, have them again raise their hands. Then, have the student at the board circle that number, the difference between the two numbers. Ask them to tell you the LAST digit in the difference, the digit in the ones place.

You will then be able to tell them the whole number. If you want to “ham it up,” you can say magical words, make humming noises as you wave your hands around, and act as if it’s taking you a minute to pull it from your mind-reading brain. Then, tell them their number- magically.

I’ve found it heightens interest if you repeat this with another student, changing it up a bit. Then, it’s fun to have the entire class use paper and pencil to follow the directions- everyone at the same time. Students will be astounded when you call them one by one and easily tell them their numbers. Here is how it works, along with tips for eliciting the patterns from students. My students always wanted to try it out on one another and on parents at home, so here is a “cheat sheet” you can give to students.

Trick #2 Human Calculator

This second trick is better explained through a video. I created this one years ago when I taught an online math enrichment class. To present this trick to students, I would again perform it several times, then give hints that lead students toward figuring out how and why it works.

Over the years, some of my more mathematically-inclined students became very excited about exploring other math tricks and how they worked. Here is a resource, written by a secondary math teacher, that provides examples of more advanced mathemagic.

If you try these tricks, or if you have other math magic you can share, subscribers to this site would love it if you would leave a comment here!