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I was listening to Arthur Benjamin speak on Cara Santa Maria’s podcast “Talk Nerdy” about his passion for mathematics. [1] In it, he discusses a way to teach Algebra to students by first presenting them with a mathematical (mathemagical, if you will) trick. It goes like this:

Pick a number between 1 - 10, but don’t tell me the number.

Uhh, 7!

Double the number.

Okay, 14.

Now add ten.

Alright, 24.

Divide it by 2.

Hmm, 12.

Subtract the number you originally started with.

Sure thing, 5.

Is the number you’re currently thinking of 5?

Ahh! It is! Pretty neat.

At this point most students will realize that this number will always be five. Curious students will typically want to know why it’s always five. Of course, we can then explain it to them using Algebra.

I feel like this is the perfect introduction to Algebra and wish I was introduced to it this way. It’s a very hands-on approach to what Algebra is capable of. It stimulates curiosity in the student and makes it immediately clear that Algebra is powerful. After being tricked, most students will want to know why and how they were tricked. Algebra; Algebra is why they were tricked.

For people who already know Algebra, this mathemagic trick is just a basic equation:

((2N + 10) / 2) - N

Which always equals five for every positive integer N. It’s very basic Algebra, but to someone who has never been introduced to Algebra, it is totally unsolvable. Until the rules are learned, this equation is simply gibberish. With this this mathemagic trick, though, one could make a student eager to learn the power of Algebra in just the short amount of time it takes to perform it.

I’m extremely happy there are teachers like Arthur Benjamin in the world sparking curiosity in students and showing awesome ways to make learning cool again.


[1] Cara Santa Maria. (2016, September 12). Episode 125 - Arthur Benjamin [Audio podcast]. Retrieved from http://www.carasantamaria.com

Written on September 19, 2016