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Dear Mitch,

That's a great trick you presented last week for remembering the three types of triangles. Do you know any other fun ways to teach some properties of triangles?


Grade 3 Teacher London, UK



Absolutely! Let me share one of my all-time favorite triangle problems, which high-schoolers often get wrong, but kindergardeners often figure out (with the right guidance, of course). The question (which has appeared on so many tests from so many countries over the years that it has become like a familiar friend) is usually presented like this:

Scalene Triangle

And it's always multiple choice. It says: The side that doesn't give its measurement is which of the following lengths?

a) 14
b) 13
c) 12
d) 11

Most educated adults get it wrong. The answer is 11, because there is a rule: NO side of a triangle can EVER be equal to or greater than the lengths of the other two sides added together. 5 + 7 = 12, so the only choice that's not equal to or greater than twelve is choice d, eleven.

AND THERE'S A GREAT WAY THAT EVEN THE YOUNGEST STUDENT DISCOVERS THIS ON HIS/HER OWN: You just need a supply of Q-tips. (in England, they may be called something like 'small cotton balls on end of short stick for ear-cleaning purposes'), but that's what they are. And they now come in a mesmerizing array of party-colors – don't ask me why; they're for ear wax removal... Anyway, I have them in a jar and refer to them as line segments, which they do resemble strikingly. You point out that they're new, of course, and have never been used for their 'other' purpose. Then in groups on the floor you have them make the first two legs of the triangle, one with seven q-tips touching end to end in a straight line (each q-tip is a 'unit' of measurement), and have them make the other leg with five q-tips. (They pick out any angle they like). Then offer a big prize to any group that can complete their triangle with twelve or thirteen q-tips. 'No problem', they say, and you watch as the angle becomes more and more obtuse, until – Oh, the q-tips aren't actually touching, but he said they have to touch... try again, and they do, but then...


There's no air inside as the triangle folds SHUT into one side sitting on top of the other to meet the end points of the third side... ...oh... Hmmmmm... Is THAT why cutting a diagonal across a square or rectangle (perhaps through a building to avoid rain) is ALWAYS a shortcut, rather than going around the square building.... Just a thought.

-- Mitch