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draMATHic Five – Triangle

Hey you! Yes! You! Thank you for stopping by. Before continuing with this post, enjoy the first four here, here, here and here, so you can get acquainted with the rest of the class. Remember to subscribe to this blog to be the first to get on to my latest blog post!

Welcome back! Enjoy this one . . .

Mr T: What’s a triangle? Nana: A shape with 3 sides. Mr T proceeding to draw 3 lines that don’t close up, then asks: Is this a triangle? Nana: No Mr T: Okay, so would you like to refine your definition? Nana: A closed shape with 3 straight sides!

Mr T: And how many angles? Alex: Three Mr T: Good. That’s why it’s called a tri-angle, a 3-angle. Alex: It should be pronounced 3-angle then. As in tri-plets or tri-nity. Benny: I’m impressed you know those words, Alex. Rest of the class giggles in response.

Mr T: Enough. Back to me. Area of a triangle. Any ideas? Maddie: If you multiply one length and one width to get the area of a rectangle which has 4 sides, then for a triangle with 3 sides, you have to multiply one length and half a side to get its area. Mr T looks utterly perplexed, while the rest of the class looks totally confused.

But Nana has her head down trying to follow Maddie’s answer on paper. Mr T, finally speaking up after nearly a minute’s silence: Maddie, care to explain the logic behind your answer? Alex, trying to sound smart, interrupts: Sir, it’s not logic, it’s magic. Maddie for magic. He looks around the room, nodding his head, for someone to agree with him.

Maddie: Shut up you! Mr T: Hey! Be polite, Maddie. I think you can take it as a compliment. Maddie: No, Sir. He’s trying to be funny. Mr T: Well, don’t we all try? But can you now explain your reasoning?

Maddie: Erm, a rectangle has 4 sides but you use only 2 sides to calculate the area. Half of 4 is 2. A triangle has 3 sides, half of 3 is 1 & a half, so you use 1 side and half of another side to get the area. Mr T: I see your reasoning but . . . Nana interjects: Sir, Maddie’s reasoning would only work if the two sides she picks to times together are at 90° to each other like in a rectangle where the length and width are at 90° to each other. Mr T: That’s true Nana. So how can we refine her formula?

Benny: Because we times the base and height of a rectangle, we have to times the base and height of a triangle because those two would always be at 90° to each other. Nana: That’s correct, Benny. Benny, smiles back and blushes feeling rather smart.

Mr T: Well done, Benny. Good thinking. Maddie protests: Sir, but it was all my idea! Mr T: True, but we’re working together to refine it, aren’t we? Maddie: Fair enough.

Mr T: A triangle can also be seen as half a rectangle. So the formula would be base times half the height. Nana: Or base times height divided by 2. Mr T: Yes. I think you all have done well today. Good job y’all! Class laughs, with some students mimicking Mr T’s attempt at an American accent.

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