Mr T: The next shape to learn is a trapezium.
Alex: A trap museum? I’ve never heard of it.
Mr T, with a rather serious face: Alex, are you just pretending to be clueless to disrupt the lesson or have you really never heard of a tra-pe-zium?
Alex responds with a sorry face: No sir. I’m not pretending. I’ve not heard of trapping drum.
More class laughter ensues.
Mr T, looks in bewilderment at Alex, and towards the heavens, silently praying to be rescued from this child. Breathes deeply and proceeds to spell the word out on the board, pronouncing it as he writes.
Alex quietly attempts to pronounce along.
Mr T helps: A tra-pe-zium. It is a four-sided shape. Draws a rectangle next to it.
Mr T, asking the whole class: What’s the difference between these two?
James: All the angles in a rectangle are 90° but not the trap-museum (in jest of A’s earlier mistake).
Giggles from classmates, with Alex looking undisturbed by it.
Mr T: That wasn’t nice, James.
James: No sir, but Alex confused me.
Mr T then waits for everyone to regain their composure.
Mr T: So what can we do to work out or calculate (looking at Alex as he says that) the area of the tra-pe-zium? Discuss for two minutes with the person next to you.
Students begin discussing as Mr T goes round listening to the different conversations.
Mr T: 5, 4, 3, 2, 1. Everyone looking this way, thank you. So which group thinks they have a solution?
Alex: You can divide it (pointing at the trapezium) into two triangles and a rectangle.
Mr T: Okay, that’s a really good idea. Thanks Alex.
Maddie: You can divide it into two triangles using one diagonal. The two triangles will have the same height but the base of the other one will be the top straight side.
Mr T: Very good. One less calculation to do than Alex’s group.
Alex: What’s a die-a-gunner? I thought we were doing maths. Aren’t gunners Arsenal football fans?
Class erupts in laughter.
Mr T, doing the sign of the cross, looks fed up.
Benny the bully erupts: A Di-A-GONAL, not a die-a-gunner, you idiot!
Mr T: Oi! That’s not a fun word.
Benny: Sorry Alex. But sir, he he he is so … I better not say what I’m thinking.
Mr T: Good decision. Keep it in. So explain what a diagonal is then.
Benny: It’s a line that goes from one corner of a shape to another corner.
Mr T: Is that clear, Alex? *Alex nods* Okay then. Last group.
Nana: You can find the average of the two bases then times by the height.
Mr T: Good idea, but why do you need the average?
Nana: Because the trapezium looks like it has been adjusted from a rectangle by making the bottom length longer and the top length shorter but keeping the height the same. So the average will tell us the original length.
Mr T: So how would you calculate this average?
James: You add them together and divide by 2.
Mr T: What’s the proper name for this type of average?
Benny: Is it the mean?
Mr T: Yes it is, Benny. Be more confident next time.
Mr T: I think this is a good way to remember the formula. Find the mean average of the two parallel sides, then times by the height.