Tangrams 1

Hi there mathematicians, welcome back. We hope you're having a really delightful day, today. We're going to use our tangram pieces here to explore trapeziums. So before we get started, can you please write down in your notebook what you think a trapezium is?

So we've got a frayer model for you to fill out. What do you think are some examples of a trapezium? Some non examples of a trapezium and what you think a definition might be. So over to you.

Let's talk about what a trapezium is defined as. So a trapezium has this definition. That it's a quadrilateral with at least one pair of parallel sides. So if I take this square for example, it actually fits the definition of a trapezium.

It's a quadrilateral, meaning it has four angles and four sides and at least one pair is parallel because this side is parallel to this side. And actually this side is parallel to this side. So a square is a special kind of trapezium. And yes, that means I could also think a rectangle or an oblong, is also a kind of trapezium.

Ah ha, because its a quadrilateral that I've just made. It has four angles and four sides and at least one pair is parallel. These two lines here run in parallel. And these lines here are also parallel. Yes, so your challenge today mathematicians is to think about how many trapeziums, using this definition here, can you make using two tangram pieces?

So it could be possible that our tangrams look different. So, let's try to make oh, our trapeziums, sorry, look different. Let's try to think about making one. What are you thinking?

Ah, ok. If I take the parallelogram and the triangle. Oh yes. That forms a trapezium, doesn't it? Ok, so here's one that I can make. I've got my triangle and my parallelogram. So, a triangle and a parallelogram is equivalent to, or makes a trapezium. Yeah.

This is actually a pretty cool idea. What's another way I could to make one? Ah yeah, if I keep the parallelogram and use a triangle. What about this? Like that? Is it a quadrilateral? Let's check. One, two, three, four angles and one, two, three, four sides. Is at least one pair of the lines parallel? Well, these ones aren't parallel 'cause if we continued them they would intersect, but these ones. Yeah, so this is also a trapezium.

Yes. So, I have a triangle combined with my parallelogram. So a triangle and a parallelogram is an equivalent shape to a trapezium or equivalent in definition. Yeah, actually look, they both use the triangle and the parallelogram. I wonder if I could make it another way without using the parallelogram?

What are you thinking? Oh, ok. Like that? Ah, yes. Let's check. Has it got four angles? Yes. One, two, three, four, Does it have four sides? Yes. One, two, three, four. At least one pair of sides parallel? These ones are parallel aren't they because if we continued them they wouldn't intersect. Where as these ones we can imagine they would crossover up about here, so this was another way.

I have a square. Yes, you're right, a trapezium plus a triangle is a trapezium. That's a really nice way of thinking about it. I'm going to call it a square because it's a special kind. Plus a triangle, equals a trapezium. Alright mathematicians, it's now over to you. Your challenge is we made trapeziums using just two of the shapes. Yeah, what I wonder is can we make some trapeziums using three of our seven shapes from our tangrams? And then of course, what about using four of them, five of them, six of them, and seven of them? Yes, and there could be lots of different ways as you're seeing.

Alright mathematicians. It's now over to you. Have fun.

Ok, then mathematicians, how did you go?

Mmm, some of them really made me have to think hard too. And I had to keep coming back to this idea of what a trapezium is defined as. But it has to have, it's a quadrilateral meaning it has the four angles, which also means it has four sides and then at least one pair had to be parallel.

Yeah, so, here is just one for each that I found. I found some others but I put one in a table for you. Mostly just because you know I love organising my information into a table 'cause it helps me as a mathematician to see my thinking and to share it with other people as well.

Uh, and I kept my seventh one here just because I really liked it and it took me awhile to figure that out. But, what I did start thinking about was keeping something consistent. So I don't know if you can see this, how I had the square and a triangle and then I kept that and added something to the side to see if it worked. And then I did the same here where I kept my square and two triangles and tried adding another shape to see if, if I could just build on to keep the trapezium, yeah.

And then sometimes that didn't work so I had to like move things around and rotate. But then in these other parts you can see the square and the triangle and parallelogram, here stay the same. Yeah, and that triangle there's a little core there that remains and down on the seventh it was just a square and the triangle.

And did you notice this also with the shapes? That you can combine two-dimensional shapes to form other shapes. Yeah, and that we can partition or break apart shapes to make other shapes, just like how we can partition numbers to make other numbers. I thought this was a really cool thing that you can see a trapezium being made of a square and a triangle or a trapezium being made of a square and two triangles. Or that you could partition a trapezium to make a square and two triangles. So cool.

So mathematicians back to you to your Freya chart now to think about, now we've played around with this. What would you change? So what are some other examples or non examples of trapeziums that you could include, and what would you refine or add on to your definition and characteristics? Over to you.

Oh, and before you go mathematicians, you're right. I just took this away really quickly. But if I kept it there actually we could add another row into this table. You're right, because technically we can make a trapezium with just one. We could have made it with a square, ah ha and we could also have made it with a parallelogram. Yes, because they fit this definition of a trapezium. So let's quickly squeeze that in together.

Which one would you prefer to choose? The square or the parallelogram? The square. Ok. And that is a square. Plus nothing else. Alright over to you mathematicians.

Nice pick up.

So, what's some of the mathematics we're seeing here today? Yeah, you can combine two-dimensional shapes to form other shapes, which means that you can also decompose or partition or break apart two-dimensional shapes to form other shapes. Yes, and this reminds us of how numbers work that inside bigger numbers are smaller numbers, just like inside bigger shapes are smaller shapes.

Yes, it reminds us of that task we looked at with the you cubed number visuals where we could see things like inside a six are three twos. Inside the trapezium are two triangles, a parallelogram and a square. We also saw that shapes can look different but have some important characteristics that allow them to be classified in the same way.