Tangrams

Hello there mathematicians. We hope you're having a really nice day today.

We were playing around with our tangram pieces and we started to wonder about something, because we noticed that there's 4 triangles. 2 of them are the same size and then there's a medium triangle and a small triangle. And then there's a square and a parallelogram.

There's actually two quadrilaterals, and this made us start thinking about well what actually is a quadrilateral and how many of them can we make? So before we get started, your job mathematicians, is to fill in your Freya chart, which is in your mathematics workbook, and define what you think a quadrilateral is.

So what are some examples? What are some non examples? And then what are the characteristics? Over to you.

Okay mathematicians, welcome back. So, we're going to use this definition of a quadrilateral. That it's a shape with 4 straight sides and 4 vertices or corners. So, so a square fits this definition because it has 4 sides.

Look, 1, 2, 3, 4, they're all straight and it has 4 corners and 4 internal angles. So that's actually a quadrilateral. And so is a

parallelogram. Look, 1, 2, 3, 4 sides, 1, 2, 3, 4 corners or vertices and 4 internal angles. So, but now I started wondering well what other quadrilaterals can I make with my tangram?

And I thought well, is this a quadrilateral? Aha, look, let's check, 1, 2, 3, 3, 4 sides. 1, 2, 3, 4 vertices or corners. So then I started to wonder, mathematicians, about what are all the different shapes I could make? So if I have, yes, using some or all of my tangram pieces. So using one tangram piece I can make a square and I could also make a parallelogram. Oops, well they were already made, mm-hmm, a square and a parallelogram.

But what about if I have two pieces of my tangram? What would we call this quadrilateral? Mm-hmm, yeah it's a trapezium. So I could make a trapezium and I will draw it like this so I can see the square and the triangle, or look I could even write it like this square plus triangle equals trapezium. I know or I could just label it as a trapezium. Mm-hmm, but it's still also a quadrilateral because it fits our definition.

Uh-huh. And then, what if I did this? Does it have 4 sides? Yeah, 1, 2, 3, 4. Does it have 4 vertices? 4 corners? Mmm, 1, 2, 3, 4. So this is also a quadrilateral. Yeah, and it's actually also a trapezium, and I could label it like that if I wanted to. Is there another 4 sided shape I could make with 2 pieces? Ahh, yes.

Look, I could use 2 of my triangles to make, aha, a square. Oh this is cool. So now I have a square. Ohhhh and if I turn it, if I rotate things, oh, no, oh that makes another triangle. Oh I see, like this, oh, now it has, aha, 1, 2, 3, 4 sides and 1, 2, 3, 4 vertices so I've made another parallelogram using my triangles. But it's also using just two pieces.

Mm-hmm, so mathematicians here is your challenge, parallelogram, is how many different quadrilaterals can you make using the pieces of your tangram? And can you actually make at least 1 for 1 piece, 2 pieces, 3 pieces, 4 pieces, 5 pieces, 6 pieces and all 7 pieces? Once you've had a go at that, then come back to your Freya chart and think about revisiting it. Would you add any more information or revise your thinking? Over to you.