Super shapes

Hi Barbara.

Hello Michelle. How are you today?

I'm very well. I have got a brain sweaty problem for us that I've borrowed fromNRICH maths.

Bring it on.

And I really liked it 'cause it's got instead of numbers. It's got shapes and colors and things. I thought it looked a bit interesting and intriguing. Two things I like. So do you want to work together?

Yes, please.

Ok. So, well, I think what this is saying is that this particular shape, the green triangle, is worth seven and the orange rectangle is worth seventeen. That's its value.

Ok, and then that's interesting because we can use that information here.

I was thinking A could be a good place to start, but do you agree?

Yeah, let's start with A.

Alright. So, so this is how I was thinking, was that I would start there because we know this is seven and that's seventeen and so we just have to work out this one here.

And do you think they are being added? Is that what's happening?

Yeah, I think so because seven and seventeen if you multiplied it would be heaps more than twenty five.

You're right of course.

But if you join seven and seventeen, so from seventeen, three more is twenty and then four more we get to twenty four. So this red shape must be one.

I think so.

Ok. I think A would be seven plus one plus seventeen, which is twenty five. So, that, that works. Almost like a red pebble, look.

A red alien blob is worth one. So is red always one?

I think so.

Ok, so let's check with D.

Oh no it can't be because that would be one, plus one, plus one equals forty eight. That's crazy. Ok, no. So it must be a combination of shape and color that gives you the value. Not just colour, not just the shape and not just the colour but together. And look like something like this one here where there's four green triangles. We know that's four, sevens. We do and then another seventeen. One, seventeen. So, that's twenty eight and seventeen more. Ok, so twenty eight and two more will give me thirty and then I need to add another fifteen, so it's forty five.

So, is that correct? Yes, I think so because seven. That's the seven triangles or four triangles. And then the two and the fifteen. Yes, yeah, ok, that's the rectangle, is forty five and so then subtract that from one hundred makes fifty five. That's right.

And then we'd have to halve both of those.

It's actually got halves in. It must do. Ok 'cause I know that half of fifty is twenty five and I know that half of five is two and a half.

Yes, so that would make it twenty seven and a half.

Ok.

And twenty seven and a half, so that very messy scribbling would mean E is seven plus twenty five and a half plus seven plus seventeen plus seven plus twenty.

No, twenty seven and a half.

Twenty seven and a half. Thanks for helping me revise. Plus seven more.

Wow, and that equals one hundred.

One hundred, wow. So I actually even though this is very messy, I liked this better when we had four sevens.

Yeah.

Plus one, seventeen plus twenty, plus two, plus two, twenty seven and a halves.

Like that? I got lazy like a mathematician then. And that makes one hundred.

That equals to a hundred.

There's actually quite a lot we can work out now I think.

We know, we now know what the triangle is. We know what the orange rectangle is, and we know what the skinny oval is. So we know quite a lot. Oh yeah. And the blob and the blob. So we have, got a few more things to work out.

And so this one here would be about dividing forty eight by three.

Ok, of course, because we've, there's three equal parts.

Oh, I really like this. Ok, over to you mathematicians.

Ok, so what is the mathematics? So in this task it requires a lot of mathematical reasoning. You have to analyse problems so you can think about using what you already know to solve what you don't know yet. And there's a lot of computation as you use your additive and multiplicative strategies with all of the operations, so addition, subtraction, multiplication and division to help you crack each one of those codes. So we hope you enjoyed this challenge mathematicians. Have a great day.