# Super shapes

Stage 3 – a thinking mathematically targeted teaching opportunity focused on reasoning and using additive and multiplicative strategies to find the value of shapes.

Adapted from NRICH

## Syllabus

Syllabus outcomes and content descriptors from Mathematics K–10 Syllabus (2022) © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2024.

## Outcomes

- MAO-WM-01
- MA3-AR-01
- MA3-RQF-01
- MA3-RQF-02

## Watch

Watch Super shapes video (5:08).

[Text over a navy-blue background: Super Shapes. Beneath this, text reads: From NRICH maths https://nrich.maths.org/1056. Small font text in the top left-hand corner reads: NSW Department of Education. In the lower left-hand corner is the red waratah of the NSW Government logo.]

**Michelle**

Hi Barbara.

**Barbara**

Hello Michelle. How are you today?

**Barbara**

I'm very well.

[Two pieces of paper sit side by side in portrait orientation, the piece of paper on the right is light-blue and blank, the piece of paper on the left has the following text in a blue banner at the top of the page: Super Shapes. To the left of this, on the other end of the banner, is a sequence of progressively smaller blue squares forming a spiral, with the text:’ nrich’ to it’s right.

Beneath this is the following text: Each of the following shapes has a value: Beneath this text is a green triangle with the text: ‘= 7’ to it’s right, and an orange rectangle, with the text: ‘= 17’ to it’s right.

Beneath this is the following text: The value of the red shapes changes in each of the following problems. Can you discover its value in each problem below, if the values of the shapes are being added together?

Beneath this are 5 rows of assorted shapes labelled (a), (b), (c), (d) and (e). Row A contains a green triangle followed by a red rounded shape and an orange rectangle. To the right of these shapes is the text: = 25.

Row B contains an orange rectangle followed by two green triangles and a red rounded shape. To the right of these shapes is the text: = 51.

Row C contains 2 green triangles followed by 2 red pentagons and 2 orange rectangle. To the right of these shapes is the text: = 136.

Row D contains 3 red triangular shapes. To the right of these shapes is the text: = 48.

Row E contains a green triangle followed by a red circular shape, a green triangle, an orange rectangle, a green triangle, a red rounded shape and another green triangle. To the right of these shapes is the text: ‘= 100’.]

**Michelle**

I have got a brain sweating problem for us that I've borrowed from NRICH maths.

**Barbara**

Bring it on.

**Michelle**

And I really liked it because it's got, instead of numbers, it's got shapes and colours and things and I thought it looked a bit interesting and intriguing.

(LAUGHTER)

**Barbara**

Two things I like.

**Michelle**

So do work together?

**Barbara**

Yes, please.

[Michelle points to the green triangle and then the orange rectangle at the top of the page.]

**Michelle**

Well, I think what this is saying is that this particular shape, the green triangle, is worth seven and the orange rectangle is worth 17. That's its value.

**Barbara**

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

[Barbara points at the row labelled (a).]

**Michelle**

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

**Barbara**

Yeah, let's start with A.

**Michelle**

Alright, so this is how I was thinking was that I would start there because we know this is seven and that's 17. And so we just have to work out this one here.

[In row A, Michelle points to the green triangle then the orange rectangle then the red round shape.]

**Barbara**

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

**Michelle**

Yeah, I think so, because seven and 17, if you multiply it, it would be heaps more than 25.

[Michelle points to the green triangle then the orange square in row A, then to the text reading: = 25.]

**Barbara**

Oh, you're right, of course.

**Michelle**

But if you joined seven and 17, so from 17, three more is 20 and then four more would get to 24.

**Barbara**

So this red shape must be one?

**Michelle**

I think so. So I think A would be 7+1+17, which is 25, so that...

[Using a black texter, Michele writes: a. 7 + 1 + 17 = 25 on the blue piece of paper.]

**Barbara**

That works.

**Michelle**

Almost like a red pebble...

(LAUGHTER)

..red alien blob is 1.

[Using a red texter, Michele draws a round red shape above the number ‘1’.]

**Barbara**

So is red always 1?

**Michelle**

I think so...

**Barbara**

OK, so...

**Michelle**

Let's check with D. Oh, no.

[Michelle points to the three triangular red shapes making up row D and then to the text to the right of the row reading: = 48]

**Barbara**

No, it can't be.

**Michelle**

It can't because that would be 1+1+1=48.

**Barbara**

That's crazy. OK, no... so it must be a combination of shape and colour. It gives you the value. So not just the shape and not just the colour, but together.

**Michelle**

And look, like something like this one here where there's four green triangles.

[Michele points to the 4 green triangles and then the orange rectangle in row E.]

**Michelle**

We know that's four sevens.

**Barbara**

We do and then another 17.

**Michelle**

One 17. So it's 28 and 17 more.

**Barbara**

OK, so 28 and two more gives me 30 and then I need to add another 15. So it's 45.

[Barbara writes the following text on the blue page: e. 28 + 2 = 30. Beneath this she writes: 30 + 15 = 45.]

**Barbara**

Is that correct?

**Michelle**

Yes, I think so, because seven, that's the four triangles and then the two and the 15, yes...

[Michelle draws a line to a triangle from the number ‘28’.]

**Barbara**

Yeah, OK.

**Michelle**

The rectangle is 45 and so then subtract that from 100, makes 55.

[Michelle outlines the number 2 and the number 15, which are aligned vertically, and draws a rectangle above them. To the right, she then writes: = 55.]

**Barbara**

That's right.

**Michelle**

And then we'd have to half twice of those.

[Michelle points to the two round red shapes in row E.]

**Barbara**

So it's actually got halves in it?

**Michelle**

Must do.

**Barbara**

OK, because I know that half of 50 is 25 and I know that half of five is two and a half.

**Michelle**

Yes. So that would make it 27.5.

[Michelle draws two lines out from the bottom of the number ‘55’ and at the end of each of these lines writes: 27 ½.]

**Barbara**

OK.

**Michelle**

And 27.5.

[ On the blue piece of paper, beneath the numbers for row A, Michelle writes: e. 7+25 ½ + 7 + 17 + 7 + 27 ½ . ]

**Michelle**

So that very messy scribbling would mean E is 7+25.5 +7+17+7+27.5.

[Michelle crosses the 5 in the first 25 ½ and writes 7 above it.]

**Michelle**

Thanks for helping me revise, and plus seven more.

[Michelle adds ‘+ 7’ to the end of the equation.]

**Barbara**

Wow, and that equals 100.

**Michelle**

And that equals 100. Actually, even though this is very messy, I liked this better when we had four sevens.

**Barbara**

Yeah.

**Michelle**

Plus one 17 22

(CROSSTALK)

**Barbara**

Two 27.5.

**Michelle**

Like that.

[Beneath the previous equation, Michelle writes: 4 sevens + 1 seventeen + 2 x 27 ½.]

**Michelle**

I got lazy like a mathematician then.

**Barbara**

And that makes 100, equals to 100. There's actually quite a lot we can work out now, I think, because 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.

**Michelle**

Oh, yeah.

**Barbara**

Oh, and the blob.

**Michelle**

And the blob.

**Barbara**

And the blob, so we have got a few more things to work out.

**Michelle**

And so this one here would be about dividing 48 by three.

[Michelle points to row D.]

**Barbara**

OK, of course, because there's three equal parts.

**Michelle**

Oh, I really like this.

**Barbara**

Me too.

**Michelle**

OK, over to you mathematicians.

[Text on a blue background reads: Over to you, mathematicians!]

**Michelle**

OK, so what is the mathematics?

[Text on a white background reads:

* This task 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.

* There is also a lot of computation as you use additive and multiplicative strategies to help you crack the codes!]

**Michelle**

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.

## Instructions

- Can you discover the value of each of the shapes in each of the problems?
- Record your thinking in your workbook.