# Super Shapes

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

## Problem

Each of the following shapes has a value:

Image
| $= 7$ | Image
| $= 17$ |

Can you discover the values of the other shapes using the information below?

(a) | Image
+ Image
+ Image
| $= 25$ |

(b) | Image
+ Image
+ Image
+ Image
| $= 51$ |

(c) | Image
+ Image
+ Image
+ Image
+ Image
+ Image
| $=136$ |

(d) | Image
+ Image
+ Image
| $=48$ |

(e) | Image
+ Image
+ Image
+ Image
+ Image
+ Image
+ Image
| $=100$ |

## Getting Started

What do the other shapes add up to in each case?

So, what is left for the circle or circles?

## Student Solutions

PLEASE NOTE the problem was slightly changed in 2018 so that it was not a red circle in each of the 5 questions but a different red shape each time.

Joanne wrote:

In the **first** line the circle is worth 1.

I worked this out by adding 17 and 7 together = 24 then add 1 =25

In the **second** line the circle is worth 20.

I worked this out by adding together 17, 7, 7 =31 add 20 =51

In the **third** line the circle is worth 44.

I worked this out by adding together 17, 17, 7 and 7 =38

In the **fourth** line the circle is worth 16.

I worked this out by doing 48 divided by 3 =16

In the **fifth** line the circle is worth 27.5

I used the same method as the 1st, 2nd and 3rd lines.

**Christopher** and **Matthew** explain further about the final answer:

On the last one the total was 100. We had to add 17 + 7 + 7 + 7 + 7 = 45.

This meant there was 55 left which we halved to get the answer 27 and a half.

**Matthew** from **Worth School** agreed with the answers given above but has recorded his thinking differently:

I looked at it as an equation.

What Matthew already knows: Triangle = 7, Rectangle = 17 and he uses C = circle

**1.**

If 17+C+7=25 then C =?

This can be rearranged as:

25-(17+7)=C

25-24=C

1=C

**2.**

If 17+7+7+C=51 then C=?

This can be rearranged as:

51-(17+7+7)=C

51-31=C

20=C

**3.**

If 7+7+17+17+C+C=136 then C=?

This can be rearranged as:

136-(7+7+17+17)=2C

136-48=2C

88=2C

44=C

**4.**

If C+C+C=48 then C=?

This can be rearranged as:

48=3C

48/3=C

16=C

**5.**

If 7+C+7+17+7+C+7=100 then C=?

This can be rearranged as:

28+17+2C=100

45+2C=100

2C=100-45

2C=55

C=27.5

Thank you also to sets of Moorfield pupils, **Niall** and **Adam** , **Steven** and **Matthew, Christopher, Elliot** and **Luke, Hannah, Amy** and **Emma, Thomas** and **Robert** , as well as to **Abi** . From **Ms Flynn's class in Ringmer County Primary** in Sussex, we heard from **Nick** and **Tom.** **Ellen, Stacie, Rosie** and **Natasha** from **St. Aldhelm's Combined School** all sent in the mail their calculations to this set of problems. **Carla** and **Georgia** from **Tattingstone Primary School** in Suffolk both sent their work as email attachments. Well done also to **Mithran** .

Each one of you put a lot of effort into your work and your explanations were clear and well thought-out.

## Teachers' Resources

**Why do this problem?**

### Possible approach

This problem would make a good starter. Make sure that paper and/or mini-whiteboards are available for pupils to jot down any workings.

### Key questions

How did you work this out?

### Possible extension

Shape Times Shape involves multiplication rather than addition and requires much more sophisticated reasoning.

### Possible support

You could provide calculators if you want children to focus on the method rather than the arithmetic.