# Is a Square a Rectangle?

How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?

How many rectangles can you find in this shape?

Image

How many of the rectangles are differently shaped?

Can you find any that are 'similar' - that is the same shape but a different size?

Can you say what makes a rectangle a rectangle?

Did you know that a square is a special sort of rectangle?

Can you think what is the difference is?

Did you know that a square is a special sort of rectangle?

Can you think what is the difference is?

We have had a solution from someone who unfortunately didn't give his or her name, but it says that there are $14$ different rectangles:

Image
1 |
Image
2 |
Image
3 |
Image
4 |
Image
5 |

Image
6 |
Image
7 |
Image
8 |
Image
9 |
Image
10 |

Image
11 |
Image
12 |
Image
13 |
Image
14 |

Rectangles 1 and 4 are the same as each other.

Rectangles 5, 8, 10 and 12 are the same as each other.

Rectangles 6 and 11 (which are squares) are the same as each
other.

Rectangles 3 and 13 are also squares but they are not the same as
each other. They are similar to 6 and 11.

Rectangles 2, 7, 9 and 14 are different to each other and not
similar to any other rectangle.

### Why do this problem?

The lead question for this problem, "How many rectangles can
you find in this shape?" is an ideal way to introduce children to
consider the properties of rectangles. The aim is not to simply
count the number of rectangles but to discuss what a rectangle
is.

The problem also looks at
whether the rectangles are similar.

For more discussion on
the properties of rectangles, see this sheet.

### Key questions

Can you tell me what a
rectangle is?

Did you know that a
square is a special sort of rectangle? What is the difference
between a square and a rectangle?

How many rectangles did
you find in the shape? Which ones are the same and which ones are
different?

How many squares did you
find?