### Four Triangles Puzzle

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

### Rectangles with Dominoes

Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?

### Chain of Changes

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

# Sorting Shapes

## Sorting Shapes

These shapes can be sorted in many different ways.

In this box there is a collection of triangles:

In this box there is a collection of small blue shapes:

Now you can make your own. Think of a good name for each of your collections.

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### Why do this problem?

This problem provides an opportunity for children to sort and categorise, both of which are important mathematical processes. This open activity challenges children to find their own categories and then name them. This means it is a good way to introduce specific vocabulary associated with properties of shape, or to remind children of relevant mathematical language.

### Possible approach

You could begin by gathering the class together, perhaps on the floor where everyone can see, and showing them a set of 2D shapes. (These can be any set that you have, they don't have to match those in the interactivity!) Gather some of them together and ask the children what your group of shapes has in common. Talk with them about different ways to describe the set of shapes and try some other groups. Alternatively (or in addition), you could use the interactivity with the whole class for a similar purpose.

Ideally, children should have a set of shapes or logic blocks to handle in pairs so that they can move and sort physically. However, if you have access to a computer suite, you might want to ask learners to work in pairs at a screen. (If you do have sets of old Dienes' Logiblocks, then you'll notice they come in different thicknesses too, which adds another variable.) Listen out for children who are clearly justifying their reasons for grouping particular shapes and encourage (or introduce) useful vocabulary.

As a plenary, you could ask some pairs of children to share one of their sets for all to see on the whiteboard. Alternatively, you could challenge pairs to hold up a shape which fits your description, for example "show me a small, red circle".

You could try a similar activity with 3D shapes, too.

### Key questions

What is the same about these two blocks?
Can we find others that could go with them?
What could we call this collection?

### Possible extension

A challenging extension to this activity could be to ask children to draw another different shape which goes with their set.

### Possible support

Some children might need prompting to sort particular groups to begin with, for example "find all the squares". However, as this is an open task, they have the scope to make it as straightforward or difficult as they like, so some children may well surprise you!