# Three of a Kind

Pupils use their knowledge of geometry to describe a pattern.

# Practical details

Suitability
National Curriculum levels 3 to 8
Time
30 minutes to 1 hour
Resources
Ruler and perhaps additional paper, plain or squared; they may also request an angle measurer and/or a pair of compasses

# Key Processes involved

Representing
Use mathematics, including angles and symmetry, to describe the shapes
Analysing
Consider the relationship between the lengths of the edges of the shapes, between the areas within the shapes, and between the positions of the shapes

# Teacher guidance

Check that pupils understand the task; show it on the whiteboard and comment:

• Think about what is the same and what is different about the shapes; think especially about why the hexagons might be where they are.
• Write down everything you can think of so that I can tell what you know.

The task requires geometric skills such as reflection and properties of shapes, but can also be extended to higher level skills such as enlargement. During the work, the following probing questions may be useful:

• What do you know about regular hexagons?
• Are the two black outside lines that connect the three shapes important? What do they tell you?
• Why do you think the hexagons are placed where they are?
• How would you go about drawing the next hexagon in the sequence?

As in any open ended activity, pupils respond in different ways, but in general, pupils working at the lower levels tend to describe the shapes. More able pupils will see connections between the shapes, with the most able generalising and quantifying the relationships in ways which enable a prediction of how the pattern could continue.