A Patchwork Piece

Stage: 2 Challenge Level:

Why do this problem?

This problem encourages learners to develop their spatial reasoning. The fact that they are asked to recreate the pattern pieces gives the opportunity for mathematical construction which is perhaps quite rare at this level.

By the far easiest way to do this construction is to start with an octagon and draw the square round it. Drawing an accurate regular octagon in a set sized square requires mathematical knowledge beyond primary level. Otherwise children can make a design in which the octagon is not regular.

Possible approach

A nice way to start this activity might be to put up a picture of the final design and then of a single square.

Invite the group to talk about what they can see. (Children will often call this a diamond which gives a good opportunity to discuss the properties of a square.)

When the class begin to work on the problem itself, encourage them to work in pairs. Their conversations will help you to assess their knowledge and understanding of properties of 2D shapes, and how readily they use vocabulary associated with shape and position.

Key questions

What you can see in this design?

What different shapes are there in the picture? Tell me about them.

Which shapes are the same and which are different?

What can you tell me about the shape in the middle?

How are you going to draw regular octagon?

What size are the eight internal angles?

Possible extension

Learners could try to make this design using the same pieces or even this one called Castle wall.

Possible support

Suggest making a design in which the octagon is not regular so the triangles can be any shape. Starting with a square with sides that are readily divided into three will make a pleasing pattern.

Ruler & protractor constructions. Visualising. Tangram. Compound transformations. STEM - General. Investigations. Practical Activity. Working systematically. Measuring equipment. Interactivities.