nrich problem solving symmetry

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Why do this problem?

This problem provides an engaging challenge that requires students to work systematically at producing various symmetrical patterns. There are a variety of avenues for exploration and extension work, and learners' results can be used to brighten up the classroom walls.

Possible approach

Key questions

• What different types of symmetry do the initial grids exhibit?
• If you colour a triangle or square here, what else must be coloured in to keep it symmetrical?
• What are the possible symmetries of a finished pattern? 
• How can you be sure you have found all the symmetric patterns?

Possible support

Possible extension, you may also like.

Eight Dominoes

Using the 8 dominoes make a square where each of the columns and rows adds up to 8

Rhombicubocts

Each of these solids is made up with 3 squares and a triangle around each vertex. Each has a total of 18 square faces and 8 faces that are equilateral triangles. How many faces, edges and vertices does each solid have?

Prime Magic

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?