John draws three shapes and then a sixth one. You can see them in the picture.

Can he complete and continue the pattern so that the twelfth shape is a circle?

Can the twelfth shape be a square? Can it be a triangle?

This problem explores pattern ideas with some common plane shapes.

Students are encouraged to create and describe their own patterns, and to interpret each other's patterns.

### Problem

John draws three shapes and then a sixth one. You can see them in the picture. Can he complete and continue the pattern so that the twelfth shape is a circle?

Can the twelfth shape be a square? Can it be a triangle?

### Teaching sequence

- Read the problem to the class. Check that the children can count to 12. If that is a problem then give them the correct number of spaces to complete.
- As the children work on the problem (in pairs), ask questions that prompt correct naming and description of the shapes.
- Share problem solutions with explanations.

#### Extension to the problem

Make up their own shape problem for others to solve.

#### Other Context for the problem

Replace the shapes by any other ones, in any other order, that you wish the children to explore.

#### Solution

Three possible answers are:

The original question can be answered by:

square, triangle, circle, square, triangle, circle, square, triangle, circle, square, triangle, circle.

For the square variation you could have:

square, triangle, circle, square, triangle, circle, circle, triangle, square, circle, triangle, square.

For the triangle variation you could have:

square, triangle, circle, square, triangle, circle, square, triangle, square, circle, square, triangle (square, circle).

Consider other variations that the students may suggest.