Problem
John was playing around with some triangles, squares and circles. He had put down the first three shapes and the sixth one. You can see them in the picture. Can he finish off the pattern so that the twelfth shape is a circle?
Variation 1: Can the twelfth shape be a square? Can it be a triangle?

What is this problem about?
This problem explores pattern ideas with some basic shapes. By talking about the shapes and how they can be placed to make a pattern with a particular shape in a given position, the children will get a better idea of both shapes and patterns.

This is an open question with no right answer and will provide the opportunity for the children to exercise their imaginations.

Achievement Objectives
Geometry (Level 1)
- classify objects by shape attributes.

Mathematical Processes
- devise and use problem solving strategies to explore situations mathematically (make a drawing, use equipment).

Resources
Mosaic shapes or attribute blocks
Blackline master of the problem

Specific learning outcomes
The children will be able to:
- Identify circles, squares and triangles.
- Continue and describe a repeating pattern (algebra objective)

Teaching sequence

1. Play guess my shape (either describe or use a feely bag to introduce the 3 shapes in the problem.) As they are identified put them in an order as shown in the problem.
2. 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.
3. As the children work on the problem in pairs ask questions about the properties of the shapes.
   What is this shape? How do you know?
   What can you tell me about triangles? Can you draw me a different triangle?
   Can you see any other squares in the classroom? How do you know it is a square?
4. Share solutions. Remember that there are many possible answers to this problem. If all the children have used blocks to solve the problem discuss drawing the shapes.

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
We give possible answers to the question but these answers are not unique.

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.