And The Twelfth One Is

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?

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.

For the triangle variation you could have:
square, triangle, circle, square, triangle, circle, square, triangle, square, circle, square, triangle (square, circle)..