And the twelfth one Is

Achievement Objectives
NA1-6: Create and continue sequential patterns.
Student Activity

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?

Specific Learning Outcomes
Devise and use problem solving strategies to explore situations mathematically (make a drawing, use equipment)
Identify circles, squares and triangles.
Continue and describe a repeating pattern
Description of Mathematics

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.

Required Resource Materials
Activity

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

  1. 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.
  2. As the children work on the problem (in pairs), ask questions that prompt correct naming and description of the shapes.
  3. 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.

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