This problem solving activity has an algebra focus.
John draws three shapes and then a sixth one. You can see them in the picture. Can he continue the pattern so that the twelfth shape is a circle?
Can the twelfth shape be a square? Can it be a triangle?
- 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.
This problem explores patterns with some common plane shapes.
Students are encouraged to create and describe their own patterns, and to interpret each other's patterns.
You could also use this problem as an opportunity to introduce and/or revise 2D shape names. Replace the shapes by any other ones, in any other order, that you wish the children to explore.
- Mosaic shapes or attribute blocks (or a digital representation - search for interactive pattern blocks)
- Copymaster of the problem (English)
- Copymaster of the problem (Māori)
The Problem
John draws three shapes and then a sixth one. You can see them in the picture. Can he 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. To support students with counting, provide them with the correct number of spaces to continue the pattern.
- As the children work on the problem (in pairs), ask questions that prompt them to correctly name and describe the shapes.
- Share solutions to the problem and ask children to explain their thinking.
Extension
Make up their own shape pattern problem for others to solve. The solutions will be dependent on the problems posed.
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.