I love using shape puzzles to explore some of the principles of algebraic thinking. The examples in this blog post are from I See Reasoning – Y4 (there are shape puzzles in all the KS2 I See Reasoning eBooks) and I often use these questions with older children too. I’ve found children love completing these questions and love creating their own puzzles!
Step 1: These questions help to uncover the key strategies for working out the value of the shapes.
Left example: the second line has one more circle than the first line and its total is 5 more. Therefore one circle = 5.
Right example: a rectangle is 2 more than a diamond. The child answering this question extended the pattern to show that three diamonds have a sum of 12 and therefore one diamond = 4.
Step 2: We complete shape puzzles using the thought processes from step 1. There are prompts (which can be used or can be hidden) to suggest possible starting points.
Step 3: Children complete different puzzles, explaining their starting points.
Step 4: Time for children to design their own puzzles! I specify two things: there can’t be any rows/columns that are made using only one shape; and the designer of the puzzle must be able to explain a possible starting point.
This webpage, designed by the brilliant Jonathan Hall, enables you to automatically generate these puzzles. And this blog explains how I’ve introduced shape puzzles to children in Y2. A fantastic way to explore some of the big ideas of algebra!
For more information about Gareth Metcalfe’s INSET and twilight maths training click here or for CPD sessions about using the I See Reasoning eBooks. My passion and expertise is in developing children’s ability to reason mathematically and building children as mathematical problem-solvers.