Shape Times Shape

This problem is a motivating context in which children can practise their times tables facts, but crucially, in a way that demands reasoning too. The task may look impossible to solve at first, which helps to draw children in as they become curious about finding a way to a solution. The problem also helps expose children to the idea of a symbol (in this case a shape) representing a number.

Try to say very little as you introduce the task, just what is stated on the problem itself and then give learners a few minutes to think on their own. (You could display the task on the board, and/or give out printed copies of this sheet.) Invite them to talk with a partner and discuss their thoughts - this may involve asking questions or clarifying the task together, or it may be that they consider how to begin solving the problem.

 

Bring the whole group together to share questions/ideas.  You might like to collate all contributions on the board without giving any response other than to thank pairs.  Once you have a full list of thoughts, you can decide how to address them.  Pass any questions back to the group as a whole - can anyone answer this query? Once you feel that everyone has a good understanding of the task, give more time for pairs to work on the solution.  You might like to provide some copies of the calculations cut into strips so that learners could move them around to group or sort them. Explain that when you bring everyone together again, you will be asking some pairs to share their reasoning at various stages of the problem-solving journey.

As you circulate, listen out for clear reasoning, based on learners' knowledge of number properties.  You may wish to warn some pairs that you will be asking them to share their thinking with everyone later. It would be worth stopping everyone for a brief mini plenary before that if you notice some interesting and efficient ways to record.

Tamara Pearson, a teacher from Atlanta, US, wrote to us to say she had adapted this task and created her own version using Adinkra symbols.  You can read about her experiences of using it in the classroom on Twitter. Thank you, Tamara.

Where might you start? Why?

Now that we know that shape, how will that help?
What does that tell us? How do we know?

How are you keeping track of what you have done?

Learners could make up their own problem using shapes as symbols and test it on a friend. The problem Different Deductions requires similar thinking processes to this problem and would be a good one for pupils to try next.

Children might find it easiest to have numbered counters or cards available so that they can physically form the calculations to check their reasoning. You might want to support their recording by giving out this sheet with each of the shapes drawn on. Alternatively, this sheet has a copy of the question and space for recording (thank you to Rose Prentice for sharing it with us).