Multiplication Square Jigsaw

Why do this problem?

This jigsaw is a great way to reinforce children's awareness and understanding of the sequences contained within the multiplication square. The jigsaw format will capture children's curiosity and provides a motivating context in which to practise the times tables.

Possible approach

One way of introducing the task would be to display the jigsaw on the screen, but hide the title and explanatory text at first.  Instead, ask learners to say what they see and by taking contributions, tease out the task.

If you have access to a computer suite, or tablets, then you could ask children to try to put the jigsaw together in pairs using the onscreen interactive. Alternatively, you could print off and cut out this sheet of the grid and pieces. Ask them to keep a record of the order in which they place pieces so that this can be shared later. Warn them that you will want to know why they made the choices that they did!

The conversations the children have amongst themselves as they work will be well-worth listening in on as they will reveal any misconceptions, but also inform you as to how well the children are able to reason mathematically.

As hinted at above, in the plenary you could invite some pairs to explain how they went about solving the jigsaw, or at least to go through the first few pieces they placed. How many different ways of starting did the class find?

Key questions

Possible extension

David Longman, a teacher at Holmemead Middle School, very kindly suggested a Ripped-up Tables activity which could be used as a follow-up to the Multiplication Square Jigsaw. Not only do pupils have to put the square together, they have to complete it first! Both Mystery Matrix and Missing Multipliers would make good follow-up tasks to this one. The format of a grid is the same, but in these two problems, children are given products and have to work out the row and column headings.

Possible support

At first, children may want to use a ready-made table square to help in doing the jigsaw before trying to do again (or trying later stages) without this aid.