Tables Teaser
Tables Teaser
Have a look at this grid:
Can you see how it has been made?
Why is the 60 in that particular square?
Why does 20 appear twice?
In the interactivity below, some of the grid is filled in for you.
Can you work out which number goes in each row and column heading?
Once you know what each heading must be, drag the purple numbers to the appropriate spaces. When you think you have cracked it, click "Show the solution" to see if you are right.
Why do this problem?
The 'reverse' nature of this task (i.e. the fact that the answers to the multiplication calculations are given) will encourage children to be more curious about the mathematics, compared with being asked for answers to times tables questions. (This problem only uses the 2, 5 and 10 times tables, up to 12x.) In order to work out the row and column headings, learners will be mentally running through many tables facts or many calculations, and selecting those which could be applicable. The task requires children to make connections, notice patterns and apply their knowledge in a way that completing a list of times tables questions does not do.
Possible approach
This problem featured in an NRICH Primary webinar in April 2021.
Display the image of the completed three by three table square without saying anything by way of explanation and invite learners to consider what they see and what they notice. Give everyone chance to talk to a neighbour about their noticings and any questions that they might have before gathering as a whole group to share observations.
Facilitate discussion so that you are confident everyone understands the construction of a table square. You could then show the interactivity on the board and ask children what they notice this time. Establish the set-up so that learners know the challenge is to find the headings of the rows and columns, using the products given in the grid.
Give pairs time to talk to each other about where they might start and gradually fill in the headings as a whole group, ensuring that you demand clear reasoning from everyone.
Learners can then use the interactivity themselves in pairs, either at computers or using tablets. As they work, listen out for examples of high quality reasoning which you could then share in a plenary.
Use time at the end of the lesson to discuss which numbers are particularly helpful and why. (For example, 25 has to be 5x5.)
Key questions
Where might you start? Why?
Are there any row or column headings you know straightaway? Why?
How might that row/column heading help us now?
What do you know about numbers in the 10 times table?
What do you know about numbers in the 5 times table?
Possible support
If an adult is available to be with a few children who are struggling, they could suggest which cell to focus on first so that learners have some immediate success.
Possible extension
Mystery Matrix works in the same way, but any numbers from 2 to 12 are used to generate the products, so the answers will not just be multiples of 2, 5 and 10.
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