Why do this problem?
Sharing this trick with learners will hook them in, firing their curiosity and thereby providing the motivation to explore, and understand, the underlying mathematics. This trick will help children gain a deeper understanding of place value and may also provide an opportunity to practise column addition in a meaningful context.
Without saying much at all, play the silent video for the class, asking them to consider what is happening. You could check the multiplication using a calculator and dramatically announce the answer! Give them chance to talk to a partner about what they notice in the video and any questions they would like to ask before playing it once more. At this point, open up discussion to the whole
group, inviting comments and questions. You could write these up on the board as they are mentioned and, rather than answering or responding yourself, encourage other members of the class to do so.
Suggest that, as a class, you try a different multiple of 11 (you could invite a pupil to give you one). With the children's help, rehearse the process step by step, this time writing on the board, stating what you are doing as you go. Ask someone to check the result on a calculator.
Set pairs off on exploring further. Is the answer always going to be correct? You may wish to suggest that everyone sticks to a two-digit multiple of 11 for now (see the 'Possible extension' ideas below).
As they work, look/listen out for those children who are recording in a helpful way, or those who are beginning to explain what is happening. You may want to warn some pairs that you are going to ask them to share their work with the whole class during a mini plenary.
After a suitable length of time, bring everyone together again and ask whether anyone found an example of a calculation when the trick didn't
work. If some pairs think they have come across one, encourage them to share it and invite the whole group to check. Will this trick always work or is it just that we need more time to find examples that don't? Allow more time for pairs to
think about this, encouraging them to create a watertight argument that would convince you one way or the other.
If appropriate, you could share the approach in the 'Getting started' section
with the class. This is a different way of presenting the same underlying mathematics, which may be more accessible even though it has slightly less of a 'wow' factor!
The final plenary can involve everyone in building an explanation together, drawing on their understanding of partitioning 11 into 10 and 1. You could suggest that children amaze their family with this new trick at home!
What is the 9 worth in 594? So, rather than 5 and 4, which two numbers have been added to make that amount?
Where have these two numbers 'come from'?
If you were asked to multiply by 11 mentally, how might you do it?
How would you partition 11 to help with this calculation?
There is a slightly different way of presenting this trick outlined in the 'Getting started' section, which some learners may find more accessible.
Does the trick work for single-digit multiples of 11? What about three-digit multiples? What happens with decimal multiples of 11? Can learners make a conjecture before exploring?