Surprising Split

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

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Problem

Take a look at this silent video:

If you can't access YouTube, here is a direct link to the video: SurprisingSplit.mp4 

Click below if you would like to read a description of what happens in the video.

 



54 x 11 is written.

Below that, the 5 and 4 are written again but separated so that there is a gap between them. A curved line is drawn linking the 5 and 4 and an addition sign is written below it. The number 9 is written between the 5 and 4.

Below that, 594 = 54 x 11 is written.



What do you notice?

What would you like to ask?

You might want to watch the video again.

Can you re-create this trick for yourself for 54 x 11?

Try the trick for a different multiple of 11.  What happens?

Does the trick always work, for any multiple of 11?

This isn't really a trick, it's maths!  Can you explain why it works?

Thank you to David Frankau and Mr Hadfield from the Pointer School in Greenwich who drew our attention to a trick for the 11 times table, which we have adapted for this task.