A times tables maths trick.

I found this trick by watching a Teachers’ TV video about Primary Maths. It’s really cool but I want to know why it works and I can’t find anything about it.

You start off taking a 0-9 number line and folding it into a circle. 


Then you choose a times table, let’s say the threes as that’s where they started in the video, and write it down, underlining all of the units digits.

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36

You then plot those units digits like a dot-to-dot, 3 to 6, 6 to 9, 9 to 2 and so on until you get this:


Making predictions about another times table that would produce the same pattern you might say 6 – I did. But no, actually it’s 7:


It turns out that all pairs are number bonds to 10:

image image

image image

Another thing I noticed is that the two corresponding pictures are actually mirror images of each other – the arrows go opposite ways. This pattern-finding looks like a great way to help kids learn their times tables; there’s some great youtube videos here on how to use these number wheels for that purpose.

The thing I want to know is why does it work? Why number bonds to 10? Why mirror-images? I want to understand the maths behind it.

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2 Responses to A times tables maths trick.

  1. mikemcsharry says:

    Here’s a starter .. this is going back a long way in my grey stuff.
    Any 2 digit number xy is 10x + y
    10x is the same as 9x+x – now can someone else help to polish this off 🙂

    You’ll notice that the even number wheels are only working in 5s (obviously, because it can’t end in an odd number)

    Now the 4 and 6 pair is something to do with 4 = 10 -6 and 6 = 10-4
    the 8 and 2 pair similar.
    Obviously 5s a bit of a waste of time. 5->0->5

    The graphics are really neat by the way – how did you make those?

    • emmaldawson says:

      Ok, I understand what you’ve explained. Now need to work out how it applies and hopefully there’s someone who can take it further 🙂

      Nothing exciting to make the pictures, just wasted ages on PPT!

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