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__, 1__2__, 1__5__, 1__8__, 2__1__, 2__4__, 2__7__, 3__0__, 3__3__, 3__6__…

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:

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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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?

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!