What my children taught me about multiplication and 3-d shapes.

I had wondered if talks about the boys’ study of the story of maths would be difficult to put together. When Eldest chose to research Times Tables, I wondered how easy it would be to come up with demos.
In the event, he had plenty to say and show. I encouraged Eldest to try and find patterns of his own in the multiplication tables by colouring them in on number squares.
We explored this Japanese method of multiplying numbers by drawing lines and counting the intersections. Eldest decided not to include this in his final presentation, but I thought it was great, and much easier than drawing endless bags of sweets (my usual multiplication illustration).
He did find out about the joys of the eleven times table. He also discovered that
ab + b(10-a) = 10b
He didn’t put it like that, but I found his explanation complicated! If you set out the times tables from one to nine in a grid. Take any sum you want (except the fives), then find the sum in the same column that is equidistant from the edge (which is why you can’t use the fives). Add the answers together and you will have a number in the ten times table.
By way of example:
3×4 is the third from the top in column three.
7×4 is the third from the bottom in column three.
40 is four tens.
It’s not going to change the face of modern mathematics, but Eldest was having fun with numbers and enjoying making his own discoveries. Good enough.
Middly’s talk was on 3d shapes. He made some, using nets I gave him:

He used our plastic shapes to make some designs of his own:

He drew a plan, with a key, showing his designs.
He told us the names of many solids. He even introduced us to the concept of anti prisms (thanks to Wikipedia).
Finally he drew on our white board:
cm³ means cm cubed
Because, as he put it: ‘it’s true, but it doesn’t mean anything if you say it out loud.’
I am pretty happy with our first maths presentations. The boys have chosen to research abacuses and sand timers next!
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8 thoughts on “What my children taught me about multiplication and 3-d shapes.

  1. Another great idea! I’m going to ask my eldest if he would like to do a presentation on a maths topic of his choice and see what the response is. I’m hoping it is as enthusiastic as your children!
    Thanks so much for linking up this week.

  2. I love maths fun stuff. Sand timers are great, my youngest bought one for his big brother for his birthday. It had a 5 min, 3 min and 1 min timer in the same thing. We made our own abacuses out of shoebox lids. I love the idea of presentaion, not sure my kids would go for it though.

    • I think it depends on the child. Our boys really enjoy doing demonstrations, getting lots of attention and showing off what they know! But, one of the joys of home ed is the ability to find what motivates your children and do that.

  3. Yeah, the maths part of home ed is the most scary part for me – I have to be honest I didn’t understand the times table thing at all! Thankfully my son is so little we’re still basically on counting – I can just about manage that part! These sound like great projects.

    • I don’t think I explained the times table bit very well. But, the main point is that Eldest discovered a pattern all by himself!
      One of the joys of home ed is that you go back over all the stuff you ‘learned’ at school, and realise how much more sense it makes now!
      For me, the really daunting lesson has been music. But, I am – very slowly – learning to play the ukulele alongside the boys, and that’s pretty fun!

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