This kind of theft has a lot going for it, not least:
- The stolen things doesn't get taken away; in fact they get multiplied;
- It is so very easy to do now - no need to attend training, or snoop round classrooms - we have the Internet;
- It means that ideas keep flowing, lessons stay fresh.
1.
The first of my thefts was Five Rectangles. This came from Gary Antonick's great Numberplay column in the New York Times. (A while back I got another great lesson from Gary's column, one that originally came from Steve Humble, Triangle Mysteries.)
Five Rectangles (aka "Sol Golomb’s Rectangle Puzzle") is basically very simple: create a set of five rectangles that have sides of length 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 units. I added Cuisenaire rods, which seemed the perfect vehicle for this - they mean you can handle this question, literally; they save time in trying out options; and they make the length x width = area nature of rectangles very obvious.
The arithmetic is just right - times tables up to 9 x 10. And the addition - five numbers adding up to a number between 100 and 200 is right too. And best of all, there are more intriguing questions - what are the maximum and minimum areas? - that take the children into unfamiliar territory, and call on their mathematical intuitions.
The original puzzle was for adults - but using a manipulative - the rods - means that it's well within the children's abilities to do some of it. It even adds new possibilities, which I hadn't foreseen, like splitting the rectangles up to make a square.
The second lesson, followed on from our work on percentages perfectly.
We'd had had the computer generate a chart for us, using our data, but we needed more.
Children get to hear about a hundred percent, and know that it means "all of it". But they should experience other percentages without any confusing arithmetic coming in the way, and get to know the concept of a percentage first by examples (just as we understand "red" by examples of red things). And they should get to make pie charts without grappling with dividing by a total and multiplying by 360°. So I was really pleased when I saw this tweet:
Don't get me wrong: I think the calculation should come, that eventually children should learn how to do it. I just want them to get a feel for what it's all about first. And to not get bogged down or addled. A little struggling to get the Smarties into their circle is OK...
Seeing that he obviously had stuff to nick, I put on my cat burglar suit and snuck into Mike Ollerton's website. There was no security at all, and there were all sorts of valuable goods that had been left there. More than I could fit into my sack in fact. The one I came away with was Being a Number.
I've printed up the exact same cards, and started using them. I know I'm going to get a lot of mileage out of them in terms of mathematical thinking.
So all in all, I've had a good cache this week. If you'd like to throw any of my stolen goods into your own sack, be my guest - I can recommend this life of crime!
The original puzzle was for adults - but using a manipulative - the rods - means that it's well within the children's abilities to do some of it. It even adds new possibilities, which I hadn't foreseen, like splitting the rectangles up to make a square.
2.
The second lesson, followed on from our work on percentages perfectly.
We'd had had the computer generate a chart for us, using our data, but we needed more.
Children get to hear about a hundred percent, and know that it means "all of it". But they should experience other percentages without any confusing arithmetic coming in the way, and get to know the concept of a percentage first by examples (just as we understand "red" by examples of red things). And they should get to make pie charts without grappling with dividing by a total and multiplying by 360°. So I was really pleased when I saw this tweet:
Bar charts to pie charts #bcme8 with myself and mike Ollerton and lots of lovely peeps pic.twitter.com/aziZj7aBaf
— Helen J Williams (@helenjwc) April 16, 2014
Pie charts without the calculation! It was apparent to me that we could add a circle divided into a hundred divisions around the Smarties circle - and we would have percentages without calculation too! So that's what we did: Pie Charts and Percentages with Smarties. |
| pie charts made simple |
 |
| Percentages made simple |
3.
I've printed up the exact same cards, and started using them. I know I'm going to get a lot of mileage out of them in terms of mathematical thinking.
+
So all in all, I've had a good cache this week. If you'd like to throw any of my stolen goods into your own sack, be my guest - I can recommend this life of crime!
