Following this post, I’m blogging some lesson ideas which address some of the problems with how mathematical modelling has been taught in primary schools.

When I showed this picture to my class, I explained the concept of money-off vouchers and asked them – which one should I use? I probed a bit further and made sure that they understood the very basics of economics – that as a shopper, buying something for the cheapest price possible is desirable. I told them nothing else at this point. I had to be sure that they understood the crux of the modelling. The vast majority were adamant that the voucher to use was the £10 off one. I pushed for explanations and not many were forthcoming. The best I got was: “If it cost £10, you’d get it for free.” I clung on to that magical word ‘if’. A couple of children at this point were physically struggling with the cognitive dissonance until one bravely piped up with: “It depends!”

After a bit of probing and development of their articulations, we settled on the idea that sometimes, the 10% voucher is better and sometimes the £10 off voucher is better. I still pressed them for an answer though, in order to sharpen their thinking further. I asked: “What information do you need to know?” After a bit of discussion, they agreed on needing to know the item I intended to purchase and its price. I told them that I wanted to buy a mobile phone, but as I had not chosen the one I wanted, I was not sure how much I would spend yet.

At this point I needed to make sure that they were able to do the maths. I knew that all of my class could subtract £10 from any amount of money, and I knew that they could all find 10% of an amount of money. What was new to all of them was to work out a 10% discount. I showed them how to do this. We drew up success criteria etc. They practised. A lot. Then I gave them the prices of the phones (screen shots from Tesco’s website – I had simplified the prices for some children and I had a great question for those that grasped the concept quickly).

I asked – If I were to buy this one, which voucher should I use? What about this one? This one? etc. Some needed a little more time than others on this so here was the tricky question. At which price should I switch vouchers from £10 off to £10 off? Thanks to a post and comments on Dan Meyer’s Blog, I also had this question ready (although unused in the lesson): If you can use both vouchers to buy the phone, does it matter which one you use first?

An alternative approach to what I did could have been giving them a worksheet of questions like this:

A mobile phone costs £79. You have a £10 off voucher and a 10% off voucher. Which voucher should you use?

I think, had I given my class this ‘word problem’ in this manner, not as many of them would have been successful. They would not have done as much thinking and reasoning; they would not have understood the concept of the modelling as much; they would not have done as much necessary practise of calculations.

Once again, thanks to Dan Meyer (@ddmeyer) for his input on 3 Act Maths.