## ....and boy was I surprised!

We were using the coloured centicubes to represent simple fractions (1/2, 1/4, 1/10 etc) when I decided to spice it up a bit with a crazy challenge."Alright then," I said. "Who can show me 31/100?"

I was anticipating some neat 10 x 10 squares with 31 squares of an alternate colour to represent the numerator - the way I would have handled the problem Well, I was in for a shock!

Here is what the kids came up with. I was determined not to get involved in how they did it, to see what they would invent, and only advised that their fraction needed to be easy to see and simple to explain. I did suggest that colour might be a good way to do this.

*Here's a 10 x 10 square with 31 green squares.*

*I was expecting to see lots of variations on this theme.*

*There was only one other that looked similar.*

*There's 10 groups of 10 cubes. One lime green cube*

*is broken off and put with the yellow group to make 31.*

*This one had 2 lines of 50. The top line has 31 orange cubes.*

*This is interesting. If you subtract 31 from 100 you get 69.*

*69 can be divided into 3 multicoloured lines of 23 cubes.*

*The long line at the top is 31 brown cubes.*

*And here is something special - use a metre ruler to represent 31 (red) cubes*

*and 69 (blue) cubes.*

## And then, out of left field we get...!

*Angry Birds??!*

*This is really creative but how do I get it to link to fractions?*

*Interestingly, each of the birds is made up of 23 cubes, and 3 x 23 = 69.*

*Was this intentional??!!*

*And if it was, where are the 31 cubes to make it up to 100??!!*

I like the idea of getting students to 'show' you a fraction - great for assessing their understanding and for them to see multiple representations of the same thing - thanks for sharing this!

ReplyDeleteI like that you give your students some freedom to develop their own models. Not only is this good for students, but it reminds us teachers that the way we model mathematics might not be a natural starting point for students. We need to approach our curriculum recognizing that students need help moving from less formal, less organized ways of using to models towards more organized models and eventually formal mathematics. (In RME-speak, "progressive formalization.")

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