I’m currently working on Light It Up, a puzzle game that teaches fraction concepts. It’s based very closely on Refraction, but for various reasons I wanted to create a different version.

Currently in this game there is a piece that takes two fractional lasers and adds them together in to one laser. In order for the piece to add the fractions the fractions must have a common denominator.

Using this approach forces students to add fractions by creating a common denominator and can effectively teach the idea that a common denominator is necessary through the rule, but because the piece simply requires this to happen, students likely aren’t going to understand why finding a common denominator is necessary, just that it is necessary.

This isn’t the end of the world. Once the pattern is firmly established then it makes it much easier to explore the explanation of why a common denominator is necessary. Still I would much rather find a way for the students to figure out that a common denominator is necessary rather than simply forcing such a rule.

You could imagine having students try to add fractions without a common denominator. They might just add the numerators and the denominators. You could create a situation where there would be a natural feedback loop showing that this doesn’t reflect reality and help them explore how to do the calculation more accurately. I just haven’t yet figured out a good practical metaphor and feedback loop to accomplish this.

I’ll continue to think about it. If anyone has any ideas I would love to hear them.

*Projects, Puzzles, The Puzzle School*

Jasper Palfree (@wellcaffeinated)

November 8, 2012

I don’t know if this helps, but this is the way I think about it…

You can’t add apples and oranges. Sometimes you can turn apples into oranges and then add those, but sometimes, you just have to turn everything into grapes…

I’m picturing some sort of box that only accepts _one type_ of object. But you have 2 apples and 5 oranges (representing two 1/3rds and five 1/4s, for example). You can’t just put them both in the box… it will just spit them out again (it doesn’t like to mix foods). So you have to convert them into grapes. two apples is the same as eight grapes (2/3 == 8/12), and five oranges is 15 grapes (5/4 == 15/12). Now you have a total of 23 grapes (23/12), which you can put into the box, and it accepts it.

Not sure if that helps…

irrationaljared

November 8, 2012

I’d like to come up with something that is a little more closely tied to reality. If I were a student such an example might make me ask “why can’t I add different fruits to the box?”

This is exactly the problem I’m wrestling with. I don’t want the software to just dictate that you can’t add fractions with different denominators, I want the students to figure out that it doesn’t make sense to add fractions with different denominators, that it’s hard to figure out what the result is…

I’d also be worried that students would find it hard to take the analogy of the fruit and connect it back to fractions.

I don’t know. Do you think such concerns are unwarranted?