Final post on ratios. I had a game idea pop in my head during the Twitter chat tonight. People were saying that fractions are a topic students should revisit before starting ratios, especially equivalent fractions. You could make up some kind of game where students practice equivalent fractions. During the game, students earn points for answering questions correctly.

I’m not sure if I would do this at the beginning or the end of the game, but I would have the students also select a rate to convert their points to money. The winner of the game is not the person with the most points, but the person with the most money. Or maybe I would randomly give them their conversion rate. I’m making this up as I go, so I’m not sure at the moment which would be ideal. Basically I would want rates like this:

- 3 points for every $1
- 5 points for every $3
- 2 points for every $1
- 6 points for every $3

If I let students choose the rates, some might figure out the best ones immediately, and that might be fine. If I assign them their rate randomly, that would also work. It just depends on whether I want some kids in the class to have the chance to figure it out right away.

Either way, at the end of the game, we would look at how much money people had and compare it with the number of points they had. I’m hoping that by reviewing a prior knowledge skill, many students would be earning the maximum number of points. The interesting discussion occurs when we see how students with the same number of points ended up with different amounts of money. Or a student who had less points than someone else ended up with more money.

Off the top of my head, I might have students graph their rate and a partner’s rate to see who would come out ahead based on different point values. Just because you won with 100 points, would you still win if you both had 50 points? 25 points? 200 points? How many points would you each need to end up with the same amount of money?

Having all the students graphing would also help us draw some conclusions about what graphs of rates look like. I’d ask them if they could play the game again, which rate of the four rates they would choose and why. After they choose, I might throw out a fifth rate and ask them if they would keep their choice or pick the new rate I just offered. To bring in more equivalent ratios, I might ask what’s another rate that would yield the same dollar value as 2/1 and 6/3.

Whew. I’m done talking about ratios and rates for tonight. The chat just got so many ideas going, and even more came out as I started writing. Brain dump complete!