Tuesday, January 17, 2017

My Closest Neighbor Fraction game

Denise Gaskins recently flagged a post about a good fraction game: My Closest Neighbor. I tried this out in class today.

A pre-test
First, I wasn't sure whether the level of the game would be right for the kids. I was considering it for the 3rd and 4th graders, but had some alternative activities planned in case. To start, I posed the following questions:
• Which is closest to one-half: 1/3 or 2/5? The third graders really struggled with this, so I left it alone and went to my plan B games. The fourth graders were all confident on this one.
• Which is closest to 3/4: 5/11 or 11/12?  This was a challenge for the fourth graders, but I thought it would be ok to play the game.
In our discussion of the second question, we explored two strategies:
1. making a common denominator
2. comparing with reference numbers
The common denominator is a bit of a pain, since 11 is prime, though at least we have the fact that 4 is a factor of 12. One student soldiered through this approach, but it was difficult for the other kids to follow.

For the second strategy, we made use of some observations that were more elementary for the kids:
(a) 5/11 < 5/10 = 1/2
(b) 3/4 is halfway between 1/2 and 1
(c) 11/12 < 1

Combining these, it was easy for us to draw a rough number line, place 5/11, 1/2, 3/4, 11/12, 1 and see that 11/12 must be closer.

The game
We played three rounds: target 0, target 1/3 and target 1/2. I think this game was very challenging for the kids.  Everyone had to work to figure out the best play from their hand and didn't always make the right (local) choice. For example, whether to choose 5/8 or 5/9 for a 1/2 target.

Once everyone had played, the challenge was still just starting. They had to figure out who was closest. I structured the discussion by helping them figure out which plays were lower than the target and which were higher. For the ones that were lower, they could put them in order and only needed to consider the highest. Then, we worked on the ones higher than the target and got the lowest of those.

In the course of this discussion, we added a third strategy to the ones listed above:

• making a common numerator
Summary thoughts
Fraction comparison like this was still too difficult for the kids to make an engaging game. If I were to do it again, I would change to make it more of a puzzling exercise, removing competition and any sense of time pressure.

Once the kids gain a bit more experience, though, I think this game has some nice features. It is particularly good for practicing fraction sense, and the multiple rounds allow some scope for strategic play.