The teacher who normally plans our 7th grade extended day tutoring was out today, so we were on our own. I could have just picked a page from the workbook for the kids to work on, but instead, I wrote out a bunch of fractions and decimals on index cards. I put 0 at one end of the table, 1.0 in the middle, and 2.0 at the far end. Then they had to place the other fractions and decimals one at a time on the number line. I increased the difficulty as we went along, starting with tenths and ending with 0.001, 3/20, and the like. When we'd used up all the cards, I gave each student a blank card and a marker and challenged them to make up new fractions between 0.4 and 0.5. I let them come up with decimals first, then convert their answers to fractions. Some of the kids got really into it and made two or three cards. Finally, I gave each student three blank cards and told them to write any new decimals or fractions that they wanted to. Pretty soon, I had kids begging me for more cards, trying to add the most devilish fractions and decimals they could think of.
I collected all the index cards into a pile, shuffled them, and dealt each student 5 cards. Then I turned over the top card on the deck. The goal was to select a card from your hand as close as possible to the target card; if your card was closest, you got to add the target card to your hand.
Two astonishing things took place:
1. The kids got raucously enthusiastic about the game.
2. The kids got better at playing it as time went on, comparing decimals with something resembling ease.
We are SO playing this game again.