One of my fun projects this year is to support a teacher who is introducing more game-based learning into his teaching. We’re trying to invent and implement games that get students doing some of the core reasoning within Integrated Math, Year 1. The textbook is Core Plus Mathematics, and hopefully we’ll track pretty well with the Common Core, also.

## September

### Pattern Predictions (updated & improved 9/10/2013)

**Format: **1-on-1 (or 2-on-2)

**Materials:** Slips of paper or cards with numbers on them. Start with natural numbers, then introduce zeros, negative numbers, and non-whole rational numbers (both greater than and less than one). Recording sheet to record starting number, operating number, each team’s bet, and the outcome.

**Downloads: **Possible set of cards (not yet play-tested!) and game board (including a sample game on the 2nd page).

**Basic Gameplay: **

- Player 1 randomly draws a number. This will be the “start” number.
- Player 2 randomly draws a number. This will be the “change” number.
- Player 1 randomly draws a number. This will be the “number of times” number.
- Each player (privately) writes down their bet as to whether addition or multiplication will lead to a larger outcome after iterating the “start” number by the “change” number the requested number of times.
- Each player carries out the requested number of iterations of each operation and they compare results. A player gets a point if his or her bet was right.

**Variations/Extensions:**

- Start by having players choose their operation before they’ve seen the numbers. Let the students be the ones to request seeing the numbers first!
- Start by modeling the game to the whole group. Have one person in each pair choose addition and the other multiplication, then reveal three “randomly” generated numbers. Students calculate and decide which player wins. You can display this game board to facilitate the process:

- When negative or non-whole number cards come up in the “number of times” role, decide whether teams should re-draw or if the class can come up with a sensible meaning for those rounds. Or teach the mathematician’s interpretation of those cards. Note: Don’t say “that’s impossible!” just say “we haven’t learned that yet… what do you think it could mean?”
- Teams can wager different numbers of points they’ve earned if they’re very confident (e.g. double-or-nothing rounds).
- Teams can bet on which outcome will be closer to a specific target number, such as 21.

what if the “number of times” is negative? or not an integer? Perhaps have a separate set of cards only for “numner of times”?

Great questions — my hope is that they will come up and the students will have those same questions. In our curriculum negative exponents come up pretty early in the exponents unit. I’d be curious if students had any intuitions about this (though I doubt they would). Fractional exponents don’t come up ’til later in the curriculum, but I bet students might be able to think about what multiplying by 5 half a time might mean. See, for example: http://christopherdanielson.wordpress.com/2013/04/11/rational-exponents-third-grade-style/