So, I thought asking the question backward might be a good way to attack it. Instead of here's the graph, what's the D and R? ask, here's a D and/or R, draw a graph. I mean, I know this is pretty standard fare. The thing is, I didn't want to do examples and a worksheet, or hold-up-your-whiteboard so I could somehow assess 22 graphs in a split second. It seemed like there should be a better way.
So I did what I do, which is ask on Twitter. And I got lots of helpful ideas, but this was the one that I latched onto and ran with:
@k8nowak make it a game? Charades-ish: Each student puts in 2 requirements. Team draws two and has a minute to make a function that fits.The end result is, I'd argue, more like Apples to Apples than Charades (hence the title).
— John Golden (@mathhombre) November 17, 2014
To prep: Make game cards. I printed each page (docx pdf) on a different color card stock. Student play in groups of 4-ish, so plan accordingly. I printed 6 sets. (John suggested having students submit constraints, but, for this crew, I decided to unload that part and create cards with the constraints.) You'll also need a mini-whiteboard, marker, and eraser for each student. Check your dry erase markers, because nothing kills a math game buzz like a weaksauce marker. (I'll admit to a minor teacher temper tantrum where I uttered (okay, yelled) the words "I'M NOT THE MARKER FAIRY! I DON'T POOP MARKERS!" Teacher of the year, right here, folks.) Also, you'll need some kind of token that players can collect when they win a turn. I use these plastic counting chips that I use for everything, but anything would work, candy, whatever.
Doing a demo round with a few kids playing and everyone watching will pay off, in the more-kids-will-know-what-is-up sense.
Here's how the game plays:
- Someone is the referee.
- To begin the turn, the referee turns over two (or one, or three) different-colored cards, and reads them out loud. (I feel the reading aloud is important practice for interpreting inequalities.) You could do, like, first round is one card, second round is two cards, third round is three cards. Whatever suits your needs.
- The other players have one minute to sketch a graph meeting the constraints on the cards. The referee is responsible for timing one minute.
- The players hold up their mini-whiteboards so the referee can see.
- The referee disqualifies any graphs that don't match the cards, and explains why. Other players should police this, too.
- Of the remaining graphs, the referee picks his favorite. This player wins a token.
- The turn is over, and the player to the referee's right becomes the new referee.
It was great! Here are things I liked about it:
- 100% participation 100% of the time. At no point should anyone be kicking back.
- Nowhere to hide. There were a couple kids who had to come to me and say, "Miss Nowak, I really don't know what's going on." which I don't think they'd be compelled to do if we were just doing some practice problems.
- Good conversations. Especially reasons for why graphs were disqualified. "You need an arrow there! The domain goes to infinity!" That sort of thing.
- Students were necessarily creating and evaluating. Take that, Bloom!
- Built-in review of what makes a graph a function vs not a function.
- My chronic doodlers had a venue to express themselves. Especially if the graph didn't have to be a function.
- Authentic game play. You could use your knowledge of what a referee liked to curry favor.