Integer Games

As we consider games for the classroom, there are several possible purposes:

• they’re fun.
• skill practice with engagement that worksheets can’t match.
• sometimes the game can support the underlying concept development.
• sometimes they can be the context to help conceptual understanding.
• provide an opportunity for problem solving in the context of game playing strategy.

I often launch a game by playing me vs. the entire class. It tends to communicate more of the rules than just explaining them. I’ll often have students play in two person teams to start, as their discussion helps work out understanding of the game and the mathematics. After the lesson, I’ll try to engage students in a conversation about what they noticed, what their strategy was, and if they would change anything about the game.

The games for today: you will rotate through the tables, spending a few minutes trying out the game at each stop. This may not be enough to finish a game, but will hopefully give you an opportunity to get a good taste.

Game - Presenter - Content

• Consecutive Capture - Emily Trybus - Integer representation on the numberline
• Tug of War - Anne Harkema - Integer small number addition, especially positive + negative.
• Close to Zero - Jill Beauchamp - Two digit integer addition, especially positive + negative
• Zero Rummy - Cassie Becker - Integer addition with more than two summands, especially zero pairs and sums.
• Gridfight - Kirsten Clemans - Integer multiplication
• Honeycomb - Nick Smith (game coauthor) - Integer multiplication and addition
• +/−24 - Emily Scothorn - Integer operations mixed plus order of operations

At the end we’ll try to come back together to discuss which games you liked the best for your classroom and why.

Files for the day.  Click on these links to see or download the games. (Finally updated to Google Drive to get rid of Scribd links. Some PDF, some Word.)

• Handout - including the Product Game and adapted Integer Product Game
• Treasure Hunt
• Integer Card Games - includes Consecutive Capture, Close to Zero, Zero Rummy and +/- 24
• Tug of War
• Gridfight
• Honeycomb

I tinkered a lot with the Product Game to adapt it for integers, and then found the exact same version I came to on the Connected Math Project website.  Sigh.

The most interesting games to me are Gridfight and Honeycomb.  My preservice middle school math teachers helped with the playtesting of these games, and gave a lot of valuable feedback.  Consecutive Capture is a nice variation of Fraction Catch... which I was about to link to, but I guess I haven't written about yet... and the preservice teachers were fond of it.  Most of the games had someone who really liked them, with the possible exception of Treasure Hunt, which is meant to be a quick and easy introduction game, and indeed the preservice teachers found it simple.

The idea behind Gridfight came from wanting to get at the area model for multiplication.  I like the way it kind of presages Algebra Tiles.  The goal of filling in rows enables you to win even when the other person gets more areas to fill in.  The strategy of it appealed to students, and it had a lot of replay value.

Nick Smith, one of the preservice teachers and the presenter for the game, came up with a lot of the idea for Honeycomb.  He was sold on the hexagonal grid, and had the idea of flipping and replicating stacks of two color chips to get the feel for multiplication by a negative.  We wound up making it a pen and paper game as it was clumsy with the chips.  It's got a large luck component with the dice, but enough strategy to keep people engaged.  This is a game I'd be interested in seeing implemented on the computer.

I hope you enjoy the games, and would love to hear what you think if you get a chance to try them.

Math in Action 2010

Grand Valley State University sponsors a terrific little math conference each year called Math in Action.  I think started by Jan Shroyer back in the whereupon.  It has 30ish workshops for K-12 math teachers, mostly very practical.

I'm hosting 6 wonderful preservice teachers presenting geometry games for K-8 teachers, so I'm posting the electronic versions here for people to be able to download.  If you were a participant and wanted a Word file to edit instead of a pdf, just email me.  The address is available on my workpage, linked on the right.

Anne Harkema: Rope Charades
Lauren McKee: Quadrilateral Concentration and the required Quadrilateral Cards
Emily Trybus: Area Block (link to a previous post)  
Rebecca Sochacki and Brynne O’Connell: Polygon Capture
Jill Dzierwa: Triangle Detective (link to a previous post)

As a bonus, here are the two bonus games from the Quadrilateral Concentration sheet.  Both are other uses of the Quadrilateral Cards.  Not included here is Quadrilateral Euchre, which is Euchre for a partially ordered card set.  Verrrry geeky in a midwest sort of way.

Quadrilateral Go Fish

Materials:  Deck of Quadrilateral cards. Best with 3-5 players.

Setup:  Deal 5 cards to each player.  Put the rest face down in the middle, either in a neat stack, or mixed up in a big pond.

Gameplay:  Start to the left of the dealer.  On a player’s turn they can ask a particular player for a specific property.  For example:  “Do you have a shape with opposite angles congruent?”  You can not ask for a shape by name.  (“Do you have a rectangle?”)  If the player has a card like that, they have to give it over.  If they have more than one, they get to choose which card to give away.  If you have a matched pair of the same type, you can play them down. 

Winner:  First winner is the first player to go out.  Second winner is the player with the most pairs.

Variations:
•    Instead of asking by properties, ask by name.
•    Start with 7 cards.
•    Allow players to play cards on other people’s pairs.  (If you have a pair of rectangles I can play a rectangle.)

Quadrilateral Guess Who

Materials:  Quadrilateral card deck.  2 players.

Setup:  Sort the quads by type.  Each player puts one quadrilateral of each type face up in front of them, and the others go face down in the middle.  Each player draws a card from the middle and keeps it hidden from the other player.

Gameplay:  On your turn you can ask one question about the other player’s hidden quadrilateral.  That player answers yes or no.  Turn face down the quads you have that don’t match.

Winner:  first player to guess the other player’s card.