Linear War

So many things to write about to catch up... but it's been a while since I posted a game, so with an impending Math Teachers at Play at Math Mama Writes. The submission form seems to be wonky, so submit directly to Sue. Plus this kind of fits with U.S. Independece Day, as we have been known to fight a war or two.

This game is good already, but could be great. So if you have feedback, let me know, please! As is, it's probably best used as a review game, but I'll comment afterward about how it could be used as a framework for a unit.

Set up: Make your own deck: 11 lines. Each line should be drawn so that it passes through at least two points with integer coordinates, such as (-2,4) or (5,5).

Claim your deck! Mark each line card on the graph side with your insignia. Initials, emoticon, math symbol, etc. – your choice. Tip: make your cards NICE and personalized. Decorations and alterations that do not obscure the line or the math are not only permitted but encouraged.


War: 2-4 players. Each player needs a deck of 11 face down cards, shuffled or not – it’s up to you. Set aside any extras, make one more if you need it.

Players roll the die for the combat. (2nd roll and beyond, the winner of last battle rolls.) Flip over the top card of your deck and follow the combat rule. On a tie, flip over one more card to determine the winner of the battle. If more than two are playing, this is only on ties for best and only the people who are tied.

Play through the deck once. The winner is the player at the end with the most cards. Give cards back to the owner. Except for the Spoils of War.

Spoils of War: Out of the cards the winner captured, they take one card from the opponent’s deck to keep. Add your mark and cross out theirs. This may mean the loser needs to make a new card for their deck for the next game.

Example: The first roll is a 2. Least slope. -2 < 1

(The X and lemniscate are the players' personal marks.)

Math notes:

• Use the cards for sorting activities before playing.
• Have players keep track of hard to determine battles.
• Discuss card design strategies.
• What about undefined and zero slope lines?
• What other combat rules could you have?

Handouts: as a Scribd file, and the graphs template. At the right is an image (larger when you click on it) that you could also print for the graphs.

Discussion: Ted, one of the excellent summer grad student/teachers, tried this cold as an end of year activity with a small group, and they struggled with it.  He felt like it had a lot of promise, but that the math requirements kept students from the game since they were rusty with it.

Trying this with teachers convinced me of it's potential, as it even uncovered math for them to discuss, and generated situations they had to think about. 

I could see this game being at the end of a linear unit, where students have been generating graphs as examples as they go through the topics, using them for activities like finding slope, sorting from least to greatest x-intercept, y-intercept and slope. Use them to construct tables or find equations.  Non-contextual, but strong on representation.  What do you think?

I'm trying hard not to use too many unlicensed images but this is too perfect. God bless you Bill Waterson, wherever you are.

Coordinate Connect

This is a modification of a game that I can not remember where I saw. EDIT:  Yeah, remembered!  It was at NRICH, the game of the month.  They have a java implementation.  Give it a go.

Modifications by Jill, Leah, Lauren, Ashley, Megan, Nick, Jenn, Alyssa (Preservice geometry K-8 class) and myself.

Game:  Coordinate Connection

Materials:  10x10 grid with no axes, pen (or colored writing utensils)

Gameplay:  The idea of the game is players take turns naming a coordinate pair and then filling in the point.  The first player to make four in a row, wins.

The first point of the first player is the origin, (0,0).  It still counts as their point and can be one of the four in a row.  Later points are given by naming a coordinate pair.  For example, (2,-3), is two to the right of the origin and 3 below it.

Players take turns naming a point and then marking it.  If it's not where you thought, too bad, so sad, that's where it goes.  (Unless another point is already there - lucky.)  If players are having a tough time just verbalizing it, they can be required to write the coordinates down before drawing the point.

The winner is the first player to get four in a row, vertically, horizontally or diagonally.  The loser decides whether they want to go first or second in the next game.

Hints:

• consider blocking your opponent from getting three in a row. 
• get and stay on the offensive
• use a special mark

Variations:

• Play with three or four people.  (This was surprisingly fun and complex.)
• Allow any 4 consecutive collinear points to win.  For example, (-3,-3), (-2,-1),(-1,1), and (0,3)
• Play with younger students by giving directions from home, such as 2 left and 3 up.
• In the original game, you marked the point then said the coordinates, losing it if you were incorrect.

Give it a go, and let us know what you think!

Paper for playing - 2 sided, 4 10x10 grids each side.

Sample game:

Other People's Geogebra

Transformations on a Graph
I've been looking for Geogebra applications for function transformations, and wanted to share a couple of the neat sketches I've found.

Michael Higdon, a math teacher at Kincaid, a college prep school in Texas, has a quadratic function in vertex form, y=a(x-h)^2+k, with a, h and k as sliders to study transformations.
Geogebra webpage: Transformation of Functions

Mike May, a Jesuit math teacher at St. Louis University, has a beautiful applet where you can input the function, and control vertical and horizontal shifts and scaling with sliders.
Geogebra webpage: Translation Compression

An overall great collection of interactive webpages appears at The Interactive Mathematics Classroom. It has a nice search feature and a good breakdown by area of mathematics.

My first attempt at a transformations sketch is with a cubic as the starting function. Although you can change the function.

As a webpage, and as the geogebra file.

Slope in Linear Equations
A nice collection of middle school or Algebra I activities for linear equations from mathcasts.org: Slope Explorations
Mathcasts are screencasts of writing with voice-overs. They have mathcasts for K-12, and a nice collection of interactive math activities.

Here's my first slope sketch. It tries to get at the idea of the slope being constant on a line regardless of what points are selected.

As a webpage or a geogebra file.