Okay, here’s a game I came up with off the cuff today. It kinda worked, but I guess if other people tried it and gave feedback, that’d be swell.
Players: 2 (or 2 teams), each with two colors
Board: A 10×10 grid.
The game is played in two phases. In the first phase, each team takes turns placing points on the grid, until each team has placed 5 points. The origin always is claimed as a neutral point. Every point has to be on a lattice point. (In the example below, I was blue and my student was yellow.)
In the second phase, on their turn, each player may place a new lattice point and form a line with one of their original 5 points. If that line then passes through one (or more!) of the opponent’s original 5 points, those points are stricken. If one player can strike out all of the other player’s points first, they win. (If not, then whoever strikes out the most.)
There is one caveats to round 2 – when a line is drawn, determine the slope of that line and write it below. That slope can’t be used again.
After playing the first time, it became clear that much of the game came down to placing the points. If you could place one of your points so it was collinear with two of your opponents, you can strike them both with a single line. (But this only works if there is space for a 4th, alternate color point in phase 2 to form the line.) You also want to place your points defensively, with weird slopes that don’t pass through a lot of lattice points, to keep them safe. The second player definitely has an advantage when placing points, but the first player has an advantage when drawing lines, so I’m hoping those balance out.
Thoughts?
James Cleveland-Tran
The Roots of the Equation 
Comments on: "Slopes and Lattices Game" (10)
What if it was turns based, with like a 5 turn game? 2 points for getting a primary point, 1 point for a secondary point. I really like the figuring out of points on the same line. it makes slope and the constant rate of change for lines very concrete.
I enjoyed trying this game! One question I had was when you say that the slopes cannot be repeated, do you mean at all? Or just for each player? An example is if I had a slope of 1/2 for my line, could you use it? What about if the sign is negative?
The intention was at all – so that you can block your opponent from using a particular slope by using it yourself. I hadn’t thought about whether the sign matters – I suppose I would treat +1/2 and -1/2 differently, and both could be used once.
I thought this game was really fun and had a lot of mathematical thinking behind it! One comment I do have is maybe elaborating on the use of multiple colors or figuring out a way to not have multiple colors. I feel like having all the colors on the board during the game might get slightly confusing for the younger students as it was for me! Overall, this game was really fun and I enjoyed it a lot once I figured out the concept!
For sure, the colors were a bit confusing. John had the suggestion of keeping two colors and doing two different shapes for the points (like closed circles and open squares) which I agree is much clearer.
I actually liked the suggestion of using different colors because it helped to have some guidelines on which points and lines could be used. When we played, we also crossed out the points that were “stricken” sort of like you pull chess pieces off the board when they are captured. There would probably be more plays available to students if you were able to use your second points already on the board as starting points for new lines because sometimes if one player fell behind or got two marks stricken right away, it was difficult to find a next move. Overall, it is a really creative idea for a graphing game!
I enjoyed playing this game with my classmates! We had a comment on where should the origin would lie, it could be chosen or just in the middle of the 10×10 grid. Also, to add onto if there is a clear origin would players be able to use that point as one of their points, as well as both teams if that was allowed.
I think I understand what you mean by the game, but I wish I could see the image. I’ve cleared my cache and reloaded the page and everything else I can think of. Do I need some kind of special viewer app?
Strange. Does this direct link work? https://pbs.twimg.com/media/EwOxtwDXMAEKCeE?format=jpg&name=large
Yes, the direct link works. Thank you!
But for some reason, Firefox won’t display the image for me. I wonder why…