## Trying to find math inside everything else

### The Integral Struggle

I had an extra day to fill for one of my sections of calculus, thanks to the PSAT, so I set about thinking up a game I could play. I gotta tell you, as much as there is a paucity of good content-related math games out there, it’s extra so as you move up the years in high school. I can still find a good amount of algebra and geometry games online, but Algebra 2? Precalc? Calc? Fuhgeddaboutit. Well, I’m teaching both Pre-Calc and Calc this year, so I guess I’ll just have to make them myself. (I brainstormed two more during said PSAT, so those might happen soon enough.)

We just covered function transformations and how they affected integrals, so this game hits on that topic. (Yeah, we’re doing integrals first.) Here’s how it works: there are 3 functions/graphs, each of which has a total area of 0 on the interval [–10,10]. One team is Team Positive, and the other is Team Negative. Teams take turns placing numbers from –9 to 9 that transform the function and therefore transform the area. Most importantly, they also place the numbers in the limits of integration, so they can just look at a specific part of the graph.

With three functions, it becomes a matter of best of 3 – if the final integral evaluates to a positive number, Team Positive gets a point, and vice versa. If it’s a tie at the end of the game, because one or more of the integrals evaluated to 0 or were undefined, then redo those specific integrals. (I discussed with the students whether it would be better to have it be the total value of all 3 integrals instead of best of 3, but I think that makes the vertical stretch too powerful.)

That’s it! Let me know what you think. Materials below.

### Crossing the Transverse

Oh my god, I haven’t blogged since August! This has been a hell of a year, let me tell you. But maybe I’ll tell you in another post, because this one is about the new game I made in my Geometry class. (My first non-Algebra game!)

So the game is called Crossing the Transverse. The goal of the game (pedagogically) is to help identify the pairs of angles formed by lines cut by a transversal, even in the most complex of diagrams. The goal of the game (play-wise) is to capture your enemy’s flagship.

Here’s the gameboard:

I printed out the board in fourths, on four different pieces of card stocked, and taped them together to make a nice quad-fold board. Then I made the fleet of ships out of centimeter cubes I had, by writing in permanent marker on the pieces the letter for each ship.

Here’s the rules.

In the game, each type of ship moves a different way, which makes it feel a lot like chess – trying to lay a trap for the enemy flagship without being captured yourself.  Many of my students really enjoyed it when we played it yesterday. Today, though, to solidify, I followed up with this worksheet where they had to analyze the angles of a diagram much like on the game board. They did pretty well on it, so I’m satisfied!

## Materials

Crossing the Transverse Rules

Printable Map (Prints on 4 pages)

No Stars Printable Map (If printing the background galaxy is not for you, here’s a more barebones version.)

Zip File with Everything, including Pages, Doc, and GGB files

### Fighting for the Center

At the Math Games morning session at Twitter Math Camp 15, we’ve been created curricular games that hit on some topics that there aren’t really good games for. I came up with the idea for this one, and worked on refining it with the help of Paula Torres (@lohstorres1) and John Golden (@mathhombre).

This game is about measures of central tendency (and range for good measure). Not only do students have to determine all of those over and over as they play the game, but they can see how changing the data set changes the values, especially as the size of the data set increases or decreases. It seems really good because it drives the need to make those calculations.

All you need is two decks of cards. The game is designed as a two-player game, but it would definitely be best done as two pairs playing against each other, so they can talk to each other about their strategies and calculations. We also recommend having students keep a running tally of the values.

### The Factor Draft

Last year at #TMC13, I ran a session called Making Math Games. I stared off with an overview of what makes a game a good game, while still being good math pedagogy as well. Then we spent most of the session in two groups brainstorming idea for games for topics that are somewhat of a drag to get through. The other group worked on something in Algebra 2, though I don’t recall what – I must say both groups were supposed to write up what we did and neither did. (But I do think Sean Sweeney was in the other group, so maybe he remembers.)

My group worked on a game for factoring, focusing on Algebra 1. I took the ideas from the session and made a mostly operational game. Then, about 2 months ago, Max Ray came to visit me on the day I was unveiling that game in class. He saw it and it worked out…okay, but here was definitely improvements to be made. So we talked over lunch (about many things, not just the game – he’s great to talk to!) and then tried out some changes with my lunch gang. The changes seemed to work and I went forward with the new version in my afternoon classes to great success. By the end I think I had a really wonderful game, and so I wanted to share it with you.

### The Materials

A set of Factor Draft cards includes 3 differently-colored decks. Mine, pictured here, were green, blue, and yellow. One deck (green here) is the factor cards, with things like (x + 2) and (x – 1) written on them. Another deck (blue) is the sum cards, with numbers like 10x or -4x. The last deck (yellow) is the product cards, with numbers like +36 or -15.

### The Set-up

Lay out the cards as follows: make a 3 x 6 rectangle of factor cards, a 4×3 rectangle of sum cards, and a 4×3 rectangle of product cards, all face up. Place the remaining cards in separate piles next to the playing area.

In the cards I printed, I didn’t put the Xs on the blue sum cards. Max suggested I do because it’s easy to be confused on which is which.

### The Objective

The goal of the game is to collect 4 cards that can be used to complete a true statement of the following form: (factor card)(factor card) $= x^2$ + (sum card) + (product card).

### Gameplay

Each turn, a player may select any card from the playing field and place it face-up in front of them. They then replace that card with a new card of the same color from the deck. Play passes to the left. A player may have any number of cards in front of them, and may use any four cards to build a winning hand.

The cards I collected after turn 5. There’s two possible cards I could pull to win the game – can you see which ones?

If at any point a player achieves victory, if they had more turns than the other players, they must allow the other players additional turns to attempt to tie. Upon a tie, discard the winning cards and continue play as a tie-breaker.

A winning hand.

My co-teacher, when we were testing the game, said that it felt like Connect 4, in that with each move you have to decide whether to go on the offense to try and complete your four cards, or go on the defense and block the other players’ sets. But as each player gets more and more cards in front of them, it’s hard to see all of the connections and effectively block, so the game will always eventually lead to victory.

I may need to adjust the number of cards and type of cards in the decks, but I think what I currently have works well – if you have any feedback on the card distribution, let me know. The sum cards go from -10 to +10, with the numbers closer to 0 more common. The product cards go from -60 to +60, with each product card being unique. And the factor cards go from (x-10) to (x+10), also with the ones closer to 0 being more common. (There are no (x+0) cards.)

I did a whole little analysis to determine how many of each type of card to include…but maybe that’s a post for another day.