## Trying to find math inside everything else

### Math Games

Back in January I participated in a panel on Math Games over at the Global Math. I meant to write this follow-up post shortly after, but January was a hell of a month for me and it slipped to the wayside. See my talk here, at the 2:55 mark.

I sorta hit the same point over and over, using six different games as examples, but that’s because I truly believe it is the most important point in both designing math games as well as choosing which games to use in your classroom. If the math action required is separate from the game action performed, then it will seem forced and lead students to believe that math is useless.

This can be fine if you want. Maybe you want to play a trivia game, where the knowledge action is separate from the game action. But if you pretend that they are the same, then you have problems.

This is the same essential argument as the one against psuedocontext. It may seem like you could say “It’s just a game,” but students see it as a shallow way to spice something up that can’t stand on its own. (I’m not saying review games and trivia games don’t have their place, but they can’t expand beyond their place.)

Below are the six examples I gave, with the breakdown of their game action and math action. I hope to use what I learned in this process to have us make a new, better math game in the summer, during Twitter Math Camp.

### Example 1 – Math Man

A Pac-Man game where you can only eat a certain ghost, depending on the solution to an equation.

If we apply the metric above and think about what is the math action and what is the game action? Here, the math actions are simplifying expressions and adding/subtracting, but the game actions are navigating the maze and avoiding ghosts. If I’m a student playing this game, I want to play Pac-Man. The math here is preventing me from playing the game, not aiding me, which makes me resentful towards that math.

### Example 2: Ice Ice Maybe

In this game, you help penguins cross a shark filled expanse by placing a platform for them to bounce over. Because of a time limit, you can’t calculate precisely where the platform needs to go, so you need to estimate. That skill is both the math action and the game action, so that alignment means that this game accomplishes its goal.

Verdict: Good

### Example 3: Penguin Jump

Here you pick a penguin, color them, and then race other people online jumping from iceberg to iceberg. The problem is that the math action is multiplying, which is not at all the same. The game gets worse, though, because AS the multiplying is preventing you from getting to the next iceberg, because maybe you are not good at it yet, you visibly see the other players pulling ahead, solidifying in your mind that you are bad at math, at exactly the point when you need the most support. A good math game should be easing you into the learning, not penalizing you when you are at your most vulnerable point, the beginning of your learning.

Verdict: Terrible

### Example 4: Factortris

This is a game that seems like it has potential: given a number, factor that number into a rectangle (shout-out to Fawn Nguyen here in my talk), then drop the block you created by factoring to play Tetris.

Again, the math action is factoring whole numbers and creating visual representations, which are good actions. But the game action is dropping blocks into a space to fill up lines. As Megan called it, though, we have a carrot and stick layout here, and often in many games. Do the math, and you get to play a game afterwards. (Also, the Tetris part doesn’t really pan out, because all the blocks are rectangles, which is the most boring game of Tetris ever.)

### Example 5: Dragonbox

I’ve written about Dragonbox before, so I won’t write about it too much here. The goal of Dragonbox is to isolate the Dragon Box by removing extraneous monsters and cards. The math actions include combining inverses to zero-out or one-out, or to isolate variables. The game action is to combine day/night cards to swirl them out, or isolate the dragon box. The game action is in perfect alignment with the math action, which makes the game very engaging and very instructive.

Verdict: Good

The board game I created last year (and you can also make your own free following instructions here, or buy at the above link). In this game, the game actions were designed to match up with math actions. Simplifying a radical by moving a root outside the radical sign, as in the picture above, is done by playing the root card outside and removing the square from the inside (and keeping it as points). You also need to identify when a radical is fully simplified, which you do in game actions by slapping the board (because everything is better with slapping) and keeping the cards there as points.

Verdict: Good

### Final Note

One of the real challenges of finding good math games, as a teacher, is curriculum. Most math teachers know of several good math games, like Set or Blokus. While these games are great and very mathematical, they’re not the math content that we usually need to teach in our classes. So the challenge falls on us to create our own games, but making good math games is hard. (Making bad ones is pretty easy.) On that note, if you know of some good math games (that meet the criteria mentioned in this post), drop a line in the comments!

### Algebra Taboo

I remember reading about the idea of Math Taboo on Sam Shah’s blog, this post by Bowman Dickson. I feel like I had the idea independently, but it seems like many people have, by doing a cursory Google search of the phrase.

Unfortunately, there are lots of posts ABOUT math taboo, but no real materials provided. If I have seen anything, it’s a lesson plan on having the students make their own. Or I saw one for sale, but it was for the elementary level. So I made one myself.

My co-teacher and I went through all the Integrated Algebra regents given since 2008 and pulled out any words that it’s possible a student might not know. I also went through my own lessons and pulled out any vocabulary I had given them. Below is the .pdf for printing your own (I used card stock and laminated), and two .doc templates if you’d like to make more, or alter the ones I have. I made a total of 126 cards (63 double sides – maybe slightly overboard).

Since I found no others, it makes sense to share.

Math Taboo (full pdf)

Math Taboo Pink  Math Taboo Blue (doc template)

### Egyptian Fractions

As I stated earlier, I’ve been trying hard this to integrate the other subjects more into my math lessons (and the other teachers are happy to work vice versa, because I’m on a great grade team). This process is made easier by actually having a Special Ed co-teacher for one section, and she specializes in math (and sees every subject, so can comment on all of them). So my first lesson explicitly tying history to math just went off, a lesson on Egyptian Fractions.

My goal for this lesson was really to get some fraction practice in while still learning something new, while also highlighting the “symbol that represents the multiplicative inverse,” , which I’d tie in on the next lesson about exponents (aka an exponent of -1). We worried, though, that the translation process would be too tough while dealing with fractions. That’s when we came up with this:

The Fraction Board has 60 square on it (which will be good reference for when I deal with sexagesimal Mesopotamian numbers soon), so each piece is cut to fit the amount of square that will cover that fraction of the board. To make the boards, I just made a 6×10 table in word as square-like as I could, printed on card stock. Then I cut the pieces out of the extra boards and had slave labor student volunteers color them in for me.

Each fraction have multiple pieces to represent the different ways you can fit them. (For example, 1/2 is 30 square, so I have a 3 x 10 piece and a 5 x 6 piece). But each fraction is also colored the same, because in Egyptian Fractions you can only use one of each unit fraction.

Then I would put up a slide like this on the board:

And the students would have to make that shape on their boards, with no overlapping and only using each color once. For the first one I shared a possible solution:

But I got really excited when the students could come up with multiple different solutions for each problem. And I would increase the difficulty of each one, until I would just get to a fraction with no picture:

And they still nailed it. Eventually I would move away from the boards and show the process of how to do it without the boards. We’d do some simultaneous calculation (using the greedy algorithm or more natural intuition) and checking on the board. Then we’d try with non-sexagesimal fractions. And every time we would translate our answers into hieroglyphics as well. So by the end of the lesson they could work on a worksheet where I just gave a fraction and they gave me hieroglyphics in return. (Not all of them could do this completely, but most could do some of the sheet). I think, overall, it went pretty well.

Egyptian Fraction Slides (Powerpoint)

Egyptian Fractions Slides (pdf)

(WordPress doesn’t seem like it’ll host my slides in their original Keynote form. That’s bothersome.)

### Habits of Mind Survey

Tomorrow is the first day of actual math class, so I’m starting off with my Habits of Mind survey that I created last year at the beginning of the year. I give some statements to the students and they can determine which habit of mind they represent. Then I’ll present them the challenge of forming themselves into groups so that each habit of mind is present in someone’s highest or second highest score. With 5 students per group and 8 habits, this shouldn’t be too challenging, but we’ll see how it goes….

Habits of Mind Survey

### Crimes and Mathdemeanors

I’ve made a post about history and science, I guess now it’s time for ELA. I think ELA is, in a way, the easiest to connect to math, but that might just be my background at Bard and working with the Algebra Project. But I wanted to talk about a book I used this past year that fits the bill.

This is a book of mysteries akin to Encyclopedia Brown. but with a more mathematical twist. The protagonist, Ravi, is a 14-year-old math whiz, athlete, and son of the Chicago DA. He often runs across mysteries that he can help solve and the reader gets a change to solve, as well.

I used this book in class to, I think, great effect. Most students enjoyed the prospect of the mysteries and got into attempting solutions. It allowed them in guess at a solution (such as who the murderer is from three suspects) without necessarily having to first grasp the math involved, which worked as a hook. Some students did not get into it but that was from rejecting the very premise of reading a story in math class. Many of those students eventually got past their misgivings.

For each story (I used the book about 6 times throughout the year) I asked the students to underline or circle anything they thought might be relevant to the mystery as we read it out loud. Then we compiled what we knew as a class and discussed what we still needed to know to solve the mystery, and then they worked in groups to come up with a solution, often with some prodding (but occasionally with none, which was nice).

I’m thinking of starting with the stories earlier next year (I didn’t this year because I only received the book in December for my birthday) to set it as normal when we use it. I also hope I can find some other books that might act similarly. If anyone reads this and has suggestions, let me know.