G.L.A.S. Game

 I'm very excited to share this game with you. Jenisa Henry invented it for our senior math game seminar, and it shows a LOT of promise.  As she pitches it, it's an early elementary game, but it is highly suited for variations I'll discuss after you hear from Jenisa.

Her rules printout in on Google drive: bit.ly/GLASrules. She writes this about the game development:

My brainstorming for G.L.A.S. first started because I knew I wanted to create a game I can play in my future lower elementary classroom. Knowing that these years it is important to learn simple addition and subtraction facts while understanding equalities I toyed around with the first version of this game. It started with players using their top four cards to create an equality, then use their biggest sum to compare to the opponents biggest sum. It was rough to begin with, until I found the game more or less. This game solidified my idea on wanting to pursue designing a game with equalities. Though, I knew I wanted to add in another element to it, that was the addition and subtraction. Once I added that element to the game, I knew I had to think of a method for making the calls. I knew adding this element would offer choice to the players. I’ve learned to value games that have choices for the players as it makes them feel more active in playing. Once I added that, the game was great. I loved it and it was fun to play.

However, there was still something missing. An element of surprise was just what the game needed and that is when the Queen chance card came into play. This added the perfect amount of randomness that the game needed. After the playtesting went well, I knew it was exactly what I wanted the game to become.

G.L.A.S. is a great game that all teachers for 2nd-3rd grade should have their students playing. There are many reasons students should play this game, many benefits for the students to gather. Most simply, addition and subtraction facts are majorly important for the students to recall as they progress through their schooling. Additionally, the exploration of greater than and less than is the beginning of a building block for equalities. It is also a game of strategy. By using the cards in the players’ hand they need to strategically pick what they want to call. Further, they have to decide what two cards to operate on to get a sum that may satisfy the called equality. My personal favorite is when we have greater than for the equality and subtraction for the operation or less than and addition.

There is another variation to this game that has an emphasis on place value. Players will still call an equality, though instead of an operation they’ll pick the desired length of the number 1 digits-4 digits. All other rules still apply as far as card values, though 10’s do represent 2-digits. This game is very interesting as many variations can be created. As another example, this game can be played where the operation is strictly multiplication, a fraction version could even be created. Changing the game in these ways extends it to reach more grade levels as well as more areas within the mathematics realm.

For me, the break through of this game is the double choice. Giving both players significant choices each turn really makes this one of the best computation games I've seen. The adaptability is significant. In addition to place value, they experimented with multiplication and division, which would be good 5th-8th grade. You could do two digit computations (draw 6 cards), or even mix, 2 cards +/– 1 card.

Also for the course, teachers make a video for a game they want to promote. Jenisa chose +/– 24.

Explaining why this game, she writes: 

+/- 24 makes a phenomenal classroom game because of its quick nature and simple materials. Only requiring three simple materials that typically already reside in the classroom requires less preparation time for any teacher or helper. With simple rules, students will be able to grasp the game fairly easily. With there being many ways to create the desired outcome, there are multiple entry points for any and all students. This allows for students to stick to addition and subtraction, if they need or use the alternative operations if they feel comfortable. This is also a great game to use to bring attention to the associative and commutative properties. All the while, students are manipulating numbers to get their desired result. There is both strategy and critical thinking within this game, allowing students to be challenged when playing.

I agree! 

If you get a chance to play GLAS or try it with kids, I would love to hear about it!

Binomial Battleship

Some years I'm fortunate to be able to lead a capstone seminar where future teachers research math games and develop a math game of their own.

One such is this high school algebra game from Lucas Pohl. He writes about this in what follows.

When thinking about creating a math game myself, I knew I had a couple goals in mind. We had done multiple readings about what makes a good classroom game, and obviously I wanted to fulfill those criteria. Things such as being engaging, strategic, and grounded in coursework were very important to me. I had two initial thoughts: at first, I wanted to do a game that is based on statistics. Statistics is one of my favorite areas of math, and I think that it could lead to a great board game. However, I ended up going to my second thought, which was an adaptation of Battleship.

The initial idea was that the coordinate system used in battleships reminded me of different methods I had seen to multiply polynomials together. In school I remember myself and classmates having trouble multiplying polynomials together, so I thought that would be a good context of the game. Luckily, making an adaptation of a game checks some game design criteria for you. Because of this, I felt like I could focus on the subject area of the game. After trial and error, I had figured out the best setup for the game. Each team gets two grids, an attack and defense grid. The attack grid had the binomials on the sides, and the attackers would have to calculate the trinomials to attack, however, the defense grid was completely filled out. The sequence and fluidity of gameplay was then discovered through playtester feedback.

I think that teachers should want their learners to play this game because it is very effective at its job. Even creating the game, I became much more efficient multiplying binomials together. There is very little to suggest that playing this game is off topic, or unuseful. The game essentially is essentially getting students to do homework level repetitions, but in a context that makes it more competitive and fun. Another reason for teachers to implement this game is the opportunity for variations, and classroom connections. I feel this game has great flexibility and potential to be implemented in not only a lesson plan, but even lecture, or assessment questions. For example, teachers could use this game to get into conversations about common factors, and factoring trinomials. The game could become more engaging by letting students choose their own binomials for the grid.

These are just a few examples of the advantages of implementing Binomial  Battleship into the classroom. The truth is, this game is very young, but the potential it has to advance student learning is very high.

Handout: https://bit.ly/BinomialBattleship-handout 

Game board: https://bit.ly/BinomialBattleship-board 

These teachers also make a video to promote an excellent math game they found. I couldn't agree more with this one, a classic from Joe Schwartz. I first saw it in this blogpost.

Lucas writes: The hundreds chart game is a great game for you to bring into your classroom for many reasons. I am going to give you three reasons why you should adopt this game into your classroom. First of all, it is incredibly engaging for students. This game will have students thinking of math in a more fun way, and they will likely find themselves enjoying math. Second, it encourages strategic thinking, and helps students develop that part of their brain. Developing this type of critical thinking will not only help them in your class, but all of their classes. Thirdly, it is incredibly easy to set up. There are almost no required materials for it. All you need is a 10x10 grid, and two different color pens. This game is the definition of minimal time and setup for the teacher, and maximum benefit for the students.

Block Market

How much is that number worth? It's all about location, location, location.

This is another story of impulsive teaching. I'm not recommending that, but we got to a good place, so I want to tell someone.

In my preservice elementary course, we were headed towards decimals, passing through place value, so it was time for the base 10 blocks. A wise elementary teacher taught me that new manipulatives should always start with play time. (If you can't, tell them when they will be able to play. Chris's other lesson was to use each new manipulative as a chance for the students to tell you the rules about using them. Pro tip.) The wooden Base 10 blocks we have are particularly good for building.  But playtime always ends with: 'so what did you notice about these?'

They found the 10 fit into the next one pattern, and noticed irregularity in these old, hand-cut materials.

I love when manipulatives are used for a purpose or a problem rather than a set of exercises. So I asked how many blocks were in each tub, in terms of the small cubes as the unit.   3510, 4873, 4508, 4508, 3377. Hey! That's not very fair. Ooh, I have an idea: what if each group gave the next group half of their blocks? 4191, 4691, 4003, 4508, 3443. Is that any better? Some say yes, some no.  Let's give half again! 4441, 4500, 3741, 4256, 3817. Still disagreement about what's happening.


Okay. Let's settle this like mathematicians. Make a display of the data that proves your point. We collected one more round of give half away.

 I was really impressed at the diversity of displays by happenstance. It made for a great discussion of results. As we often do, I asked for each group to get feedback from the other students: one specific thing you like about their work, and one thing that would make it stronger.
 I missed one of the graphs, but here are the other three.

The first graph shown, people liked how it made the visual comparison of the round by round numbers. Convinced people that the numbers each round were getting closer.

This display charted each group's round by round count compared to the mean.

The classic lineplot follows each group's total round by round. People agreed that this showed convergence to the mean the most strongly.

But while people were making their graphs, I noticed something, and had groups record their total for each block on the back board. What's the problem?

Our individual block distribution is out of wack. Two groups don't even have enough to compose the next unit! We had to make some trades to get a better balance. We could play...

BLOCK MARKET!

We went table by table with people proposing trades. The whole class decided if a trade was fair. It was the most fun I've ever seen composing and decomposing by place value. Trading was heavy and fast paced. But occasionally we had to stop to check fairness. We even had one crazy three way trade. There was lots of interesting reasoning about the quantities and how they got out of whack even while the totals converged. Final count - not bad.

The idea of social relevance in math class has always been an interest. My colleague Georgi Klein made great use of Marilyn Frankenstein's algebra work. And we almost got a chance to hire Mathew Felton who looks at the political aspect of math learning. So I closed with an observation that with so many math problems about maximizing or candy, it might be nice to address big issues, and disparity is something that's going to be an issue. I got a little preachy, really. But it felt like a good day, with some real values in our place value.

Epilogue

Transitioning to decimals, after work with a fixed unit, we traditionally do something like the top part of this next activity. (Probably originated with Jan Shroyer.) It starts the idea of shifting the unit for different situations. Pretty effective. This time around I added the problems at the bottom as puzzles. They were very interesting for the students to think about, and seemed to push consolidation of their decimal strategies. It really requires a lot of reunitizing. I'd love to know how middle school students thought about them. Each group made up a puzzle of their own to swap, and that also seemed beneficial.


I'd love to hear your thoughts about political values in math class, block market trading for place value, or the representation puzzles.