Boxzee - Flexible Computation Game

All this month I'll be posting games from the Fall 2023 GAMES seminar at GVSU. This senior capstone was begun by Char Beckmann. See many of the games in this YouTube playlist. Many of the games completed in my seminar are in this playlist. In the seminar, we play lots of games and math games, the future teachers make a first video to promote a class math game that already exists, we develop a group game (a monster-themed middle school Desmos escape room and Math Heads, a number mystery game), and they develop a game of their own.

Jordan Burnham selected Close to Zero, and integer addition game for her first video. Handout and original blogpost.

Jordan's original game Boxzee crosses one of my favorite classroom games, Number Boxes by Jenna Laib, with the classic Yahtzee. What follows is Jordan's explanation of the game and thoughts on why play games in math class.

Boxzee

When I was first brainstorming games, I had absolutely no idea what kind of game I wanted to make. It wasn’t until one day when I was sitting on my bedroom floor that the starting ideas of Boxzee came to me.

Originally I imagined the game to have more moving parts. I first had players each being dealt 4 cards. From there they would roll a dice twice to determine a specific operation they would be using (odds = subtract, evens = add). Then after finding out those operations you would choose 3 cards from your hand to find a largest total value for that specific round. I found that this became a little confusing and players wouldn’t necessarily be able to truly “compete” if all of their rounds operations were different than each other. If one player only rolled odd values then they would be predetermined to loose solely because the other players would have a better chance of having larger numbers if they rolled more even values. 

Moving on from here, I decided to instead come up with the number box sets. Rather than using the dice to determine operations I decided this was a more structured way that players could still affect the total value by the cards they put in without having so many moving parts. I first came up with the idea to have four different rounds. The players would both have 4 cards in their hands and needed 3 to fill into the number box sets. I also decided that they would both fill in the top box row, then move downward. After playing this a couple of times I realized it could be very common to tie. So then I chose to create a number box set that would be the final round and would use all of the cards in the players hand. I liked this much more. 

Then to incorporate more of a feel of Yahtzee, I decided that players should be able to substitute their cards into any of the top 4 number box sets of their choice in any order. This gives them more of a chance to use higher cards and lower cards when they have them for specific rows that those cards would be more valuable for each round. 

Some final touches were made after play testing with Professor Golden and my classmates. These included allowing players to chance any of the cards they have in their hand. I really enjoyed this change because it gives players more risk opportunities. The queen card was introduced as being a wild card during this time as well. I appreciated this idea because I feel like it allows players to more strategic and intentional about where they substitute certain card values into the number boxes. Finally I made a coupe of variations. I came originally came up with the addition and subtraction version of the game. I then decided to toy around with the idea of multiplication and division and made the multiplication and fractions versions.

I think that teachers should play this with their students because it makes basic operations more exciting. I think that allowing students to have so much control over placing values into expressions and solving these is something they will enjoy. I also believe that it allows students to grasp where they may rather place a larger value versus a smaller value. Since the goal is to have the largest total value for each number box set, it will look different for each set. Placing a 9 in the same value that you place a 1 or a 0 has much different affects. 

I believe that this game can be adapted and used for so many reasons. The framework of the rules and rounds is something that creates such a great skeleton to then use with multiple content areas. I have thought about creating a Binomial Boxzee and think that this would be a great next step as well.

Why Play Math Games?

Math can sometimes be a very intimidating subject area for some students. Because of this, I believe that it is important to keep the classroom environment exciting and reassuring that every student has the ability to be a mathematician no matter what level of skills they may think they have. To do this, incorporating games into the classroom can be very beneficial.

Math games are a great resource for teachers to use to introduce and practice content. When playing games in the classroom in allows students to learn content in a more relaxed environment. This allows students to feel less pressure when making mistakes. This is important because students will be more likely to try and continue trying even after making mistakes which will help them master content areas. Similarly, playing these games allows students to build their strategic and problem solving skills. They want to perform their best and win, so they are able to develop strategies that can help them succeed throughout the game.

I also believe math games are beneficial in the classroom because they can be interactive. This allows students to also help each other in teaching the math skills. By not only performing the skills needed for the game, but also using their skills to help teach their classmates they develop a deeper understanding for the content. 

Finally, playing math games allow students to build a love of math. When students are engaged and having fun playing these games, this is when they will be doing the most learning. Exposing students to games that are centered around math subjects, they will be able to see that math is more than just what they may be learning to compute in class.

Now seeing some of the benefits associated with math games, it is also important to identify what makes a good game. One of the biggest things that I believe makes a good math game is having minimal time constraints. When students are practicing their math skills within a certain amount of time some may start to feel discouraged if they are not as fast as their other classmates. With this in mind, choosing games that give students the same opportunity to be successful at completing the game whether they are fast thinkers or need some extra time is very important. 

I also believe that a good math game allows for catch up. This means that even if a student is “down” in a game or is behind, there are aspects of the game that allow the players to quickly catch up and still have an opportunity to win. Since some students may not succeed right away, offering an opportunity for them to catch up and still have a chance to win this makes the game more fun for all players. This also makes students more likely to want to play and in turn allows them to practice and learn without the fear of losing. 

In conclusion, math games being incorporated into the classroom that I urge many educators to try. Not only to practice content, but also to help build up students’ love for the subject and confidence in their own skills.

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!

Wimbledon

Quick game idea dreamed up while watching tennis. I'm excited about it, but it's untested. Maybe someone will playtest with me at TMC16?

Wimbledon
2 or 4 players (doubles, naturally)

Materials: deck of playing cards, score sheet.

Set up: deal each player 5 cards. Randomly determine who is serving first.

Tennis scoring:

• In a game, you score love (0), 15, 30, 40, game. But games have to be won by two points. If you get to 40-40 it is deuce (tie). One point from there is Ad (advantage). If the player with ad wins, it's game. If the other player wins it's back to deuce. 
• It takes 6 games to win a set, but you have to win by two games. 
• If you get to 6-6, there's a tiebreaker. The server serves once, then players take turns serving twice. First to 7 points wins the tiebreaker and the set, but, everyone say it, you have to win by two points.

(Game design aside: having to win by two points is one of the best remove first player advantage mechanics ever. The tennis tiebreaker was also a great innovation.)

A match can be one set, best of three or best of five. I recommend playing one set to start.

Playing a point: players draw up to 5 cards. The server can play a card or flip over the top card. Each card played has to be higher than the card before. Players can play two cards together as a sum. If a player can't play or chooses to pass, the other player wins the point. The same player or team serves for an entire game, then the other player or team serves the next game. Continue alternating serve throughout the match. When the deck runs out of cards, shuffle the played cards to continue.

Special cards:
Ace: 1 on a serve (flipped from the deck) 11 any other time.
Face cards: count as 10, but can only be played as part of a sum. However, King beats Queen beats Jack beats 10, so Queen+2 beats 10+2.

Variation: card pairs are multiplied rather than added.

Doubles: in a doubles match, either player on a team can play a card, or play a sum, or a sum can be made with one card from each player.

Notes: The weird scoring is the downside, but kids learning tennis scoring is not a bad thing. And it's a classic for a reason. I'm really excited by the strategy here. When to give up on a point, how to get rid of low cards, which pairs to form and play.

Safe or Sorry

Penrose Impossible Triangle
(best source I can find)

There was no specific math goal for today, so that always puts me in mind for number sense, mental math and operational fluency.

I've been interested in push your luck games (Farkle, Zombie Dice. Pig from the Interactive Mathematics Poject..) but those mechanics can be lame for a whole class math game. Students get bored waiting for the turn to come around. Not enough decisions to make. So I thought of a variation that offered a little better opportunity for mental math, and more activity for the players. The game was a moderate success, but the game design discussion at the end was even better.

Safe or Sorry
Dice game for two or more players.

All the players roll a die. Add them up for a total.
If the total is a multiple of 5 –  turn is over, zero points.
You can stay and take that many points, or keep rolling.
Whoever is still in, rolls again and adds the points to your first total.
If the new total is a multiple of 5 –  turn is over, zero points.
After each roll you have to decide:  stay safe and take the points or keep rolling. If the total is a multiple of 5, though, sorry, the turn is over and you get zero points.

Winner is the first player to 150. If more than one player is over 150, they all win.

Example: 3 players: Ann, Bill and CeCe.
Ann rolls 3, Bill a 4 and CeCe a 5. Total 3+4+5=12
Bill stays and scores 12. Ann rolls a 2, CeCe rolls a 6. 12+2+6 =… 20! That’s a multiple of 5.
Score: Ann =0, Bill = 12, CeCe = 0.

Next turn: Ann, 4; Bill, 4, CeCe, 3: 4+4+3 = 11. Ann stays and scores 11. Bill and CeCe roll: 3 and 5. 11+3+5=19. Bill stays and scores 19. CeCe rolls again: 5. 19+5=24. She rolls again: 5. 24+5=29. She rolls again: 6. 29+6 =35! She loses all the points.
Score: Ann = 11, Bill = 12+19 = 31, CeCe = 0.

You have to know when to stop, CeCe!

Pretty bare bones, but it's the end of the year so I want them doing more of the game design work.

I played a game against the class (Golden vs guys vs girls) to introduce it. The main confusion was whether the multiple of 5 was the total on the roll or the total for the turn. Maybe I need better terminology?  It wasn't a persistent confusion, though. The original game was to 100, but they wanted to 150, and that worked pretty well for the playtest.

The mental math level was appropriate and pretty diverse: some adding the single digit dice for some and writing down the two digit sums, mentally keeping the running total, or considering their score + running total.  Having multiple dice to add gives options for summing, the group nature had people doing it in different ways. I saw everything from counting on to efficient fact use (doubles or sum to ten).

The game was mostly engaging. One group couldn't get into it, two groups played a full game then stopped, and four groups played until awwww, time was called. But, interestingly, the discussion afterward was full engagement, even the group that tried it the least. They all agreed that the game was a keeper, even though it needed some work. There was a fair amount of discussion about the zero condition. Some people wanted it to come up more often, others felt it was okay as is. One student suggested, "what about on multiples of 5s and 10s?" which led to a quick but strong class discussion about that. Some students wanted as hard a condition as even numbers. They recognized that the more common the condition, the more risky continuing to roll, the more often you should stop. The strategy discussion was strong; I was surprised that they recognized they were not stopping enough, but the fun of rolling was worth it. Most of the stories they were telling were of the "I got to 147 on one turn! Then 155 for a zero, of course."

One interesting rules discussion was about whether players who were out be able to come back in. At first the majority thought yes, but then someone pointed out that this made the decision to stay or keep rolling less important. That changed public opinion, but there was an interesting suggestion: when someone else opts out you can choose to come back in.

There does need to be a catch up mechanic, because when you're behind, the risky behavior is not enough to get back in. The opt in might be one way to do it. Other suggestions were that the risk should elevate. A really interesting idea was that there should be extra zero conditions the farther they go. One cool idea was that the zero condition should be a multiple of the number of players!

The game could use a context. The best idea the class had might not be suitable for school! "What about, you're a burglar, and you keep doing jobs, but you might get caught and go to jail. That's the zero." I do like that as a pushing your luck context; would it bother teachers to have their students playing criminals? Do you have a better idea for a context?

I think this is how I'd try it for the next iteration, adding in the extra zero condition:

Safe or Sorry
Dice game for two or more players.

All the players roll a die. Add them up.
If the your total for the turn is ever a multiple of 5 – the turn is over, everyone who rolled gets zero points. Now you can take your points and be safe, or keep rolling.
Whoever is still going rolls again and adds the points to their turn total. If the new total is a multiple of 5, the turn is over, zero points.
After each roll, you have to decide:  stay safe and take the points or keep rolling. If the total is a multiple of 5, though, sorry, the turn is over and you get zero points.
But the longer you stay in, the riskier it gets! If the total is over 50, multiples of 3 also give you zero.

Winner is the first player to 150. If more than one player is over 150, they all win.

2024 Update!

At the GAMES seminar yesterday we tried this game. Jeremy Schultz had an awesome selection. After each roll, you show if you're in or not by holding out a closed hand. Everyone reveals at the same time - if you have the die in your hand, you're still in.

To be clearer about the end condition. The game is over on the turn when someone has banked 150 or more points. But the winner is the person who has the most points on that turn. So you can stop with 159, but what if someone else keeps going?

Also think the catch up is just fine. You're never out till the game is over. You keep rolling and those are moments of actual excitement, even if you lose.

Math-wise, it's really pretty good practice. You're adding, others are also adding and you need to agree on totals. The seminar participants rated the game pretty highly, and thought how could it not be fun, "it's gambling for kids!"