Math Hombre

 I once again am getting to teach the math game design seminar (at some point they'll realize it's too fun to count for my workload) and I wanted to try and capture my design thinking on a promising new game.

Phil Shapiro shared on Bluesky his math pairs game. A randomized list of 1 to 100 where you find pairs that add up to 100. 

For whatever reason, that made me wonder about a game finding differences. In elementary there's often a default to subtraction=take-away (Separate Result Unknown si parlez vous CGI) (I don't speak French) So a game that focused on the difference would be a good thing. I thought, what if you roll a die and need to find a pair that is that far apart?

For kids I like a number board that has a structure, so kids can use patterns to find what they want. (Nothing against Phil's game, where the Where's Waldo feeling is a lot of the fun.) My first try was a double spiral.

The other thing you can see here is pretty typical for me when I have a mechanic idea. Try out the mechanic and worry about the win condition as you go. The above image was my first try. I asked on Bluesky who won, and Phil responded probably yellow, since it seemed to have more territory. Biggest block of squares? Longest path? I stuck with that for a while. Eventually I realized the game is about differences, the win condition should be, too. What if the path with the biggest difference won?

Mechanically I really liked that. Then there's an advantage for the first player. And it raises questions: what's a path? I thought it should be only edge to edge, but it became too easy to cut someone off. Having squares connect corner to corner gave some of that Blokus energy. I did wonder about the sum of two paths, but that's unnecessarily complicated.

I'm still trying different play rules. Should one of your new squares have to be adjacent to one of your old squares? Currently I'm saying no, because that makes more interaction possible as well as opening up more strategy with more choice.

The board was 9x9 originally because I wanted that double spiral, so it had to be odd x odd. I can see this being on a hundred board. Great representation, and I love to have kids spend time with it. I like that +/-9 are above each other, because 10s are often comfortable already, and it feels like 9s still makes for lots of interesting patterns. It does make a game around 20 turns - which is long for 2nd & 3rd grade. Although kids play Joe Schwartz's Hundred Board Game (definitely a Best of Math Games awardee; video explaining it) is more turns, but the turns are quicker. 

Why I think this is worth developing is because as I play, I have to think! Looking for pairs, any in good strategic placement, what is possible... a lot to consider. Too much for middle elementary? I hate to underestimate the players. Towards the end of the game, there are surprisingly frequent times that you can't take the number you would first take. The number rolled makes a difference in play, as well as providing some variance that helps with surprise.

Current rules text: 

Two teams. Roll a 10 sided die (0=10) or flip a Tiny Polka Dot card. High number goes first and gets 10. Team 2 rolls and takes 90 and then 90 minus their number. 

On your turn, find two numbers whose difference is the number you rolled and color them in your color. After 10 and 90, teams can choose any pair of numbers with the difference they rolled.

Game ends when both teams have to pass because there is no pair with that difference. Both teams draw a path connecting the biggest difference that can find. Squares connect edge to edge or corner to corner. Winner is the team to have the biggest difference in their path.  For example if team 1 makes a path from 10 to 71 (71-10=61) and team 2 makes a path from 24 to 90 (90-24=66) team 2 wins! If tied, the winner is the team with the longest 2nd path that doesn't overlap their first.

The 10 and 90 start is trying to remove that first turn advantage. It's also is a step towards understanding strategy, which can be nice to bake into the rules.

Definitely want to try with a d20 as well. Maybe as a 4th and 5th grade variation? On a 0 with Tiny Polka Dot cards, you could be allowed to pick a single number - which definitely could be useful. Another variation for high school + players could be the sum of two paths victory rule.

Two games with the most recent rules. 10/90 start is working well. 

PS. I make some references here to the criteria I use for thinking about games. Definitely a part of my design thinking.

PPS. I also like the name, which is unusual for me, but am open to suggestions. 

I'm still posting games from the Fall 2023 GAMES seminar at GVSU. This senior capstone was begun by Char Beckmann. See many of the games from her seminar 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 this year), and they develop a game of their own.

Ryan Brummel made a video for Math Heads, our group game as mentioned above, a game he tested extensively with his algebra students.

I brought this very rough idea to my Math 496 math games class at Grand Valley. From there my professor and classmates did a great job helping me brainstorm and try to arrange my setup so that it would be as user friendly as we would get it to be. We came to the conclusion of a rough idea of a game with two teams trying to solve a linear equation and create the biggest output.

I took that idea to my Honors class and had them try it. It went over surprisingly well, The students had a blast. They found holes in the game that needed to be addressed, and they begged me to play the next week. I brought their comments back to class and we continued to playtest and mess around with the rules and setup of the game. Once I thought we had a final product I brought it back to my students and had them play it one more time. Having honed in on some of the minor issues of the game a lot better, it went very well and my students were very self-sufficient and able to play in teams of 2-3 the whole hour without my help. That is when I knew the game was pretty well set in stone.

From there the game needed a name. My students did not have any bright ideas like I thought, however my 496 class gave me the idea of “Variable Kings” as the name since the game is all about winning variables and the king cards are the ones that count as variables. From that point I did what I never thought I would really do which was create my own math game that I can effectively use in my 8th grade classroom.

Why Play Math Games?

Coming into the Grand Valley education program I was completely foreign to the idea of math games in the classroom. I have a dad who just retired as a high school math teacher and spent 30 years in the classroom. I went all throughout my 12 year educational journey from kindergarten to high school not remembering any semblance of math games in the classroom as I know of them today. However now that I have taken math education courses, taken a math games course, and have taught in my own classroom I now can see the importance of games in the classroom.

Math classes at the primary or secondary level tend to get the reputation of being very boring. As someone who was good at math, I did well in my math classes and enjoyed them but I enjoyed them more because of my classmates and friends in the class rather than the content itself and the way the classes were run. There were some teachers that had good personalities that made the classes more engaging but again, that is nothing to do with the content and most of my classmates didn’t even feel the way I did. What happens when students say class is “boring”. That means they are not engaged, and don’t have any desire to be engaged. Students who are not engaged have no chance at success. These students who tend to not be engaged, whether it be in math or any class, are the students that are the toughest to reach, but the students we have to try and reach. What I have found when using math games in my classroom is that a lot of the students that normally tune out, or misbehave, will perk up when there is a game to be played rather than the traditional notes or worksheet. I believe the reason for this is that a lot of these games that teachers use in the classroom have a very low entry point. This means that students who feel like they struggle in math or don’t want to share for fear of getting an answer wrong, are much more likely to engage in mathematical conversation during a math game. Math games invite students of all achievement levels to participate and also have fun which is something not always associated with a math class.

The engagement piece is huge when it comes to math games in the classroom. However, if I played dodgeball every day in my Algebra class I’m sure students would be engaged, but they wouldn’t be learning any math. The thing that surprised me the most about math games is that I really feel like students get more out of it. When you pick a good math game it gets students to think deeper about mathematical concepts without even realizing it. With good scaffolding and discussion facilitation students really start to notice things about math while playing games that they wouldn’t using a textbook. The more students are engaged and are invested in the activity they are doing the more they will dig deeper and get out of said activity.

Overall I think that math games are super essential to any math classroom. Not every single part of every day has to be a game, but I think that using math games in your classroom is super beneficial to the students and the teacher. With my experience, math games cause engagement and the depth of mathematical thinking to skyrocket. Both of these are things that can be lacking in traditional math classrooms. I wish my teachers and classrooms would have incorporated math games a lot more in my education experience. And I know classmates that would have benefited greatly from that!

 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 from her seminar 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 this year), and they develop a game of their own.

Keri Herman chose Tens Go Fish, a classic addition fluency game. As an extra feature, she demonstrates the game with Tiny Polka Dot cards. (Find them here at Math for Love.)

Keri's original game was a new idea for the seminar: she was interested in making a puzzle. I recently saw a description of a puzzle as a game for one person.  That certainly fits here. The puzzles are available on a Google doc here. What follows is Keri's story of making the game, and her ideas on why we should play games in math class.

Story of my Game

I knew when I got the opportunity to create my own game, I wanted to develop something that was related to quick multiplication facts. The reason being that my memory of learning my multiplication tables was always timed and quite stressful for me as a young student. I wanted to create a game where students could get great practice of their multiplication facts, and build in aspects of a good game; strategy, any player can win, etc. 

My first idea was a game board, moving the amount of spaces of the product. However, I was then drawn to the idea of more of a maze. I started with a small grid and filled in very small multiplication facts, students would have to find their way to the end. This turned into the development of three mazes, 5 x 6, 7 x 8, and 9 x 10, all with their own unique solution. To figure out how to design these mazes took a lot of different approaches, starting from scratch, and overall just thinking about how to make them work. I believe that the final product of these mazes will provide students with a very fun way to practice their multiplication, while being able to try to solve the maze. 

The goal was to have a large mathematical objective for the game. Students will be focused on trying to find the solution, even if they are going the wrong way, or have to start over, they are still constantly doing the math and getting practice of their multiplication facts. I think this game would be something that teachers should play with their learners because you can never have enough practice with multiplication. Especially in the 9 x 10 maze, all multiplication facts are used from 1 through 9 (not including zero). These mazes will also help students recognize patterns between multiples, factors, and products. 

These games could be used within a lesson, if students finish early, or simply just given as an opportunity for more practice, without time constraints. I also share within my video the development process of these mazes. With students who have learned multiplication facts,  I think it would be a great idea to turn this into a project or performance assessment. Students can work to develop their own maze. Not only does it take strategy, but at the same time students are able to continue working with the facts themselves and continue to recognize patterns. Overall, I am very proud of the way these mazes have turned out. I want to continue to show these to math educators and I hope that students will enjoy solving them as much as I had hoped. 

Why Play Games in the Math Classroom?

As a future math educator, incorporating games into the classroom is something that I want to use and will continue to encourage others to consider as well. It is often looked over to play games in the classroom, but the reasons as to why they are beneficial to student education should be considered. There are few specific reasons that are important to point out, including; building mathematical knowledge and skills, collaboration with peers, student engagement, critical thinking skills, and more. Each one of these reasons in its own makes games in a math classroom worthwhile. 

Building Mathematical Knowledge

Math games all are built upon their own goals and mathematical objectives. Teachers have the option to choose a game that targets the content that is being focused on. To find a game that can build mathematical knowledge, choosing a game that is relevant to your current learning goals within a classroom can help students extend their skills. There are so many aspects built within games that students can pick up on mathematically, without noticing. This can be beneficial to students because they are still learning, but without the title of class, homework, or assessments. 

Collaboration with Peers

It is important for a classroom to have communication among students that can lead to quality discussions. Discussions can uncover so many helpful aspects to student learning. In a game setting, a lot of times students will play with each other in teams, or against each other. In both cases, students are able to communicate and learn from each other. Students are able to pick up on each other’s strategies and build off of them. When playing with each other, this can help build a more positive classroom environment. This is because this type of communication is not usually seen in a regular lecture or discussion. 

Student Engagement

Oftentimes we hear negative assumptions about math and negative attitudes are common when stepping into a classroom for some students. It is important as teachers that we are able to increase student interest by engagement and participation. Incorporating math games into the classroom is a great way to develop student engagement. A lot of times, the mathematical objective of games are mixed in with aspects of interaction, surprises, and fun. A game can also change the view of many students. All students can participate and it is important to use games where any student can win. In math class, students can often point out the “smartest” students and become discouraged. When using games that are designed that anyone can win, not just based on skill, this can build a lot of confidence in students. 

Critical Thinking Skills

In many situations, students become disengaged after they reach the level of knowledge and understanding. However, it is things like analysis, critical thinking, and application that get students to really push past that level of reasoning for the content that they are learning. Math games provide a different way to push students to build upon their critical thinking skills. Having to figure out a strategy to finish or win the game is a very important tool when it comes to building these skills. With that being said, games that are chosen to play in a class should have aspects that involve strategy. 

Overall, math games have so many advantages when it comes to incorporating them into the classroom. Being able to play different types of games this semester has taught me so much about what a good math game should look like. Being able to develop and create our own group game, and my own game has changed my perspective on math games. Math games can help students learn in a unique, fun, and interactive way. 

 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 from her seminar 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 this year), and they develop a game of their own.

Kacy Jeffries chose Number Boxes from Jenna Laib for her first video. See Jenna's blogpost for it here. This game was really influential to the seminar this year. Corrina Campau made a high school/college focused video for it, and Jordan Burnham made a game built on that structure, Boxzee.

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.

This post is sharing Corrina Campau's games - she was also the lead Desmos engineer on the escape room!

Her first video was for Jenna Laib's Number Boxes. Really an all time great classroom math game, it was extra influential to this year's seminar. Like Jordan Burnham's game Boxzee.

Corrina's original game has an original deck of cards, which would have multiple uses, but is great in her Math Spoons (Cards and Rules). What follows the video is her story of making the game, and some thoughts on why to play games in math class and which games are effective.

The Story of Algebra Spoons

Whenever I take a class at GV I am always trying to see how I can use the class to become a more effective, engaging math instructor.  In thinking about what my course content entails I became enthralled with the idea of having students differentiate between different function families.  We study linear, quadratic, exponential and logarithmic functions and so this became my starting point.  I wanted a game that would allow students to think about all of the function families as a whole.  After playing some of the games in class I decided that one of the games that could work would be to design a game like SET where students must match cards based on different attributes.  I kept thinking about SET and how I felt when I played the game.  Although I like the game, I don’t always have fun playing it because I am not necessarily the fastest player when looking at 12 cards and trying to find matching ones.  John mentioned Spoons in class one day, and I thought that was a really great idea.  I have always enjoyed playing Spoons and so decided to roll with the idea.  Thus, Algebra Spoons was born.  I began to think of the number and type of cards needed.  I decided to use linear, quadratic, and exponential function families with 4 cards in a set and 4 of each function family giving me a total of 48 cards per deck.  I knew I needed to include graphs, stories, equations, and tables, but I wasn’t sure if I should choose a theme or not.  I decided to use stories that related to GV students and even chose some stories like they had modeled in class – like the equation of the water as it comes out of the drinking water fountain.  I hoped that the stories would appear somewhat familiar to them even if the story was new.  Once the stories were written then I needed to make sure that the graphs showed the important characteristics of each story so that students would be able to determine the graphs that matched the stories with relative ease.  I also examined the tables and made sure to include the portion of the table that made the most sense when trying to match the cards.  For some of the quadratic functions I used vertex form and for some I used standard form.  In retrospect, I wish I had included factored form as well.  But making these cards took a considerable amount of time and thought, and unfortunately when I thought about factored form it was too late to change.  Having finalized the front of the cards, I decided to make something on the back to make the cards more visually interesting.  Thus, the spoons motif was added.  Ten sets of cards were printed on card stock and printed out in color.  

When I played the game with two of my MTH 109 classes, I first had them sort the cards so they could become familiar with them.  After they had a chance to match all the cards, I then passed out the spoons, and they started playing the game.  The students had so much fun!  I was overjoyed to see how they embraced this game, and this was so much more fun than doing a standard final exam review.  I would encourage all teachers to play this game as it really gives students a fun, enjoyable, and deep conceptual learning of different function families.

Why Play Games in the Math Classroom and What Makes a Game Effective?

Research shows that Games Based Learning (GBL), either digital or non-digital, in education is now one of the major learning trends of the 21st century.   So, why are teachers playing more games in the classroom, and what makes a game effective as a learning tool?  

First, for a game to be effective, a game needs to meet learning targets.  Once an instructor has decided upon what the game should help students learn then a game can be found or created that allows students to meet those goals.  In thinking about LeBlanc’s Taxonomy of Game Pleasures, we can understand the eight “primary pleasures” that arise from playing games and see how these game pleasures help to make games more enjoyable and when games are more enjoyable, they are often more effective.  

A game that requires fewer materials is typically better because there is less set-up and typically less time spent learning to play the game.  Having fewer rules or simplifying the rules is also important so students are not overwhelmed before they begin playing the game.  Games where students’ interaction with other players affects their play attract different types of players and can make the game more fun to play for all players.  A game that generates different situations or has the element of surprise can be more exciting and make players want to keep playing the game, and a game where an early advantage always causes a player to win is not as fun or effective as a game that allows all players an equal chance of winning.  

When I play games in my classroom, I look for games that yield the best results in the least amount of time.  I ask myself – what game can I play that allows students to understand, apply, analyze, evaluate, and create?  Games always make learning fun and interactive, so when I tell students we are going to play a game there is always some excitement in the atmosphere.  Games, if set up correctly, can provide low risk competition and meet learning targets in a manner that is more motivating for students.  The structure of the game allows students to engage in problem solving in a way which is typically more enjoyable and more effective.  Games create a more engaging learning environment and cause more students to pay attention to the teacher’s lessons, and they help students understand the concepts and retain the material better.  Games are also able to reach students of all levels and function as confidence builders.  In addition, game play encourages and deepens strategic mathematical thinking.  Playing games in the classroom also allows educators to easily include active learning in the classroom.  

Spending time creating games or selecting games that are already made is time well spent and worthwhile for students and a very effective way of presenting concepts, creating deep thinking, and motivating and encouraging students, and GBL should be included in every classroom.

Reference

Hui HB, Mahmud MS. Influence of game-based learning in mathematics education on the students' cognitive and affective ___domain: A systematic review. Front Psychol. 2023;14:1105806. Published 2023 Mar 28. doi:10.3389/fpsyg.2023.11058

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.

 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.

+/- 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.

As my preservice teachers have had the opportunity to work with a K/1 classroom this year, I've been thinking a lot more about early math games. Mostly I'm trying to tie these to the components of number sense. 

Number Sense

In our class we discuss these as: 

• one-to-one correspondence - as learners count, they have one (and only one!) number assigned to each object being counted.
• hierarchical inclusion - (worst name candidate) the idea that a number contains smaller numbers. If you have 6 you also have 5, etc.
• subitizing - visual recognition of quantities. Perceptual subitizing is immediate recognition of quantities, most commonly up to 5 or 6. Conceptual subitizing is visual chunking of a collection into smaller groups that can be perceptually subitized.
• cardinality - the center and core. Recognition of numbers as quantities, a characteristic of a collection that doesn't change with rearrangement. Kids can have most of these other concepts but still not have assembled them into cardinality.
• magnitude/comparison - both being able to directly compare quantities, and identify relative size - like locating where 7 is between 5 and 15.

If possible, my favorite thing for many of these games is for kids to have number cards which they have a hand in making. Similar to Tiny Polka Dot cards, which are a great commercial version. The idea is to make four suits, 0 or 1 to 10, where the suits are different representations of the numbers. Ten frames, symbols or shapes organized into patterns, randomly placed or groups of shapes to encourage subitizing, etc. You can have numerals or tally marks or number words if that's something you want your learners working on. I tend to prefer cards that involve counting and supportive structures. I used to have my own cards I'd print, but the opportunity for creativity, ownership and doing mathematics is strong with kids making the cards. (Not to mention some sneaky assessment.)

General Educational Game Advice

Many traditional games have a rule that when you're successful, you go again. I recommend against this because it increases wait time for other players, works against catch up, and can discourage the kids we want most to engage.

Similarly, I try to avoid games that emphasize speed, or require correctness to score and advance. I love for games to be an opportunity for collaboration and discussion, not a stand in for a quiz.

Staircase  (Counting, counting on, hiearchical inclusion)

Materials: optional gameboard, a lot of stacking cubes and a die.

Play: roll a die, and build a stack of that many cubes, then roll another (or reroll) and add that many, with the two summands in different colors. Put them on your team’s track on the sum. If you already have that number, that’s okay, put it on the same space. Winner is the first to get three spaces in a row (make a staircase). Some students lay them down, some stand them up. Variation 1: If the three step game is too short, play to four or five steps. Variation 2: if you roll a sum you already have, you can choose to remove the same sum from your opponents’ board. (Increases interaction.) Variation 3: Playing with number cards 1-10. If you get a 1 or a 2 first card, you must take another. Otherwise it’s your choice. Bigger than 12 is a bust, you lose your turn. Probably best with a four or five step win condition, and can be combined with variation 2 as well. Lots of opportunity to notice and wonder. Notice the different ways to get the same sum, wonder how much you have together, notice that 2+5 is the same as 5+2, ask what you hope to get on that second die roll…

How many behind? (Decomposing, hiearchical inclusion, part part whole stories) Materials: 10 (or 12!) unifix cubes.

Show and count how many cubes in the stack. Now put the whole stack behind your back, and bring 1 cube out front. Ask: how many cubes behind my back? Next time, keep 1 behind your back, then show the rest. (If your partner’s there, have them go.) Learners and teachers take turns being the hider. If you want, you can always start with the same amount shown in front, or let people show a different number, then hide some behind. If the learners haven’t got the one less idea, try that one a few more times.

Big Three (Magnitude) Materials: deck of number cards. Idea: Players start with 3 face down cards. On your turn, draw a card from the deck or the top card of the discard pile. Replace one of your face down cards with it. No peeking! The goal is to find the biggest cards you can. The card you replace is then discarded, even if it was a high card. When someone thinks they have the biggest cards, they call “Last Turn” and everyone else takes one more turn. Players add up their cards to see who has the Big Three. Option: need more challenge? Play Big Four!

(Riff on Rat-a-Tat-Cat, a great commercial math game.)

Moving to Story & Operation

As kids have started to acquire number sense, we move into stories that provide the context for operations. The Cognitively Guided Instruction Framework, based on research analyzing how children acted out elemental math stories.

• Join. One quantity, increasing over the story. Unknown could be the start, the change or the result.
• Separate. One quantity, decreasing over the story. Unknown could be the start, the change or the result.
• Comparison. Two quantities, related by the difference between them. Unknown could be the referent, the difference or the compared quantity.
• Part Part Whole. Two quantities that are part of a group. Unknown could be either part or the whole.
• Grouping. A number of groups, each group with a number of things, and a total. If the total is unknown, it's multiplication; if the number in the group is unknown, it's fair share/partative division; if the number of groups is unknown, it's measure/quotative division.

Comparison Game

Materials: number cards, especially if you have organized ones like dice face, hashmarks (if those are good for your kids), or ten frames. Plus 50-60 unifix cubes. Both players flip a card and build a stack that tall. Compare the stacks. Count the difference and take it off the taller stack. The player with more scores the difference. First player to 20 scored cubes wins. If it’s a tie, no score. Afterwards be sure to describe the score as 8 is 3 more than 5, or 5 is 3 less than 8. You could write down 5+3=8 (or 8-5=3 if they seem familiar with subtraction and super-comfortable with addition number sentence already.) Transition to them writing the number sentences and saying which is how many more than the other. If they are able to find the difference without counting blocks, make sure to have them describe their thinking. If they need challenge, don’t put the stacks together as they try to figure out how much more and less.

Making a Difference Materials: unifix cubes or counters about 30, number cards. Play: Both players have three cards. Choose a card to play. The lower card scores how many blocks it takes to make it equal to the other card - let the learners know that low cards are better.. If students can do with just numbers, that’s fine. But at least the first couple plays, build both numbers and count up how many cubes to make the difference. The person with the lower card scores those blocks. If it’s a tie, you have to play a second card from your hand. Draw back up to three cards. Winner is the first player or team to 12 cubes.

Facts

I feel like this is a place where games have made an inroad. But still, there's plenty of fun to be had.

10s Go Fish and Concentration Make 10

Pretty self explanatory. Remember to not let kids take extra turns. Both games I like to have kids score by counting their 10s.

Double Time (Doubles and counting on)

Materials: a game track, which can be numbered. 1 to 40 or 50 makes a good length with number cards, 30 is okay with dice. Bonus if you color or design the track in alternating spaces, to hint at the counting by 2s connection.

Play: students roll one die and move that plus the same. First to the finish line wins. I like to have students write down what they rolled and how far they went. 3+3=6, etc. If the track is numbered, you can start sneaking in some questions like 'Oh, you're on 24 and moving 8? Where will you end up?' For students working on counting on, this game provides lots of practice, since you don't start with 24, 1 is 25.

Ten Penny Game (Fives structure, sums to 10)

Have two ten frames out, the blocks, and some pennies or chips for scoring. Put a penny on the tenth spot of each. Players take turns rolling a die, and adding that many blocks to one of the ten frames. If they fill up the last spot, you get the penny as a point. Clear all the blocks and put on a new penny. There will be lots of opportunities for counting, counting on, and using the fives structure. "How many on this ten frame? How many more to fill it?" Are good questions here.

Cover All (Addition, decomposing)

This is the classic math game Shut the Box.

Cover All gameboard, but really all students need is a track from 1 to 10.

Play: roll two dice, and cover up any combination of numbers that add to the same amount.

With some kids, blocks help. If they set out how many they rolled, they can break them up in different ways. Consider questions to ask: what would be a good roll? What numbers might be harder to cover? What are different ways to split up our roll? (Helping them realize they have a choice.) What really makes this game a classic to me is that it really generates problems. Not how do you make 10, but how do you make 10 if I already used 7, 6 and 5. Is it even possible?