## Wednesday, May 20, 2020

### Choose Your Path, a Math Game

This past semester I got to teach a senior project class. Four preservice elementary teachers working on understanding math games, game design and making their own. Maggie wanted a game that used a graph/network as a playing board, and tried several options until coming up with this. All the games were tested with kids, and went through multiple revisions and I'm really proud of their work and the games they made.
GUEST POST by Maggie Eisenga

In my capstone with Professor John Golden I got to play and research math games. The big project of this class was to create our own math game that teachers would be able to use in their classrooms and/or parents could use at home! I created a game called “Choose Your Path.” This game is designed to help elementary students (focused more on 3rd grade but can work for other grades as well) work on their fluency in integer equations. I wanted to add strategy to my game as well, which you will see as I explain further.

The materials for this game are simple. You will need a deck of standard playing cards, small household/classroom items, and a scratch piece of paper and pencil if students need to check their answers. This is a two player game, but students can also work in teams against each other. I found it to work better as two individual players, but either works! The goal of the game is to make an equation with the cards you choose to equal the designated number in that round.

To set up the game, shuffle the cards and lay 12 cards, face up, in a 3 X 4 fashion and lay the rest of the deck face down in the middle of the two players. This picture is how it will look.

Have the students pick their household item, this will be their game piece.

To determine who goes first each player will draw a card from the deck and whoever has the bigger number will go first. In this game K=13, Q=12, J=11 and Ace=1.

The players will start at a corner of the “board”,” but they cannot start at the same corner. The player who goes first will pick up 2 cards from the deck and they get to decide what operation they want to use to get the first designated number and this can be any operation. That player then gets to decide where they want to go on the board. They only move one card at a time and can go up, down, left, and right, but not diagonal. They then pick up the card they were just on and keep it and replace it with another card from the deck.

The next player then gets to move their piece and do the same thing. This continues until one of the players believes they can make an equation with their cards to get the designated number. If they can, they discard all the cards they used in that operation and pick up the two cards that were used to make the designated number. They may keep any cards they didn’t use. The player who won that round then gets to pick up another two cards from the deck and choose any operation to get the next designated number. Whoever wins 3 out of 5 rounds wins the game.

The strategy behind the game is choosing which cards the students want to use for their equations. Having them use any operation is a good strategy as well.

In addition to all of that, if a player draws 2 cards of the same suit they may have an extra turn in that round and may use it whenever they would like but it has to be in
that round and if you land on the same card another player is on, you can kick the other player off and they will have to start their next turn at a corner of your choosing. For more difficulty, have the players win a round by using 3 or more cards and using 2 or more operations when getting the designated number. For example, they may use 3 cards but then it has to have 2 different operations. Not just adding for instance to make it simpler, use only adding and subtracting and take out the bigger numbers in the deck meaning the jack, queen, and king.

Whenever I played this with students they really enjoyed it and loved the challenge it brings! Being fluent in integer equations, I believe, is very important for students to have as they continue in their math education and this game is a good way to practice just that!
Here are the standards that involved within the game:

• CCSS.MATH.CONTENT.2.OA.B.2 Fluently add and subtract within 20 using mental strategies
• CCSS.MATH.CONTENT.3.OA.A.1 Interpret products of whole numbers
• CCSS.MATH.CONTENT.3.OA.B.5 Apply properties of operations as strategies to multiply and divide.
• CCSS.MATH.CONTENT.3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division

John's postscript: while this is similar to many computation games, there are several interesting elements that make the play more fun. One, it naturally levels as the operations the players use to make the target connect to the operations they'll use with the cards they pick up. It's turn-based, taking out the speed element to a lot of these games. And being limited to the cards they can get to helps even the playing field, with some chance involved in those replacement cards. I think there is a lot of opportunity for strategic thinking.

In addition to their own game, each teacher chose an already created math game to promote for classroom use.

Integer Solitaire

We looked at so many math games as a class and individually, but I found that the one I am about to talk about, is very beneficial for students who love a challenge and need a little more integer practice. It works for middle school, possibly late elementary (if they are ahead), and even high school students who want to be more fluent in solving integer equations. This game was created by Kent Haines back in February of 2016.

All you need to play this game is a deck of cards and a small white board and marker. If you do not have a white board, a piece of paper and pencil would work just as well! The board will look like the picture to the right.

Students can work by themselves or in pairs. I recommend using pairs because it helps build teamwork and in this game it is nice to have a partner you can bounce ideas off of. The student will draw 18 cards at random. The black cards will be positive integers and the red cards will be negative. In this particular game Ace=1, Jack=11, Queen =12, and King=13.

The goal of the game is to have the students use their 18 cards to somehow fill in
the 14 blanks on their board to make 4 correct equations. If the students finish early have them start over and pick 17 cards to make it more challenging.

Overall this game can be a challenge because they could get 3 correct equations but not be able to make a fourth. However, students are persistent to win so they will keep trying. For this reason, the fact that you don’t need a lot of supplies, the range of students who can play this is large, and because it is really good practice and fun for students who need to work with integers are all of the reasons I believe this game is a great math game for students.
A couple standards that are involved within this game are:
• CCSS.MATH.CONTENT.2.OA.B.2 Fluently add and subtract within 20 using mental strategies.
• CCSS.MATH.CONTENT.2.OA.C.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.

Cf. Kent's original post on Integer Solitaire