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Is It Fair? A Dice Game for 3rd and 4th Grades and Beyond!

An Intriguing Game for Kids and Adults

Earlier this year I was having dinner with my nephew Brandon, and his partner Patty. While we were eating, the topic of mathematics came up (Patty is a high school math teacher and Brandon is an economics professor at Stanford), and I shared one of my favorite games with them, Is It Fair? (About Teaching Math by Marilyn Burns, Heineman).

I explained to them how the game works. “You play with a partner and decide who is Player A and who is Player B. Roll 2 dice, add the numbers that come up. If the sum is even, Player A gets a point. If the sum is odd, Player B gets a point. Roll 20 times and keep track of your score.” Then I asked them, “Do you think the game is fair?”

Without any paper and pencil to help them, they proceeded to engage in an animated discussion about whether the game is fair or not. I didn’t intend for them to argue, but hey, isn’t that what we want to happen during math class? I was impressed that a math game intended for elementary kids would be so engaging for adults.

I finally let them play the game after dinner to settle their argument. Before they left, I posed what ended up being the topic of conversation on their ride home. “What about if you multiplied instead of adding? Would the game be fair?” This is the version of the game that I recently taught a group of fourth graders in Samantha Holcolm’s class in San Diego.

Spoiler Alert! Before reading on you might want to try playing both versions of the game.

Launching the Lesson with Guess My Rule

When I visited Samantha’s class, I wasn’t sure whether all her fourth graders were familiar with odd and even numbers (key to playing Is it Fair). So, I showed the class a chart (see below) on which I sorted the numbers 1-36 (the range of products you could get when playing) into two groups, odd and even. I asked the class to look at the chart and think about my ‘rule’ for sorting the numbers. “Why did I put these numbers together?” I asked, pointing to the even numbers. “And why did I put these numbers together?” I continued, pointing to the odd numbers.

I gave the class some time to think and then had them talk with their partner. When they shared out, the students agreed that the rule for sorting was ‘odd and even numbers.’ Students later used the chart as a reference when playing the game.

Guessing games are a great way to launch math lessons because students find them so intriguing, and they engage children in logical reasoning and communication. For more guessing game ideas, see our blog post, “Math Guessing Games...Kids Love Them!”

Modeling Is It Fair?

Next, Samantha and I modeled a few rounds of the game for the students. See the game directions below.

Game Directions

You need: a partner, piece of paper and pencil for each player, 2 dice.

  1. Partners choose who is Player A and who is Player B.

  2. Partners roll 2 dice and multiply the numbers that come up.

  3. If the product is even, Player A gets a point. If the product is odd, Player B gets a point.

  4. Players roll 20 times, keeping track of their scores.

Playing the Game

An essential Common Core standard for fourth grade is to ‘use the four operations with whole numbers to solve problems.’ For third graders, it’s essential that they learn to multiply numbers within 100. Playing Is It Fair gives students many opportunities to practice these important skills.

Samantha’s fourth graders dove into the game with enthusiasm. Many knew how to multiply the single digit factors 1-6 but benefitted from the practice, while a few needed their multiplication table as a reference. The odd/even chart was also helpful when players were deciding who would get a point.

After a few minutes, it became obvious to students that the game wasn’t fair. Samantha and I heard lots of giggles and comments like, “I’m losing every time!” “There are more even products!” “I want to be Player A!” Everyone seemed to be enjoying the game.

Collecting and Analyzing the Data

When most partners had rolled about 20 times, we stopped the game and collected the results. As I elicited the number of points that each player had won, Samantha recorded the tallies using her document camera (see below). Then we gathered the class on the rug at the front of the room.

“Look at the data we’ve collected from our games,” I told the class. “What do you notice? What do you wonder?” After a few seconds of think time, students shared their thoughts with a partner. During our class discussion that followed, I was impressed at students’ wonderings. Many in the group were curious about why the data behaved as it did. Why were there so many more tallies for the even products?

“Did anyone who was Player B have more points at the end?” No one raised a hand. This really stumped the class. “How can we figure out why even products happen more often?” This question led us to figuring the likelihood of odd and even products using a matrix as a tool for organizing.

Figuring the Likelihood of Odd and Even Products

Using the matrix below, I guided the class through figuring out what would happen when we rolled two dice and multiplied the numbers. This exercise provided yet another opportunity for students to both practice essential multiplication skills, but also to learn ways to organize data to answer a question. The matrix revealed just how much more likely it is to get an even product in the game Is It Fair?

Student Letters

Knowing that I would soon be sharing Is It Fair? with teachers in Lakeside, California, I asked Samantha’s students to write letters to the teachers and make recommendations for winning the game. The letters served as an exit ticket and provided students with an authentic audience to communicate what they learned. Following are a few examples.

Is It Fair? A Rich Math Task

Is It Fair? is a prime example of a rich math task. The game requires problem solving, critical thinking, practicing essential standards, and using mathematics to find a solution or answer a question. It is naturally differentiated so that any student can play and be challenged, even a high school math teacher or an economics professor! Is It Fair? allows students to visit several topics in mathematics, including numbers and operations, representing and interpreting data, as well as probability. Finally, the game is intriguing. Students were curious from the get-go, which caused them to be engaged and motivated.

Kids love things to be fair. So, if you find that one of the versions of Is It Fair? isn’t fair, ask your students to find a way to make it fair. It’s a nice challenge they’ll be ready to tackle.

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