Games Open the Door to Complex Problem-Solving in Middle School

Math Teacher Sarah introduces games to her Middle School classes early each year, and the Factor Game is always a favorite. Much more than fun icebreakers, these games help Lowell students develop number sense and flexibility with how numbers and operations can connect and combine. 

In the Factor Game, players take turns selecting a number from a grid labeled 1–30, for which they collect the matching point value. The opponent then marks off all the factors that can combine to create that number, collects those points, and selects a new number for the other player. No number can be used twice, and the game ends when the grid runs out of options. The player with the most points wins. (Learn how to play and try it yourself here).

 

“We give students the rules and objectives of the game and let them try it out. Someone always starts their play with the number 30, thinking it will result in the highest point value, but they quickly realize it opens up a lot of factors to their opponent, which already total more than 30.” After a few rounds, the class will analyze the strategies they tried, which succeeded or failed, and why. Together they figure out the best opening moves and ideas for responding to the other player’s choices.

 

Post-game analysis comes into play in the game CONTIG as well. After rolling three dice, players can use any mix of addition, subtraction, multiplication, and division to combine the three values into one, which is then marked on a numbered game board. The next player rolls the dice and tries to combine their values into a number directly adjacent to the marked spaces on the board. Points are awarded based on how many marked spaces your sum touches. “They’re reviewing basic operations, order of operations, and envisioning expressions at the same time,” says Sarah. This newfound fluency leads into all the other work for the year. “We move quickly into real-world problems, and the more flexible they can be in recognizing rules, the easier everything else becomes for them,” she adds.

 

In her second-trimester math enrichment seminar, such flexibility came into play as students explored Fermi problems, or hypothetical situations, without one exact answer, among other activities. “After years of math courses, the students have a lot of practice finding the right formula for the right answer. The Fermi problems are interesting because they have to get comfortable with not knowing,” she says. “They have to figure out everything, from a starting point through a whole process for how to get to some sort of logical answer. Fluency with operations is really helpful in this situation too, like what sort of multiplication to put together to figure out how many tennis balls could fill our classroom.”

 

Math games in the Middle School can be played in ways that are fun and challenging for every student, regardless of where they are in their math journey. They can choose to push the games further by expanding the playing boards (think about the Factor Game going up to 49 rather than 30), by improving on strategy, or by increasing the pace of the game. Ultimately, every student will develop a toolkit of skills that will serve their mathematics and problem-solving needs, both in and out of the classroom.