Math is more fun when students get to do it together! Turning a lesson into a game lesson encourages peer learning and provides new ways to discuss math strategies. When students discuss math in the context of a game, the discourse becomes an especially fun way to process the math they are learning.
Games can also become opportunities for formative assessment. Data collected from the games can be used to inform your instruction in the moment by offering up individual or small group differentiation opportunities, or the data can be a longer-term guide for future classroom differentiation. In addition, math games can make repeated practice fun rather than students soldiering through problem after problem in a worksheet.
Factor Game Rules and Descriptions
In this article, we present three games that get students making sense of math with their classmates. Each game includes rules, ideas for differentiating instruction, benefits of playing, and free downloadable resources. The games come from Math Games for Number and Operations and Algebraic Thinking, published by Heinemann, along with Math 180, our math intervention program for Grades 5 and up.
Factor Game 1: Finding Factors
The concept of factors can serve as a foundation for higher-level mathematics that many students will encounter. Factors are a part of the far-reaching abstract idea of decomposing one entity into its constituents. Whether kindergarteners are recognizing doubles or high schoolers are rewriting polynomials, practice around breaking mathematical objects apart can benefit students of all grade levels. Try the Finding Factors game for accessible, fun practice that doesn’t require many materials and encourages rich math discussion.
Key Objective: Identify factors for products through 50.
How to Play: In this game, students take turns selecting numbers on a game board and identifying their factors. First, Player 1 circles a number on the game board, then Player 2 circles all of its factors. Then, Player 2 circles a number on the game board, and Player 1 circles all its factors. Players continue alternating between circling a number and its factors until there are no more numbers with remaining factors. The player with the highest score upon adding up the numbers they have circled in their color is the winner.
Differentiating Instruction: Finding Factors includes two different game board variations, 1–30 and 1–50, allowing you to differentiate around your students’ levels of mathematical proficiency. Yet there are plenty of other ways that you can differentiate instruction with this game. For example, you could extend the board to 100 and only have the board contain even numbers. Or you could give students a blank grid and have them pick numbers to fill in before playing.
Benefits of Playing: Throughout play, you may want to pause the game to pose questions around strategy and gather how the students are tackling the math. Good math discussion can easily be facilitated throughout this game to strengthen students’ understanding around products and factoring.
Factor Game 2: Target 300
If some of your students are right now working on factors that are multiples of 10, try the Target 300 game for especially relevant practice. In addition, if instead of finding factors, your goal is to get students more fluent in multiplying factors, Target 300 is a multiplication game where students choose the factors and play the game by multiplying them.
Key Objective: Build fluency with addition, subtraction, and multiplication through 300.
How to Play: In this game, students roll a number cube to determine one factor but get to choose the other from a list of multiples of 10 that the teacher provides (for example, 10, 20, 30, 40, and 50). Next, students record the product on their recording sheet. They record both their own multiplication equation and their partner’s. By recording both, they are being provided more opportunities to practice multiplying factors to find a product. In this game, students also have the opportunity to practice addition and subtraction as they add up their products and strategize around the difference between their current total and 300. The objective of the game is to get as close as they can to 300 without going over.
Differentiating Instruction: If you are looking for ways to differentiate Target 300 for individual or groups of students, consider allowing the factor set to continue through 100 instead of just 50 or changing the target from 300 to 3000 with multiples of 100 instead of multiples of 10. Target 300 is a great game to play as a whole group when you have just 5–10 minutes to spare at the end of class, or it can be intentionally offered as a workshop or center in your classroom for students to play with a partner.
Benefits of Playing: Students not only have fun playing, but they also learn quite a bit along the way. It allows them to see patterns in numbers and practice addition and subtraction as they strive to hit the target of 300. Students also practice estimation and mental math. They benefit from thinking ahead and observing what happens to a product when one of the factors is a multiple of 10.
Factor Game 3: Tic-Tac-Go
The previous two games are from the professional learning book, Math Games for Number and Operations and Algebraic Thinking, published by Heinemann. However, factoring practice is not limited to printed books and can be found throughout all of our math programs! The classroom board game Tic-Tac-Go is part of Math 180, an intervention program for students in Grades 5 and up.
Key Objective: Multiply single-digit factors with products through 100.
How to Play: In this game, students are presented a 4 × 5 grid of numbers that represent products, along with a list of 5 factors below the grid. Player 1 begins by selecting two factors with counters and putting an X over their product in the grid. Player 2 moves one counter to a different factor, leaving one of the counters on one of the original factors, and places an O over the new product. Players take turns moving the counters, one factor at a time, until one player completes a path from one side of the grid to the other.
Differentiating Instruction: While Math 180 already has three levels of the game established that increase in difficulty, a teacher could create additional variations of the game board to focus on larger products, larger factors, or products with a greater number of factors.
Benefits of Playing: By virtue of being an intervention program, Math 180 is particularly careful in making strategic scaffolding a nonnegotiable part of its design. In Tic-Tac-Go, a student’s cognitive load is lightened by having one factor provided but requiring strategic thought about the other.
Algebra and Beyond
Algebra is not a one-off area of study, siloed from the rest of mathematics. Rather, it is a progression of ideas that has foundational pieces that are initially taught in kindergarten, builds up to an algebra course taken at the secondary level, and can continue into undergraduate courses and beyond. Since algebra is so deeply woven into mathematical learning, it is important to continually offer opportunities that develop number sense and practice decomposing numbers so that students are prepared for more complex and abstract mathematical ideas like combining like terms or factoring polynomials.
At HMH, we pride ourselves in offering math solutions that offer a path to algebra, even when students are performing several years behind grade level. Whether it’s students breaking numbers apart in lower elementary or finding missing factors in upper elementary—the target grade range for the games listed here—playing a factor game can lay the foundation for students understanding higher mathematics in the future.
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