Activities to Teach Students to Factor Variable Expressions: Area Models

As a math teacher, one of the challenges you might face is teaching students to factor variable expressions. Although the process may seem straightforward, it can be daunting for students who aren’t familiar with the concept. One way to make the learning process fun and engaging is through using area models.

What are Area Models?

Area models refer to diagrams that help students understand the relationships between different parts of an equation by visualizing a two-dimensional layout. To factor variable expressions using area models, you must divide the rectangle into sections of different sizes that represent the different terms of the equation.

1. Using Manipulatives

To make this activity, you can give students squares or rectangle cutouts and ask them to manipulate them to create different expressions. For instance, you can create an equation such as x² + 5x + 6 and ask students to create a rectangle that represents that equation. After students complete the rectangle, they must divide it into rectangular sections of different sizes to represent the terms x², 5x, and 6 respectively. Students should then color-code each rectangular section to represent each term.

2. Collaborative Activity

This activity involves group work. Students work in groups to create area models that represent different equations. Each group will create an equation of their choice, and the other groups will try to factor it. The group that factors the most equations within a given time limit will be declared the winner.

3. Using Games

Games are a fun and engaging way to reinforce concepts learned in class. For instance, you can create a game where students would draw two cards from a deck, and each card would represent a coefficient or variable. Students would then have to construct an area model that represents the equation.

4. Using Technology

Technology has revolutionized the learning process. You can use online tools such as Geogebra or Desmos to teach your students to factor variable expressions using area models. These tools enable students to visual the equation and manipulate its elements to understand how they relate to each other.


Teaching students to factor variable expressions using area models is not only fun but also a practical way to help them visualize a concept that is otherwise abstract. By using manipulatives, collaborative activities, games, and technology, you can make learning math a fun and interactive experience.

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