# Rational Equation Activities

Instructor: Clio Stearns

Clio has taught education courses at the college level and has a Ph.D. in curriculum and instruction.

Working with rational equations is an important of high school algebra. This lesson offers activities that will make it more interesting for students to work with and resolve rational equations.

## Teaching Rational Equations

If you are a high school algebra teacher, then you already know that a rational equation is an equation that has at least one fraction with polynomials for the numerator and denominator. Rational equations vary in their complexity, but understanding how they work is a significant aspect of algebra at the high school level.

As you work with your students on understanding what a rational equation is and how they can go about solving one, it can help to have some activities to incorporate into your instruction. Activities not only make math learning more fun, they also allow students a variety of ways to access the same material. The activities in this lesson appeal to different learning styles while teaching students what a rational equation is all about.

## Simple Equations

Here, you find activities that will help students solve and comprehend the simplest of rational equations.

### Put It In Words

Sometimes, simply translating a mathematical expression into words can go a long way for students. Have students work with partners for this activity.

Give each pair a set of simple rational equations to work with. Usually, it is a good idea to give them five to ten to start. For example, you might ask students to solve (2-x) / (3+x) = 1/2.

Before they solve these equations, though, students' job is to 'translate' the numerical notation into language that makes sense. For instance, for the above example, students might write, 'X less than two divided by x more than three is equal to one half'. After students have put all of their equations into words, they should go back and solve them.

### Draw It

Here is a visual activity you can use to help your students work with simple rational equations. This activity is another good one for partnerships or independent work.

Give each student or pair one to three different rational equations to start with. Then, ask them to illustrate a step by step guide, using icons and images to show what they are doing to solve each step of the equation. Students can also use manipulatives to work on their solutions, as long as they find a visual way to represent the strategies they are using. Finally, bring students together to share their drawings and discuss overall strategies for rational equations.

## Intermediate Equations

These activities can be used for slightly more complex equations, where there may be multiple variables.

### Tell a Story and Represent It

Ask students to begin by reading and solving a few different story problems that make use of rational equations. In small groups, have them write their own stories that make sense and are authentic. Each story should be represented by a rational equation that contains two variables.

Before students solve their story problems, have them create short skits to use their bodies to enact the stories. Then, have them swap with other groups, write the rational equations, and solve each other's problems.

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