Simplifying Expressions with Product Rule and Quotient Rule Lesson Plan

Overview

In this lesson, students will review the product rule, quotient rule, zero exponent rule, and negative exponent rule. Then, we’ll expand on students’ knowledge of exponent rules by simplifying expressions with product rule and quotient rule. You can expect this lesson with additional practice to take one `45`-minute class period.

Grade 8

Exponents

8.EE.A.1

How to Teach Simplifying Expressions With Product Rule and Quotient Rule

For teaching students how to combine exponent rules, we have broken up the lessons for students: product and quotient rule, then product and power rule, then quotient and power rule. If students are ready to combine all of the exponent rules, you can also include examples from the other linked lessons!

Bell Ringer

To start the lesson, students will review the exponent rules they already know: product rule, quotient rule, zero exponent rule, and negative exponent rule.

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Encourage discussion!

Students can check their work with a partner or table group. Encourage students to explain their reasoning if there are disagreements. As students work, you can circulate to listen to conversations to help determine where students may be struggling with these prerequisite skills.

Combining product and quotient rule

To foster student discussions, give students a couple of minutes to look at the expression to discuss how they might try to simplify the expression with a partner. This will encourage your students to use what they already know to help simplify expressions with product rule and quotient rule.

Using product rule first

Students should recognize they need the product rule and quotient rule. When students work through the expression, they may use simplify using different strategies; however, encourage students to simplify the expression by starting with the product rule first so there is only one term in the numerator and denominator to help avoid confusion.

Including negative exponents

Some students may choose to simplify the expression by using the negative exponent rule first to make all of the exponents positive. This can be a point of discussion for students, and ideally students will recognize that it requires more steps. Let students know that simplifying the numerator or denominator as needed first helps reduce the number of steps.

Product rule in the denominator (and numerical bases!)

Allow students an opportunity to work through the next example. Students may need to be reminded that with numerical bases, they should fully simplify the expression to find their final answer.

Class activity

Consider showing the slide above from the Slideshow and encouraging students to try each problem with a different person so that students’ hear each others’ perspectives. This also gives students the opportunity to move around the room if needed. Once students have completed the problems, review them as a class. Encourage students to explain their reasoning to their peers for each problem

Common misconceptions

When working with students, consider these potential misconceptions:

Students may have arithmetic errors with negative values.
Students may think a base raised to the power of `0` is `0` instead of `1`.
Students may not recognize that a base without an exponent has an exponent of `1`. For example, `y` is `y^1`.
If the base is a numerical value, students may not fully simplify the expression. For example, they may answer `2^3` instead of `8`.

Simplifying Expressions With Product Rule and Quotient Rule Practice

After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn gives you access to tons of practice problems for simplifying expressions with product rule and quotient rule. Check out the online practice and assign to your students for classwork and/or homework!