# Understanding Negative Exponents

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## Objective

SWBAT simplify expressions and equations with negative exponents and understand that a negative exponent can be expressed with positive exponents using the inverse reciprocal.

#### Big Idea

This lesson will help students gain understanding about negative exponents and how they relate to fractional representations.

## Warm-Up: Continuous Improvement Quiz #3

22 minutes

As with each Wednesday, we begin class with a Continuous Improvement (CI) Quiz (see My Resource folder for an explanation about CI Quizzes).  Students have 15 minutes to complete the quiz.  After students pass in their answer sheets, I go over the questions.

## Discovering Properties of Negative Exponents

15 minutes

In this lesson, we are tackling negative exponents and the different ways they can be expressed.  I introduce negative exponents by revisiting the "2-string" from the previous day's lesson on zero exponents.  We simplify each, stopping at 2^0.  I reminded the students that in the previous lesson we saw that each simplified equation was half the previous one so that 2^0 was equivalent to 1.  I then asked, "What is half of one?" When students respond with one-half, I write it down next to 2^-1 and then write: 1/2^1. I ask the students if these are equivalent.  I ask for a volunteer to explain how they know. We then move on to 2^-2 and 2^-3.  I ask if anyone sees a pattern.

I then show them several examples of equivalent exponents and their inverse reciprocals and ask students to talk at their tables about what they notice. After a few minutes, I bring the class back together by asking for volunteers to share what they saw.

Typically, at least one group notices that the fraction "flips and changes signs." I ask students to recall the name for a "flipped" fraction (reciprocal).  I then ask what term we use to explain a sign change (inverse).  I then point to the word wall where I have already added the term inverse reciprocal.

I then ask students to practice writing negative exponents as positive by using inverse reciprocals.

## Wrap-Up

8 minutes

After completing the six Let's Practice problems, I provide five additional practice problems for them to complete independently.  As students work, I circulate the room, looking for and correcting any misconceptions.