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# Understanding Negative Exponents

Lesson 3 of 10

## 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.

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.

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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.

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#### Wrap-Up

*8 min*

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.

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- UNIT 1: Welcome Back!
- UNIT 2: Rules of Exponents
- UNIT 3: How Big? How Small?
- UNIT 4: So What's Rational About That?
- UNIT 5: The Fabulous World of Functions
- UNIT 6: Shapes On A Plane
- UNIT 7: What's at the Root?
- UNIT 8: Playing Around with Pythagoras
- UNIT 9: Quantum of Solids
- UNIT 10: It's All About the Rates
- UNIT 11: Oni's Equation Adventure

- LESSON 1: Organizing Rules of Exponents
- LESSON 2: Zero As an Exponent
- LESSON 3: Understanding Negative Exponents
- LESSON 4: Simplifying Power to a Power
- LESSON 5: Exponents with Coefficients
- LESSON 6: More Exponents with Coefficients
- LESSON 7: Let's Play a Game of Hoops! Rules of Exponents Review
- LESSON 8: Quick Quiz- Rules of Exponents
- LESSON 9: Extending the Use of Exponents Part I
- LESSON 10: Expanding the Use of Exponents Part II