Understanding Negative Exponents

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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.



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.