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.
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.
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.
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.