Real Number Exponents

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Students will be able to simplify real number exponents and solve equations with real number exponents.

Big Idea

It's not enough to be rational, let's get real with exponents.

Warm Up and Homework Review

5 minutes

I include Warm ups with a Rubric as part of my daily routine. My goal is to allow students to work on Math Practice 3 each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. This lesson’s Warm Up- Real Number Exponents asks students  to correct the thinking of a fictional person who is doing a rational exponent problem.   This warm up highlights one of the most common problems surrounding student understanding of multiplying exponents.

I also use this time to correct and record the previous day's Homework.  

Real Number System

10 minutes


The goal of today’s lesson is to extend the student’s knowledge of exponents into real number exponents. Our first task is to construct a diagram of the relationship between real numbers (Math Practice 7).  This is a conversation that has happened earlier in the year so it should be a review. 

I give the students a couple of minutes.  If they all seem to be floundering, then I provide some hints as to what real numbers are.  I then pick a couple that have fairly different samples and have them put them on the board making sure to include someone how has irrational numbers.  This is a great time to pick students who are reluctant to talk in class.  Sometimes, I help a student who usually struggles to get a good example and then ask them to put it on the board.  Please check out my Video Narrative about this task.

Real Number Exponents

30 minutes

The remainder of the lesson involves Guided Practice of the specific skills important to the fruition of the day's objective.  I have found this method to work the best for me when it comes to introducing students to new skills. 

I start with something they know or give a basic introduction so they have some confidence.  Each successive problem either reinforces a new that skill or strategy or adds a new twist.  This works well since they go into each problem feeling like they already have some skill.  It is also extremely important to follow to needs of a particular class.  I regularly skip through problems or add more as needed.  By the time we are done, they have had experience solving a wide range of problems for a particular skill.  I  try to include an extension in the homework that was not part of the day's instruction as this forces them to do some synthesis of what they have already done.   

Detailed presentation notes can be found in the PowerPoint.

Homework Assignment

This Assignment includes a variety of expressions and equations that include real number exponents.

Exit Ticket

2 minutes

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.  

Today's Exit Ticket asks students to solve an equation similar to the problems worked on in the guided practice.