Quotients of Monomials

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Objective

Students will be able simplify quotients of monomials.

Big Idea

Investigate the concepts behind, as well as the numerical limitations of, the simplest form of a rational expression.

Warm up and Homework Review

10 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. Please watch my Video Narrative which explains this lesson’s Warm Up- Quotients of Monomials.

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

Rational Numbers

17 minutes

This lesson in a support/scaffolding lesson for my unit on rational functions.  Though these concepts have been mapped in the Common Core into the Algebra 1 standards, they are fundamental to my students’ success in the upcoming lessons. Since this is a skills based lesson, it does include guided practice.  To balance this, I have included conceptual activities that provide an opportunity to deal with the WHY as we talk about the HOW.

The first activity asks students to spend two minutes writing down everything they know about exponents.  The goal of this is to activate all their prior knowledge of exponents which will increase their success in this lesson.

Next, we discuss the concept behind rational numbers as well as their major limitations, namely a zero in the denominator. We look at two reasons why this can't happen (Math Practice 2).  

Please see the PowerPoint for detailed presentation points.

Quotients of Monomials

17 minutes

Next, I have the students investigate the pattern xa/xb = xa-b (Math Practice 8) using several sample problems.  After trying a couple of examples, the students look at reasoning behind a0=1. 

Our next task is looking at 00.  After consulting with their partner, I have the students raise their hands if they think 00 = 0 or if 00 = 1.  This discussion provides an opportunity to see how mathematics isn’t always black and white and gives the students an opportunity to defend their own reasoning (Math Practice 3).  Here is a website with some great information on this topic. 

Finally, we discuss negative exponents and look at several examples combining all of these concepts. 

Exit Ticket

3 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 simplify a quotient of monomials that include negative exponents.

Homework

This homework begins with eight problems which provide a small amount of practice to reinforce the day’s lesson.  Next, the students identify a quotient that has a variable with a constraint not equal to zero.  This is a preview into the next lesson which includes binomial denominators.  Finally, they determine whether  a quotient has been simplified properly (Math Practice 3).  

This assignment was recreated with Kuta Software, an amazing resource for secondary mathematics teachers.