Laws of Exponents

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Students will be able to identify and correct errors in problems using the laws of exponents.

Big Idea

Error analysis helps students reinforce their understanding of the laws of exponents.

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.  The Video Narrative explains how this lesson’s Warm Up- Laws of Exponents draws on students prior knowledge of exponent rules.

I also use this time to correct and record any past Homework.  

Laws of Exponents

17 minutes

I begin this lesson by explaining the goal of this unit is to make sure my students' algebraic tools are sharp and prepared.   Exponent rules are introduced in Common Core Grade 8 and Algebra 1 yet I find many students have conceptual understanding issues.  Therefore,  I approach this lesson from an error analysis point of view in hopes of addressing misconceptions in advance.  

The first activities ensure that students are confident with the laws of exponents.  Rather than have students write down formal definitions and do practice problems, we approach the work from a conceptual point of view and derive patterns ourselves (Math Practice 7).  I want students to know the laws (or shortcuts) but I encourage them to write things out.  For example, (2x2y)3(5x3y6)2 can be rewritten as (2x2y) (2x2y)(2x2y) (5x3y6) (5x3y6).  This takes longer but I prefer that to plethora of errors that come up when students depend formulaically on rules (exponent laws). 

For each law, I give the students simple practice problems reflecting that law and ask them to determine the pattern.  We then try several more difficult problems including ones with variable exponents (Math Practice 1 and 8).

We then extend this knowledge to distribution using a monomial and a polynomial.  Again, the final problem uses variables as exponents.   I have specifically avoided dealing with integer and rational exponents as these will be covered later in the course.

Find the Error

20 minutes

The remainder of the class will be spent on an activity that asks students to identify the error in an exponent problem, explain why it is a mistake, and correct it (Math Practices 1 and 3).  I chose to do this activity because  students tend to feel confident in their ability to simplify these types of problems but also tend to make a lot of errors.  By having to identify not only the error, but WHY the error was made, students will deepen their own understand and hopefully avoid these errors in the future. 

I have my students work on these in pairs.  I expect complete sentences in their explanations.  Anything not finished in class will be homework.  

Some great links that identify common mistakes students make using exponents can be found here and here.  I used these websites in planning this activity.

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 find (3x2yz)3(-10x5y7z)2.