Delta Math and Multiplying Exponents

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Objective

SWBAT to apply the laws of exponents to multiply polynomials

Big Idea

We can encourage our students to master 8th grade topics by differentiating up and challenging them

Start Up

10 minutes

This lesson is meant as another opportunity to challenge students and assess how they are doing with current 8th grade standards. My students completed a similar lesson on Adding Exponents a few days ago. I start off by reviewing a string that exposes students to some challenging expressions that cane be analyzed and simplified using the properties of exponents. 

String:

(2^2)^3

(2^3)^2

(2^4)^2

(2^2)^4

2^6

2^8

(2^2 * 3^2)^2

(2^4 * 3^4)

The string starts with four problems that directly relate to the 8th grade standards and show that x^ab = x ^ba. This helps students understand the exponent powers are commutative. As the string develops, it progresses to (2^2 * 3^2)^2. When students compare this to 2^4 * 3^4 and see how they can multiply and "distribute" the exponent to all the exponents in the parenthesis. This is a necessary step to understand the Algebra 1 problems like (2x^2y^3)^2.

After students complete the string, we talk about these types of algebra problems and how they connect to the expressions in the string. I then give students a key choice. They can use this time to review content that we have already covered or they can take on the Delta Math challenge and try these Algebra 1 exponent problems. 

If students choose to practice more 8th grade problems, I print out worksheets from sites like Kuta Software: http://www.kutasoftware.com/freeipa.html

If students decide to take on the challenge, I give them a laptop and have them log into Delta Math (completely free): http://www.deltamath.com

The Delta Math Challenge

25 minutes

My goal is to have students attempt a challenge beyond our standard curriculum. Delta Math is a great way to differentiate up and accomplish this goal. I like to customize it so that students can attempt to get at least 5 problems correct. There are unlimited examples and I track and share progress with the class. 

Problems look a bit like this: Multiplying Exponents

It is a wonderful activity and a great opportunity to introduce choice into your lessons. Here students can choose this challenge. I am always amazed by the level of honesty that can be accomplished in a successful classroom. If students are ready to move to the next level, they almost always go for it. No one who is able to do the tough work says, "I am going to take it easy and review stuff that I already know." Instead, students who need real support sit together and review content that we already covered (I allow students to arrange themselves in groups for these types of activities)

Summary

20 minutes

I use this time to review some of the problems from the 8th grade set and the Delta Math challenge set. I usually have two students present on problems that led to interesting conversations during class. 

I like to show some of the Delta Math Data. Then we talk about the choices they made and how they went. I ask questions like: 

  • Did any students at first pick the challenge and then decide that they needed to go and review? Is it alright to change your mind? 
  • Did any students start by going over review material and then go for the challenge? When did you decide to change? 
  • What was surprising about the problems you chose? Were you successful? Do you like having these types of choices?"

These types of questions remind students that learning is something we should do with intent. We shouldn't just sit and let everyone decide what we should learn. Instead, all students can participate in the process.