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# Delta Math and Adding Exponents

Lesson 4 of 17

## 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

*55 minutes*

#### Start Up

*10 min*

This lesson is meant as an opportunity to challenge students and also assess how they are doing with current 8th grade standards. I will start off by reviewing a string that bridges the middle school and high school standards for exponents. I find that early exposure to this type of a challenge using strings helps many students master 8th grade content.

**String:**

(3^2)(3^3)

(3^2)(3^4)

(3^2)(3^5)

(2^2)(3^2)

6^2

(4^2)(2^2)

8^2

The string starts with four problems that directly relate to the 8th grade standards and then progresses to (2^2)(3^2). Here the bases are different. Students will most likely multiply 4 x 9. However, I use this string to help students realize that this is also the same as the next expression, 6^2. This is a necessary step to understand the Algebra 1 problems like (2x^2)(3x^3). 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

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#### The Delta Math Challenge

*25 min*

My goal is to have my 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.

The problems look a bit like this: Delta Math Multiplying

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)

#### Resources

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#### Summary

*20 min*

I use the time at the end of this lesson 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 also like to show some of the Delta Math Data. Then, we talk about the choices the students made and how they went. I'll ask questions like:

- Did any one at first pick the challenge and then decide that they needed to circle back and review?
- Did any one start by going over review material and then go for the challenge?
- What was surprising about the problems you chose?
- Were you successful in your work today?
- 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 others decide what we should learn. Instead, students should learn to participate in the process, from setting a course to assessing results.

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- UNIT 1: Starting Right
- UNIT 2: Scale of the Universe: Making Sense of Numbers
- UNIT 3: Scale of the Universe: Fluency and Applications
- UNIT 4: Chrome in the Classroom
- UNIT 5: Lines, Angles, and Algebraic Reasoning
- UNIT 6: Math Exploratorium
- UNIT 7: A Year in Review
- UNIT 8: Linear Regression
- UNIT 9: Sets, Subsets and the Universe
- UNIT 10: Probability
- UNIT 11: Law and Order: Special Exponents Unit
- UNIT 12: Gimme the Base: More with Exponents
- UNIT 13: Statistical Spirals
- UNIT 14: Algebra Spirals

- LESSON 1: Pay it Forward
- LESSON 2: Stringing in Zero
- LESSON 3: Khan Academy on Positive and Zero Exponents
- LESSON 4: Delta Math and Adding Exponents
- LESSON 5: Zettabytes
- LESSON 6: Stringing Strings with Stringy Strings (A Project)
- LESSON 7: Delta Math and Multiplying Exponents
- LESSON 8: Khan Exponent Rules
- LESSON 9: Diablo 3 - The Marquis Emerald
- LESSON 10: Ordering Exponents
- LESSON 11: The Depths and Death of Space
- LESSON 12: Khan Academy and Squares
- LESSON 13: Exponent Study Time (Game)
- LESSON 14: Finding Ones and Zeros
- LESSON 15: Review Day Problem Set
- LESSON 16: Cutting Apple Pie
- LESSON 17: Ongoing Assessments in Exponents