## How much is enough? - Section 4: Finishing Up

*How much is enough?*

*How much is enough?*

# Simplifying Exponential Expressions, Day 2

Lesson 4 of 14

## Objective: SWBAT simplify algebraic and numeric expressions involving rational exponents.

## Big Idea: Students persevere in solving problems as they use their knowledge of the properties of exponents to simplify expressions involving rational exponents.

*50 minutes*

#### Sprints!

*10 min*

Hand out the double-sided "Power Sprints" 5 & 6, with sprint 6 facing up. By now the students have figured out the routine, and many should be close to 100% on these. Make the most of this motivation and encourage them just like a coach would before a race; I ham it up sometimes by doing some fake stretches, deep breaths, and acting like a runner about to come out of blocks.

On "Go!" students flip the sheet over and have 2 minutes to solve as many of the problems on Sprint 5 as they can.

Next, give the class about 2 minutes to consider & discuss strategies for increasing their efficiency.

Time for the second sprint! On "Go!" the students flip the sheet and race through Sprint 6.

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#### Simplifying Exponents

*20 min*

Begin by checking the solutions to the front of "Exponents and *n*th Roots" worksheet. I read the answers once through, and students mark their own work. If a number of students are confused by a particular problem, I'll write it on the board and then ask other students to explain how to solve it. (**MP 3**) For example,

There are almost always questions about the problems in section V, especially the ones that do not simplify to a rational number. So, be prepared for questions!

Once this is done, hand out Rational Exponents and ask students to begin this problem set individually and *without* calculators.

#### Resources

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#### Checking Progress

*10 min*

Like yesterday, I'll share some of the answers about half-way through the class period. I'll also emphasize the strategic use of the properties of exponents for simplifying these expressions. If students are *looking* for the most efficient solution, not just *any* solution, they'll improve much more quickly.

To illustrate this, it might be good to select one problem as an example, like this one. Discuss the variety of ways you might go about simplifying it, and have students discuss whether one way is better/simpler/more efficient than another.

Alternatively, I might simply set out the solutions for students to check on their own. In this case, I would wait until everyone is about half-way done, and I would encourage students to check their progress and think carefully about any mistakes they've made. Doing it this way tends to take the emphasis off of the "answer" and put it more firmly on the simplification process. After all, if the answer were the most important thing, why would I just give it away like this!

Typically, I assign all of these problem, but it would take more than one class period to complete them. If you want to do fewer problems, you might split the class up into groups, assigning some students in each groups the even-numbered problems, and the others the odd-numbered problems. There whole group will be responsible for all of the problems, but the work will be divided.

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#### Finishing Up

*10 min*

After checking our progress, it's time to get back to work. Again, I'll use these final ten minutes for formative assessment. Primarily, I'm interested in who's still struggling with the simple problems on the top half of the sheet. These are the ones that involve a pretty straightforward application of one property or another, and it's important that everyone be comfortable with simplification at this level.

The final problem on this sheet are intended to challenge the best students in the class, so I'm not concerned that everyone complete them all today. If some students need an extra night or two to finish up, that's okay with me. (**MP 1**) See this video for some more of my thoughts on this.

#### Resources

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- UNIT 1: Modeling with Algebra
- UNIT 2: The Complex Number System
- UNIT 3: Cubic Functions
- UNIT 4: Higher-Degree Polynomials
- UNIT 5: Quarter 1 Review & Exam
- UNIT 6: Exponents & Logarithms
- UNIT 7: Rational Functions
- UNIT 8: Radical Functions - It's a sideways Parabola!
- UNIT 9: Trigonometric Functions
- UNIT 10: End of the Year

- LESSON 1: Opening Day Exponential and Logarithmic Functions Unit
- LESSON 2: Rational Exponents
- LESSON 3: Simplifying Exponential Expressions, Day 1
- LESSON 4: Simplifying Exponential Expressions, Day 2
- LESSON 5: Graphing & Modeling with Exponents
- LESSON 6: Comparing Growth Models, Day 1
- LESSON 7: Comparing Growth Models, Day 2
- LESSON 8: Comparing Growth Models, Day 3
- LESSON 9: Logarithms - Napier's Wonderful Invention!
- LESSON 10: Getting to Know Logarithms
- LESSON 11: Properties of Logarithms Day 1 of 3
- LESSON 12: Properties of Logarithms, Day 2 of 3
- LESSON 13: Properties of Logarithms, Day 3 of 3
- LESSON 14: The Number e