##
* *Reflection: High Quality Task
Zero and negative exponents - Section 2: Play of the Day

This year, I've raised the bar for what I expect for students to demonstrate their understanding. In the days following this lesson, I ask kids to "prove" the various properties of exponents using an annotated example that proves that you can, for example, subtract exponents when you divide exponential amounts with the same base.

This has led to a much deeper understanding of the various properties of exponents, and also created so much more understanding around both the zero property and negative exponents.

In this video, a student just models one way to prove the zero property of exponents, which can be done in conjunction with the quotient property.

*High Quality Task: Getting Students to Prove the Zero Property of Exponents - video of a student*

# Zero and negative exponents

Lesson 2 of 10

## Objective: SWBAT explore zero and negative exponents.

## Big Idea: Use logic to prove the rules of zero and negative exponents. These rules are not made up - they make mathematical sense!

*75 minutes*

#### Warm Up

*10 min*

Each day, students complete a warm-up that usually consists of spiraling the previous day's material, in addition to older material. Warm-up problems also sometimes extend lessons that students have encountered before to more unfamiliar contexts.

For a video narrative about how I structure each lesson, and how the warm-up fits in, click here.

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#### Huddle

*10 min*

In this lesson, I like to close the lesson by asking two kids to come up to the board and prove that:

1) anything to the zero power is 1; and

2) the properties of negative exponents.

The first one is generally much easier than the second; the second one requires quite a bit of guidance, but it is pretty powerful to get kids to do this. I try to do this over the course of a few days to ensure spiraled review.

*expand content*

#### Homework

*15 min*

Homework is to be completed at home and should take students approximately 15 minutes.

*expand content*

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- UNIT 1: FLUENCIES AND THE LANGUAGE OF ALGEBRA
- UNIT 2: SOLVING LINEAR EQUATIONS
- UNIT 3: INTRODUCTION TO FUNCTIONS
- UNIT 4: INTERPRETING AND COMPARING LINEAR FUNCTIONS
- UNIT 5: SYSTEMS OF LINEAR EQUATIONS
- UNIT 6: EXPONENTS AND SCIENTIFIC NOTATION
- UNIT 7: PARALLEL LINES, TRANSVERSALS, AND TRIANGLES
- UNIT 8: CONGRUENCE AND SIMILARITY THROUGH TRANSFORMATIONS
- UNIT 9: PATTERNS OF ASSOCIATION IN BIVARIATE DATA
- UNIT 10: SLOPE REVISITED
- UNIT 11: VOLUME OF CYLINDERS, CONES, AND SPHERES
- UNIT 12: POLYNOMIALS AND FACTORING
- UNIT 13: QUADRATIC FUNCTIONS

- LESSON 1: Laws of exponents
- LESSON 2: Zero and negative exponents
- LESSON 3: Apply properties to general equivalent expressions
- LESSON 4: Scientific Notation
- LESSON 5: Perform operations with scientific notation 1
- LESSON 6: Perform operations with scientific notation 2
- LESSON 7: Scientific notation - How many times larger?
- LESSON 8: Flexible problem solving with scientific notation
- LESSON 9: Review exponents and scientific notation
- LESSON 10: Assessment #11 - Exponents Unit Assessment