Laws of exponents

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Objective

SWBAT prove and apply properties of integer exponents.

Big Idea

Use logical reasoning to prove the properties of integer exponents. These rules are not made up - they make mathematical sense!

Lesson Author

Jeff Li MTP

New York, NY

Grade Level

Eighth grade

Subjects

Math

Number Sense and Operations

Exponents

Standards

8.EE.A.1

Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3-5 = 3-3 = 1/33 = 1/27.

8.EE.A.3

Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger.

8.EE.A.4

Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

MP2

Reason abstractly and quantitatively.

MP7

Look for and make use of structure.

Warm-Up

10 minutes

Before asking students to complete today's Warm-Up, I want to do something a little bit silly to help students accomplish the change in mindset that I want them to undertake as we begin to talk about exponents. I provide an overview of my plan for launching class in this video narrative.

Here is the ice-breaker that I show in the video narrative:

Source url: https://www.youtube.com/watch?v=leH7IU4yOWE (accessed April 2, 2014)

Play of the Day

40 minutes

Huddle

10 minutes

Getting Students To Prove the Laws of Exponents

5 - 5 student work sample prove quotient property.pdf

In this lesson, I like to review the silver problem (see 6 - 1 huddle image). Not only do I ask for the correct answers, I ask students to say what was most likely to be popular wrong answers. By doing this, I try to highlight key misconceptions so students deepen their understanding.

The silver and gold problems are from Holt Algebra I.