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Copyright © Swun Math Grade 8 Unit 2 Lesson 5 C TE

Properties of Exponents:

Zero and Negatives

Conceptual Lesson

Grade 8 · Unit 2 · Lesson 5
MC: 8 .EE. 1 

Problem of the Day

Objective: I will explore patterns with positive and negative exponents.

Vocabulary Teacher Resources

Negative Exponent: indicates the number of

times to divide by the base

푥푥−2

The negative sign says to do the inverse.

Dividing is the inverse of multiplying.

Reciprocal: what to multiply a value by to get 1;

multiplicative inverse

A negative exponent is equivalent to the inverse of

the positive of the same number.

x−3 is the reciprocal of x^3

4 −5 is the reciprocal of 45

Properties of Exponents

Zero Exponent a^0 = 1

Negative Exponent a−n=a^1 n

Considerations:

Create a chart like the one being created today to post on

the wall. Students should explore the patterns found in

the chart. Allow time for discussion on the use of

multiplication when there is a positive exponent and

division when there is a negative exponent.

It is critical for students to understand that decreasing

an exponent by one is the same as dividing by the base.

Use other bases to construct the same chart if students

continue to struggle.

Steps:

1. Complete the chart.


2. Use expanded form to identify the standard
   notation.


3. Identify the pattern.


4. Use the pattern to identify the standard notation.

Application of MPs:

MP3: Why is any number to the zero-power equal to 1?

Any number to the zero power is equal to 1

because.

MP 8 : What patterns do you notice?

The patterns I notice are.

MPs

Applied MP

* Embedded MP

1 2 3 4 5 6 7 8

* ^ *

Student Journal Pages

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