Unit 7, Lesson 5
Negative Exponents with Powers of 10
Grade 8
Preparation
Lesson Narrative
In this lesson, students make sense of the rule that and extend the rules they have developed for working with values with exponents to include situations with negative exponents. This type of reasoning appears again in a later course when students extend the rules of exponents to make sense of exponents that are not integers.
Students develop their fluency as they mentally determine missing values from equations involving powers of 10. Next students complete a table comparing expressions written using exponents with those written as a decimal and as a fraction. The table includes both large values and values less than 1. By looking at the multiplier required to increase or decrease the exponent by 1, students correspond a power of 10 with a negative exponent to repeated multiplication by (MP8).
Students reinforce this understanding by matching a series of expressions written with negative exponents to a corresponding expression written using repeated multiplication (MP7).
- Describe (orally and in writing) how exponent rules extend to expressions involving negative exponents.
- Describe patterns in repeated multiplication and division with 10 and $\frac{1}{10}$, and justify (orally and in writing) that $10^{\text-n}=\frac{1}{10^n}$.
Let’s see what happens when exponents are negative.
Required Preparation
Create a visual display (or add to an existing display) for to be displayed for all to see throughout the unit. A sample display can be seen in the Activity Synthesis.