Unit 7, Lesson 2
Multiplying Powers of 10
Accelerated 7
Preparation
Lesson Narrative
In this lesson, students make use of repeated reasoning to discover the exponent rules and .
Students begin by relating base-ten diagrams to exponents, specifically powers of 10. This allows students to consider the meaning of quantities and not just how to compute them (MP2).
Next, students expand expressions written as the product of two powers of 10 or written as a value with an exponent raised to another power, and notice patterns when asked to write the expression using a single power of 10 (MP8). Students will extend this exponent rule to cases where the exponents are zero or negative in following lessons, but the focus here is on cases with positive exponents.
- Generalize a process for finding a power raised to a power, and justify (orally and in writing) that $(10^n)^m = 10^{n \boldcdot m}$.
- Generalize a process for multiplying exponential expressions with the same base, and justify (orally and in writing) that $10^n \boldcdot 10^m = 10^{n+m}$.
Let’s explore patterns with exponents when we multiply powers of 10.
Required Preparation
Create a visual display of the exponent rule to be displayed for all to see throughout the unit. A sample display can be seen in the Activity Synthesis.