Logarithms Lesson 1 Episode 6 (Teachers)

This episode features the first use of exponents that are not whole numbers [1:30]. If students have not yet had opportunities to make sense of these types of exponents, it is recommended that you provide some opportunities for them to do so. The Project MathTalk unit on exponentials offers a great starting point for that, particularly Lessons 5 through 7.

For use in a classroom, pause the video and ask these questions:

1. [Pause the video at 0:14] Interpret the expression (3⁴)(3⁶) = 3¹⁰ using a number line. Then, watch the video to see how your number line compares to the one drawn by Arobindo and Josh.
2. [Pause the video at 1:34] Interpret the expression (3^7.2)(3^0.4) = 3^7.6 using a number line. Then, watch the video to see how your number line compares to the one drawn by Arobindo and Josh.

After watching the video, ask students to discuss how Josh and Arobindo interpreted the exponential equations (3⁴)(3⁶) = 3¹⁰ and (3^7.2)(3^0.4) = 3^7.6. What was similar in their interpretations and what was different? How did their interpretations compare to your interpretation?