Logarithms Lesson 1 Episode 1 (Teachers)

Making Sense

The students create two equivalent expressions that both represent the height of the beanstalk 5 days after Day 2, and create a number line to represent these expressions.

Episode Supports

Students’ Conceptual Challenges

Josh and Arobindo readily tackle the challenge of expressing the height of the beanstalk five days after Day 2, coming up with two equivalent expressions: 9 × 35 and 1× 3(2+5). Some students may have trouble expressing this height, particularly if they are not familiar with the beanstalk context. The Project MathTalk Exponentials Unit helps students build foundational ideas about exponential functions. If you notice your students struggling unproductively with the tasks in this episode, consider spending some time reviewing exponentials.

Focus Questions

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

1. [Pause the video at 2:25] How does Arobindo interpret and represent the growth of the beanstalk in comparison to the initial height? What is the significance of the numbers he uses in his expression and how do they link to the context?
2. [Pause the video at 4:10] How does Josh’s explanation for the expression 1 × 3(2+5) utilize the repeated tripling of the beanstalk context?

Supporting Dialogue

[Pause the video at 3:30] Ask students to compare Josh and Arobindo’s expressions: 9 × 35 and 1 × 3(2+5). Are these two expressions equivalent? Encourage your students to make an argument to support their claim.