Exploring
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Arobindo and Joshua use an applet to determine how a new beanstalk is growing.
Episode Supports
Students’ Conceptual Challenges
The introduction of a new applet, one that displays tick marks corresponding to the height of the beanstalk on an earlier day, poses some new challenges for Josh and Arobindo. First, the students must interpret these new markings. Initially Arobindo and Josh count only the tick marks above the tick mark indicating the original height, which leads to them incorrectly guess that the growth rate is 2 [3:14]. Additionally, the students need to reinterpret the tick marks as quantifying distances or heights, in this case the number of distances equal to the height of the beanstalk on the earlier day. They resolve this challenge by calling each of those distances “one unit” and using circles to show those units, rather than just counting the tick marks [4:33].
Focus Questions
For use in a classroom, pause the video and ask these questions:
- [Pause the video at 1:10] Based on the observations of Day 0 and Day 1, what do you think is the growth factor of this new beanstalk? Can you provide evidence for your claim?
- [Pause the video at 3:36] Tell a partner what you think Josh and Arobindo meant when they said they could count the first one. What does that first tick mark represent? What about the second and third tick marks? (Push students to be precise with their language and highlight responses that discuss those tick marks in terms of the height of the beanstalk or as a distance.)
Supporting Dialogue
- As students work to determine the growth rate for the new beanstalk, ask them to make note of what features of the context and the representation they are using to help them make their determination. At [1:36], the students in the video claim they can check the heights of the beanstalk on any two consecutive days. Encourage your students to investigate this claim—how does that help reveal the growth rate of the beanstalk?
- Later, Josh and Arobindo use non-integer days to check the growth rate. Ask your students to discuss this strategy and why it may or may not differ from checking two consecutive integer days.