The students explore an applet to think about the area of a new garden when the length of the original garden is increased by 5 ft, 2 ft, and 3.5 ft. They provide a verbal explanation of a general method for finding the area.
Episode Supports
Students’ Conceptual Challenges
In this episode, Mauricio and Emily are asked to begin generalizing their method for finding the area of a garden after one dimension has been increased. Generalizing can be challenging for students, so provide plenty of opportunities for them to gather data from specific examples (for example, in this episode Emily and Mauricio find the area after increasing the length by 5 ft, 2 ft, and 3.5 ft before being asked to generalize). Notice how they are not asked to reason with variables, yet they still have some difficulty describing a method for finding the area of a garden with an unknown increase in length [7:00].
Focus Questions
For use in a classroom, pause the video and ask these questions:
[Pause the video at 6:25] The teacher has a number in mind for an increase in the length of the garden, but she isn’t saying what that number is. How could you express the area of the new garden with the number she is thinking of, but not telling?
[Pause the video at 9:10] Compare your method from before with the one Mauricio and Emily just described. Are they the same? If not, how are they different?
Supporting Dialogue
[Pause the video at 4:07] Mauricio and Emily seem to have developed a method for finding the area of the new garden after any increase in its length. Talk with a partner about what seems to be the same each time they find the new area and what changes. Describe the method Emily and Mauricio seem to use in your own words. Do you think this method always works?
