Case Overview: Sequences
Background on the Classroom Lesson
This video comes from a thirdyear high school math class using an integrated curriculum.
Student Activity
Suppose you are building a sequence of towers, and you want the difference in height from one tower to the next to be the same. Find a formula that gives you the height of the tallest tower (hn), given the number of towers (n), the difference in height between each tower (d), and the height of the first tower (h1).
Overview of the Video
In the video, the students are discussing their ideas for how to find the height of the tallest tower. When watching (or rewatching), focus on how students think about the problem and how they use the cubes to help illustrate their thinking. Consider how the students understand the relationship between variables.
Questions to Consider about Student Thinking
We think some of the richest student thinking in this video includes Allison's initial formula and other students' responses to her formula. In what follows, we provide sets of questions about these ideas to scaffold analysis of students' ideas.

Allison's Initial Formula:

What formula does Allison suggest for determining the height of the tallest tower?

How does Allison use cubes to model her initial idea?

Which towers does Allison reference in her demonstration?


Thinking about the Relationship between Height of First Tower and Difference in Heights:

How do different students think the height of the first tower relates to the difference in heights between the towers?

What does Carol mean when she says, "Well the first one would have to have negative one, that's why?"

Sherin, M. G., Russ, R. R., Walkoe, J., & Dyer, E. (2023). Algebra classroom video cases. Freezing Time Research Group. https://www.freezingtime.sesp.northwestern.edu/videocases. © 2023. Licensed under Creative Commons AttributionNonCommercialShareAlike 4.0 International.