NOTICE Lab - Video Club 6: Root Graph

Video Club 6: Root Graph

In this video, a group of students discuss a square root graph and whether it can have negative inputs, and what that might look like if it did. This is a more formal classroom setting than some previous clips, where students in a school classroom discuss this under the guidance of a teacher.

Video Club Overview

Video Club Goals:

- Teachers will attend to, make sense of, and see distinctions between the ways in which students represent possible inputs and outputs for the graph y=rt(x)

Materials:

- Video loaded on Anotemos and shared with all participants
- If watching in person, each participant should have a device on which they can view the video and headphones

Get ready (5 mins). Use Desmos or a similar tool to graph the function y = sqrt(x). What are the key features of this graph? How do you think students might talk and reason about what they see in this graph?

Exploring the Math

Moving between representations- In order to make conjectures about how negative inputs might be plotted on y=x, it is important to consider how to make sense of this problem with other representations. For example, from a numerical perspective, what happens when you try to compute -5? It is also important to consider the equation representation and how the definition of a function contributes to this representation. Students in the video try to justify their response by thinking about the relationship between y=x and y2=x. How does the definition of a function impact this relationship?

Reflection- Students in the video consider the different ways that the graph might reflect if negative inputs were allowed. What does each possible reflection mean (over the x-axis, over the origin, over the y-axis) and why are each of these not plausible? Are any of these more plausible than others?

Definition of a function: The domain of the function f(x)=rt(x) is bounded to [0,∞). Why is that the case?

Viewing and Discussing the Video

Have participants watch the approx. 6 minute video clip individually on the Anotemos platform. Participants should be encouraged to draw and comment on the video when they see interesting moments of student thinking.

Description of Goal:

Teachers will attend to, make sense of, and see distinctions between the ways in which students represent possible inputs and outputs for the graph y=rt(x)
Teachers will practice previously introduced skills such as noticing and responding to student gesture, and considering seeds of algebraic thinking.

Table - Video Key Moments

VC6 table

Potential Discussion Questions:

How do students use gesture to reason about the negative inputs on the square root graph?
Are there instances when the students are moving from one representation to another?
Why might Pete draw the graph as a reflection over the y-axis? How might you respond to him?

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