## Preview of Module 3

**Module 3: Qualitative Analysis of Representations of Functional Relationships **

This module engages PSMTs with a popular Desmos Activity – Function Carnival.

PSMTs first engage with the task as a learner and discuss their solution strategies as they relate to the mathematical goals of the task.

TRY OUT FUNCTION CARNIVAL HERE

Next PSMTs go through a series of activities that provide opportunities to analyze authentic samples of students’ engaged with the task and to practice pedagogical skills including using the Desmos Activity Teacher Dashboard to select, sequence, and connect examples of student work for whole class discussions.

What follows is a PREVIEW of one task in the module. The purpose of this particular task is for PSMTs to have an opportunity to examine the strategies of one pair of students as they work through the Function Carnival car simulation from beginning to end and consider how these strategies are related to the mathematical goals of Function Carnival.

#### 3.4 Analyzing and Supporting Emergent Student Thinking - Function Carnival

In this task you are going to watch Emily and Ella as they work through the Function Carnival: Cars simulation. Like many students, they make a series of attempts, working between their graph and watching the simulation, before landing on a final graph. Emily and Ella created multiple graphs before they were satisfied with their response. For each of the attempts shown below, you are asked to reflect on the ways in which they work to make sense of creating a graphical representation of the car simulation.

**Emily and Ella's First Attempt**

They are trying to create the graph shown below

**Q1.** Watch the video of Emily and Ella creating this graph linked above. Identify the “issue” Emily and Ella encounter while creating this representation of the car simulation.

**Q2.**Describe what they do with the technology, see in the simulation and graph, and say as they work to make sense of the “issue” you identified in Q1.

**Q3.** Based on your explanation in Q2, describe Emily and Ella’s current understanding of the relationship between the car’s movement in the simulation and its representation on the graph.

**Emily and Ella's Final Attempt**

Emily and Ella reach a point where they have an increasing line segment that ends when the car crashes. (See the picture below.) They are still trying to figure out how to represent the stopped car.

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Q10**. Watch the video of Emily and Ella creating their final graph. Identify the “issue” Emily and Ella encounter while creating this representation of the car simulation.

**Q11. **Describe what they do with the technology, see in the simulation and graph, and say as they work to make sense of the “issue” you identified in Q10.

**Q12.** Based on what you described in Q11, how would you characterize Emily and Ella’s current understanding of the relationship between the car’s movement in the simulation and its representation on the graph.

**Q13.** Ella and Emily successfully complete the car simulation while thinking about it as a game. This is not uncommon. What is difficult though is knowing whether or not they learned anything mathematical from the experience. That is where you come in! What questions might you pose to assess their understanding and support them in making connections between their graph (which is great!) and the mathematical ideas underlying it?