## Reflection: Advanced Students Compare and Contrast Graphs of Piecewise Functions - Section 2: Investigation and New Learning

So I really messed up this Extension with my advanced students during this lesson. I gave them way too much of a hint to get started, and by the time they understood how to set up the graphs, the Extension was basically too easy. I realized that it is essential not to explain to them how to set up the graphs, but only to ask them questions about what the graphs will represent and how to set up the scales and the axes for the graphs.

With my advanced students during this lesson, they were initially perplexed by the situation and seemed confused about how they could create a two different graphs to represent the same description. I mistakenly jumped in and showed them an example, which was really unfortunate, because once they had seen the example, they basically didn't have to do any more thinking.

In this future, I think this is still an interesting extension, especially because it previews such an important part of calculus, thinking about functions and their derivatives. When I use this extension again, I will ask many more questions to my advanced students, and let them struggle a lot more, before I show them any examples:

• How could you create 2 graphs to show the same situation?
• How could you turn this situation into a data table?
• What kind of function will you use to represent this situation?
• How could you scale the axes here?
• What are some interesting quantities and relationships to consider in these situations?

Hopefully with more of these questions, the advanced students would have to think a lot more and even though the actual calculations and graphs are easy to create, they would still have to struggle to make sense of the big ideas behind the graphs.

Getting the Most Out of the Extension
Advanced Students: Getting the Most Out of the Extension

# Compare and Contrast Graphs of Piecewise Functions

Unit 2: Piecewise Functions
Lesson 5 of 12

## Big Idea: Students get lots of practice in this lesson, but the focus is on thinking about the functions and their graphs, not just doing the steps.

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Standards:
Subject(s):
Math, modeling, Inequalities (Algebra), Precalculus and Calculus, piecewise-defined functions, PreCalculus, absolute value
70 minutes

### Hilary Yamtich

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