## Reflection: Problem-based Approaches Introduction to Piecewise Functions: Dance-a-Thon Question - Section 1: Launch

This segment of the lesson ran longer than I expected.  I was impressed how students were certainly able to approach the problem from many different perspectives in order to find the rate of change.  This led to some rich conversations both during the launch and during the full class discussion.  Students struggled with making the leap to showing how to graphically and numerically represent money being made at twice the rate (\$60).  Many students approached this by first finding values and plotting points and then sketching their graph.  I anticipated that more students would be able to come up with the actual functions f(x)=30x and g(x)=60x-240.  This was a struggle for most students in the class and so that portion of the discussion took more time than anticipated.  Students were still a little unsure of how to find the function g(x).  Most students could see why it worked but thought they might struggle if they had to build a function like that on their own.

Launch-Reflection
Problem-based Approaches: Launch-Reflection

# Introduction to Piecewise Functions: Dance-a-Thon Question

Unit 1: Functions
Lesson 11 of 18

## Big Idea: By looking at a situation in context students will discover the need for piecewise functions.

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Standards:
Subject(s):
Math, Algebra, domain, range, rate of change, input, output, piecewise-defined functions, function
40 minutes

### James Bialasik

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