## Reflection: Developing a Conceptual Understanding The Tortoise and the Hare Piece-wise Functions - Section 1: Warm up and Homework Check

I found the range of responses I got to today's warm-up very interesting.  It was obvious that some students had a much better conceptual understanding than others.  My goal with this warm-up was to get them thinking about the idea that all portions of the function might not have to touch.  I think it was important to have students share their ideas afterward as there were many great correct, and incorrect, ideas.  Student Work 1Student Work 2, and Student Work 3 each highlight some of the different conceptual and algebraic takes students had.  I was pleased with the number and range of correct descriptions.   Student Work 4 reflects the response similar to many other incorrect responses.  The discussion was particularly important for these students to build the idea that a function doesn't have to be continuous everywhere.  I found Student Work 5 particularly interesting as the student used a correct continuous piece-wise function as proof that all functions are continuous.

Developing a Conceptual Understanding: What makes something a function?

# The Tortoise and the Hare Piece-wise Functions

Unit 2: Modeling with Functions
Lesson 16 of 24

## Big Idea: Will the tortoise win again? Students will not only find out but write a mathematical story about it.

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Standards:
Subject(s):
Math, graphing equations, Algebra, Algebra 2, master teacher project, piecewise, function
50 minutes

### Amelia Jamison

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