## Reflection: Intervention and Extension Exploring Distance Functions - Section 2: Investigating Distance Functions using Number Lines

I really like the way these levels come together. I have found that using the levels as a differentiation tool is really effective, especially as students are able to choose their level. In some cases, I tell students to skip easy levels and in other cases I ask everyone to start at Level A, to ensure that even the accelerated students learn the basic skills before trying to extend them.

For my struggling students, I would try to talk through one or two input and output pairs with them, using the number line kinesthetically (physically counting spaces) to show them how the distance worked. A challenge for these students was to choose inputs that would show the whole function. It was common for students to choose a few inputs, find the outputs correctly, and then connect these points to make a linear function.

Sometimes I hastily responded just by correcting them, which I wish I had not done! I want to figure out what questions I could ask them to help them realize that it is possible to choose inputs that will prove that this function is not linear. I often ended up saying something like, "Choose inputs on either side of the key number." This is definitely not the way I would want to teach this--so I am still thinking about good questions to ask.

On this day, for students who worked on the Level C material, they spent a lot of time writing piecewise functions to fit the graph, which was a good starting point. However, I wanted to push them to understand that we are dealing with a new kind of function-- a "Distance function." So at some point in this lesson, for students who had already worked through Level A and Level B, I started asking students what symbols are used to express distance. Some students had already made the connection to absolute value, while others had not. I didn't expect or even want students to realize this today, but for those who had mastered Level A and B, it was a good next step.

Intervention and Extension
Intervention and Extension: Intervention and Extension

# Exploring Distance Functions

Unit 3: Absolute Value Functions and More Piecewise Functions
Lesson 1 of 9

## Big Idea: Instead of memorizing the definition of absolute value, students work with the concept of distance and the number line to develop transformed absolute value functions.

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Standards:
Subject(s):
Math, Algebra, Graphing (Algebra), graphing functions, continuity, absolute value functions, piecewise functions, function
70 minutes

### Hilary Yamtich

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