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
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Exploring Distance Functions

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

Objective: SWBAT graph absolute value functions using a verbal description of the relationship. SWBAT write piecewise functions to match these graphs.

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.

  Print Lesson
Math, Algebra, Graphing (Algebra), graphing functions, continuity, absolute value functions, piecewise functions, function
  70 minutes
student using number line distance function
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