More Distance Functions

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SWBAT write both piecewise and absolute value functions to match verbal descriptions and graphs of distance functions.

Big Idea

Students go deep in this lesson--really sticking with challenging problems that force them to look at the same types of functions and problems from multiple perspectives.

More Making Piecewise Functions Continuous

30 minutes

I will give my students Piecewise and Absolute Value Functions Warm-up at the start of class today. 

The big idea behind the focus on making piecewise functions continuous is that at certain inputs, we need the outputs of the different parts of the function to match up with each other. In today's lesson I want students to work on developing purely algebraic methods to solve these problems (MP1, MP2). In order to support this goal, I will encourage students to use graphing technology to check their answers. In this instance, using technology also helps to reinforce the idea that we can represent the same things either graphically or algebraically (MP5). As the students develop their own methods, I will keep referring students back to the big idea I will give the students 20 minutes or so to look at these problems before encouraging them to move on to the next section.

More Distance Functions

30 minutes

Today's investigation is really set up to allow students more time to investigate the big ideas of the previous days, with an additional task available for students who have already mastered the other tasks.

I start off a workshop session like this by making sure that each student has clear expectations--for some students, this will be continuing to work on the Level A problems from the Exploring Distance Functions Assessment. For other students, this might be trying a more challenging level of this assessment. Still for others, it will be to investigate these new problems in the Challenging Absolute Value Equations.

Once each student is clear on their expectations, have everyone get started and circulate to make sure that each student is engaged in their task. I often make changes to what I want students to accomplish throughout the class period based on what I see--I identify some students who should be working on a more challenging level, or other students who should focus on some easier problems. 


10 minutes
As we prepare for the class to end, I say to students, "From time to time, I am going to give you a grade not on your actual work, but on your own reflection on and analysis of your work." I explain that this is another way I can communicate the value of metacognition and deep thinking, over mindless repetition. No matter how many times I say that I want students to think about what they are doing, if the grade they get is for doing a certain number of problems correctly in a certain amount of time, I am not really putting my money where my mouth is.

So today’s closing is an activity that I plan to grade where I ask them to use the day’s tasks as a source of evidence to answer four questions (see below). I tell them that I want them to show me honest and thoughtful reflection, and I care about this more than I care about lot of work getting done, or many problems being done correctly.

  • Did you work on problems that challenged you?
  • Did you make sense of those problems?
  • What evidence do you have that you really stuck with challenging problems?
  • What evidence do you have that you really made sense of those problems?

I circulate quickly as students are answering these questions to make sure they are on track, and I may ask one or two students to share their evidence, or to ask them to look at their partner’s work and to see whether or not he or she actually is referring to evidence to explain their answers.