Sometimes, Always, Never with Absolute Value

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SWBAT determine whether statements involving absolute value are sometimes, always or never true using justifications and counterexamples.

Big Idea

How can you test your theories? Students work at different levels of abstraction, either working with numerical examples or algebraic generalizations.


30 minutes

I arranged this warm-up differently because I want to make sure my students can do all the problems on the front of the warm-up. In doing so, I am actually putting a lot of responsibility into the hands of my students; they will make the decision about whether they need this practice or not. For today, I ask students to decide whether to do Level A, Level B or Level C for each section. I will encourage my students to push themselves to fully understand all the problems in this section.

My purpose is not simply for students to master the content of the warm-up. I want them to be metacognitive about their learning:

  • What is a good challenge for me?
  • How can I make sure I master the skills I need? 
  • How can I assess my own level of understanding? 

I want students to ask themselves these questions. In order to promote this habit, I will ask them these same questions over and over throughout the lesson. I find it important to ask these questions whether students appear to be working on the right level or not. Just as with their answers to content related questions, I want students to justify their choice of level whether I deem it "right" or "wrong."




40 minutes


5 minutes

Because we are nearing the end of the unit, I like to use the closing of this class to ask students to reflect on the knowledge they have gained and to assess their understanding so far. This can be done in many ways.

One way to do this is to ask students to reflect on their understanding of absolute value functions and to write about their strengths and weaknesses related to the learning target. Another way to do this is to ask students to do a quick Partner Interview:

  1. What do you understand well?
  2. What do you still need to understand better?
  3. What is one new thing that you figured out today?
  4. What is still a struggle for you?

I walk them through the interview process with a quick timer (a few minutes per person). Then, I give them time to see if partners can help each other fill in any gaps.

Teaching Note:

It is difficult to enforce accountability when using this strategy. Some will put good effort into this process, others will drag themselves through it. So, if you feel like students are not invested in the lesson, it might work better to ask students to take notes.

One strategy for following up on the the interview is by asking each partner to share one thing their partner said as they leave the class.  Or, if technology allows, you can even ask them to record the interviews on a computer or a phone (even if you don't listen, this makes them more accountable).

Ideally, if they find the peer interview process helpful, they will be invested in it even without the external accountability measures.