Absolute Value Equations

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Objective

Students will be able to model and solve absolute value equations. How cold is it?

Big Idea

Modeling a range of solutions is the goal of this lesson on absolute values. How cold is it?

Warm Up and Homework Check

10 minutes

I include Warm ups with a Rubric as part of my daily routine. My goal is to allow students to work on Math Practice 3 each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative specifically explains this lesson’s Warm Up- Absolute Value Equations which asks students to model an absolute value situation.  

I also use this time to correct and record the previous day's Homework

Modeling Absolute Value

20 minutes

This lesson is a precursor to the Common Core Algebra 2 standards.  Absolute value equations are part of the Algebra 1 standards but this is something my students need to see before studying transformation of absolute value functions which are in the Algebra 2 standards.

We are going to begin our discussion of absolute value by looking at this situation: The average monthly temperature in a northern Canadian city is 0 degrees Fahrenheit. The actual January temperature for that city may be about 5 degrees Fahrenheit warmer or colder.  I will ask my students to determine the maximum and minimum temperature, an easy task, and then write an equation with algebra to model this situation, which is not so easy (Math Practice 1).  I will be doing the Note Card Activity with this problem.   

There is a good chance that you will get someone who comes up with an absolute value equation.  If not, ask some guiding questions to the class like “What math concept do you think this is modeling?”  

Once the students have gone through this introduction to absolute value equations, there are three additional modeling situations temperature, assessment grades and biology(Math Practice 4). The first two problems are relatively simple.  My goal with these problems is to give the students an opportunity to experiment with building the absolute value models.  Students will struggle with building the equation properly (Math Practice 2).  I recommend to students that they test their equations to ensure that their model works.  Depending on the speed that the students learn the model, I will continue to do the note card activity or not.

The final scenario will require some additional reasoning.  A portion of the model is given and the students must use it to build the complete absolute value model.  This problem should provide some great discussion around appropriate models. My lesson Absolute Value Equations presentation includes detailed presenter notes. 

Solving Absolute Value Equations Guided Practice

17 minutes

The remaining portion of this lesson has students review solving Absolute Value Equations.  I have build this portion very carefully using increasing levels of difficulty.  The final problems deal with absolute value equations that may have extraneous solutions.

Please see the PowerPoint for detailed presentation plans.

Exit Ticket

3 minutes

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.  

This Exit Ticket asks students to solve a multi-step absolute value equation. 

Homework

The goal of this Assignment for this section is to reinforce the day’s lesson.  The first six problems are straight absolute value problems of varying difficulty.  The next two are modeling problems similar to those seen in the lesson.  The final problem gives the students an absolute value equation and asks them to write a scenario to model it.