Reflection: Modeling Absolute Value Equations - Section 2: Modeling Absolute Value


The highlight of this class was the Modeling Temperature problem.  The students had just had a basic introduction to absolute value and worked with a simple modeling problem.  I introduced the Problem and asked them to write a model that found the maximum and minimum temperatures.  I then walked around the classroom writing down their models on a personal white board which I then transferred to the large whiteboard. 

Here are the Models from one class.  While close, none of the students hit a precise model.  I padded the list with two accurate models (the fifth and eighth ones). 

Once they were all of the board, I asked the students to talk to their partners about which of the eight models they thought were accurate, which were not, and why. This is the key to the entire process.  I don't tell them which is correct or incorrect, I follow their lead.  I do insist that they raise their hand to offer an opinion as this allows me to manage the flow and not allow specific students to dominate.  An example of the conversation, one student who wrote │x│= 80, and claimed it as his to the class, eliminated it as a possibility since it doesn't model either the min or the max.   It was interesting that many students initially hit on │x - 5│= 80.  We discussed the necessity of checking our models for reliability and the students quickly saw that this only modeled the max but not the min.  Many of the other models had the same issue.

Finally, we narrowed it down to │x – 80│= 5 which proved to find 75 and 85.  One student asked whether │80 – x│= 5 would produce the same results or not so I had each partner discuss this (I like to turn question like this back on the students).  After checking, we found that it did.

One of the best things occurred at the end of this activity when I asked the students to discuss with each other why this model works.  A student in the discussion stated that it worked because the 80 is the average and the five is the difference between the average and each extreme.  This really struck the other students and when asked to model the next Problem, most of the students immediate wrote the correct equation.  

  Modeling: Multiple Models
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Absolute Value Equations

Unit 2: Modeling with Functions
Lesson 18 of 24

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?

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Math, Algebra, absolute value, Algebra 1, Algebra 2, master teacher project, Absolute Value Equations, transformation of absolute value functions
  50 minutes
image absolute value equations
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