Reflection: High Expectations Absolute Value Equations and Inequalities - Section 1: Workshop


I wanted to try throwing in a new skill and a new set of ideas even though I did not give students much time to learn this. 

In thinking about the Common Core, I have been thinking about these key mathematical concepts: 

Expressions, Equations and Functions

I am trying to understand the best way to put these together for students. One idea is to start with expressions, which I guess are like phrases: "two more than x", and are the most basic in some ways. The expressions are the building blocks for both equations and functions. 

Beyond this, to me, equations are born from functions. Equations can be created by looking at specific cases of a function--a function is a relationship between two variables, and an equation comes from fixing one of those variables with a certain value, and then figuring out what the other variable must be to make the relationship hold.

I was trying to use this idea to help my students make sense of equations, and I think this was a good attempt, though I would like to investigate further. Basically, my thinking was that if they could understand a relationship like this:

"y is equal to 3 times the distance between x and -2."

I thought that they could extend this understanding to a relationship like this:

"12 is 3 times the distance between x and -2."

Or even:

"12 is less than 3 times the distance between x and -2."

I want to spend more time within each unit having students apply their understanding of functions to equations and inequalities. This lesson was a start, and it was pretty fluid and straight-forward for students. Hopefully by building this into more units, students will be able to understand the relationship between functions and equations.

  Extending Understanding
  High Expectations: Extending Understanding
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Absolute Value Equations and Inequalities

Unit 3: Absolute Value Functions and More Piecewise Functions
Lesson 8 of 9

Objective: SWBAT demonstrate their knowledge of absolute value functions and apply this understanding to absolute value equations and inequalities.

Big Idea: Put it all together -- students use a lot of strategies and make a lot of connections to hopefully demonstrate their mastery of the skills and ideas of this unit.

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abs value eqns inequalities
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