##
* *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*

# Absolute Value Equations and Inequalities

Lesson 8 of 9

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

#### Workshop

*30 min*

Today's lesson offers a chance for students to review the unit content before tomorrow's quiz. I find that students are generally pretty focused on this day. I don't have to work too hard to facilitate. I just circulate and ask lots of probing questions as students work on the Absolute Value Practice Quiz.

If things get off course, some options I might pursue include:

- Giving students 30 minutes to work with their chosen team/table and then partnering them with some one whom they have not been working with to compare their work. I find that even this simple transition can be reinvigorating, provoking fruitful conversations with the new partner.

- Asking students to choose two key areas to work on that are challenging and having students write their questions before getting started. Giving students the opportunity to answer their own questions is often powerful. (It can be hard for them to write their questions, so another way to do this is to circulate and ask them to tell you one question they have--that you don't answer--and then seeing if they can use their resources to answer the question during the workshop.)

- Assign each person one or two problems to become the "class expert" on and giving them 10-15 minutes to work. Then, I list class experts on the board and let people walk around the room to ask the experts for help with the problems they don't understand. This makes the "Experts" feel more accountable to a higher level of understanding, and it often gets people to use more academic vocabulary because they have to really talk to each other about what they are doing.

This workshop can take the entire class period.

#### Resources

*expand content*

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- UNIT 1: Linear and Nonlinear Functions
- UNIT 2: Piecewise Functions
- UNIT 3: Absolute Value Functions and More Piecewise Functions
- UNIT 4: Introduction to Quadratic Functions through Applications
- UNIT 5: More Abstract Work with Quadratic Functions
- UNIT 6: Rational Functions
- UNIT 7: Polynomial Functions
- UNIT 8: Exponential Functions
- UNIT 9: Ferris Wheels
- UNIT 10: Circles
- UNIT 11: Radical Functions
- UNIT 12: Cubic Functions

- LESSON 1: Exploring Distance Functions
- LESSON 2: Further Exploration of Distance Functions
- LESSON 3: From Descriptions to Graphs without Data Tables
- LESSON 4: More Distance Functions
- LESSON 5: Comparing Piecewise and Absolute Value Functions
- LESSON 6: Comparing Absolute Value Functions
- LESSON 7: Sometimes, Always, Never with Absolute Value
- LESSON 8: Absolute Value Equations and Inequalities
- LESSON 9: Absolute Value Summative Assessment