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06_15_07 algebra1 - absolute value equations and inequalities.doc

Teacher: Austin Anderson

Group Members: Jamila Alexander, Austin Anderson, Peter Muller, Karl Nastrom

Subject: Algebra I

Date: June 15, 2007

Approximate Time: 50 minutes

Objective(s): The students will…

• solve and graph absolute value equations and inequalities (3c)
• determine the absolute value equation or inequality from its graph (3c)

Materials:

• students have pencils, notebooks, and textbooks

(Algebra I: Applications and Connections, Merrill, 1995) – examples adapted from text

• whiteboard and dry-erase markers & eraser

Schedule:

1. warm-up
2. intro
3. examples & explanations:
4. closure

Warm-Up:

Simplify:

Set:

Do you ever look at the labels on the food you eat? Did you know that food almost never comes in exactly the same amount that it says on the package? This is because it is very difficult to measure (or package) something exactly. In fact, in the real world, there is almost no such thing as exact, just closer and closer. When a bag of potato chips says it has 16 oz. of potato chips, it may have slightly more or slightly less than that. The error might go either way. We you absolute value for this, and the amount the packaged contents might differ from the ideal is called the tolerance.

 (The ideal is 16 and the tolerance is 0.02.)

You should know that the  symbol means, since that is what we studied in the previous lesson. But what do the straight vertical lines mean? (absolute value—what is that?) Againt means, again, that the error could go either way, above or below the ideal. Today we are going to be studying stuff like this. In particular, we will solve absolute value equations and inequalities. We will also graph their solutions on the number line.

Procedures:

1. Lecture: Absolute value means it could be positive or negative. So to get rid of absolute value sign in an equation, make two equations, one for the positive, one for the negative.
2. Examples and try now: Teacher demonstrates method (also graphing on the number line), engaging students with questions each step of the way. Then teacher gives “try now” example problem(s) and asks students to work on their own. Teacher circulates to observe and help students as needed.
3. Lecture: Absolute value inequalities have two basic types:
   1. Less-than points inward.

e.g.

2. More-than points outward.

e.g.

4. Try now:
5. Lecture: The graph of an absolute value equation or inequality will always make two dots on the number line. The center between those two dots on the distance from the center to each dot can be used to write an equation or inequality.

i.e.  (where c is the center and b is the distance from the center to each dot)

6. Examples and try now: (Demonstrate writing absolute value equation or inequality from its graph.)

Homework: p. 202: 26-42 even

Closure:

In this lesson, we have learned to solve and graph equations and inequalities involving absolute value. How do we solve absolute value equations? Which type of absolute value inequality points inward? Which points outward? In the next lesson, we will begin to solve systems of equations, where you have more than one equation with more than one variable.

Assessment/Evaluation:

Informal: Teacher circulates the room to observe student responses on small-group activity and “try now” guided practice, assessing their ability to solve given equations and inequalities and graph them with accuracy.

Formal: Students are formally assessed on homework, as well as the upcoming quiz and unit test, for their ability to solve equations and inequalities and graph them accurately, and their grades are recorded in the grade book.

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