Subject Area: Mathematics
Lesson Design
Mathematics
Grade Level: Algebra I & CAHSEE
Benchmark Period
Duration of Lesson: 1st of 2
Standard(s): 3.0 Students solve equations & inequalities involving absolute values. (1 CAHSEE)
Learning Objective: Students will successfully solve linear equations & inequalities involving absolute
value.
Big Ideas involved in the lesson: If n is any positive real number, |x| = n results in two points on the
number line, at n or -n. |x| < n results in the region on the number line between n & its opposite. |x| > n
results in a region on the number line greater than n or less than –n.
As a result of this lesson students will:
Know:
 Vocabulary: variableabsolute value, reciprocal, opposite, linear inequality, linear equation, solve, simplify,
expression, inequality, coefficient, equivalent inequalities, greater than, less than, greater than or equal to,
less than or equal to, not equal to, line graphs, and, or, intersection, union
 Symbols: <, >, , , , |absolute value|.
 Addition & Multiplication properties of equations and Inequalities.
Understand:
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Absolute value measures distance from zero, it does not measure direction.
The solution set for a linear absolute value equality could be no solution, one solution or two solutions.
The solution of a linear absolute value inequality is a set of points on the number line.
The endpoints of the solution of inequalities are either an open or closed set depending on the inclusion
or exclusion of the equal sign in the inequality symbol.
Why, when an inequality is multiplied or divided by a negative number, the inequality sign changes
direction.
The relationship between the absolute value linear and inequality (symbolically) and the number line
solution.
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Be Able To Do:
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Identify properties used in the solution of linear equations and inequalities
Solve linear absolute value equations and inequalities in one variable.
Justify each step in the solution of a linear absolute value equation or inequality in one variable.
Translate a word problem involving absolute value into a mathematical model, apply the model and
determine a solution or solutions to the problem.
Check and verify solutions to linear absolute value equations and inequalities in one variable, whether
within the context of a word problem or not, for accuracy and reasonableness.
Graph the solution to a linear absolute value inequality in one variable, determine if the endpoint(s) of
the solution set is closed or open, and if the solution is an intersection (“and”) or a union (“or”).
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Assessments:
What will be
evidence of
student
knowledge,
understanding &
ability?
Formative:
 ABWA
 CFU
 Whiteboards
Summative:
 Teacher
generated quiz
or test
CFU Questions:
1. Describe the purpose of the grid?
2. What is the measure of the Equator?
3. Which ship is north of the equator? South?
4. Which ship is furthest from the equator? Explain.
5. How can the difference be used to find the distance?
6. Distance is always, never or sometimes positive?
7. Define the absolute value.
8. Use student whiteboards and ask students to find the absolute value of 3.2, -4.5
& -0.1.
9. Explain why the solution of x  2 is x=2 or x=-2
10. If zero is not one of the endpoints how would we find the distance?
 
11. What is 8  2 ?
12. Use student whiteboards to CFU what is the distance between -2 and -8?
1
Lesson Design
Mathematics
13. Explain why the order of the coordinates is not important when finding the
distance between two points.
14. Use whiteboards to CFU 5  3  8
15. What equation can we use to express the distance between x and 2?
15. Explain why -3and 7 satisifty the equation x  2  5 ?
16.
17.
18.
19.
20.
Why is 2 the midpoint of the segment between-3 and 7?
What is the midpoint of the segment between -4 and 10?
What is the distance between the two unknown endpoints?
What is the midpoint between the two unknown endpoints?
What happens when the expression inside the absolute value is negative.

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21. What two equations are equivalent to x  5 when x  5  0 and
x  5 0 ?
22. What does 55 represent in the expression h  55  3 ?
Lesson Plan
Anticipatory Set:
a. T. focuses students
b. T. states objectives
c. T. establishes purpose of the
lesson
d. T. activates prior knowledge
Instruction:
a. Provide information
 Explain concepts
 State definitions
 Provide exs.
 Model
b. Check for Understanding
 Pose key questions
 Ask students to explain
concepts, definitions,
attributes in their own words
 Have students
discriminate between
examples & non-examples
 Encourage students
generate their own examples
 Use participation
Use PowerPoint: Absolute Value
Objective: Today we will learn to successfully solve linear equations involving
absolute value. (slide 1)
Poem from PowerPoint: Song of values (slide 2)
Continue using PowerPoint: Absolute Value
(slide 3)
RiverDeep: Mastering Algebra Course I, Module I, The Language of Algebra,
Unit 2: Linear Equations in one variable, Session 3: Solving absolute value
equations, Screen 1-3. (*refer to this tutorial when using RiverDeep)
a.
 Model problems from screen 1 thru 3 as you go along
b. CFU
 Have student work with whiteboards for CFU
 Teacher ask the following check for understanding questions via
random selection as they progress through RiverDeep.
1. Describe the purpose of the grid?
2. What is the measure of the Equator?
3. Which ship is north of the equator? South?
4. Which ship is furthest from the equator? Explain.
Explain how the number line supports the problem?
5. How can the difference be used to find the distance?
6. Distance is always, never or sometimes positive?
7. Define the absolute value.
8. Use student whiteboards and ask students to find the absolute value of 3.2, 4.5 & -0.1.
9. Explain why the solution of x  2 is x=2 or x=-2
10. If zero is not one of the endpoints how would we find the distance?
11. What is 8  2 ?
 
12. Use student whiteboards to CFU what is the distance between -2 and -8?
13. Explain why the order of the coordinates is not important when finding the
distance between two points.
14. Use whiteboards to CFU 5  3  8
15. What equation can we use to express the distance between x and 2?
2
Lesson Design
Mathematics
15. Explain why -3and 7 satisifty the equation x  2  5 ?
16.
17.
18.
19.
20.
21.
Why is 2 the midpoint of the segment between-3 and 7?
What is the midpoint of the segment between -4 and 10?
What is the distance between the two unknown endpoints?
What is the midpoint between the two unknown endpoints?
What happens when the expression inside the absolute value is negative.
What two equations are equivalent to x  5 when x  5  0 and
x  5 0 ?


22. What does 55 represent in the expression h  55  3 .7?
c. Model how to use graphic organizer with RiverDeep problems and
PowerPoint problems.
 Direct students how to use graphic organizer
 Students complete an individual problem using graphic organizer.
(slide 4)
Examples 1,2 and 3
 Model how to describe what the problem is asking.
 Model how to solve the problems
CFU
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Guided Practice:
a. Initiate practice activities
under direct teacher
supervision – T. works
problem step-by-step along
w/students at the same time
b. Elicit overt responses from
students that demonstrate
behavior in objectives
c. T. slowly releases student to
do more work on their own
(semi-independent)
d. Check for understanding that
students were correct at each
step
e. Provide specific knowledge
of results
f. Provide close monitoring
What opportunities will students
have to read, write, listen & speak
about mathematics?
Closure:
3
“What must be done first if the absolute value is not isolated?”
“What step must be done every time when eliminating absolute value
symbols?”
“How many solutions do you usually obtain when solving an absolute
value equation?”
“If there are two solutions, is one always positive and the other
always negative?”
“How can you check your work?”
Use PowerPoint: Absolute Value
(slide 6 -7)
Use student whiteboards to work out this problems
CFU
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“What must be done first if the absolute value is not isolated?”
“What step must be done every time when eliminating absolute value
symbols?”
“How many solutions do you usually obtain when solving an absolute
value equation?”
“If there are two solutions, is one always positive and the other
always negative?”
“How can you check your work?”
Completing the graphic organizer includes reading, writing, listening.
Guided practice includes all aspects as students use whiteboards and
explain work.
Lesson Design
Mathematics
a. Students prove that they
know how to do the work
b. T. verifies that students can
describe the what & why of
the work
c. Have each student perform
behavior
(slide 8 - 9)
Summarize what the students have learned.
 Definition of Absolute Value
CFU: Give a definition for Absolute Value

Problems related to objective on PowerPoint using multiple representations
for students to complete using (slides 5 – 7)
a. Graphically
b. Verbally
c. Algebraically
CFU:
What does x  2 look like graphically?
Translate the equation into words?
What is the solution?
Use student whiteboard
RiverDeep: Mastering Algebra Course I, Module I, The Language of Algebra,
Unit 2: Linear Equations in one variable, Session 3: Solving absolute value
equations, Problem 2. (Problem related to temperature range of sleeping bag)
CFU:
Frame1: What is the meaning of temperature extremes for a sleeping bag?
Frame2: What temperatures in Fahrenheit might make sense as extremes?
Frame3: Does the range -20 to 32 make sense? Is this sleeping bag better for
summer or winter camping?
Independent Practice:
a. Have students continue to
practice on their own
b. Students do work by
themselves with 80%
accuracy
c. Provide effective, timely
feedback
Resources: materials needed to
complete the lesson
4
Error Analysis worksheet
RiverDeep access, computer, LCD projector, ppt presentation, white boards,
associated worksheets.