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Planning Step 1: Lesson Curriculum: What are the Learning Goals for this lesson?

Lesson Standards

Always include a writing standard.

AII.4a: The student will solve, algebraically and graphically, absolute value equations and inequalities.
AII.7: The student will investigate and analyze functions algebraically and graphically.
MP3: Construct viable arguments and critique the reasoning of others.

Students Will Be Able To… (Do)

  • Skills from standards including thinking (cognitive verbs).
  • This is not activities.
  • One or more goals should be Higher Order Thinking (Levels of Learning 3 or 4), and/or Reading Comprehension.
  • Sequence these goals in the order in which they should be learned.

Solve absolute value equations and inequalities algebraically and graphically
Apply an appropriate equation to solve a real-world problem
Evaluate given solutions for errors
Construct arguments supported by reasons and facts

Students Will Know

Knowledge from standards such as vocabulary, facts, formulas.

Absolute value inequalities can be solved graphically or by using a compound statement
Real-world problems can be interpreted, represented, and solved using equations and inequalities
Error points for solving for absolute value

Lesson Essential Question

  • A question that communicates the Learning Goals.
  • Reflect the Higher Order Thinking and/or Reading Comprehension Learning Goal(s).

How do you analyze absolute value functions?

Planning Step 3: Lesson Instruction: How will students learn?

Activating Strategy

  • Plan this after you plan your Learning Activities. How will you introduce the Lesson Essential Question?
  • How will you draw attention to important vocabulary in the Lesson Essential Question?
  • How will you build/link background knowledge?
  • What prerequisite content might students need to know before the lesson?
  • >Which key vocabulary from the Learning Goals needs to be explicitly taught?
  • Are there other vocabulary words that you think need to be taught?
  • Which vocabulary strategy will you use?
  • Previewing:
    • Advance Organizer
    • Prerequisite Content
    • Vocabulary

Ask students to take a guess at the age of prominent figures in the news. Give the actual ages for students to record. Who in our class got the closest to the actual ages? How can you tell? Think Pair Share. Model a graph using one group’s data on board.

Previewing (what, who, when):
Whole Group: Preview the steps for using the graphing calculator.
Key Vocabulary (for explicit instruction):
parent graph absolute value function

Vocabulary Strategy:
Compare and Contrast Parabola and Absolute Value Graphic Organizer

Previewing (what, who, when):

Scaffolding (what, who, when):

Graphic Organizer

  • How will students store and organize information as they learn during this lesson?
  • Base the organizer on the Higher Order Thinking or Reading Comprehension in the Will Be Able To… (Do) Learning Goals.
  • Determine how the organizer will be previewed for struggling students.
  • Determine how the organizer will be scaffolded for struggling students.

Compare and Contrast Parabola and Absolute Value

Previewing (what, who, when):
Struggling Students: Preview the visual of the parabola on a graph

Scaffolding (what, who, when):

Learning Activity 1

The Learning Goal(s) for this Learning Activity and Assessment Prompt:

Consider:

  • Explicitly teach Higher Order Thinking and/or Reading Comprehension Strategy (if didn’t in a previous Learning Activity)
  • Content students need to learn
  • Chunk activity:
    • Several opportunities for thinking, talking, writing to learn
    • Distributed summarizing and/or practice
    • Questions to ask
    • Higher Order Thinking and/or Reading Comprehension Questions to ask
  • Active engagement:
    • Collaborative Pairs, Numbered Heads, Think-Pair-Share, etc.
    • Variety
    • Movement
  • Previewing prerequisite knowledge/skills
  • Scaffolding content and process

Ask students to solve for x in |x| = 7. Verify that there are two solutions. Working with a partner, solve |x-3| = 7. Share strategies whole group. Lecture/notes on how the definition of absolute value. “The definition of absolute value (for any real numbers a and b, where b ≥ 0, if |a| = b, then a = b or a = – b) is used in solving absolute value equations and inequalities.”

Model the solution of two equations and two inequalities. Identify half the students as “parabolas” and the other half as “absolute values”. Parabola/Absolute value pairs work together to solve 5 absolute value equations/inequalities. Locate another Parabola/Absolute value pair and compare answers.

Previewing (what, who, when):
Struggling Students: Preview an Anchor Chart to demonstrate and Think Aloud the steps in the process for solving for absolute value and inequalities algebraically and graphically.

Scaffolding (what, who, when):
Struggle Students: Provide task analysis organizers for the steps in solving for absolute value and inequalities (both algebraically and graphically).

Assessment Prompt for Learning Activity 1

  • Formative assessment of the Learning Goal(s).
  • Ensure the task meets the expectation of the Higher Order Thinking and/or Reading Comprehension Learning Goal.
  • Remediate: What is an additional learning opportunity for students who did not master the Learning Goal(s) before proceeding?

Summary Point Writing: How do you solve absolute value equations and inequalities algebraically?

Learning Activity 2

The Learning Goal(s) for this Learning Activity and Assessment Prompt:

Consider:

  • Explicitly teach Higher Order Thinking and/or Reading Comprehension Strategy (if didn’t in a previous Learning Activity)
  • Content students need to learn
  • Chunk activity:
    • Several opportunities for thinking, talking, writing to learn
    • Distributed summarizing and/or practice
    • Questions to ask
    • Higher Order Thinking and/or Reading Comprehension Questions to ask
  • Active engagement:
    • Collaborative Pairs, Numbered Heads, Think-Pair-Share, etc.
    • Variety
    • Movement
  • Previewing prerequisite knowledge/skills
  • Scaffolding content and process

Students complete Pairs Checking with the Graphing and Writing Absolute Value Thinking Sheets. Students solve real-world problems involving equations and inequalities.

Previewing (what, who, when):

Scaffolding (what, who, when):
Struggling Students: Vary the complexity of the real-world problems.

Assessment Prompt for Learning Activity 2

  • Formative assessment of the Learning Goal(s).
  • Ensure the task meets the expectation of the Higher Order Thinking and/or Reading Comprehension Learning Goal.
  • Remediate: What is an additional learning opportunity for students who did not master the Learning Goal(s) before proceeding?

Students continue to fill in applicable sections of the matrix graphic organizer. Teacher monitors for accuracy.

Learning Activity 3

The Learning Goal(s) for this Learning Activity and Assessment Prompt:

Consider:

  • Explicitly teach Higher Order Thinking and/or Reading Comprehension Strategy (if didn’t in a previous Learning Activity)
  • Content students need to learn
  • Chunk activity:
    • Several opportunities for thinking, talking, writing to learn
    • Distributed summarizing and/or practice
    • Questions to ask
    • Higher Order Thinking and/or Reading Comprehension Questions to ask
  • Active engagement:
    • Collaborative Pairs, Numbered Heads, Think-Pair-Share, etc.
    • Variety
    • Movement
  • Previewing prerequisite knowledge/skills
  • Scaffolding content and process

Using the matrix organizer, students graph several absolute value equations and analyze the graphs they have created (translations, stretch, orientation). Provide solved equations and ask students to evaluate for accuracy (Error Analysis). For the incorrectly solved equations, students must construct an argument through a “Note to the Student” to identify errors, explain the mistake that was made, explain how to avoid the mistake, and then correctly solve the equation. Facts and reasons must be included in the argument. Students fill in any blank spaces on the organizer as they go.

Previewing (what, who, when):

Scaffolding (what, who, when):
Struggling Students: Provide a writing frame for the note that helps students structure their argument and include facts and reasons to support it.

Assessment Prompt for Learning Activity 3

  • Formative assessment of the Learning Goal(s).
  • Ensure the task meets the expectation of the Higher Order Thinking and/or Reading Comprehension Learning Goal.
  • Remediate: What is an additional learning opportunity for students who did not master the Learning Goal(s) before proceeding?

“Absolute values” find another “Absolute value”; “Parabolas” find another “Parabola”. Explain how to find a graphic solution to an absolute value equation, a common mistake that could be made when finding the solution, and how to avoid the mistake. Teacher circulates to hear discussions.

Planning Step 2: Lesson Assessment: How will students demonstrate understanding of the Learning Goals for this lesson?

Assignment

  • Plan this before planning Lesson Instruction.
  • How will students demonstrate their knowledge of the Will Know Learning Goals and the skills in the Will Be Able To… (Do) Learning Goals (especially the Higher Order Thinking and/or Reading Comprehension)?
  • How will the Assignment be differentiated for support and challenge?
  • Which students receive differentiation?
  • For students who struggle with the Assignment, how will you remediate this lesson?

A billiard ball travels at an angle from Wall A of a billiards table to its parallel wall, Wall B. The distance of the ball from Wall A is modeled by y = –|x – 3| + 2, where the point of reflection on Wall B is (3, 2), and x is the location
(x, 0) of the ball when it touches Wall A. Give an algebraic solution and sketch and label a graphic solution for the ball’s position as it leaves Wall A and returns to Wall A. What is the equation of the location of Wall B?
Below, the problem has been solved for you. Does your solution match this one? If not, analyze the solution for errors. Identify the error(s) made, and construct an argument to the teacher as to why this solution cannot be correct. Explain the mistake that was made and how it can be avoided.

Differentiated Assignment for Struggling Students:
Provide the position of the ball and students solve for the algebraic solution.

More Challenge: Students create and solve absolute value equations and inequalities algebraically and graphically. Problems should be then rewritten to contain an error. Partners exchange problems and determine where the error is located.

Remediation: Provide solved equations and ask students to evaluate for accuracy (Error Analysis). Provide several “Note to Student” samples from Learning Activity 3 and ask students to work to match the error to the problem. Pairs Checking: partners work to check each other’s’ answers.

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