Created byMonisha Lordson millar

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Solve Absolute Value Equations

Grade 9Math1 days

In this 9th-grade math project, students tackle absolute value equations by understanding 'distance from zero' and employing strategic problem-solving. Beginning with an escape room challenge, students learn to represent absolute value mathematically, solve equations, and verify their solutions. The project culminates in students unraveling and solving absolute value equations, demonstrating their understanding through a set of verified solutions.

Absolute ValueEquationsProblem-SolvingDistance from ZeroVerificationMathematical Notation

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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can understanding distance from zero and strategic problem-solving help us find and verify solutions to absolute value equations in various mathematical contexts?

Essential Questions

Supporting questions that break down major concepts.

How can we represent distance from zero using mathematical notation?
What strategies can be used to solve equations involving absolute value?
How can we verify the solutions to absolute value equations?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:

Students will be able to represent distance from zero using mathematical notation.
Students will be able to solve equations involving absolute value.
Students will be able to verify the solutions to absolute value equations.

Entry Events

Events that will be used to introduce the project to students

The Great Escape Room Challenge

Students are presented with a seemingly impossible escape room scenario where the locks are coded with absolute value equations. Cracking the codes requires them to understand absolute value, setting the stage for the project's math concepts.

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Portfolio Activities

These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.

Activity 1

Equation Unravelers: Basic Absolute Value Equations

Students solve simple absolute value equations using the concept of distance from zero.

Steps

Here is some basic scaffolding to help students complete the activity.

1. Review the definition of absolute value.

2. Present example equations like |x| = 3 and |x| = 7.

3. Explain that 'x' can be both positive and negative.

4. Solve for 'x' in each equation, showing both possible solutions.

5. Check if the solutions are correct by plugging them back into the equation.

Final Product

What students will submit as the final product of the activityA set of solved absolute value equations with both positive and negative solutions verified.

Alignment

How this activity aligns with the learning objectives & standardsLearning Goal: Students will be able to solve equations involving absolute value. Learning Goal: Students will be able to verify the solutions to absolute value equations.

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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Absolute Value Equation Mastery Rubric

Category 1

Conceptual Understanding

Demonstrates understanding of absolute value as distance from zero and its implications for solving equations.

Criterion 1

Definition of Absolute Value

Understanding and application of the definition of absolute value.

Exemplary

4 Points

Demonstrates a sophisticated understanding of absolute value as distance from zero and explains its relevance to solving equations with clarity and precision.

Proficient

3 Points

Demonstrates a thorough understanding of absolute value as distance from zero and applies it correctly to solving equations.

Developing

2 Points

Shows an emerging understanding of absolute value as distance from zero but struggles to consistently apply it in solving equations.

Beginning

1 Points

Shows a limited understanding of absolute value and its connection to distance from zero.

Category 2

Problem-Solving Strategies

Application of appropriate strategies to solve absolute value equations.

Criterion 1

Solving Absolute Value Equations

Ability to solve equations by considering both positive and negative possibilities.

Exemplary

4 Points

Solves absolute value equations accurately and efficiently, demonstrating a deep understanding of the process and considering all possible solutions, including extraneous solutions if any.

Proficient

3 Points

Solves absolute value equations accurately, considering both positive and negative solutions.

Developing

2 Points

Solves absolute value equations with some errors or omissions, showing an inconsistent understanding of the need to consider both positive and negative solutions.

Beginning

1 Points

Struggles to solve absolute value equations, demonstrating a limited understanding of the process.

Category 3

Solution Verification

Ability to verify the correctness of solutions by substituting them back into the original equation.

Criterion 1

Verification of Solutions

Checking the validity of solutions through substitution.

Exemplary

4 Points

Verifies solutions meticulously and explains why each solution is valid or invalid with clear mathematical reasoning.

Proficient

3 Points

Verifies solutions correctly by substituting them back into the original equation.

Developing

2 Points

Attempts to verify solutions but makes errors in the substitution or calculation process.

Beginning

1 Points

Does not verify solutions or demonstrates an inability to do so.

Reflection Prompts

End-of-project reflection questions to get students to think about their learning

Question 1

How did your understanding of absolute value as 'distance from zero' influence your approach to solving the equations?

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Question 2

What was the most challenging aspect of verifying the solutions to the absolute value equations, and how did you overcome it?

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Question 3

To what extent do you feel confident in your ability to solve and verify absolute value equations?

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