Linear Equations & Inequalities

Unit Context

Unit: Exploring Functions and Relations
Lesson: 4 of 4
Duration: 90 minutes
Class Size: 30 students
Grade Level: Algebra 1 (approx. ages 13-15)
Curriculum: International Baccalaureate (IB) Middle Years Programme (MYP) Mathematics: Analysis and Approaches

Learning Objectives (MYP Mathematics Criterion B - Investigating Patterns)

By the end of this lesson, students will:

Apply algebraic methods to solve linear equations and inequalities with one variable accurately.
Represent solutions of linear equations and inequalities on a number line with clarity.
Interpret the meaning of inequalities as solution sets and analyze their real-world context.
Communicate reasoning clearly using appropriate mathematical language and symbols.
Demonstrate an understanding of the relationship between equations, inequalities, and their graphical representations.

Key Concepts and Related Concepts

Key Concept: Relationships
Related Concepts: Change, Expression, Representation

Approaches to Learning Skills

Thinking: Critical thinking to solve equations and inequalities logically.
Communication: Mathematical language and symbolic notation for clear explanations.
Self-Management: Time management to complete exercises independently and collaboratively.
Collaboration: Group discussion to solve complex problems and reflect on strategies.

Materials Required

Whiteboard and markers
Graph paper and number line handouts
Student math notebooks
Mini whiteboards with markers (for quick formative checks)
Tablets or laptops (optional - for virtual graphing tools or inequality solvers)
Colored sticky notes

Lesson Structure

1. Introduction and Prior Knowledge Activation (10 minutes)

Activity: Warm-up with a quick interactive quiz using mini whiteboards
- Simple recall: What is a linear equation? What does it mean to solve one?
- Brief review of concepts from previous lessons on functions and relations, including variable expressions and what equality means.
IB connection: Connect the concept of equation balance to fair relationships (Key Concept: Relationships)

2. Direct Instruction: Techniques for Solving Linear Equations (20 minutes)

Explain step-by-step simplifying, isolating variables, and balancing equations.
Introduce one-step and two-step equation examples.
Model solving equations using the “balance scale” analogy for visual and conceptual understanding.
Check for understanding: Pose a problem, have several students solve on mini whiteboards with immediate feedback.

3. Guided Practice: Solving Inequalities (15 minutes)

Introduce inequalities: symbols (<, >, ≤, ≥) and their meaning.
Explain how solving inequalities parallels linear equations, but with special attention to reversing the inequality sign when multiplying/dividing by negative numbers.
Demonstrate graphing solutions on number lines using arrows and open/closed circles.
Students practice 3-4 problems in pairs, graphing their answers on number line handouts.

4. Exploration & Group Activity: Real-World Inequality Scenario (20 minutes)

Present a real-life context (e.g., budgeting money, height restrictions, or speed limits) where inequalities are used.
Students work in groups of 4 to:
- Write an inequality representing the scenario.
- Solve the inequality.
- Graph the solution.
- Use colored sticky notes to label key points and solution intervals on a large number line posted on the board.
Groups share their reasoning with the class to promote mathematical communication and reflection.

5. Independent Practice and Formative Assessment (15 minutes)

Individually solve a mix of linear equations and inequalities with graphing.
Use structured problems with increasing difficulty to enable differentiation.
Teacher circulates, providing scaffolding and probing questions.
Exit ticket: Write one sentence explaining the difference between an equation and inequality solution.

6. Reflection and Summary (10 minutes)

Class discussion guided by teacher questions:
- Why do we flip the inequality sign when multiplying/dividing by a negative?
- How does graphing help us visualize equation and inequality solutions?
- How can inequalities be used to represent real-world constraints?
Highlight how this lesson connects to the IB learner profile attributes, such as “Reflective” and “Thinkers.”
Preview next unit or assessment connections.

Assessment and Success Criteria

Success Criteria	Assessment Method	IB Criterion Alignment
Solve linear equations accurately.	Mini whiteboards responses, homework	Criterion B (Investigating)
Solve and graph inequalities.	Guided practice and independent work	Criterion B (Investigating)
Explain reasoning using mathematical language	Exit ticket reflection, group presentation	Criterion C (Communicating)
Use equations and inequalities to model real-world situations	Group activity presentation	Criterion D (Applying Math in Context)

Differentiation Strategies

Support:
- Provide equation-solving templates and step reminders.
- Use visual aids such as the balance scale model.
- Peer tutoring during group work.
Challenge:
- Extension problems involving compound inequalities or inequalities with variables on both sides.
- Encourage students to create their own real-life inequalities and explore solutions.

Reflection for Teacher

Did students demonstrate clear understanding of inequality graph conventions?
Who needs extra support with negative coefficient manipulation?
Were students able to connect abstract algebraic concepts to real-life applications?
Adjust pacing or scaffolding accordingly in next unit or review lessons.

This detailed IB-aligned lesson plan incorporates inquiry, collaboration, and authentic contexts designed to engage Algebra 1 students deeply while cultivating essential IB learner profile traits and international-mindedness.