Solving and Graphing Inequalities

Overview

This 90-minute lesson is designed for Algebra 1 students (typically 14-15 years old) following the International Baccalaureate (IB) Middle Years Programme (MYP) framework. Students will explore how to solve linear inequalities, graph solutions on a number line, and combine solutions using "and" / "or" statements. This lesson ties directly to the MYP mathematics objectives emphasizing reasoning, communication, and application in real-world contexts.

Learning Objectives (MYP Mathematics Criterion C & D)

Solve linear inequalities involving one variable using algebraic methods (MYP Criterion C: Applying mathematics in real-life contexts).
Demonstrate understanding of inequality solution sets by representing them graphically on number lines (MYP Criterion D: Communicating mathematics effectively).
Apply logical connectives “and”/“or” to combine inequalities and interpret solutions in context.
Use precise mathematical language to explain and justify steps and solutions.
Develop critical thinking skills by creating and solving compound inequalities.

Materials Needed

Whiteboard/markers
Graph paper or printed number line templates (one per student)
Colored markers/pens (e.g., red and blue for different solution sets)
Student notebooks
Mini whiteboards and expo markers for small group work
Prepared inequality problem cards (see activity section)

Lesson Outline

Introduction & Prior Knowledge Review (10 minutes)

Begin with a short interactive quiz using mini whiteboards:
Example prompts:
- Solve: 3x + 2 > 8
- Graph the solution x > 2 on a number line
Discuss quickly: What does it mean when an inequality sign changes direction?
Recap the difference between inequality signs: >, <, ≥, ≤

IB Focus: Activate prerequisite knowledge, scaffold new learning through recall.

Direct Instruction (15 minutes)

Explicitly explain:
1. How to isolate the variable in a linear inequality step-by-step focusing on inequality rules (flip the sign when multiplying/dividing by a negative number).
2. How to represent solutions on a number line: open dots for strict inequalities (<, >) and closed dots for inclusive (≤, ≥).
3. Introduction to compound inequalities: "and" means intersection (both conditions must be true), "or" means union (either condition can be true).
Use visual models on the board to show solutions of inequalities individually and combined (‘and’ / ‘or’).
Model examples:
- x > 2 and x ≤ 5
- x < 1 or x ≥ 4

IB Focus: Emphasize communication with mathematical symbols and visuals following Criterion D.

Guided Practice (20 minutes)

Students work in small groups (4-5 per group) with assigned inequality problem cards. Each card presents:
- One linear inequality to solve and graph.
- One compound inequality using “and” or “or” to solve and graph.
Each group will:
- Solve algebraically.
- Graph on printed number lines with colored markers (one color per inequality).
- Verbally present their solution and graph to the class for peer feedback.

Example problem card:

Solve: 2x - 3 < 7
Solve and graph: (x + 1 > 0) and (x - 4 ≤ 3)

IB Focus: Collaborative learning and use of communication skills (Criterion D) while applying math in new contexts (Criterion C).

Independent Practice (15 minutes)

Provide individual worksheet with a range of inequalities to solve, including:
- Simple inequalities (e.g., 4x + 1 ≥ 9)
- Compound inequalities requiring “or”/“and” solutions
Students graph solutions on the number line and write a brief explanation of the solution including reasoning for intersection/union in compound inequalities.

IB Focus: Individual application and reflection aligning to MYP criterion C and D.

Inquiry & Extension Activity (15 minutes)

Pose a real-world problem that involves inequalities:
Example: "A company offers two types of service contracts. Contract A requires monthly usage greater than 10 hours but less than or equal to 20 hours. Contract B covers any usage below 5 hours or above 25 hours. Graph the possible usage hours for both contracts and determine if there is an overlap in coverage."
In pairs, students:
- Write inequalities describing each contract.
- Graph solutions on number lines.
- Discuss if any hours are covered by both contracts (using “and”).
Debrief as a class to connect inequalities with meaningful real-world applications.

IB Focus: Apply mathematics in authentic contexts and develop analytical thinking (criterion C).

Summary & Formative Assessment (10 minutes)

Quick formative assessment quiz:
- Solve an inequality and graph on the whiteboard.
- Write “and” / “or” compound inequality solutions based on given graphs.
Exit ticket prompt:
- “Explain in your own words how to solve a compound inequality involving ‘and’ and how it differs from ‘or.’”

IB Focus: Assess conceptual understanding and communication skills (Criterion D).

Reflection and Differentiation

Scaffold learners who need more support with color-coded steps and concrete number line models.
Challenge advanced learners by having them create their own real-world compound inequalities for peers to solve.
Continuous formative feedback during group presentations and individual work ensures concepts are understood.

Alignment with IB MYP Mathematics Guide (2020)

MYP Objective	Description	Activity Connection
Criterion C	Apply math in real-life contexts and problem solving	Real-world contract problem & solving inequalities
Criterion D	Communicate mathematical ideas effectively	Verbal group presentations, written explanations, and graphical representations
Approaches to learning (ATL)	Communication, critical thinking, collaboration	Group work, peer feedback, creating explanations

This lesson plan seeks to engage Algebra 1 students in developing deep understanding of linear inequalities, algebraic manipulation, and graphical representation through interactive, collaborative, and authentic learning experiences — core tenets of the IB approach.