Working with Inequalities

Unit Context

This is Lesson 13 of 30 in the unit "Algebra in Everyday Life" for Year 7-10 students working at levels between Year 2 to Year 7. The lesson focuses on understanding inequalities, solving them, and graphing the solutions. The lesson aligns with the NSW Mathematics Curriculum, particularly addressing algebraic concepts relevant to Years 7 and 8, adaptable to the diverse needs of learners with autism, behaviour and mental health challenges.

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Learning Objectives

By the end of this 45-minute lesson, students will be able to:

1. Understand what inequalities represent and distinguish between inequality symbols (>, <, ≥, ≤).
2. Solve simple linear inequalities involving one variable.
3. Represent inequality solutions on a number line.
4. Relate inequalities to real-life situations through authentic examples.

NSW Curriculum References

• Years 7-8 Mathematics (Algebra):
• Use algebraic expressions to represent and describe relationships between variables.
• Solve linear equations and inequalities with one variable, graph the solutions on a number line.
• Use mathematical modelling to interpret and solve practical problems involving algebraic expressions and inequalities.

Referencing achievement standards for Year 7 and 8 emphasizing solving linear inequalities and graphing solutions using tables and graphs.

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Lesson Duration

45 minutes Class size: 20 students

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Resources Needed

• Whiteboard and markers
• Printed number lines (dyslexia-friendly: wide spacing, clear font, high contrast)
• Worksheets with examples and practice problems (large text, simple language)
• Real-life scenario cards for inequality contexts (e.g., budgeting money, speed limits)
• Counters or tokens for hands-on inequality activities
• Graphing paper

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Lesson Plan Breakdown

1. Introduction and Recap (5 minutes)

• Begin with a brief recap of algebra basics: What are variables? What do equality (=) and expressions mean?
• Introduce the concept of inequalities as statements about relative size or amounts, explaining symbols using visual aids:

Symbol	Meaning
>	greater than
<	less than
≥	greater than or equal
≤	less than or equal

• Use clear, simple language and concrete examples (e.g., "If you have more than 3 apples, you have at least 4").

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2. Direct Instruction: Understanding Inequalities (10 minutes)

• Demonstrate how to solve a simple inequality step-by-step:

Example: x + 3 > 5 Step 1: Subtract 3 from both sides → x > 2 Step 2: Interpret solution: all numbers greater than 2 satisfy the inequality.

• Show how to graph the solution on a number line:

• Open circle for > or < (not including the number)

• Closed circle for ≥ or ≤ (including the number)

• Shade in the direction of the solution set.

• Use visual aids and repeat examples to reinforce learning.

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3. Guided Practice (15 minutes)

• Hand out worksheets with 5 inequalities that students solve collaboratively in pairs, with physical counters to represent values visually.

• Problems include both strict inequalities (>) and inclusive inequalities (≥).

• Circulate around the classroom to support students, using questioning techniques:

• "What happens if x is 3? Does it satisfy the inequality?"

• "How do you show this on your number line?"

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4. Real-Life Connections (5 minutes)

• Present simple, authentic scenarios that require inequality reasoning:

• "You have $20 and want to buy snacks costing more than $5 but less than $15."

• "The speed limit is less than or equal to 60 km/h. Show the speeds you can legally drive."

• Students write the inequalities corresponding to these situations, either verbally or in written form.

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5. Independent/Extension Activity (5 minutes)

• For students who finish early or are more advanced:

• Create their own inequality problems based on real or imagined scenarios.

• Graph compound inequalities on a number line (e.g., 2 < x ≤ 5).

• Use trial and error to check if specific values satisfy an inequality.

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6. Review and Reflect (5 minutes)

• Class discussion: What did you learn about inequalities today?
• Clarify any misconceptions.
• Outline how these skills will connect to future lessons in algebra and everyday problem-solving.

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Differentiation Strategies

• For diverse learners including students with autism and behavioural challenges:

• Use clear, step-by-step instructions with visual cues.

• Allow frequent breaks if needed.

• Use concrete objects (counters, tokens) to represent inequalities physically.

• Provide printed notes and visual aids with high contrast and dyslexia-friendly fonts.

• Reinforce learning with repetition and simple language.

• Use consistent routines and structure in lesson delivery.

• For students with dyslexia:

• Provide worksheets with clear fonts (e.g., Arial or Comic Sans), off-white paper to reduce glare.

• Use bullet points and short paragraphs.

• Include colour coding for inequality symbols and number line regions.

• For advanced learners:

• Challenge students with compound inequalities and real-world modelling tasks.

• Introduce the idea of solving inequalities with variables on both sides.

• Explore graphing inequalities in two variables (if applicable to capability).

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Assessment

• Formative:

• Observation during guided practice and pair work.

• Questioning to check understanding of inequality symbols and solutions.

• Quick exit ticket: Write an inequality representing a real-world scenario or graph a given inequality.

• Summative Informal:

• Completed worksheets with correctly solved inequalities and number line graphs.

• Ability to explain reasoning verbally or through written reflection at lesson end.

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Teacher Reflection Prompts

• How well did students grasp inequality concepts and symbols?
• Were the real-life examples effective for engagement and understanding?
• Did the differentiation strategies support all learners effectively?
• What adjustments are needed for the next lesson on inequalities or algebra?

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This lesson is structured to meet the NSW Curriculum goals, providing layered support to meet the needs of students working below expected year level while offering extension for advanced learners, all embedded in authentic contexts for engagement and relevance to everyday life. The use of tactile materials, visual supports, and clear language respects students' diverse needs, including those with autism, behavioural conditions, and dyslexia. This approach supports skill development in both mathematical reasoning and real-world application, which is crucial for post-school transition and career readiness.