Creating and Solving Equations

Year Level

Differentiated for Years 7-10 (students working between Year 2 to Year 7 levels)

Duration

45 minutes

Unit Context

Unit: Algebra in Everyday Life (Lesson 7 of 30)

NSW Mathematics Curriculum Reference

Relevant Content Descriptions

Year 7: Use algebraic expressions to represent situations, describe relationships, substitute values, and solve simple linear equations.
Year 8: Solve linear equations with rational solutions algebraically and graphically; use algebraic properties to manipulate expressions.
Year 9: Solve linear equations and apply algebraic methods to real-life contexts.
General capabilities: Developing problem-solving, reasoning, and numeracy skills through authentic real-world contexts.

Achievement Standards

Students create and solve linear equations from practical situations, explaining their reasoning and choosing appropriate strategies

Learning Objectives

By the end of the lesson students will be able to:

Understand key vocabulary: variable, coefficient, equation, solution.
Translate simple word problems into algebraic equations.
Apply step-by-step problem-solving strategies to solve one-variable linear equations.
Check solutions by substituting back into the original problem.
Relate algebraic equations to real-life contexts relevant to students’ daily experiences.
Build confidence by mastering foundational algebra skills with repetition and scaffolded support.

Resources Needed

Whiteboard and markers
Printed word problem cards (real-life scenarios)
Calculators for checking work (optional)
Visual maths aids/dyslexia-friendly worksheets with clear fonts and colour-coded parts of equations
Manipulatives like algebra tiles (optional for hands-on support)
Timer for pacing activities
Digital tools (optional) for extension activities (e.g., simple algebra apps or interactive games)

Lesson Structure

Time	Activity	Description	Teacher Notes	Differentiation
5 min	Warm-up & Review	Quick oral revision of variables and simple equations: e.g., “If x + 3 = 7, what is x?”	Use gesture and visuals, repeat key terms	Use flashcards or symbols for vocabulary; allow verbal or physical responses
10 min	Modelling creation of equations	Teacher reads aloud word problems related to everyday life (e.g., shopping, sharing snacks). Together, break down language and write an equation on the board.	Emphasise one step at a time. Use simple sentences. Use real objects if possible.	Use visual word maps; highlight key words (“total”, “left”, “each”) in colours; pair students for peer support
15 min	Guided practice: solving equations	Stepwise solving of equation created. Use “think aloud” approach to explain balancing operation (doing the same on both sides). Demonstrate substitution checking.	Repeat key concepts, pause for questions, allow use of manipulatives	Provide sentence starters and equation templates; use scaffolded worksheets with space for visual thinking
10 min	Independent or paired activity	Students receive word problems to translate and solve independently or with a partner. Teacher circulates offering individual support.	Encourage students to verbalise their thinking; use concrete examples if stuck	Use simplified problems for some; provide hint cards; for advanced learners, add two-step problems
5 min	Review and reflection	Discuss solutions, common mistakes, and real-world application. Ask for one thing learned/from confusion. Reinforce the life skill of algebra as problem solving.	Praise effort; use positive reinforcement	Accept answers in different forms (verbal, written, drawn); use a “thumbs up/down” check-in to gauge confidence

Detailed Activities Description

Warm-up & Review (5 mins)

Begin with simple equations involving addition/subtraction. Use concrete objects or drawings.
Use repetition and prompt students to say key words aloud.
This sets a calm, low-pressure start and checks prior knowledge.

Modelling Equations from Word Problems (10 mins)

Present a relatable scenario, e.g., “Sarah has some apples. She buys 3 more and now has 7 apples. How many did she have before?”
Write down what is known and unknown. Introduce variable x to represent unknown.
Write the equation: x + 3 = 7.
Use drawings or physical objects to visualise.
Highlight the meaning of each part of the equation.
Invite suggestions from students to name parts (variable, constant, total).

Guided Solving of Equations (15 mins)

Show how to isolate x by subtracting 3 from both sides.
Explain performing operations on both sides to maintain balance.
Solve step-by-step, writing neatly.
Substitution check: show by plugging in x = 4 that equation balances.
Use manipulatives if helpful for kinesthetic learners.
Invite students to explain steps back to the class or in pairs.

Independent or Paired Activity (10 mins)

Provide 2-3 short word problems with scaffolding (some visual, some simplified).
Examples:
“Tom has x stickers. He gives 2 to a friend and now has 5. How many stickers did Tom have?”
“A pizza is cut into pieces. Each person gets 3 pieces. If there are 4 people, how many pieces (p) are there? Write an equation.”
Encourage students to:

Underline key facts.
Write equation.
Solve.

Teacher provides prompts or hints as needed.
For advanced learners, offer a two-step problem or one requiring rearrangement.

Review and Reflection (5 mins)

Call on volunteers to share solutions and explain reasoning.
Discuss common issues like forgetting to subtract on both sides.
Emphasise that these skills help solve practical problems such as budgeting, sharing, or working out time.
Use simple exit questions like “What did I learn today?” or “What was tricky?”

Differentiation Strategies

Use clear, dyslexia-friendly fonts and layouts: avoid clutter, use short sentences, bullet points.
Provide coloured overlays or colour-coded steps to visually separate operation stages.
Repeat instructions and key vocabulary multiple times; use multisensory cues (oral, visual, tactile).
Incorporate manipulatives (algebra tiles, counters) for concrete understanding.
Pair stronger students with those needing support for peer modelling.
Break down complex problems into smaller chunks.
Scaffold with sentence stems for students to formulate equations: “I know ___ plus ___ equals ___, so I write ___.”
Allow extra processing or response time.
Use frequent positive reinforcement to build confidence.
For students working below Year 2 levels, use concrete counting and simple addition/subtraction before algebra introduction.
Extension activities for advanced learners included below.

Extension Activities for Advanced Learners

Create and solve two-step equations from more complex word problems.
Explore simple inequalities related to everyday decisions (“if x > 5, then…”).
Introduce solving equations graphically using plotting points (if digital tools available).
Challenge students to write their own word problems and exchange with peers to solve.
Integrate basic function notation or substitution of multiple values into formulas (in simple contexts).

Career & Life Skills Connection

Emphasise algebra as a tool used in daily decisions such as budgeting, shopping, cooking (measuring ingredients), and planning.
Discuss how solving equations relates to figuring out “unknowns” in real world tasks — helping manage finances, time, or work tasks.
Build social and emotional learning by encouraging respectful partner collaboration, sharing ideas kindly, and being patient when others need help.
Encourage goal setting: “Algebra helps me learn to think logically, which helps me in my future career, whatever I choose.”

This lesson plan provides targeted support for students with learning and behavioural challenges while keeping content aligned with NSW curriculum standards for Years 7-10 mathematics, focusing on fundamental algebra skills. The approach is highly scaffolded and multisensory, with explicit connection to authentic everyday contexts to engage students meaningfully and build confidence progressively.

Teaching Instructions