Equations and Rearranging

National Curriculum Links

• Physics KS3/KS4 (Years 7-9, Year 9 transition to GCSE): Use and rearrange formulae to solve problems, understand the importance of equations in describing physical relationships and quantities (National Curriculum for England, KS3 Science Programme of Study (Physics)).
• Mathematics Links: Apply mathematical techniques required for Physics such as rearranging algebraic equations, substitute values, solve simple linear equations.
• Focus here is on developing algebraic skills necessary for GCSE Physics, meeting the statutory requirement to use and manipulate equations.

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Learning Objectives (WALT)

• WALT: Understand why equations are fundamental to Physics.
• WALT: Identify examples of equations used in everyday life.
• WALT: Develop skills to rearrange simple Physics equations to solve problems.
• WALT: Apply rearranged equations confidently to calculate physical quantities.

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Success Criteria

• I can explain why equations are essential in Physics.
• I can give examples of equations I already use or encounter daily.
• I can rearrange given Physics equations step-by-step.
• I can solve straightforward Physics problems by substituting values into rearranged equations.
• I can self-assess my understanding using provided criteria and ask for help or extension appropriately.

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Resources

• Whiteboard/Smartboard
• Printed worksheets with equations and questions (dyslexia-friendly fonts, clear spacing)
• Colour-coded equation cards
• Mini whiteboards for student responses
• Interactive 'hide-the-learning' envelopes/boxes
• Visual aids with everyday life equation examples (e.g., speed calculation, currency conversions)
• Step-by-step scaffolding guide printouts
• Laptops/tablets (optional) or paper for extension tasks

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Lesson Structure (60 minutes)

Starter (10 minutes)

Activity: “Equation Detectives”

• Present a slide/board with common everyday statements involving relationships between quantities (e.g., “Speed = Distance ÷ Time”, “COST = Price × Quantity”, “BMI = Weight ÷ Height²”).
• Ask students to discuss in pairs and identify what these statements all have in common (equations).
• Discuss how equations help us understand and calculate things in everyday life.
• Differentiation: Provide printed statements with colour-coding; posters with pictures for SEN/dyslexic learners.
• Outcome: Activate prior knowledge and get students thinking about the importance of equations beyond physics.

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Chunk 1: Why Use Equations in Physics? (8 minutes)

• Mini Lecture:

  • Introduce the concept that Physics explains how the world works by showing relationships between measurable quantities using equations.
  • Highlight that equations condense complex relationships into simple, powerful tools for predicting and understanding phenomena.
  • Example: speed = distance ÷ time – explains how these concepts connect.

• Visuals and Interactive Questioning:

  • Show real-life physics examples: e.g., calculating speed on a journey, estimating time for a ball to fall, etc.
  • Ask students to predict the outcome if some variables change.

• Differentiation:

  • Use simple language and visuals.
  • Dyslexia-friendly handout of key points with bullet lists and icons.
  • Advanced learners: Challenge with asking how an equation might change if conditions vary (e.g., speed if time halves).

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Chunk 2: Introducing Rearranging Equations (8 minutes)

• Define rearranging: changing the subject of the equation to isolate a different variable.

• Use a simple, familiar example: rearranging speed = distance ÷ time to find distance or time.

• Stepwise demonstration of algebra:

  • Start with speed = distance ÷ time
  • Multiply both sides by time
  • distance = speed × time

• Guide students to follow on mini whiteboards.

• Differentiation:

  • Provide colour-coded algebra steps (e.g., red for what you do to both sides).
  • Use physical equation cards to ‘move’ parts around physically for kinaesthetic learners.
  • SEN: Highlight keywords, use clear font.
  • Advanced learners: Introduce inverse operations or rearranging more complex equations briefly.

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Hide-the-Learning Activity: Equation Puzzle Challenge (10 minutes)

• In groups of 3-4, students receive envelopes containing cards:

  • Cards with parts of equations,
  • Cards with steps in rearranging,
  • Cards with everyday physics problems.

• Task: Match and order the cards to reveal correct rearranged equations and solve the problems.

• Rotate roles: reader, matcher, calculator, recorder to engage all.

• Teacher circulates, probing understanding and offering scaffolds.

• Differentiation:

  • SEN groups receive pre-arranged partially completed sets.
  • Use tactile, dyslexia-friendly cards with symbols.
  • Extension: Challenge groups with “What if” questions to test deeper understanding.

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Guided Practice: Step-by-Step Rearranging (12 minutes)

• Use a worksheet with three simple equations frequently used in physics (e.g., density = mass/volume; pressure = force/area; speed = distance/time).

• Scaffold each question with hints and partial steps.

• Teacher-led walkthrough first equation on board, then students attempt next two in pairs.

• Emphasis on verbalising the steps as they rearrange.

• Use mini-whiteboards for immediate formative assessment; teacher gives quick feedback.

• Differentiation:

  • SEN: Sentence starters provided for explanations, use of calculator if needed.
  • Dyslexic learners: Worksheets with dyslexia-friendly font, clear spacing.
  • Advanced: Add a question asking to rearrange two-step equations combining units or formulas.

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Plenary (7 minutes)

• Self-Assessment with Success Criteria:

  • Show each success criterion.
  • Students tick what they feel confident with using coloured cards (Green = confident, Amber = some help needed, Red = need more support).

• Discuss answers aloud, clarify misconceptions.

• Quick quiz: Give a simple Physics problem, ask two students to volunteer to explain rearranging and solving.

• Extension/Homework prompt:

  • Research and bring an example of an equation used outside of school or physics (e.g., in cooking, sports, or finance).

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Differentiation Summary

Learner Type	Strategies
SEN	Colour-coded notes, physical/moveable equation cards, sentence starters, step-by-step scaffolds, peer support
Dyslexic learners	Dyslexia font worksheets, visual aids, high contrast materials, oral instructions and check-ins
Mixed Ability pairs	Pair stronger with less confident students for peer learning, clear roles in group activities
More Able learners	Extension questions, “what if” investigations, rearranging multi-step equations, explaining reasoning in writing and verbally

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Teacher Reflection/Notes

• Ensure pace allows sufficient time for scaffolded practice.
• Circulate actively during group activities to address misconceptions.
• Monitor self-assessment carefully to plan next lesson focus.
• Encourage all students to verbalise their thinking for deeper conceptual understanding.

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This structured approach incorporating hands-on manipulation, careful scaffolding, interactive group work, and clear success criteria aligns well with the England National Curriculum’s emphasis on using mathematical skills to solve Physics problems and builds vital foundations for GCSE study.