Homeschool Guide: These lesson plans are a guide for parents. Content may contain errors — always cross-reference with official exam board specifications.

modelling with algebra

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4 detailed 50-minute lessons with teaching scripts, worked examples, parent guides, and assessment criteria.

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Lesson Overview

Total Lessons: 4
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, OCR, Eduqas, CCEA

Learning Objectives

Prerequisites

Materials & Equipment

Lesson 1: Introduction: modelling with algebra

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Write down everything you already know about modelling with algebra. Then check against the key terms: Mathematical modelling. Use a mini-whiteboard or paper.

Main Content (35 minutes)

Parent/Teacher Guide:
Before lesson: Read the script below. Pre-teach key vocab: Mathematical modelling.
If stuck: Re-read the revision notes (link above), then break the content into smaller steps.
Extension: See the Stretch & Challenge ideas in Lesson 4.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: modelling with algebra. By the end you will be able to answer exam questions on it unaided. It connects to the rest of Mathematics because the ideas here recur across the spec."
Mins 5-20 - Direct Instruction: Work through the core ideas below one at a time; after each, ask your student to explain it back in their own words.
Mins 20-30 - Guided Practice: Model the worked example together, then let your student attempt the first practice question with guidance.
Mins 30-35 - Independent Practice: 2-3 practice questions from Lesson 3 below, with immediate feedback.
First Look

Start with the revision notes summary, then attempt: I think of a number, double it, then subtract 5. The result is 17. Find the number.

Plenary (5 minutes)

Check Out

Your student states one thing they learned and one question they still have about modelling with algebra.

Lesson 2: Core Concepts: modelling with algebra

Duration: 50 minutes

Starter Activity (5 minutes)

Review Previous Lesson

Quick recap: write 3 key points from Lesson 1 on modelling with algebra. Check them against the notes below.

Main Content (35 minutes)

Mathematical modelling: Using algebra to represent real-life situations. This involves: Defining variables Writing expressions or equations Solving to find unknown values Interpreting solutions in context

Practice (10 minutes)

Q: I think of a number, double it, then subtract 5. The result is 17. Find the number.

Answer: 11

Plenary (5 minutes)

Explain Back

Your student teaches the key points back to you without looking. Fill any gaps immediately.

Lesson 3: Application: modelling with algebra

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Recall the key terms: Mathematical modelling. Define each in one sentence.

Main Content (35 minutes)

Parent/Teacher Guide: Let your student attempt each question alone first, then compare with the model answer. Award method marks for correct working even if the final answer is wrong.

Q1: I think of a number, double it, then subtract 5. The result is 17. Find the number.

Answer: 11

Q2: A rectangle has sides x and 2x - 1. The perimeter is 32 cm. Find x.

Answer: x = 5.5 cm

Q3: Tickets cost £12 for adults and £8 for children. A group of 10 people pays £96. How many adults?

Answer: 4 adults (and 6 children)

Q4: Sarah is 3 times as old as her brother. In 12 years, she will be twice his age. How old is Sarah now?

Answer: Sarah is 36, brother is 12

Q5: A phone contract costs £20 per month plus 5p per text. Write a formula for monthly cost C with t texts.

Answer: C = 20 + 0.05t

Q6: Three consecutive numbers add to 78. What are they?

Answer: 25, 26, 27

Plenary (5 minutes)

Error Review

Review any questions answered incorrectly. Identify whether the error was knowledge, method, or reading the question.

Lesson 4: Exam Practice: modelling with algebra

Duration: 50 minutes

Starter Activity (5 minutes)

Command Words

Review what these command words require: state (one point), describe (say what happens), explain (say why), compare (both sides), evaluate (judgement).

Main Content (35 minutes)

Extended Answer

Extended question: Extended Answer 6 marks: A school trip costs £200 per adult and £120 per child. The total cost for a group is £2800. There are 20 people in total. (a) Write two equations. (b) How many adults and children are in the group? (c) If 2 more adults join, what is the new total cost? <div class="

(a) a + c = 20 and 200a + 120c = 2800 (b) From (1): c = 20 - a. Substitute: 200a + 120(20 - a) = 2800 → 200a + 2400 - 120a = 2800 → 80a = 400 → a = 5, c = 15 5 adults and 15 children (c) New cost = 7 × 200 + 15 × 120 = 1400 + 1800 = £3200 Mark scheme: (a) 2 marks. (b) 2 marks. (c) 2 marks.

Exam Tips: Always define your variables (let x = ...) | Read the question carefully - what do you need to find? | Check your answer makes sense in context | State your final answer clearly with units | Verify by substituting back into the problem
Common Errors: Watch Out! 1. Wrong: "5 more than x" written as 5x Correct: "5 more than x" means x + 5 (5x means 5 times x) 2. Wrong: Forgetting units in the final answer Correct: Always state units (cm, £, kg, etc.) and interpret the answer in context 3. Wrong: Ignoring whether the answer is realistic (e.g., a negative number of people) Correct: Check your answer makes sense in context — you can't have -5 children
AO3 - Reasoning & Interpretation: Reasoning and Interpretation A gardener has 40 m of fencing to make a rectangular enclosure. The length is 4 m more than the width. (a) Write an expression for the perimeter. (b) Find the dimensions. (c) If the gardener wants the area to exceed 80 m², will this enclosure work? Answers: (a) Let width = w. Length = w + 4. Perimeter = 2(w + w + 4) = 4w + 8. (b) 4w + 8 = 40 → w = 8 m, length = 12 m. (c) Area = 8 × 12 = 96 m² > 80 m². Yes, it works.
Stretch & Challenge (Grade 8-9):
  • Synoptic links: explain how modelling with algebra connects to another Mathematics topic you have studied
  • Real-world: research one real-world use or example of modelling with algebra
  • Critical: "What are the limitations of the models used in modelling with algebra?"

Plenary (5 minutes)

Assessment Criteria
  • Got it: Confident explanation + correct worked examples
  • Getting there: Main points OK, needs support with detail
  • Not yet: Confused on key concepts - re-run Lesson 2

Homework & Consolidation

Recommended Resources

🎓 Smart Lesson (Guided)