straight line graphs
4 detailed 50-minute lessons with teaching scripts, worked examples, parent guides, and assessment criteria.
Lesson Overview
Total Lessons: 4
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, OCR, Eduqas, CCEA
Tier: Foundation and Higher
Duration: 50 minutes per lesson (200 minutes total)
Exam Boards: AQA, Edexcel, OCR, Eduqas, CCEA
Learning Objectives
- Explain the key ideas of straight line graphs
- Apply straight line graphs to exam-style questions
- Develop independent study skills
- Build cross-topic connections
Prerequisites
- Read the revision notes for straight line graphs first (GCSE Revise summary)
- Key vocab to pre-teach: Linear equation
- Basic skills: reading the summary notes and answering the practice questions there
Materials & Equipment
- Exercise book, pencil, ruler
- Scientific calculator
- Pair of compasses and protractor (geometry topics)
- Graph paper
- Printed revision notes (link below)
Lesson 1: Introduction: straight line graphs
Duration: 50 minutes
Starter Activity (5 minutes)
Quick Recall
Write down everything you already know about straight line graphs. Then check against the key terms: Linear equation. Use a mini-whiteboard or paper.
Main Content (35 minutes)
Parent/Teacher Guide:
Before lesson: Read the script below. Pre-teach key vocab: Linear equation.
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.
Before lesson: Read the script below. Pre-teach key vocab: Linear equation.
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: straight line graphs. 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.
Mins 0-5 - Hook: "Today: straight line graphs. 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: State the gradient and y-intercept of y = 4x - 3.
Plenary (5 minutes)
Check Out
Your student states one thing they learned and one question they still have about straight line graphs.
Lesson 2: Core Concepts: straight line graphs
Duration: 50 minutes
Starter Activity (5 minutes)
Review Previous Lesson
Quick recap: write 3 key points from Lesson 1 on straight line graphs. Check them against the notes below.
Main Content (35 minutes)
Linear equation: An equation of the form y = mx + c produces a straight line graph.
| Term | Meaning | Example |
|---|---|---|
| y | -3 | -1 |
Practice (10 minutes)
Q: State the gradient and y-intercept of y = 4x - 3.
Answer: Gradient = 4, y-intercept = -3
Plenary (5 minutes)
Explain Back
Your student teaches the key points back to you without looking. Fill any gaps immediately.
Lesson 3: Application: straight line graphs
Duration: 50 minutes
Starter Activity (5 minutes)
Quick Recall
Recall the key terms: Linear equation. 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: State the gradient and y-intercept of y = 4x - 3.
Answer: Gradient = 4, y-intercept = -3
Q2: Find the gradient of the line passing through (2, 1) and (5, 10).
Answer: Gradient = 3
Q3: Find the equation of the line with gradient -2 and y-intercept 5.
Answer: y = -2x + 5
Q4: Find the equation of the line passing through (0, 3) and (2, 11).
Answer: y = 4x + 3
Q5: Find the equation of the line parallel to y = 5x - 2 passing through (0, 1).
Answer: y = 5x + 1
Q6: Find the gradient of a line perpendicular to y = 3x + 1.
Answer: - 1 ⁄ 3
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: straight line graphs
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: Line A passes through (0, 4) and (6, 0). (a) Find the equation of Line A. (b) Line B is perpendicular to Line A and passes through (3, 7). Find the equation of Line B. (c) Find the coordinates where Line A and Line B intersect. <div class="
(a) m = 0-4 ⁄ 6-0 = - 2 ⁄ 3 . y-intercept = 4. So y = - 2 ⁄ 3 x + 4 (b) Perpendicular gradient = 3 ⁄ 2 . y = 3 ⁄ 2 x + c → 7 = 3 ⁄ 2 (3) + c → 7 = 9 ⁄ 2 + c → c = 5 ⁄ 2 . So y = 3x ⁄ 2 + 5 ⁄ 2 (c) Set equal: - 2 ⁄ 3 x + 4 = 3 ⁄ 2 x + 5 ⁄ 2 . Multiply by 6: -4x + 24 = 9x + 15 → 9 = 13x → x = 9 ⁄ 13 . y = - 2 ⁄ 3 ( 9 ⁄ 13 ) + 4 = 50 ⁄ 13 . Point ( 9 ⁄ 13 , 50 ⁄ 13 ) Mark scheme: (a) 2 marks. (b) 2 marks. (c) 2 marks for solving simultaneous equations.
Exam Tips: y = mx + c: m is gradient, c is y-intercept | Use y = mx + c or draw a table to plot lines | Parallel lines have equal gradients | Perpendicular gradients multiply to -1 | Horizontal lines have gradient 0 | Always check your line passes through the given points
Common Errors: Watch Out! 1. Wrong: Calculating gradient as x₂-x₁ ⁄ y₂-y₁ Correct: Gradient = y₂-y₁ ⁄ x₂-x₁ (change in y over change in x) 2. Wrong: For y = 3x - 2, the y-intercept is (2, 0) Correct: The y-intercept is (0, -2) — it's where x = 0, not where the number appears 3. Wrong: Parallel to y = 5x + 2 has gradient -5 Correct: Parallel lines have the SAME gradient: m = 5
AO3 - Reasoning & Interpretation: Reasoning and Interpretation Company A charges C = 25h + 50. Company B charges C = 40h + 20, where C = cost (£), h = hours. (a) Which company is cheaper for 2 hours? (b) After how many hours do both companies charge the same? (c) A customer needs 5 hours of work. Which company should they choose and how much do they save? Answers: (a) A: £100, B: £100 — same cost. (b) 25h + 50 = 40h + 20 → 30 = 15h → h = 2 hours. (c) A: £175, B: £220. Choose A, saving £45.
Stretch & Challenge (Grade 8-9):
- Synoptic links: explain how straight line graphs connects to another Mathematics topic you have studied
- Real-world: research one real-world use or example of straight line graphs
- Critical: "What are the limitations of the models used in straight line graphs?"
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
- Consolidation: Re-answer any Lesson 3 practice questions answered incorrectly (20 mins)
- Retrieval: Write flashcards for the key terms: Linear equation (10 mins)
- Exam practice: One past-paper question on straight line graphs from the board websites (15 mins)
- Extension: Explain straight line graphs to someone else in your own words (10 mins)