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coordinates

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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: coordinates

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Write down everything you already know about coordinates. Then check against the key terms: Coordinates. Use a mini-whiteboard or paper.

Main Content (35 minutes)

Parent/Teacher Guide:
Before lesson: Read the script below. Pre-teach key vocab: Coordinates.
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: coordinates. 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: In which quadrant is the point (-4, 3)?

Plenary (5 minutes)

Check Out

Your student states one thing they learned and one question they still have about coordinates.

Lesson 2: Core Concepts: coordinates

Duration: 50 minutes

Starter Activity (5 minutes)

Review Previous Lesson

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

Main Content (35 minutes)

Coordinates: Pairs of numbers (x, y) that specify a position on a grid. The x-coordinate comes first, then y.
Remember: "Along the corridor, up the stairs" - x first, then y.
TermMeaningExample
1st (top right)++
2nd (top left)-+
3rd (bottom left)--
4th (bottom right)+-

Practice (10 minutes)

Q: In which quadrant is the point (-4, 3)?

Answer: 2nd quadrant

Plenary (5 minutes)

Explain Back

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

Lesson 3: Application: coordinates

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

Recall the key terms: Coordinates. 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: In which quadrant is the point (-4, 3)?

Answer: 2nd quadrant

Q2: What are the coordinates of a point 3 units right of (-2, 5)?

Answer: (1, 5)

Q3: Find the midpoint of (4, 2) and (10, 8).

Answer: (7, 5)

Q4: Find the midpoint of (-2, 3) and (6, -5).

Answer: (2, -1)

Q5: Point A is (3, -2). Point B is on the x-axis, directly below A. What are the coordinates of B?

Answer: (3, 0)

Q6: What is the distance between (-3, 5) and (-3, -1)?

Answer: 6 units

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: coordinates

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(2, 3) and B(8, 7) are opposite vertices of a rectangle with sides parallel to the axes. (a) Find the other two vertices C and D. (b) Find the midpoint of the diagonal AB. (c) Find the area of the rectangle. <div class="

(a) The other vertices must share x and y coordinates with A and B: C = (8, 3) and D = (2, 7) (b) Midpoint = ( 2+8 ⁄ 2 , 3+7 ⁄ 2 ) = (5, 5) (c) Length = |8 - 2| = 6, Width = |7 - 3| = 4. Area = 6 × 4 = 24 square units Mark scheme: (a) 2 marks for both vertices. (b) 2 marks. (c) 2 marks for length, width and area.

Exam Tips: Always write coordinates in brackets with a comma: (x, y) | x comes first: "along the corridor, up the stairs" | Negative x = left of origin; negative y = below origin | Points on x-axis have y = 0; points on y-axis have x = 0 | For midpoint, find the average of x-values and average of y-values
Common Errors: Watch Out! 1. Wrong: Writing coordinates as (y, x) Correct: Always (x, y) — x comes first 2. Wrong: (-2, 5) is in the 4th quadrant Correct: (-2, 5) is in the 2nd quadrant (x negative, y positive) 3. Wrong: Midpoint formula adds coordinates and doesn't divide by 2 Correct: Midpoint = average of x-values, average of y-values — must divide by 2
AO3 - Reasoning & Interpretation: Reasoning and Interpretation A phone mast at point M has signal covering all points within 5 km. Town A is at (2, 4) and Town B at (8, 4) on a map where 1 unit = 1 km. (a) If M is at (5, 4), does Town A get signal? (b) Does Town B get signal? (c) Where should M be placed so both towns just get signal? Answers: (a) Distance = |5 - 2| = 3 km
Stretch & Challenge (Grade 8-9):
  • Synoptic links: explain how coordinates connects to another Mathematics topic you have studied
  • Real-world: research one real-world use or example of coordinates
  • Critical: "What are the limitations of the models used in coordinates?"

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)