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

P7: Possibility Spaces

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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: Possibility Spaces

Duration: 50 minutes

Starter Activity (5 minutes)

Quick Recall

3 quick questions to activate prior knowledge about possibility spaces. Use mini-whiteboard or paper.

Main Content (35 minutes)

Parent/Teacher Guide:
Before lesson: Read script below. Prepare materials. Pre-teach key vocab: P7.
If stuck: See Troubleshooting below. Break into smaller steps.
Extension: See Stretch & Challenge section.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: Possibility Spaces. Goal: by the end you can two fair coins are flipped. List the sample space and find P(exactly one head), using the method shown step by step. Connects to listing (N5) because you'll reuse its method throughout today's work."
Mins 5-15 - Direct Instruction: 1) Define: "Possibility Spaces is..." 2) Key principle: "Most important:..." 3) Draw diagram, label live. 4) Real example: "Like Two fair coins are flipped. List the sample space and find P(exactly one head). - a real example worked through in full..."
Mins 15-25 - Guided Practice: Ex1: Teacher models. Ex2: Student tries with guidance. Ex3: Student independent.
Mins 25-35 - Independent Practice: 3-5 questions. Immediate feedback.
Worked Example 1: Basic

Q: Two fair coins are flipped. List the sample space and find P(exactly one head).

  1. What is asked? Two
  2. Recall knowledge: Sample space = every possible outcome; count it for the denominator; Grids: two dice = 6 × 6 = 36 equally likely cells
  3. Apply: Sample space: HH, HT, TH, TT (4 equally likely) P(exactly one head) = 2/4 = 1/2
  4. Check: Check the units named in the question and sense-check the size of your answer.
  5. Answer: 1/2

Tip: "Show working - method marks > answer marks."

Worked Example 2: Multi-step

Q: Two dice: find P(product is even).

  1. Break down: Separate parts?
  2. Solve each: P(odd product) requires both odd: 3 × 3 = 9 of 36 → P(odd) = 1/4 P(even) = 1 − 1/4 = 3/4
  3. Combine: The parts chain: each answer feeds the next step of the question.
  4. Final answer: M1 for the complement, A1 for 3/4. 'At least one even' questions often fall to 1 − P(both odd).
Worked Example 3: Data/Application

Q: Two dice: find P(product is even).

  1. Read data: Axes, units, scale
  2. Patterns: Trends, anomalies
  3. Explain: Why? Using possibility spaces
  4. Conclude: Evidence-based

Common Questions & Troubleshooting

Q: "Why does Sample space = every possible outcome; count it for the deno work this way?"
A: Analogy: "Two fair coins are flipped. List the sample space and find P(exactly one head).". Try re-draw or re-write the worked example from memory, then check it against the model answer.
Q: "Wrong answers on calculations."
A: Checklist: units? formula? calculator mode? sig figs?
Q: "Can't remember key terms."
A: Flashcards (term front, def+diagram back). Spaced repetition: day 1, 3, 7.
Q: "Exam wording confuses me."
A: Commands: Describe=what you see; Explain=reasons; Evaluate=pros/cons+judgement; Calculate=working+units.
Q: "Running out of time."
A: 1 mark/min. Skip hard, return. Attempt all - partial marks count.

Assessment & Model Answers

Mastery Checklist:
  • [ ] Define Possibility Spaces in own words
  • [ ] Identify features in diagram
  • [ ] Explain process step-by-step
  • [ ] Apply to unfamiliar context
  • [ ] Score 80%+ on past paper question

Model Answer: Past Paper Question

Q: Two fair coins are flipped. List the sample space and find P(exactly one head).

  • 1 mark: [Key terminology]
  • 1 mark: [Mechanism/process]
  • 1 mark: [Application/example]
  • 1 mark: [Evaluation - Higher]

Model response: "[Complete answer with expected detail/terminology]"

Why full marks: [What makes this strong]

Stretch & Challenge (Grade 8-9):
  • Synoptic links: Connect to P6-systematic-listing / P8-tree-diagrams
  • Real-world: Research use in industry, medicine or research
  • Advanced calc: Try a more challenging variant
  • Critical: "Evaluate limitations of today's model"
  • Research: Recent discovery on possibility spaces, summarise 100 words

Plenary (5 mins)

Label the Diagram

Unlabelled diagram - write all parts in 1 min

Assessment Criteria

Lesson 2: Core Concepts: Possibility Spaces

Duration: 50 minutes

Starter Activity (5 minutes)

Review Previous Lesson

Quick recap: write 3 key points from last lesson on possibility spaces. Use mini-whiteboard or paper.

Main Content (35 minutes)

Parent/Teacher Guide:
Before lesson: Read script below. Prepare materials. Pre-teach key vocab: P7.
If stuck: See Troubleshooting below. Break into smaller steps.
Extension: See Stretch & Challenge section.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: Possibility Spaces. Goal: by the end you can two fair coins are flipped. List the sample space and find P(exactly one head), using the method shown step by step. Connects to listing (N5) because you'll reuse its method throughout today's work."
Mins 5-15 - Direct Instruction: 1) Define: "Possibility Spaces is..." 2) Key principle: "Most important:..." 3) Draw diagram, label live. 4) Real example: "Like Two fair coins are flipped. List the sample space and find P(exactly one head). - a real example worked through in full..."
Mins 15-25 - Guided Practice: Ex1: Teacher models. Ex2: Student tries with guidance. Ex3: Student independent.
Mins 25-35 - Independent Practice: 3-5 questions. Immediate feedback.
Worked Example 1: Basic

Q: Two fair coins are flipped. List the sample space and find P(exactly one head).

  1. What is asked? Two
  2. Recall knowledge: Sample space = every possible outcome; count it for the denominator; Grids: two dice = 6 × 6 = 36 equally likely cells
  3. Apply: Sample space: HH, HT, TH, TT (4 equally likely) P(exactly one head) = 2/4 = 1/2
  4. Check: Check the units named in the question and sense-check the size of your answer.
  5. Answer: 1/2

Tip: "Show working - method marks > answer marks."

Worked Example 2: Multi-step

Q: Two dice: find P(product is even).

  1. Break down: Separate parts?
  2. Solve each: P(odd product) requires both odd: 3 × 3 = 9 of 36 → P(odd) = 1/4 P(even) = 1 − 1/4 = 3/4
  3. Combine: The parts chain: each answer feeds the next step of the question.
  4. Final answer: M1 for the complement, A1 for 3/4. 'At least one even' questions often fall to 1 − P(both odd).
Worked Example 3: Data/Application

Q: Two dice: find P(product is even).

  1. Read data: Axes, units, scale
  2. Patterns: Trends, anomalies
  3. Explain: Why? Using possibility spaces
  4. Conclude: Evidence-based

Common Questions & Troubleshooting

Q: "Why does Sample space = every possible outcome; count it for the deno work this way?"
A: Analogy: "Two fair coins are flipped. List the sample space and find P(exactly one head).". Try re-draw or re-write the worked example from memory, then check it against the model answer.
Q: "Wrong answers on calculations."
A: Checklist: units? formula? calculator mode? sig figs?
Q: "Can't remember key terms."
A: Flashcards (term front, def+diagram back). Spaced repetition: day 1, 3, 7.
Q: "Exam wording confuses me."
A: Commands: Describe=what you see; Explain=reasons; Evaluate=pros/cons+judgement; Calculate=working+units.
Q: "Running out of time."
A: 1 mark/min. Skip hard, return. Attempt all - partial marks count.

Assessment & Model Answers

Mastery Checklist:
  • [ ] Define Possibility Spaces in own words
  • [ ] Identify features in diagram
  • [ ] Explain process step-by-step
  • [ ] Apply to unfamiliar context
  • [ ] Score 80%+ on past paper question

Model Answer: Past Paper Question

Q: Two fair coins are flipped. List the sample space and find P(exactly one head).

  • 1 mark: [Key terminology]
  • 1 mark: [Mechanism/process]
  • 1 mark: [Application/example]
  • 1 mark: [Evaluation - Higher]

Model response: "[Complete answer with expected detail/terminology]"

Why full marks: [What makes this strong]

Stretch & Challenge (Grade 8-9):
  • Synoptic links: Connect to P6-systematic-listing / P8-tree-diagrams
  • Real-world: Research use in industry, medicine or research
  • Advanced calc: Try a more challenging variant
  • Critical: "Evaluate limitations of today's model"
  • Research: Recent discovery on possibility spaces, summarise 100 words

Plenary (5 mins)

Label the Diagram

Unlabelled diagram - write all parts in 1 min

Assessment Criteria

Lesson 3: Application: Possibility Spaces

Duration: 50 minutes

Starter Activity (5 minutes)

Review Previous Lesson

Quick recap: write 3 key points from last lesson on possibility spaces. Use mini-whiteboard or paper.

Main Content (35 minutes)

Parent/Teacher Guide:
Before lesson: Read script below. Prepare materials. Pre-teach key vocab: P7.
If stuck: See Troubleshooting below. Break into smaller steps.
Extension: See Stretch & Challenge section.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: Possibility Spaces. Goal: by the end you can two fair coins are flipped. List the sample space and find P(exactly one head), using the method shown step by step. Connects to listing (N5) because you'll reuse its method throughout today's work."
Mins 5-15 - Direct Instruction: 1) Define: "Possibility Spaces is..." 2) Key principle: "Most important:..." 3) Draw diagram, label live. 4) Real example: "Like Two fair coins are flipped. List the sample space and find P(exactly one head). - a real example worked through in full..."
Mins 15-25 - Guided Practice: Ex1: Teacher models. Ex2: Student tries with guidance. Ex3: Student independent.
Mins 25-35 - Independent Practice: 3-5 questions. Immediate feedback.
Worked Example 1: Basic

Q: Two fair coins are flipped. List the sample space and find P(exactly one head).

  1. What is asked? Two
  2. Recall knowledge: Sample space = every possible outcome; count it for the denominator; Grids: two dice = 6 × 6 = 36 equally likely cells
  3. Apply: Sample space: HH, HT, TH, TT (4 equally likely) P(exactly one head) = 2/4 = 1/2
  4. Check: Check the units named in the question and sense-check the size of your answer.
  5. Answer: 1/2

Tip: "Show working - method marks > answer marks."

Worked Example 2: Multi-step

Q: Two dice: find P(product is even).

  1. Break down: Separate parts?
  2. Solve each: P(odd product) requires both odd: 3 × 3 = 9 of 36 → P(odd) = 1/4 P(even) = 1 − 1/4 = 3/4
  3. Combine: The parts chain: each answer feeds the next step of the question.
  4. Final answer: M1 for the complement, A1 for 3/4. 'At least one even' questions often fall to 1 − P(both odd).
Worked Example 3: Data/Application

Q: Two dice: find P(product is even).

  1. Read data: Axes, units, scale
  2. Patterns: Trends, anomalies
  3. Explain: Why? Using possibility spaces
  4. Conclude: Evidence-based

Common Questions & Troubleshooting

Q: "Why does Sample space = every possible outcome; count it for the deno work this way?"
A: Analogy: "Two fair coins are flipped. List the sample space and find P(exactly one head).". Try re-draw or re-write the worked example from memory, then check it against the model answer.
Q: "Wrong answers on calculations."
A: Checklist: units? formula? calculator mode? sig figs?
Q: "Can't remember key terms."
A: Flashcards (term front, def+diagram back). Spaced repetition: day 1, 3, 7.
Q: "Exam wording confuses me."
A: Commands: Describe=what you see; Explain=reasons; Evaluate=pros/cons+judgement; Calculate=working+units.
Q: "Running out of time."
A: 1 mark/min. Skip hard, return. Attempt all - partial marks count.

Assessment & Model Answers

Mastery Checklist:
  • [ ] Define Possibility Spaces in own words
  • [ ] Identify features in diagram
  • [ ] Explain process step-by-step
  • [ ] Apply to unfamiliar context
  • [ ] Score 80%+ on past paper question

Model Answer: Past Paper Question

Q: Two fair coins are flipped. List the sample space and find P(exactly one head).

  • 1 mark: [Key terminology]
  • 1 mark: [Mechanism/process]
  • 1 mark: [Application/example]
  • 1 mark: [Evaluation - Higher]

Model response: "[Complete answer with expected detail/terminology]"

Why full marks: [What makes this strong]

Stretch & Challenge (Grade 8-9):
  • Synoptic links: Connect to P6-systematic-listing / P8-tree-diagrams
  • Real-world: Research use in industry, medicine or research
  • Advanced calc: Try a more challenging variant
  • Critical: "Evaluate limitations of today's model"
  • Research: Recent discovery on possibility spaces, summarise 100 words

Plenary (5 mins)

Exam Question Speed Round

5 quick questions, 1 min each. Mark together.

Assessment Criteria

Lesson 4: Exam Practice: Possibility Spaces

Duration: 50 minutes

Starter Activity (5 minutes)

Review Previous Lesson

Quick recap: write 3 key points from last lesson on possibility spaces. Use mini-whiteboard or paper.

Main Content (35 minutes)

Parent/Teacher Guide:
Before lesson: Read script below. Prepare materials. Pre-teach key vocab: P7.
If stuck: See Troubleshooting below. Break into smaller steps.
Extension: See Stretch & Challenge section.
Teaching Script (35 mins):
Mins 0-5 - Hook: "Today: Possibility Spaces. Goal: by the end you can two fair coins are flipped. List the sample space and find P(exactly one head), using the method shown step by step. Connects to listing (N5) because you'll reuse its method throughout today's work."
Mins 5-15 - Direct Instruction: 1) Define: "Possibility Spaces is..." 2) Key principle: "Most important:..." 3) Draw diagram, label live. 4) Real example: "Like Two fair coins are flipped. List the sample space and find P(exactly one head). - a real example worked through in full..."
Mins 15-25 - Guided Practice: Ex1: Teacher models. Ex2: Student tries with guidance. Ex3: Student independent.
Mins 25-35 - Independent Practice: 3-5 questions. Immediate feedback.
Worked Example 1: Basic

Q: Two fair coins are flipped. List the sample space and find P(exactly one head).

  1. What is asked? Two
  2. Recall knowledge: Sample space = every possible outcome; count it for the denominator; Grids: two dice = 6 × 6 = 36 equally likely cells
  3. Apply: Sample space: HH, HT, TH, TT (4 equally likely) P(exactly one head) = 2/4 = 1/2
  4. Check: Check the units named in the question and sense-check the size of your answer.
  5. Answer: 1/2

Tip: "Show working - method marks > answer marks."

Worked Example 2: Multi-step

Q: Two dice: find P(product is even).

  1. Break down: Separate parts?
  2. Solve each: P(odd product) requires both odd: 3 × 3 = 9 of 36 → P(odd) = 1/4 P(even) = 1 − 1/4 = 3/4
  3. Combine: The parts chain: each answer feeds the next step of the question.
  4. Final answer: M1 for the complement, A1 for 3/4. 'At least one even' questions often fall to 1 − P(both odd).
Worked Example 3: Data/Application

Q: Two dice: find P(product is even).

  1. Read data: Axes, units, scale
  2. Patterns: Trends, anomalies
  3. Explain: Why? Using possibility spaces
  4. Conclude: Evidence-based

Common Questions & Troubleshooting

Q: "Why does Sample space = every possible outcome; count it for the deno work this way?"
A: Analogy: "Two fair coins are flipped. List the sample space and find P(exactly one head).". Try re-draw or re-write the worked example from memory, then check it against the model answer.
Q: "Wrong answers on calculations."
A: Checklist: units? formula? calculator mode? sig figs?
Q: "Can't remember key terms."
A: Flashcards (term front, def+diagram back). Spaced repetition: day 1, 3, 7.
Q: "Exam wording confuses me."
A: Commands: Describe=what you see; Explain=reasons; Evaluate=pros/cons+judgement; Calculate=working+units.
Q: "Running out of time."
A: 1 mark/min. Skip hard, return. Attempt all - partial marks count.

Assessment & Model Answers

Mastery Checklist:
  • [ ] Define Possibility Spaces in own words
  • [ ] Identify features in diagram
  • [ ] Explain process step-by-step
  • [ ] Apply to unfamiliar context
  • [ ] Score 80%+ on past paper question

Model Answer: Past Paper Question

Q: Two fair coins are flipped. List the sample space and find P(exactly one head).

  • 1 mark: [Key terminology]
  • 1 mark: [Mechanism/process]
  • 1 mark: [Application/example]
  • 1 mark: [Evaluation - Higher]

Model response: "[Complete answer with expected detail/terminology]"

Why full marks: [What makes this strong]

Stretch & Challenge (Grade 8-9):
  • Synoptic links: Connect to P6-systematic-listing / P8-tree-diagrams
  • Real-world: Research use in industry, medicine or research
  • Advanced calc: Try a more challenging variant
  • Critical: "Evaluate limitations of today's model"
  • Research: Recent discovery on possibility spaces, summarise 100 words

Plenary (5 mins)

Exam Question Speed Round

5 quick questions, 1 min each. Mark together.

Assessment Criteria

📝 Mark Scheme Guidance

How examiners mark P7: Read the command word carefully — State = one word/phrase (1 mark), Describe = pattern or detail (2 marks), Explain = reason with "because" (2–3 marks), Compare = similarities AND differences, Evaluate = both sides + conclusion. Method marks are awarded for correct working even if the final answer is wrong. Always show your working — unexplained answers score zero for AO2.

Success on P7 questions: Underline the command word, count the marks (one mark per point expected), and answer in the format the command word demands.

Board Notes & Revision Links

This lesson is examined by: AQA 8300 | Edexcel 1MA1 | OCR J560 | Eduqas C300 | CCEA M-units. Tier and paper details vary - always check your board's current specification.

Follow-up revision: P7-possibility-spaces on GCSE Revise (notes, flashcards and auto-graded target tests for this exact topic).

📐 Reference Diagram

START Condition true? Yes No Do A Do B

✏️ Draw-Along Instructions

Parent/teacher: Draw the key diagram for probability: start with the main structure, add labels with arrows, then annotate with the key facts from the lesson. Use a ruler for straight lines.

Display the reference diagram (or draw it live) while pupils copy. Check each label as it is added.

Homework & Consolidation

Recommended Resources

🎓 Smart Lesson (Guided)