Lesson: Probability and Outcomes
Year: 7 | Subject: Mathematics | Time Allocation: 100%
Class/Set: ____________ Date/Term: ____________
LO (WALT): To analyse the likelihood of outcomes using the formal probability scale from 0 to 1.
Success Criteria (WILF):
- I can define and apply key probability vocabulary (Impossible, Unlikely, Even Chance, Likely, Certain).
- I can accurately place events on a linear 0–1 probability scale.
- I can express simple probabilities as fractions, decimals, and percentages.
1. Starter (15%)
- Activity: 'The Likelihood Line-Up'.
- Action: Students are presented with five scenarios on the board: 1. It will rain in London at some point this year; 2. You will grow a tail tomorrow; 3. Rolling a 4 on a standard six-sided die; 4. Tossing a coin and getting 'Heads'; 5. Picking a blue marble from a bag of 10 red marbles.
- Challenge: Students must rank these from 'least likely' to 'most likely' on mini-whiteboards and justify their choice for the middle scenario.
2. Main Activity (70%)
Teacher Input:
- Define: Introduce the five Tier 3 vocabulary terms: Impossible (0), Unlikely, Even Chance (0.5), Likely, and Certain (1).
- Model: Draw a horizontal 10cm line on the board. Label the left extremity '0' and 'Impossible' and the right extremity '1' and 'Certain'.
- Explain: Demonstrate that 'Even Chance' sits exactly at 0.5 (or 1/2). Explain that all probabilities are numerical values between 0 and 1; they cannot be negative or greater than 1.
- Demonstrate: Show how to convert a worded probability into a fraction and a decimal. Example: A bag has 4 sweets; 1 is lemon. The probability of picking lemon is 1/4, which is 0.25. Place this on the scale between 'Impossible' and 'Even Chance'.
- Check: Ask students to identify the decimal value for 'Likely' if it is halfway between 'Even Chance' and 'Certain' (0.75).
Student Task:
- Task 1: The Master Scale:
- Construct: Draw a precise 20cm probability scale in exercise books using a sharp pencil and ruler.
- Label: Mark 0, 0.25, 0.5, 0.75, and 1.0. Annotate each point with the correct British English probability term.
- Task 2: Scenario Mapping:
- Calculate: Determine the numerical probability (as a fraction and decimal) for the following:
a) Rolling an even number on a standard die.
b) Picking a 'Heart' from a standard deck of 52 cards.
c) Selecting a vowel from the word 'MATHS'.
- Plot: Place each of these outcomes accurately on the scale created in Task 1.
- Task 3: Probability Reasoning:
- Justify: Write a short paragraph explaining why a probability of 1.2 is mathematically impossible. Use the term 'certainty' in the explanation.
3. Plenary (15%)
- Check: 'Hinge Question' - If the probability of an event happening is 0.3, is it more likely to happen or not happen? Students hold up 'Heads' (Likely) or 'Tails' (Unlikely) using a coin or hand gesture.
- Consolidate: Exit ticket - Students must write down one event that has a probability of exactly 0.
4. Resources
- Rulers and pencils.
- Mini-whiteboards and pens.
- Scenario cards/Deck of cards for demonstration.
- Probability Scale templates (for SEND support).
⚠ TEACHER’S GUIDANCE
💡 Pedagogical Pulse
- Delivery: Conduct the starter as a 'stand up if...' activity to encourage oracy and debate before moving to formal scale construction.
- Misconception Alert: Year 7 students often confuse 'unlikely' with 'impossible'. Emphasise that any value above 0 has a mathematical chance of occurring, no matter how small.
- Scaffolding: For lower-attainment groups, provide a pre-drawn 0–1 scale divided into tenths to assist with decimal placement.
🎯 Task Answers & Solutions
Task 1 Answer: The Master Scale
- 0 = Impossible
- 0.25 = Unlikely
- 0.5 = Even Chance
- 0.75 = Likely
- 1 = Certain
Task 2 Answer: Scenario Mapping
- a) Answer: 3/6 or 1/2 (0.5). Position: Even Chance.
- b) Answer: 13/52 or 1/4 (0.25). Position: Unlikely.
- c) Answer: 1/5 (0.2). Position: Between Impossible and Unlikely.
Task 3 Answer: Probability Reasoning
- Answer: A probability of 1 represents total certainty (100%). It is impossible to be more than 100% certain that an event will occur, therefore 1.2 is not a valid probability.
📋 Lesson Readiness Checklist
- ☐ Ensure all students have a ruler for Task 1; precision is key for the 0-1 scale.
- ☐ Check that 'standard deck' definitions are understood (some students may not know there are 52 cards or 4 suits).
- ☐ Prepare 'Tier 3' word mats for EAL students containing the keywords: Outcome, Probability, Scale, Certainty.