Scheme of Work: Probability and Experiments

Subject: Mathematics | Year: 7

Class/Set: ____________ Date/Term: ____________

Intent: Students will develop a secure understanding of the probability scale, transitioning from qualitative likelihood descriptions to calculating theoretical probabilities and conducting experiments to compare relative frequency against expected outcomes.

Timeframe / Lesson	Lesson Title	Learning Objective (LO)	Key Activities / Assessment
Lesson 1	The Language of Chance	To use and interpret the probability scale.	Define: certain, likely, even chance, unlikely, and impossible. Place: various real-life events on a 0-1 probability scale.
Lesson 2	Quantifying Probability	To express probabilities as fractions, decimals, and percentages.	Convert: between FDP to describe chance. Match: numerical values (e.g., 0.25) to verbal descriptions (unlikely).
Lesson 3	Theoretical Probability	To calculate the probability of equally likely outcomes.	Apply: the formula P(Event) = (Number of favourable outcomes) / (Total outcomes). Calculate: probabilities for fair dice and spinners.
Lesson 4	Sum of Probabilities	To understand that the sum of all mutually exclusive outcomes is 1.	Calculate: the probability of an event NOT happening. Solve: missing probability problems using the 'sum to 1' rule.
Lesson 5	Mid-Unit Assessment	To demonstrate proficiency in theoretical probability.	Complete: Formative Assessment (see Checkpoint below). Review: common misconceptions via peer-marking.
Lesson 6	Experimental Probability	To calculate relative frequency from observed data.	Record: results from a series of trials. Calculate: relative frequency as (Number of successful trials) / (Total trials).
Lesson 7	The Coin Toss Experiment	To carry out a simple probability experiment.	Execute: 50 coin tosses in pairs. Tabulate: results using a tally chart and calculate the running relative frequency.
Lesson 8	Evaluating Results	To compare theoretical and experimental probability.	Analyse: why experimental results differ from theory. Explain: the effect of increasing the number of trials (sample size).

Resources Needed:

• Standard fair dice and coins.
• Probability scale wall-charts.
• Scientific calculators.
• Multi-coloured counters and opaque bags.

Formative Checkpoint: Probability Task

Task A: A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles.

1. Calculate: The probability of picking a red marble. Give your answer as a fraction in its simplest form.
2. Calculate: The probability of picking a marble that is NOT blue.

Task B: Sarah flips a coin 20 times. It lands on 'Heads' 14 times.

1. State: The theoretical probability of landing on Heads.
2. Calculate: The experimental probability (relative frequency) of landing on Heads in Sarah's experiment.
3. Explain: One reason why these two values might be different.

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⚠ TEACHER’S GUIDANCE

💡 Pedagogical Pulse

• Misconception Alert: Many Year 7 students believe that if a coin has landed on 'Heads' five times in a row, it is "due" to be 'Tails'. Explicitly teach the concept of independent events to dismantle the "Gambler's Fallacy" during Lesson 7.
• Scaffolding: For lower-attaining students, keep probabilities as fractions with denominators of 10 or 100 before moving to more complex simplification.
• Greater Depth: Challenge GDS students to design a "biased" experiment using weighted dice or unevenly distributed counters to see if they can identify the bias through relative frequency.

🔑 Answer Key & Solutions

Task A Answer: Marbles

1. P(Red): 3/10. (Total marbles = 3+5+2=10. Favourable = 3).
2. P(Not Blue): 5/10 or 1/2. (Total - Blue = 10 - 5 = 5. Or Red + Green = 3 + 2 = 5).

Task B Answer: Coin Flip

1. Theoretical Probability: 1/2 or 0.5.
2. Experimental Probability: 14/20 or 7/10 (0.7).
3. Explanation: Sarah used a small sample size (only 20 flips); experimental results rarely match theoretical probability exactly in short runs due to randomness.

📋 Delivery Checklist

• ☐ Prepare: Ensure every pair has a coin and a tally chart for Lesson 7.
• ☐ Check: Confirm students can simplify fractions before starting Lesson 3.
• ☐ Differentiate: Provide "Probability Word Mats" for EAL students to support the qualitative-to-quantitative transition in Lesson 1.