|
|
- 1Ask learners: If you toss a coin, what are all the possible outcomes? Write H and T on the board; ask learners to call out what each means.
- 2Show a bag with 5 red and 3 blue counters. Ask: If I pick one counter without looking, which colour am I more likely to pick? Why?
|
- INTRODUCTION TO SAMPLE SPACE AND EVENTS
- 1Define sample space: Write on board 'Sample space = all possible outcomes of an experiment'. Use coin toss: sample space = {H, T}.
- 2Define event: An event is one or more outcomes we are interested in. Example: Getting heads = 1 outcome from 2 possible.
- 3Guide learners to understand that probability measures how likely an event is to happen.
- 4Use concrete examples: tossing a coin, rolling a die, picking marbles from a cloth bag.
- EXPRESSING PROBABILITY AS A FRACTION
- 5Write on board: Probability = (Number of favourable outcomes) / (Total number of possible outcomes).
- 6Modelled example: Kofi has a spinner with 4 equal sections: red, blue, green, yellow. What is the probability the spinner lands on red? Answer: 1/4 (1 favourable outcome, 4 total outcomes).
- 7Guided practice: Give each pair of learners a die. Ask: What is P(rolling a 3)? What is P(rolling an even number)? Learners write fractions in exercise books.
- 8Use the spinner and dice as physical manipulatives. Emphasize that each section/face must be equally likely.
- CONVERTING FRACTIONS TO DECIMALS AND PERCENTAGES
- 9Show: 1/4 = 0.25 (divide numerator by denominator using calculator). Write this step-by-step on board.
- 10Show: 0.25 = 25% (multiply decimal by 100). Write 0.25 × 100 = 25.
- 11Guided practice: Learners convert P(red on spinner) = 1/4 to decimal (0.25) and percentage (25%). Repeat with P(even on die) = 3/6 = 1/2 = 0.5 = 50%.
- 12Demonstrate calculator use: 1 ÷ 4 = 0.25. Repeat for 3 ÷ 6.
- EXPRESSING PROBABILITY AS A RATIO
- 13Introduce ratio notation: P(event) can also be written as 'Favourable outcomes: Total outcomes'. Example: P(red on spinner) = 1: 4.
- 14Show equivalence: 1/4 = 0.25 = 25% = 1: 4.
- 15Learners in pairs: Write down one more example (e.g., rolling a 2 on a die) and express it as fraction, decimal, percentage, and ratio.
- 16Emphasize that all four forms express the same probability.
|
- 1Coin
- 2Six-sided die
- 3Spinner with 4 equal coloured sections
- 4Cloth bag
- 5Coloured counters (red and blue)
- 6Calculator
- 7Whiteboard and marker
|
- 1Ask: What does sample space mean? Invite one learner to explain to the class.
- 2Ask: How do we convert a fraction to a percentage? One learner models on the board: 1/2 = 0.5 = 50%.
Exercise
- 1A spinner has 6 equal sections: 3 blue, 2 green, 1 red. Write the probability of landing on green as a fraction, decimal, percentage, and ratio.
|
|
|
- 1Quick quiz: Show learners a die. Ask: What is P(rolling a 4)? Learners write the answer as a fraction on mini-whiteboards and hold up.
- 2Peer check: Learners swap mini-whiteboards with a neighbour. Check: 1/6. Ask 2 learners to explain why the numerator is 1 and denominator is 6.
|
- DEEPER PRACTICE WITH NON-EQUALLY LIKELY OUTCOMES
- 1Present: Ama's bag contains 4 red balls, 2 yellow balls, 3 green balls. Total = 9 balls. What is P(picking red)?
- 2Learners solve: P(red) = 4/9. Convert to decimal (≈0.44) and percentage (≈44%). Use calculator.
- 3Error analysis activity: Show wrong working on board: 'P(red) = 4 balls, so probability is 4.' Ask learners: What mistake was made? Why is this wrong? Discuss: probability is a fraction between 0 and 1, not just a count.
- 4Reinforce: probability must be expressed as a ratio or fraction, not as a raw count.
- REAL-LIFE PROBLEM SOLVING WITH TWO-STAGE EVENTS
- 5Scenario: Kwame buys a lottery ticket at Makola Market. The lottery seller says 50 tickets are sold. Only 1 ticket wins a prize. What is the probability Kwame's ticket wins?
- 6Guided solution: P(win) = 1/50 = 0.02 = 2%. Write all forms on board.
- 7Second scenario: Yaa attends a raffle at school. 200 raffle tickets are sold. She buys 5 tickets. What is the probability she wins? P(win) = 5/200 = 1/40 = 0.025 = 2.5%. Learners calculate in pairs using calculator.
- 8Use real Ghanaian market context. Emphasize that more tickets = better chance.
- EXPRESSING PROBABILITY AS A SIMPLIFIED RATIO
- 9Teach: Ratios can be simplified. Example: 4: 9 cannot be simplified further (GCD is 1). But 4: 8 can be simplified to 1: 2.
- 10Guided example: A trotro driver picks passengers randomly. In a trotro with 15 seats, 10 are occupied. P(picking an empty seat) = 5/15 = 1/3 = 1: 3.
- 11Learners in pairs: Simplify ratios. Start with 6: 12, 8: 10, 3: 9. Write simplified forms and corresponding probabilities as fractions.
- 12Use trotro and market contexts to make scenario relatable.
- MIXED PRACTICE AT VARIED DIFFICULTY
- 13Assign learners mixed problems: (a) Simple: P(odd on a die). (b) Moderate: P(picking a specific colour from a bag with unequal numbers). (c) Harder: Express probability of an event and its complement (e.g., P(not landing on red) on a 4-colour spinner).
- 14Learners work individually, then peer-mark using a simple checklist: Did they write as fraction? As decimal? As percentage? As ratio?
- 15Complement: P(not event) = 1 - P(event). Introduce briefly, focus on conversion accuracy.
|
- 1Calculator
- 2Mini-whiteboards and markers
- 3Exercise books
- 4Dice
- 5Spinner
- 6Coloured counters in a cloth bag
- 7Ruler
|
- 1Exit ticket: Each learner writes on a slip of paper one thing they learned today and one question they still have. Collect and review 3-4 slips aloud.
- 2Invite one learner to share their 'one thing learned' with a partner.
Exercise
- 1Kofi runs a fruit stall at Kejetia Market. He has 8 mangoes, 5 pawpaws, and 7 oranges. A customer picks one fruit without looking. Express the probability of picking a mango as a fraction, decimal, percentage, and ratio.
|
|
|
- 1Speed challenge: Display 5 quick questions on board. Learners answer in pairs on mini-whiteboards. Example: 'A bag has 2 red and 8 blue balls. Write P(red) as a fraction.' (Answer: 2/10 = 1/5). Check answers together.
- 2Team game: Divide class into two teams. Call out a fraction (e.g., 3/4). Each team races to convert to decimal (0.75) and percentage (75%). First team with correct answer scores a point.
|
- INTRODUCTION TO TREE DIAGRAMS FOR TWO-STAGE EVENTS
- 1Model: Toss a coin, then spin a spinner with red and yellow. Draw a tree diagram on board step-by-step. First branch: H or T. Second branches from each: R or Y. Label outcomes: HR, HY, TR, TY.
- 2Count: Total outcomes = 4. P(H and R) = 1/4 = 0.25 = 25%. Write on diagram.
- 3Guided practice: Learners draw a tree diagram for: Roll a die (1-6), then pick a card (Red or Black). How many outcomes? What is P(rolling a 3 and picking Red)?
- 4Use ruler. Label branches clearly. This prepares for multi-stage probability calculations.
- USING A TWO-WAY TABLE TO ORGANIZE OUTCOMES
- 5Draw a 2×2 table on board: Rows = Coin outcomes (H, T), Columns = Spinner outcomes (Red, Yellow). Fill cells with all outcomes: (H,R), (H,Y), (T,R), (T,Y).
- 6Count: 4 outcomes total. P(T, Y) = 1/4 = 0.25 = 25%. Write in cell.
- 7Learners create their own table: Pick a card from a deck (Red or Black) and roll a die (Odd or Even). Complete the 2×2 table. Calculate P(Black and Odd).
- 8Tables are clearer than diagrams for some learners. Both methods express the same probability.
- REAL-WORLD SCENARIO: CUSTOMIZING A SCHOOL LUNCH
- 9Scenario: At school canteen, learners choose one starch (Jollof Rice, Banku, Tuo Zaafi) and one protein (Fish, Chicken, Beans). How many meal combinations?
- 10Create a table: Rows = 3 starches, Columns = 3 proteins. Total cells = 9 combinations.
- 11Questions: What is P(choosing Banku and Chicken)? Express as 1/9 ≈ 0.111 ≈ 11.1%. If a learner is told no Tuo Zaafi, how many outcomes now? P(Banku and Chicken | no Tuo) = 1/6.
- 12Learners apply: Create their own real scenario using tree or table (e.g., choosing a trotro route: Accra-Kumasi or Accra-Takoradi; and time: Morning or Evening).
- 13Use Ghanaian food and transport. Introduce conditional probability gently without heavy notation.
- LEARNERS CREATE AND SWAP EXAMPLES
- 14In pairs: Each pair designs their own two-stage probability scenario (e.g., pick a number 1-5, then pick a colour). They draw a tree diagram or table and calculate 3 probabilities.
- 15Swap: Pairs exchange with another pair. The receiving pair solves the given problems and checks answers.
- 16Share: 2-3 pairs present their scenario to the class. Whole class checks the calculations.
- 17Peer teaching deepens understanding. Scaffold by providing a template.
|
- 1Ruler
- 2Graph board
- 3Whiteboard and marker
- 4Mini-whiteboards and markers
- 5Exercise books
- 6Calculator
- 7A coin and spinner
- 8Template for tree diagram (printed or drawn on board)
|
- 1Celebrate mastery: Ask 2-3 learners to share one key insight from today's lesson. Examples: 'A tree diagram helps organize all outcomes.' 'A table makes it easy to count.'
- 2Confidence check: Learners hold up 1-5 fingers to show how confident they feel about drawing a tree diagram and calculating probabilities (1 = not confident, 5 = very confident). Acknowledge growth from Day 1.
Exercise
- 1Abena spins a spinner with 3 equal sections (Red, Blue, Green) and rolls a four-sided die numbered 1-4. (a) Draw a tree diagram showing all outcomes. (b) How many total outcomes? (c) Express P(Green and rolling a 2) as a fraction, decimal, and percentage.
|
|
|
- 1Learner-created problems: Ask 3-4 learners to pose a probability question they invented at home (or during a break). Class solves on mini-whiteboards. Check answers together.
- 2Reflection question: Which method do you prefer to organize outcomes—a tree diagram or a table? Why? Learners discuss in pairs.
|
- CROSS-TOPIC CONNECTION: PROBABILITY AND RATIO SIMPLIFICATION
- 1Review: Simplify the ratio 12: 18. (Answer: 2: 3). Now express 2: 3 as a fraction and decimal. (Answer: 2/5 is incorrect; 2/(2+3) = 2/5; clarify: the ratio 2:3 means out of 5 parts, 2 are favourable, so probability = 2/5 = 0.4 = 40%).
- 2Guided example: Kwesi's chop bar has 15 customers: 9 order waakye, 6 order red red. Express as a ratio (9:6 = 3:2). If a random customer enters, P(orders waakye) = 9/15 = 3/5 = 0.6 = 60%. Ratio form: 3: 5 (where 5 = total parts).
- 3Learners solve: A farmer plants 20 fields: 12 with maize, 8 with cassava. Express P(picking a maize field) in all forms. Simplify ratio first.
- 4Clarify: probability ratio shows (favourable) : (total), not part-to-part ratio.
- INVESTIGATION: FAIR VS. UNFAIR (BIASED) EVENTS
- 5Question: Is tossing a fair coin fair? (Yes, each outcome has equal chance: P(H) = P(T) = 1/2.) Is pulling a ticket from a raffle fair? (Yes, if all tickets are in the drum and one is drawn randomly.)
- 6Introduce bias: Suppose a spinner has sections of different sizes: Red occupies 60%, Blue 40%. Is this fair? (No. P(Red) = 0.6, P(Blue) = 0.4, not equal.) Explain: fairness means all outcomes equally likely.
- 7Real scenario: At Makola Market, a trader claims their die is fair, but when rolled 60 times, 6 appears 25 times. Is it fair? Calculate P(rolling 6) = 25/60 ≈ 0.42 ≈ 42%. Is this close to the fair probability of 1/6 ≈ 16.7%? No—suspect bias.
- 8Learners investigate: Given simulated roll data (e.g., from a previous class or provided table), calculate observed probabilities for each face and compare to fair probability of 1/6.
- 9Introduce fairness concept. Connect to critical thinking: question claims; check with data.
- PROJECT: DESIGN A FAIR GAME FOR A SCHOOL FETE
- 10Scenario: The school fete committee asks learners to design a probability-based game using a spinner, die, or bag of counters. The game must be fair (equal chance of winning for all players).
- 11Learner groups (3-4 per group): Design the game setup, draw a tree diagram or table, calculate P(winning) in all forms, and write a rule card explaining the game.
- 12Gallery walk: Post designs on walls. Learners circulate, read each design, and verify fairness by checking the probabilities. Provide sticky notes for feedback.
- 13Whole class: 2-3 groups present their game to the class. Classmates ask: 'Is this fair? How do you know?' Presenters justify using probability calculations.
- 14Authentic, creative application. Learners explain and defend reasoning—high-order thinking.
- MIXED REVIEW: ALL FOUR REPRESENTATIONS
- 15Give each pair a multi-part task: Scenario involves two stages (e.g., 'Yaw picks a snack from a tray with 4 cookies and 6 groundnuts, then plays a game with a coin'). Learners must: (1) Draw a tree diagram. (2) Create a two-way table. (3) List all outcomes. (4) Calculate 3 given probabilities as fractions, decimals, and percentages.
- 16Peer review: After completion, pairs check a neighbour's work using a rubric (Is the diagram complete? Are conversions correct? Is work shown clearly?).
- 17Consolidates all four representation methods and conversion skills.
|
- 1Ruler
- 2Graph board
- 3Whiteboard and marker
- 4Mini-whiteboards and markers
- 5Exercise books
- 6Calculator
- 7Spinners, dice, bags with counters
- 8Sticky notes
- 9Template for game design (printed)
- 10Rubric for peer review
|
- 1Gallery walk summary: Invite 1-2 learners to share what they learned from reviewing peers' game designs. Did any design surprise them? Why?
- 2Whole-class reflection: Ask 'What is one concept from this week that you now understand better than on Tuesday?' Learners raise hands and share briefly. Celebrate growth.
Exercise
- 1Design your own two-stage probability scenario using a local Ghanaian context (e.g., choosing a meal at a chop bar, picking items at a market). (a) Draw a tree diagram or two-way table. (b) Calculate the probability of one specific outcome in all four forms: fraction, decimal, percentage, and ratio. (c) Explain whether the scenario is fair or biased, and why.
|
