Lesson Notes By Weeks and Term v3 - Primary 5
Tossing coins and throwing of die
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Tossing coins and throwing of die
Download the Lessonotes Mobile Nigeria 2025 app for faster lesson access on Android and iPhone.
Subject: General Mathematics
Class: Primary 5
Term: 2nd Term
Week: 4
Theme: Everyday Statistics
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
Pupils should be able to: Record in data from, experiments on coin to ssing and dice throwing Identify various chance events in the ir daily life activities
This section explains the core ideas necessary for understanding and teaching the topic.
A. Chance Events: A chance event is an event whose outcome cannot be predicted with certainty. When something happens by chance, it means there is an element of unpredictability about what the result will be. For example, when playing "ludo," one cannot predict with certainty which number will appear on the die.
B. Experiment: In the context of probability, an experiment is an activity or process that produces an observable result or outcome. Examples include tossing a coin, throwing a die, or spinning a spinner.
C. Outcome: An outcome is any one of the possible results of an experiment.
Example 1 (Coin Toss): When a coin is tossed, the possible outcomes are either a "Head" (H) or a "Tail" (T).
Example 2 (Die Throw): When a standard six-sided die is thrown, the possible outcomes are the numbers 1, 2, 3, 4, 5, or
6. D.
Tally Marks (Tallying): Tally marks are a quick and easy way to record counts in groups of five. They are used to count occurrences of specific outcomes during an experiment.
Counting System: 1: | 2: || 3: ||| 4: |||| 5: |||| (The fifth mark crosses the previous four to form a bundle, making it easy to count in fives). 6: |||| |
E. Tossing Coins: When a fair coin is tossed, there are two equally likely outcomes: Head (H): The side of the coin showing the national emblem or a notable figure (e.g., the Nigerian Coat of Arms or a national hero).
Tail (T): The other side of the coin (e.g., the numerical value or another design). The set of all possible outcomes for a single coin toss is {Head, Tail}. Worked
Example: Tossing a Coin A pupil tosses a N10 coin 10 times and records the outcomes.
Step 1: Prepare a recording table. | Outcome | Tally | Frequency | | :------ | :---- | :-------- | | Head (H)| | | | Tail (T)| | | Step 2: Perform the experiment and record.
Let's assume the results were: H, T, H, H, T, H, T, T, H,
H. Toss 1: H -> | Toss 2: T -> | Toss 3: H -> || Toss 4: H -> ||| Toss 5: T -> || Toss 6: H -> |||| Toss 7: T -> ||| Toss 8: T -> |||| Toss 9: H -> |||| (This is the fifth Head, so bundle it)
Toss 10: H -> |||| | (This is the sixth Head)
Step 3: Complete the table. | Outcome | Tally | Frequency | | :------ | :------ | :-------- | | Head (H)| |||| | | 6 | | Tail (T)| |||| | 4 | | Total | | 10 |
F. Throwing a Die: A standard die is a cube with six faces, each marked with a different number of spots from 1 to
6. When a fair die is thrown, each of these six outcomes is equally likely. The set of all possible outcomes for a single die throw is {1, 2, 3, 4, 5, 6}. Worked
Example: Throwing a Die A pupil throws a die 15 times and records the outcomes.
Step 1: Prepare a recording table. | Outcome | Tally | Frequency | | :------ | :---- | :-------- | | 1 | | | | 2 | | | | 3 | | | | 4 | | | | 5 | | | | 6 | | | Step 2: Perform the experiment and record.
Let's assume the results were: 3, 5, 1, 2, 4, 6, 3, 5, 1, 2, 4, 6, 3, 5,
1. Throw 1: 3 -> | Throw 2: 5 -> | Throw 3: 1 -> | Throw 4: 2 -> | Throw 5: 4 -> | Throw 6: 6 -> | Throw 7: 3 -> || Throw 8: 5 -> || Throw 9: 1 -> || * Throw 10: 2 | | | 6 | | | Step 2: Perform the experiment and record.
Let's assume the results were: 3, 5, 1, 2, 4, 6, 3, 5, 1, 2, 4, 6, 3, 5,
1. Throw 1: 3 -> | Throw 2: 5 -> | Throw 3: 1 -> | Throw 4: 2 -> | Throw 5: 4 -> | Throw 6: 6 -> | Throw 7: 3 -> || Throw 8: 5 -> || Throw 9: 1 -> || Throw 10: 2 -> || Throw 11: 4 -> || Throw 12: 6 -> || Throw 13: 3 -> ||| Throw 14: 5 -> ||| * Throw 15: 1 -> ||| Step 3: Complete the table. | Outcome | Tally | Frequency | | :------ | :------ | :-------- | | 1 | ||| | 3 | | 2 | || | 2 | | 3 | ||| | 3 | | 4 | || | 2 | | 5 | ||| | 3 | | 6 | || | 2 | | Total | | 15 | This section outlines a sequence of activities to facilitate learning.
Phase 1: Introduction and Engagement (10 minutes)
Teacher Activity: Begins by asking learners questions about daily events that are uncertain.
Examples: "Will it rain today?", "Who will win the football match between Kano Pillars and Enyimba?", "What number will I get if I throw this ludo die?". Explains that these are "chance events" – events whose outcomes cannot be precisely predicted.
Student Activity: Learners respond to the teacher's questions and share their own examples of uncertain events from their daily lives in Nigeria.
Phase 2: Concept Development and Demonstration (15 minutes)
Teacher Activity: Introduces a N10 or N20 coin and a standard die. Asks learners about the possible outcomes when tossing the coin (Head, Tail). Writes these on the board. Asks learners about the possible outcomes when throwing the die (1, 2, 3, 4, 5, 6). Writes these on the board. Explains and demonstrates how to use tally marks to record frequencies, emphasizing the group of five system (||||). Performs a short demonstration of tossing a coin 5 times, recording the results using tally marks on the board. Performs a short demonstration of throwing a die 5 times, recording the results using tally marks on the board. Ensures learners understand the structure of the tally table (Outcome, Tally, Frequency).
Student Activity: Observe the coin and die. Participate in discussions about possible outcomes. Pay close attention to the teacher's demonstration of tallying. Ask questions for clarification.
Phase 3: Group Experiments and Recording (30 minutes)
Teacher Activity: Organizes learners into small groups (e.g., 4-5 learners per group).
Distributes materials to each group: one N10 or N20 coin, one standard die, plain paper or exercise books, and pens/pencils. Provides clear instructions for the first experiment: "Each group will toss the coin 20 times." "Design a tally table in your book for Head and Tail." "One learner tosses the coin, another records the tally, and others observe." "After 20 tosses, count the frequencies and fill in the 'Frequency' column." Monitors groups, provides assistance, and ensures correct tallying techniques are applied. After the coin experiment, provides instructions for the second experiment: "Each group will throw the die 20 times." "Design a tally table in your book for outcomes 1 to 6." "Repeat the process: one throws, another records, others observe." "After 20 throws, count the frequencies." Encourages groups to discuss their results.
Student Activity: Work cooperatively in groups. Draw appropriate tally tables in their books. Take turns performing the experiments (tossing the coin, throwing the die). Accurately record the outcomes using tally marks. Calculate and record the frequencies for each outcome. Discuss findings within their groups.
Phase 4: Class Discussion and Real-life Connections (15 minutes)
Teacher Activity: Calls on groups to share their results from both experiments. Notes some results on the board to highlight variations between groups. Facilitates a discussion on why results might differ slightly between groups (randomness). Guides learners to identify other chance events in their daily lives.
Prompts with questions like: "When your parent decides who fetches water, what do they sometimes do?" (Coin toss), "What about when Nigeria plays Ghana in football – can you predict the exact score?" (No, chance event), "Is it guaranteed that a particular politician will win an election?" (No, voting outcomes can be uncertain). Emphasizes that understanding chance helps in making informed decisions, even when outcomes are uncertain.
Student Activity: Present their group's tally results to the class. Participate in the class discussion, comparing results and understanding variations. Brainstorm and share examples of chance events they observe in their Nigerian communities and daily routines. The teacher guides learners through these questions, providing immediate feedback.
Question 1: A pupil tossed a N50 coin 12 times.
The results were: H, T, T, H, H, T, H, H, T, H, T,
H. Create a tally table and record these results.
Solution 1: Step 1: Create the table. | Outcome | Tally | Frequency | | :------ | :---- | :-------- | | Head (H)| | | | Tail (T)| | | Step 2: Record the tallies. H, T, T, H, H, T, H, H, T, H, T, H Heads: |||| ||| Tails: |||| | Step 3: Complete the table. | Outcome | Tally | Frequency | | :------ | :------- | :-------- | | Head (H)| |||| ||| | 7 | | Tail (T)| |||| | | 5 | | Total | | 12 |
Commentary: This question directly assesses the ability to record outcomes using tally marks, a core performance objective.
Question 2: A ludo player threw a die 10 times.
The numbers obtained were: 6, 2, 4, 6, 1, 3, 5, 6, 2,
4. Record these results in a tally table.
Solution 2: Step 1: Create the table. | Outcome | Tally | Frequency | | :------ | :---- | :-------- | | 1 | | | | 2 | | | | 3 | | | | 4 | | | | 5 | | | | 6 | | | Step 2: Record the tallies. 6, 2, 4, 6, 1, 3, 5, 6, 2, 4 1: | 2: || 3: | 4: || 5: | 6: ||| Step 3: Complete the table. | Outcome | Tally | Frequency | | :------ | :------ | :-------- | | 1 | | | 1 | | 2 | || | 2 | | 3 | | | 1 | | 4 | || | 2 | | 5 | | | 1 | | 6 | ||| | 3 | | Total | | 10 |
Commentary: This reinforces the tallying skill with a die, which has more outcomes than a coin, requiring more attention to detail.
Question 3: Which of the following is a chance event? A. The sun rising in the East. B. Throwing a die and getting a '5'. C. The day after Monday is Tuesday.
D. Boiling water at 100 degrees Celsius will produce steam.
Solution 3: The correct answer is
B. Throwing a die and getting a '5'.
Explanation: A, C, and D are certain events that will always happen under normal conditions. Throwing a die involves an unpredictable outcome, as any number from 1 to 6 could appear. Getting a '5' is one of the possible chance outcomes.
Commentary: This assesses the ability to identify chance events in daily life.
Question 4: A teacher asked students to predict if their local football club, 'Kaduna United', would win their next match.
The predictions were recorded: | Prediction | Tally | Frequency | | :--------- | :---- | :-------- | | Win | |||| || | 7 | | Lose | |||| | 5 | | Draw | ||| | 3 | How many students predicted that Kaduna United would lose the match?
Solution 4: From the table, the 'Lose' row has a tally of |||| , which corresponds to a frequency of
5. So, 5 students predicted that Kaduna United would lose the match.
Commentary: This requires learners to interpret pre-existing tally data, applying their understanding of frequency from tally marks. ---
Sports and Games: Coin Toss for Kick-off: In Nigerian football leagues (e.g., NPFL), a coin toss is used to decide which team starts with the ball or which goal they will attack. This is a common chance event observed by many.
Board Games: Games like Ludo, Snakes and Ladders, or Whot (card game) heavily rely on the chance outcomes of throwing a die or shuffling cards. Understanding that the outcome is random helps manage expectations and appreciate the fairness of the game.
Decision Making: Arbitration: When two children in a Nigerian home disagree on who should do a simple chore (e.g., wash plates, sweep the compound), an adult might suggest a coin toss to decide fairly, recognizing the equal chance of Head or Tail. This teaches them about random selection for impartial decisions.
Everyday Predictions and Expectations: Weather: While advanced weather forecasting exists, simple daily observations ("Will it rain today in my village?") are chance events. Learners can relate the unpredictability of a coin toss to the unpredictability of daily weather, especially during the rainy season.
Market haggling: While skillful, the final agreed price in a negotiation in a Nigerian market can have an element of chance, depending on the mood of the seller, the buyer's persistence, and unseen factors.