Mathematics
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50 mins
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+95 XP
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IWB/Projector/Large Screen
Dice
Coin

Chance: Likely, Unlikely, Certain, Impossible

Discover where everyday events sit on the certain-to-impossible scale. Investigate fair and unfair spinners, sort real-world examples, and learn why chance takes time to even out.

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    1 - Getting Started ~4 mins

    Illustration for Getting StartedHands up: if I roll this die once, how sure are you that a 6 comes up? Would you bet your break-time snack on it?

    Key point

    Some things always happen. Some never happen. Most things sit somewhere in between. Today we sort them.

    👇 Mark your steps as done as you complete them.

    +5 XP

    2 - Watch and Notice ~9 mins

    Look at each one on the board. As the die is rolled again and again, watch the bars for each face grow. If the die is fair, no single face runs away with the game.

    Now a spinner with four equal parts. Every part is the same size, so landing on any one is equally likely.

    Last, a spinner with one giant part. Is that a fair spinner? Watch where it wants to land.

    👇 Mark your steps as done as you complete them.

    +10 XP

    3 - Sort the Events in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy, write each of these events on its own line. Beside each one, mark it with a letter: C for certain, L for likely, U for unlikely, or I for impossible. Underline any you were unsure about.

    • The sun will rise tomorrow.
    • I will roll a 7 on this die.
    • It will rain somewhere in Ireland this week.
    • A tossed coin will land on heads.
    • Our whole class will grow wings by home time.
    • The next car past the gate will be red.
    +10 XP

    4 - Try It Together ~10 mins

    Key point

    Today we explore an unfair spinner. Half of it is red. A quarter is blue. A quarter is green.

    We'll spin it many times and watch which colour grows the tallest bar. Before each run, say aloud which colour you think will win most.

    +15 XP

    5 - Class Challenge ~8 mins

    We work through two chance jobs together at the board.

    Task 1: sort these events on the scale

    Key point

    Place each event on the certain-to-impossible scale.

    • A tossed coin lands on tails.
    • Rolling a number less than 7 on a die.
    • Rolling an even number on a die.
    • The next person through the door is wearing shoes.

    Task 2: design a fair spinner

    Sketch a fair spinner for red, blue and green so every colour has the same chance, then talk through a quick prize game on it.

    If there is time, the stretch is to explain why, even after thirty rolls of a fair die, the six bars are almost never perfectly level.

    Where does each event sit on the certain-to-impossible scale, and can you build a fair spinner?

    ['Task 1: sort the four events onto a certain → likely → unlikely → impossible line.', 'Task 2: design a spinner with three equal parts so each colour is equally likely, then play a quick prize game and check every player has the same chance.', "Stretch (if time): explain why a fair die's six bars are almost never perfectly level after thirty rolls."]

    1. Task 1: mark 'a tossed coin lands on tails' on the scale.
    2. Task 1: mark 'rolling a number less than 7 on a die' on the scale.
    3. Task 1: mark 'rolling an even number on a die' on the scale.
    4. Task 1: mark 'the next person through the door is wearing shoes' on the scale.
    5. Task 2: design a fair three-part spinner for red, blue and green.
    6. Stretch: after 30 rolls of a fair die, why are the six bars rarely level?

    Ways to start:

    • Start Task 1 by finding any event you are sure is certain or impossible — put those at the two ends first.
    • For Task 2, ask: are all the parts the same size?

    Stretch:

    • Design a spinner where blue is twice as likely as red — is it still fair?
    • How many rolls do you think you would need before the die's bars looked nearly level?

    Record: Sort cards on the board's scale line; sketch the fair spinner in the copy.

    Answers & strategies (teacher)
    1. Task 1: mark 'a tossed coin lands on tails' on the scale. — Between likely and unlikely — an even chance (about halfway).
    2. Task 1: mark 'rolling a number less than 7 on a die' on the scale. — Certain — every face is less than 7.
    3. Task 1: mark 'rolling an even number on a die' on the scale. — An even chance — three of six faces are even.
    4. Task 1: mark 'the next person through the door is wearing shoes' on the scale. — Certain — in school, everyone comes in wearing shoes.
    5. Task 2: design a fair three-part spinner for red, blue and green. — Make all three parts the same size, so each has a 1 in 3 chance.
    6. Stretch: after 30 rolls of a fair die, why are the six bars rarely level? — Chance is not a guarantee — thirty rolls is too few to even out. The bars level only over a very long run.
    +15 XP
    Pupil practice
    Module 7 · Data, Chance and the Co-ordinate Plane Data & Chance
    Lesson 100 · Chance: Likely, Unlikely, Certain, Impossible
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