Year 4 · Mathematics · Probability
Chance experiments
Running simple experiments with coins, dice and spinners, recording outcomes and comparing what happened with what was expected.
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These lessons were written around Australian Curriculum strands and matched to UK year groups by age (Year 1 is the year a child turns 6 in England). They are not mapped to the National Curriculum in England or the curricula of Scotland, Wales or Northern Ireland, so check them against your own plans.
Learning goals
Learners will
- List the possible outcomes of tossing a coin, rolling a dice and spinning a spinner.
- Predict how often outcomes might happen and run experiments to test predictions.
- Record outcomes in a tally table and compare what happened with what was expected.
Success looks like
- I can list all the possible outcomes for a coin, a dice or a spinner.
- I can predict which outcome is more likely and explain why.
- I can record results with tallies and explain why results are not always exactly as expected.
The big idea
A chance experiment is something like tossing a coin, rolling a dice or spinning a spinner. Each go is called a trial, and each possible result is an outcome.
List the possible outcomes first. A coin has 2: heads or tails. A standard dice has 6: 1, 2, 3, 4, 5 or 6. A spinner's outcomes are the colours or numbers on its sections.
If every outcome has the same chance, they are equally likely. On a fair coin, heads and tails are equally likely. On a dice, each number from 1 to 6 is equally likely. Rolling a 7 on a standard dice is impossible.
Make a spinner: draw a circle, divide it into 4 equal sections and colour 3 red and 1 blue. Put a pencil point through a paperclip at the centre and flick the paperclip. Because 3 of the 4 sections are red, red is more likely than blue. If the sections were different sizes, the bigger sections would be more likely.
Before an experiment, predict. For 20 coin tosses we expect about 10 heads, because heads is half of the outcomes. For 20 spins of the 3-red-1-blue spinner, we expect red about 15 times, because red is 3 of the 4 equal sections.
Then carry out the trials and record them with tally marks. Compare the results with the prediction. They are usually close, but rarely exact — you might get 12 heads instead of 10. That is normal. Chance means results vary.
The more trials you do, the closer the results usually get to what you expect. Combining results from several family members, or doing 50 trials instead of 10, shows this nicely.
- Coin: 2 equally likely outcomes.
- Dice: 6 equally likely outcomes.
- Spinner: bigger sections are more likely.
Worked examples
Listing outcomes
What are all the possible outcomes when you roll a standard dice?
- Look at each face of the dice.
- The faces show 1, 2, 3, 4, 5 and 6 dots.
Answer: There are 6 possible outcomes: 1, 2, 3, 4, 5 and 6.
Predicting with a spinner
A spinner has 4 equal sections: 3 red and 1 blue. If you spin it 20 times, about how many times would you expect red?
- Red covers 3 of the 4 equal sections.
- Split 20 spins into 4 equal parts: 20 ÷ 4 = 5 spins for each section.
- Red has 3 sections: 3 × 5 = 15.
Answer: About 15 spins would be expected to land on red, though the real result may be a little different.
Comparing results with predictions
A coin is tossed 20 times: 12 heads and 8 tails. Is the coin unfair?
- We expected about 10 heads and 10 tails.
- 12 and 8 are close to 10 each.
- Small differences like this happen often by chance.
Answer: Not necessarily. The results are close to what we expected; chance makes results vary.
Practice check
Have a go, then check your answers. Each answer comes with an explanation.
Answer guide for parents
How many possible outcomes are there when you roll a standard dice numbered 1 to 6?
6 — The outcomes are 1, 2, 3, 4, 5 and 6.
Rolling a 7 on a standard dice is …
impossible — A standard dice only has the numbers 1 to 6, so a 7 cannot be rolled.
A spinner is half red and half blue. You spin it 20 times. About how many times would you expect red?
about 10 — Red is half of the spinner, and half of 20 is 10.
A spinner has 4 equal sections: 3 green and 1 yellow. Which colour is more likely?
green — Green covers 3 of the 4 equal sections, so it is more likely than yellow.
Which is more likely when you roll a standard dice?
rolling an even number — An even number can be 2, 4 or 6 (3 outcomes), but a 6 is only 1 outcome.
Mia tosses a coin 20 times and gets 13 heads and 7 tails. What is the best conclusion?
Results vary by chance, so this does not prove the coin is unfair — Chance experiments rarely match predictions exactly. More trials would give a better picture.
What are the possible outcomes of tossing a coin?
heads or tails — A coin has two sides, so the outcomes are heads or tails.
You roll a standard dice 60 times. About how many times would you expect to roll a 3?
10 — Each of the 6 numbers is equally likely, so share 60 rolls into 6 equal parts: 60 ÷ 6 = 10.
Watch out for
- Believing some numbers on a dice are 'harder' to roll, such as 6. Run a 60-roll experiment to show each number comes up roughly the same number of times.
- Expecting results to match predictions exactly. Explain that chance makes results vary, especially with small numbers of trials.
- Thinking a spinner with more colours makes each colour equally likely, even when sections are different sizes. Compare a spinner with one big and one small section.
Tips for parents
- Make predictions together before every experiment and write them down so you can compare afterwards.
- Keep experiments short but combine results across days or family members to see bigger patterns.
- Ask 'Why do you think that happened?' rather than 'Was your prediction right?'
Go further
- Make a 'tricky spinner' with unequal sections and challenge someone to predict which colour will win.
- Roll two dice, add the numbers and tally the totals for 50 rolls. Which totals come up most often?
- Design a fair game using a coin or dice and explain why each player has an equal chance of winning.
About 40 minutes
You'll need
- A coin and a standard dice (numbered 1 to 6)
- Paper, a pencil and a paperclip to make a spinner
- Coloured pencils
- Paper ruled into tally tables
Key words
- outcome
- One possible result of an experiment, such as rolling a 4.
- experiment
- A test you carry out to find out what happens.
- equally likely
- Having the same chance of happening.
- trial
- One go at an experiment, such as one coin toss.
- predict
- Say what you expect to happen before you test it.
- spinner
- A circle split into sections with a pointer or paperclip that spins.
Still tricky?
For parents
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