Year 3 · Mathematics · Probability
Describing chance
Talking about whether everyday events are likely, unlikely, certain or impossible, and testing simple predictions with coin tosses or coloured counters in a bag.
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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
- Describe everyday events as certain, likely, unlikely or impossible.
- Explain choices using what they know about how often events happen.
- Make a prediction and test it with coin tosses or coloured counters in a bag.
Success looks like
- I can use the words certain, likely, unlikely and impossible correctly.
- I can say why an event is likely or unlikely.
- I can predict which colour I will pick from a bag, test it and talk about what happened.
The big idea
We can describe how likely something is to happen using four words: certain, likely, unlikely and impossible. Think of them as a line from 'cannot happen' to 'will definitely happen'.
Impossible events cannot happen: a cat will lay an egg. Certain events will definitely happen: after Monday comes Tuesday. Likely events will probably happen: it will be warm on a summer day. Unlikely events probably will not happen, but could: finding a coin on the footpath.
Ask your child to explain choices. 'Why is it unlikely?' A good answer uses what they know: 'Because it doesn't happen very often.' Some events depend on where you live or the time of year, so different answers can be right if the reason makes sense.
Now test chance with an experiment. Put 8 red and 2 blue counters in a bag. Ask, 'If you pick one without looking, which colour is more likely?' Most children will say red, because there are more of them. That is a prediction.
Pick a counter, record its colour with a tally mark and put it back. Do this 20 times. Usually red comes up many more times than blue — but not always in exactly the same way. Blue is unlikely, not impossible, so it will probably turn up sometimes.
Toss a coin too. Heads and tails are equally likely, so over many tosses you get roughly the same number of each, but you can still get several heads in a row. Each toss is a fresh chance.
- Impossible → unlikely → likely → certain.
- More of a colour in the bag makes it more likely to be picked.
- A prediction is a careful guess; an experiment tests it.
Worked examples
Describing an event
Is it certain, likely, unlikely or impossible that the sun will rise tomorrow?
- Think about every morning: the sun always rises.
- It will definitely happen.
Answer: It is certain.
Predicting from a bag
A bag has 8 red counters and 2 blue counters. Which colour are you more likely to pick?
- Count each colour: 8 red and 2 blue.
- There are more red counters, so there are more chances to pick red.
- Blue is still possible, but it is unlikely.
Answer: Red is more likely to be picked. Blue is unlikely.
Testing with a coin
Predict how many heads you will get in 10 coin tosses, then test it.
- Heads and tails are equally likely, so predict about 5 heads.
- Toss the coin 10 times, recording H or T with tally marks.
- Compare: you might get 4, 5, 6 or even 7 heads. Close to half is what we expect.
Answer: A sensible prediction is about 5 heads, and the result will usually be close to 5 but not always exactly 5.
Practice check
Have a go, then check your answers. Each answer comes with an explanation.
Answer guide for parents
A dog will grow wings and fly. Which word describes this?
impossible — Dogs cannot grow wings, so this cannot happen. It is impossible.
Tomorrow will be the day after today. Which word describes this?
certain — This will definitely happen, so it is certain.
A bag has 9 yellow counters and 1 green counter. Picking green is …
unlikely — There is only 1 green out of 10 counters, so it could happen but probably will not. It is unlikely.
A bag has 9 yellow counters and 1 green counter. Which colour are you more likely to pick?
yellow — There are many more yellow counters, so yellow is more likely.
A bag has only blue counters. Picking a blue counter is …
certain — Every counter is blue, so you will definitely pick blue. It is certain.
A bag has only blue counters. Is picking a red counter certain, likely, unlikely or impossible?
impossible — There are no red counters in the bag, so it cannot happen.
You toss a coin. Which is true?
Heads and tails are equally likely — A fair coin has one heads side and one tails side, so each is equally likely.
You toss a coin 3 times and get heads every time. What about the next toss?
Heads and tails are still equally likely — A coin does not remember earlier tosses. Each toss is a fresh, equal chance.
Watch out for
- Thinking 'unlikely' means 'impossible'. Show that the blue counter does come out sometimes, even though there are only 2.
- Believing that after several heads, tails is 'due'. Explain that each toss is a fresh chance and the coin cannot remember.
- Expecting experiment results to match predictions exactly. Talk about results being close to what we expect, not exactly the same.
Tips for parents
- Use chance words in everyday talk: 'It's likely to rain — let's take an umbrella.'
- Always put the counter back in the bag before the next pick so the chances stay the same.
- Ask your child to predict first and explain why, then test it — the reasoning matters more than being right.
Go further
- Make your own bag so that red is likely and blue is unlikely, then test it with 20 picks.
- Draw a chance line from impossible to certain and place pictures of everyday events along it.
- Toss a coin 20 times, record the results with tally marks and compare heads with tails.
About 35 minutes
You'll need
- A coin
- A non-see-through bag or sock
- Coloured counters, blocks or buttons (for example, 8 red and 2 blue)
- Paper and pencil for recording results with tally marks
Key words
- certain
- Will definitely happen.
- likely
- Will probably happen, but it is not certain.
- unlikely
- Probably will not happen, but it could.
- impossible
- Cannot happen at all.
- predict
- Say what you think will happen before you try it.
- outcome
- A result of an experiment, such as heads or tails.
Still tricky?
For parents
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