Mini Minds Hub · Free printable
Fairground Probability Fair: Free Printable Worksheet for Year 8
- ForYear 8
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Fairground Probability Fair is a free printable maths worksheet for Year 8 (ages 12 to 13) in Key Stage 3. Children unscramble the words, then test the stalls. They work out theoretical probability, read tally results and decide whether a stall is fair. Page 2 gives the grown up notes, help ideas, a stretch task and the answers.
It comes from the Mini Minds Hub, the free library of printables from Jaques of London, the British games and toy company that has been making games for families since 1795. Print both pages, give page 1 to your child or class and keep page 2 for yourself. Black and white printing works well.
What is on the sheet
Children start by unscrambling the four words, which sets up the language of the topic. Then they visit the fairground stalls. They calculate theoretical probability, read tally results and compare the two. Hook a Duck is one of the stalls. Questions ask for a number, a method or a short reason, and there is space to answer each one. Children also judge whether a stall is fair and explain their thinking in a line.
- On Hook a Duck, how many wins should you expect from 40 goes?
- Is Hook a Duck fair to players? Explain in one line.
Worked example: a different stall
A spinner has 8 equal sections and 2 of them win a prize. How many wins should you expect from 60 goes?
This is a different stall from the ones on the sheet, with different numbers. It shows two ways to work.
Method 1: use the probability- There are 8 equal sections and 2 win, so the probability of a win is 2/8.
- 2/8 simplifies to 1/4. The value stays the same.
- Expected wins = probability × number of goes.
- 1/4 × 60 = 15.
- 2 wins in every 8 goes is the same rate as 1 win in every 4 goes.
- 60 ÷ 4 = 15, so there are 15 groups of 4 goes.
- Each group gives 1 win on average, so that is 15 wins.
Why use a fairground for probability?
Fairground stalls are full of chance. A spinner, a pond of ducks or a lucky dip each have a set of possible outcomes, and players want to know their chances of winning. That gives probability a real purpose. Year 8 learners can ask a sensible question: if the stall owner gives a prize, will the stall still make money, or will players do better than they should?
Theoretical probability is what should happen when outcomes are equally likely. Relative frequency is what actually happened in an experiment, found by dividing the number of times something happened by the total number of tries. With only a few tries the two can be far apart. With many tries they usually move closer together. Comparing them is a core skill at Key Stage 3.
Skills and curriculum link
- Theoretical probability
- Relative frequency
- Judging fairness
- Expected outcomes
- Comparing theory with results
- Explaining reasoning
Ideas for helping with probability
- Probability scaleEvery probability sits between 0 and 1. An event that cannot happen is 0 and one that is certain is 1. Fractions, decimals and percentages can all describe the same chance.
- Equally likely outcomesTheoretical probability only works simply when every outcome has the same chance. Check this before counting favourable outcomes out of the total.
- Expected is an averageAn expected number is what you would get on average over many goes. A single set of goes can be higher or lower.
- Fair means balancedA game is fair when what players can expect to win matches what they put in. Ask what is paid, what is won and how often.
Key words
- ProbabilityA number from 0 to 1 that tells you how likely something is to happen.
- OutcomeOne possible result, such as a spinner landing on a certain section.
- Theoretical probabilityThe chance worked out from the situation, by counting favourable outcomes out of all equally likely outcomes.
- Relative frequencyThe number of times something happened divided by the number of tries in an experiment.
- TallyA way to record results by drawing a mark each time, grouped in fives.
- FairNot giving an unfair advantage to anyone. In a game, the chances and prizes are balanced.
How to use it
- Print both pages. Page 1 is for the child. Keep page 2, which has the notes and answers.
- Ask your child to unscramble the four words first. Talk about what each one means before moving on.
- Work through the stall questions. Ask them to show their method, not just write a number.
- Check against page 2 together. Ask, "How did you decide that?" The reasoning matters as much as the answer.
- Come back another day and redo any tricky questions. Repeating a familiar sheet builds confidence.
Help, stretch and game ideas
If it feels too hard
Draw the 10 sections of the wheel and shade the winning ones before answering. Count the shaded sections, then count all of them. Write the chance as a fraction first. Turn it into a decimal or percentage only afterwards.
To stretch confident children
Change the prize on Hook a Duck so the stall is exactly fair, and show your working. Then explain in a sentence or two why a stall owner might not want to run a stall that is exactly fair.
Make it a game
Make a paper spinner with a pencil and a paper clip. Mark equal sections, and shade some as wins. Predict the number of wins in a set of spins, then spin and tally. Compare your prediction with the result.
Mistakes to watch for
Watch forA child writes the chance of winning as wins to losses, such as 2 to 6, instead of wins out of all outcomes.
Try thisAsk, "How many outcomes are there in total?" Write the probability as wins over total, such as 2/8, before simplifying.
Watch forA child thinks the expected number must happen exactly, and says the stall is broken when it does not.
Try thisExplain that expected means the average over many goes. Run a few more tallies and see how results move around the expected number.
Watch forA child compares a tally from only a few goes with the theory and decides the stall is unfair.
Try thisAsk how many goes were tallied. Discuss why more goes give a more trustworthy relative frequency.
Talk about it
- What does it mean for a stall to be fair?
- Why might your tally results differ from the theory?
- If you did many more goes, what would you expect to happen to the relative frequency?
- How can a fraction, a decimal and a percentage all describe the same chance?
- Would you rather be the player or the stall owner? Why?
- How could you change a stall to make it fairer?
Take it off the page
Paper spinner
Make a spinner from card, a pencil and a paper clip. Split it into equal sections and shade some as winning. Spin it many times and keep a tally.
Bag of counters
Put counters of two colours in a bag. Work out the chance of picking one colour. Pick, record and replace many times, then compare your results with the theory.
Design a stall
Draw your own fairground stall on paper. Write down the outcomes, the chance of winning and a prize that would make it fair.
Who it is for
Parents
Read the sheet through first. Sit beside your child for the first few questions, then let them lead. Ask them to explain their reasoning aloud, and use page 2 to check answers together.
Teachers
Use it as a starter, a plenary, an early finisher task, supply cover or homework. It supports the probability strand at Key Stage 3. Page 2 offers support and stretch ideas for mixed ability groups.
Home educators
Print it as part of a wider maths plan. It pairs well with real experiments using dice, spinners or counters. It is free to print again for brothers, sisters or revision later on.
Where this fits in maths
Before this sheet, children meet probability as a scale from 0 to 1, list outcomes and use fractions to describe simple chances. They also need to be comfortable simplifying fractions and converting between fractions, decimals and percentages.
After this, learners move on to combined events, sample spaces, tree diagrams and the idea that relative frequency becomes a better estimate with more trials. These ideas build towards more formal probability work in Key Stage 4.
Questions parents and teachers ask
- What age is Fairground Probability Fair for?
It is written for Year 8 (ages 12 to 13) in Key Stage 3. It can also help confident Year 7 learners or Year 9 pupils who want revision on theoretical probability and relative frequency.
- What will children practise?
They practise calculating theoretical probability and comparing it with tally results in a fairground stall setting. They also judge whether a stall is fair and explain their reasoning in words.
- How do I use it?
Print both pages. Children unscramble the four words first, then work through the stall questions, comparing theory with tally results. Keep page 2 for the grown up, who can check the answers and use the notes.
- What if it feels too hard?
Let the child draw the 10 sections of the wheel and shade the winning ones before answering. Seeing the sections makes it easier to count favourable outcomes and write the probability as a fraction.
- Is it free?
Yes. It is free to print for home and classroom use. You can print it again for brothers, sisters or a revision session a few weeks later.
- Can teachers use it in class?
Yes. Teachers can use it as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing, and page 2 has support and stretch ideas for mixed ability groups.
- Do I need to print in colour?
No. It prints well in black and white on plain A4 paper. Colour is not needed to complete any of the activities, so it is easy to print at home or school.
Preview the full PDF
Made by Jaques of London, making games for families since 1795. A printable supports classroom learning and does not replace a teacher.