Mini Minds Hub · Free printable
Prime Number Pursuit: Free Printable Game for Year 7
- ForYear 7
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Prime Number Pursuit is a free printable maths game for Year 7 (ages 11 to 12), in Key Stage 3. Players use cards with numbers on them and name a prime factor to win each card. It is for 2 to 3 players, takes about 15 minutes and needs no screen. Page 2 gives the grown-up notes, help ideas, a stretch idea 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 the players and keep page 2 for the person checking. Black and white printing works well.
What is on the sheet
Players work with cards to cut out and use. Each card shows a number, and the numbers on the sheet go up to 70. On their turn, a player looks at a card and names a prime factor of it to win the card. Players also have to listen and decide whether a claim is right. Mental maths, a little bluffing and careful checking all come into play.
- 12
- 18
- 20
- 24
- 30
- 36
- 42
- 45
- 48
- 60
- 63
- 70
A worked example
Find the prime factors of 28.
This number is not a card on the sheet. It shows two ways to find prime factors.
Method 1: a factor tree- Split 28 into a factor pair: 4 × 7.
- 7 is prime, so that branch stops.
- 4 is not prime. Split it into 2 × 2. Both 2s are prime, so these branches stop.
- Divide 28 by the smallest prime, 2. 28 ÷ 2 = 14.
- Divide 14 by 2 again. 14 ÷ 2 = 7.
- 7 is prime, so stop. Check by multiplying back: 2 × 2 × 7 = 28.
What is a prime factor?
A factor of a number divides into it exactly, with nothing left over. A prime number has exactly two factors: 1 and itself. The number 1 is not prime, because it has only one factor. A prime factor is a factor that is also a prime number. So to name a prime factor of a card, you need to find a factor and check that it is prime.
Every whole number greater than 1 is either prime or can be written as a product of primes. Numbers with more than two factors are called composite numbers. Prime factors are the building blocks of a number. Later in Key Stage 3, children use them to find the highest common factor and the lowest common multiple of two numbers.
Skills and curriculum link
- Prime factors
- Mental maths
- Bluffing
- Checking by multiplying
- Reasoning out loud
This sheet supports the area below. It is matched to the published England framework. Please check it against your own school plan.
| Framework | Subject or area | Strand | Year |
|---|---|---|---|
| National Curriculum (England) | Maths | Number | Year 7 |
What children will be able to do
- I can say what a prime number is.
- I can find the prime factors of numbers up to 70.
- I can check my factors by multiplying them back.
Helpful maths ideas for this game
- Primes up to 20The primes up to 20 are 2, 3, 5, 7, 11, 13, 17 and 19. Keep them nearby. Most prime factors on the cards will come from this list.
- Divisibility cluesEven numbers divide by 2. Numbers ending in 0 or 5 divide by 5. If the digits of a number add up to a multiple of 3, the number divides by 3.
- Two is specialThe number 2 is the only even prime. Every other even number has 2 as a factor, as well as 1 and itself.
- Multiply back to checkIf you claim a prime factor, say what you multiply it by to reach the card. If the multiplication works, the factor is a real one.
Key words
- FactorA whole number that divides exactly into another number, with nothing left over.
- Prime numberA number with exactly two factors: 1 and itself.
- Prime factorA factor of a number that is also a prime number.
- Composite numberA whole number greater than 1 that has more than two factors.
- MultipleA number you get by multiplying a number by a whole number. The multiples of 5 include 5, 10 and 15.
- ProductThe answer when you multiply numbers together.
How to use it
- Print both pages. Page 1 is for the players. Keep page 2, which has the notes and answers, for the grown-up.
- Cut out the cards. Read the rules aloud together so everyone plays the same game.
- Take turns to look at a card and name a prime factor. Keep the list of primes up to 20 nearby if you need it.
- Check each claim together. Multiply back, and use page 2 to confirm answers.
- Come back another day for another round. Repeating a familiar game builds confidence.
Help, stretch and game ideas
If it feels too hard
Keep a list of primes up to 20 nearby: 2, 3, 5, 7, 11, 13, 17, 19. Try each prime in turn as a divisor. Say the division out loud. Play the first round together before players go on alone.
To stretch confident children
Ask players to give all the prime factors of a card, not just one. Then ask them to write the number as a product of its prime factors and check it by multiplying back.
Make it a game
Add a challenge: name a prime factor and say what you multiply it by to reach the card. If the group agrees the multiplication works, you win the card. If not, the card stays in the middle.
Talk about it
- How can you tell that a number is prime?
- Why is 1 not a prime number?
- Why is 2 the only even prime?
- What is the quickest way to spot a factor of a number?
- How can you check that a factor is right?
- Is a bluff easier to spot when you check by multiplying? Why?
Take it off the page
Prime hunt
Write the numbers 1 to 50 on paper. Circle the primes and cross out the rest. Say why you cross out each number.
Factor pair posters
Pick a number up to 70 that is not on the sheet. Draw every factor pair as a pair of rectangles with a pencil and ruler. Mark the prime factors with a star.
Family factor talk
At a meal, one person says a number up to 70. Everyone takes a turn to name a factor, then say whether it is prime.
Who it is for
Parents
Read the rules together, then play the first round side by side and let your child lead. Ask them how they know a factor is prime. Keep the primes list close, and praise clear reasons as well as right answers.
Teachers
Use it as a starter, plenary, early finisher task or table activity. It needs no preparation beyond printing and cutting. Page 2 gives support and stretch ideas for mixed ability groups. Listen for reasoning, not just answers.
Home educators
Print it as part of a wider maths plan. It pairs well with number talk, factor trees drawn on paper and everyday counting. It is free to print again for brothers and sisters, or for a quick revision game later.
Where this fits in learning
Children first meet prime numbers, prime factors and composite numbers in upper Key Stage 2, from Year 5, alongside factors and multiples. In Year 7, this game is a chance to practise that knowledge, recall primes quickly and use it with confidence.
Next, Key Stage 3 number work uses prime factors in more ways. Children write numbers as products of primes, and use them to find common factors and common multiples. Naming prime factors fluently and checking them by multiplying makes that work much easier.
Check it worked
Ask these when the sheet is finished. Listen for the reasoning, not just the answer.
- How can you tell that a number is prime?
- How did you find the prime factors of 60?
- How can you check that your factors are right?
Questions parents and teachers ask
- What age is Prime Number Pursuit for?
It is written for Year 7 (ages 11 to 12), in Key Stage 3. It also works as a recap game for older children, or as a stretch game for confident younger ones who know their factors.
- What will children practise?
They practise recognising prime factors of numbers up to 70. They also build mental maths, reasoning and checking by multiplying, and have some fun with bluffing, which keeps everyone listening.
- How long does it take?
It takes about 15 minutes. It is for 2 to 3 players. Keep rounds short, because two quick games work better than one long one.
- What if it feels too hard?
Keep a list of primes up to 20 nearby: 2, 3, 5, 7, 11, 13, 17, 19. Play the first round together and talk about each choice. Try each prime in turn as a divisor.
- Is it free?
Yes. It is free to print for home and classroom use. You can print it again for brothers, sisters or revision, and share it with a class or tutor group.
- Is this a screen free activity?
Yes. It is a screen free printable that needs only paper, scissors and a pencil. It works well for quiet time, rainy days and school holidays, and gets children talking and thinking.
- Do I need to print in colour?
No. It prints well in black and white on plain A4 paper. Page 2 is for the grown-up, so keep it separate until players want to check their answers.
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Made by Jaques of London, making games for families since 1795. A printable supports classroom learning and does not replace a teacher.