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Case File: Prime Suspects: Free Printable Quiz for Year 8
- ForYear 8
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Case File: Prime Suspects is a free printable maths quiz for Year 8 (ages 12 to 13), in Key Stage 3. Children play detective. They test each claim about numbers, answer multiple choice questions on primes, multiples and prime factors, then crack the key words. Page 2 gives the grown-up notes, help and stretch ideas, 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 child and keep page 2 for yourself. Black and white printing works well.
What is on the sheet
Children work through a detective style case file about number. They test claims, using a quick factor check before they tick. They answer multiple choice questions with three answers each, such as spotting a prime, finding a multiple of two numbers, or choosing the right product of prime factors. At the end, they unscramble the key words to finish the case.
- Which of these numbers is prime?
- Which number is a multiple of both 7 and 4?
- Which shows 60 as a product of prime factors?
Worked example: prime factors of 90
Write 90 as a product of prime factors.
This is a different number from the ones on the sheet. It shows two ways to find prime factors.
Method 1: factor tree- Split 90 into any two factors, such as 9 and 10.
- Split each of those: 9 = 3 × 3 and 10 = 2 × 5.
- Stop when every end of the tree is prime. The ends are 3, 3, 2 and 5.
- Write them in order and multiply back to check: 2 × 3 × 3 × 5 = 90.
- Divide by the smallest prime that fits: 90 ÷ 2 = 45.
- Divide 45 by 3 to get 15, then 15 by 3 to get 5.
- 5 is prime, so stop.
- The divisors were 2, 3, 3 and 5.
Quick tests for prime suspects
Divide by small primes
For a number under 121, try dividing by 2, 3, 5 and 7. If one of them divides it exactly, and that prime is not the number itself, the number is not prime. If none of them divides it, the number is prime. Remember that 2, 3, 5 and 7 are prime themselves. Above 120 this test is not enough, because 121 = 11 × 11.
Use divisibility clues
A number ending in 0, 2, 4, 6 or 8 divides by 2. If the digits add to a multiple of 3, the number divides by 3. A number ending in 0 or 5 divides by 5. These clues save a lot of dividing.
Grow a factor tree
Split a number into two factors. Keep splitting until every end is a prime. Then multiply the ends together to see if you get the number you started with.
Multiply back to check
After finding prime factors, multiply them all. If the answer is not the starting number, a factor is missing or wrong. This quick check catches most slips.
Why primes matter in Year 8
A prime number is a whole number greater than 1 with exactly two factors, 1 and itself. Every other whole number above 1 can be built by multiplying primes together. That is why primes are often called the building blocks of number. In Year 8, children begin to use this idea, not just spot primes in a list.
Prime factors link several topics. They help with finding common factors and common multiples, and they come back when simplifying fractions and working with indices. Detective style tasks suit this topic well. Each claim has to be tested and justified, so children practise giving a reason, not just a tick.
Prime number facts
- The list of prime numbers never ends. There is always another one.
- Every whole number above 1 is either prime or can be written as a product of primes.
- Apart from the order, a number can be written as a product of primes in only one way.
- Computers use very large primes to help keep information secret online.
- Mathematicians still use computers to search for larger and larger primes.
Skills and curriculum link
- Spotting prime numbers
- Factors and multiples
- Prime factorisation
- Testing a claim
- Reasoning and justifying
- Number vocabulary
Ideas to help with the case
- Divisibility cluesQuick tests tell you if a number divides by 2, 3 or 5 without a calculator. Learn them once and use them on every claim.
- Factor pairsList pairs of numbers that multiply to make a number. A number with a pair other than 1 and itself is not prime.
- Times tablesA multiple of a number sits in its times table. To find a number in two tables, list the first few multiples of each and look for a match.
- Factor treesA tree turns a number into primes one split at a time. Different trees for the same number end with the same primes.
Key words
- Prime numberA whole number greater than 1 that has exactly two factors, 1 and itself.
- FactorA whole number that divides another number exactly, with nothing left over.
- MultipleA number in the times table of another number. 20 is a multiple of 5.
- Prime factorA factor that is also a prime number.
- ProductThe answer when numbers are multiplied together.
- Common multipleA number that is a multiple of two or more numbers. 15 is a common multiple of 3 and 5.
How to use it
- Print both pages. Page 1 is for the child. Keep page 2 for the grown-up.
- Read the sheet together the first time. Talk about each choice before anyone ticks.
- Work alone or in pairs. Check each claim with a quick factor test before ticking.
- Unscramble the key words last, once the questions are done.
- Check against the answers on page 2. Talk about any wrong answers, then come back to the sheet another day.
Help, stretch and game ideas
If it feels too hard
Give the child a list of primes under 50. Let them test numbers by dividing by 2, 3, 5 and 7. Suggest they write the test next to each claim, so they can see which numbers pass and which fail.
To stretch confident children
Ask the child to write two new true or false claims about primes, multiples or factors. They should be sure of the answers. Then they swap them with a partner, who must prove or disprove each claim and give a reason.
Make it a game
Play in pairs. Read out a claim from the sheet. Both players race to prove or disprove it, then explain the reason aloud. A point is only won if the reason is clear and correct. Swap who reads each time.
Mistakes to watch for
Watch forA child thinks every odd number is prime, for example 9.
Try thisTest it. Ask them to find a factor other than 1 and 9. Then use divisibility clues on other odd numbers.
Watch forA child mixes up factors and multiples. They say 20 is a factor of 5.
Try thisLink the words to a direction. Factors divide into a number, so 5 is a factor of 20. Multiples are found by multiplying, so 20 is a multiple of 5.
Watch forA child stops a factor tree too early. For 36 they write 4 × 9.
Try thisAsk, "Are 4 and 9 both prime?" Keep splitting until every end is prime, then multiply back to check.
Talk about it
- How do you know that number is prime? What did you test?
- Can you find a number that passes one test but fails another?
- What is the difference between a factor and a multiple?
- Why do we keep splitting a factor tree until every end is prime?
- Which claim fooled you most, and why?
- How could you check your answer in a second way?
Take it off the page
Factor pairs hunt
Pick a number and find every pair of factors on paper. Colour the numbers that have only one pair. Talk about what those numbers have in common.
Sieve of primes
Write the numbers from 1 to 50 in a grid. Cross out multiples of 2, then 3, then 5, then 7. Look at what is left and discuss why it works.
Number detective cards
Write a clue on a card, such as a multiple of 5 with two digits and an odd number. A partner works out which numbers fit.
Who it is for
Parents
Sit with your child for the first go and let them lead. You do not need to be a maths expert. Ask them to explain each test they use, and keep the answers on page 2 covered until they finish.
Teachers
Use it as a starter, plenary, early finisher task, supply cover or homework. It needs no preparation beyond printing. Page 2 has help and a stretch idea for mixed ability groups, and the Number strand link is easy to match to your planning.
Home educators
Print it as part of a wider maths plan. It suits a topic on number, and it can be used again for revision a few weeks later or for brothers and sisters. Ask your learner to talk through their reasoning.
Where this fits in maths
Before this sheet, children learn times tables, multiples and factors in primary school. They also meet the idea of a prime number and use simple divisibility tests. Year 8 builds on this by asking for reasons and for numbers written as products of primes.
After this, children can use prime factors to find common factors and common multiples. They also meet them again when simplifying fractions and working with indices. The habit of testing a claim and explaining why is useful across all of Key Stage 3 maths.
Questions parents and teachers ask
- What age is Case File: Prime Suspects for?
It is written for Year 8 (ages 12 to 13), in Key Stage 3. It can also work as revision for older children, or as a stretch task for confident Year 7 pupils who already know their factors and multiples.
- What will children practise?
They practise spotting prime numbers, using multiples and factors, and writing numbers as products of prime factors. It is set as a detective style logic task in number, so children also practise testing a claim and giving a reason.
- How do I use it?
Print both pages, give page 1 to the child and keep page 2. Children work alone or in pairs, check each claim with a quick factor test before ticking, and unscramble the key words last. Then check with the answers.
- What if it feels too hard?
Give them a list of primes under 50 and let them test numbers by dividing by 2, 3, 5 and 7. Work through the first claim together, and talk about why each choice is right or wrong.
- Is it free?
Yes. It is free to print for home and classroom use. You can print it again for brothers, sisters, other pupils or revision later on.
- How long does it take?
It depends on the child. Children can work at their own pace, in one sitting or split over two. Page 2 gives help for children who find it hard and a stretch idea for those who finish early.
- Do I need to print in colour?
No. It prints well in black and white on plain A4 paper. You only need a pencil, and no screen is needed, so it works well for quiet time, homework or a rainy day.
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.