Mini Minds Hub · Free printable
Valid or Just True?: Free Printable Worksheet for Year 7
- ForYear 7
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Valid or Just True? is a free printable maths worksheet for Year 7 (ages 11 to 12). Children read a short argument in each file and mark two things: whether the logic is valid or broken (V or B), and whether the ending is true or false (T or F). It uses multiples, primes and other number facts, needs only a pencil, and page 2 gives the grown up the 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 the child and keep page 2 for yourself. Black and white printing works well.
What is on the sheet
Children fill in a table of classified files. Each file holds a short argument built on number facts. For every file they make two separate decisions. First they mark the Logic column V or B, by asking whether the facts force the ending. Then they mark the Ending column T or F, by checking it against real number facts. The two marks can disagree, and that is the point.
- File
- Classified argument
- Logic V or B
- Ending T or F
A worked example with no numbers
Facts: All dogs have wings. Rex is a dog. Ending: Rex has wings.
This example uses animals, so you can see the two decisions clearly before you move on to number arguments.
Step 1: mark the Logic- Pretend the facts are true. All dogs have wings, and Rex is a dog. Must Rex have wings? Yes. The facts force the ending, so the logic is V.
- Now forget the pretending and use real facts. Dogs do not have wings. So the ending is F.
Why separate logic from truth?
In maths, an argument is valid when the ending must follow from the facts. If the facts were true, the ending could not be false. Validity is about the shape of the reasoning, not about whether the ending happens to be right. An argument can be valid and still give a false ending if one of its facts is false. It can also be broken and still land on a true ending by luck.
Year 7 is a good time to meet this idea. Children start to see that a correct looking answer is not enough, and that a reason has to hold for every case. Multiples and primes give clear number facts to reason with. A single example that breaks an argument, called a counterexample, is a powerful tool and a first taste of proof.
Skills and curriculum link
- Logical reasoning
- Multiples and primes
- Justifying answers
- Testing with examples
- Separating logic from truth
Ideas that help with the files
- MultiplesA multiple of a number is in its times table. You find it by multiplying that number by a whole number.
- Prime numbersA prime number has exactly two factors: 1 and itself. Checking factors is the way to test one.
- CounterexampleOne number that fits the facts but breaks the ending shows that an argument is broken.
- Valid versus trueValid asks whether the facts force the ending. True asks whether the ending is correct in real maths. They are different questions.
Key words
- ArgumentA set of facts followed by an ending that is supposed to come from them.
- ValidThe ending has to follow if the facts are true. There is no way round it.
- BrokenThe facts do not force the ending. Another case could fit the facts and still break it.
- MultipleA number you get by multiplying a number by a whole number. The multiples of 4 are in the 4 times table.
- Prime numberA number with exactly two factors, 1 and itself.
- CounterexampleAn example that fits the facts but shows the ending does not always follow.
How to use it
- Print both pages. Page 1 is for the child. Keep page 2, which has the notes and answers.
- Read the first file together. Cover the ending and ask what the facts tell you.
- Mark Logic first. Ask, "Do the facts force the ending?" Then check the ending on its own with real number facts and mark T or F.
- Check against page 2. Where you disagree, ask for the reason before looking at the answer.
- Come back another day and redo any files that felt tricky. Repeating a familiar sheet builds confidence.
Help, stretch and game ideas
If it feels too hard
Test each ending with a real number first. Then, for Logic, ask whether a different number could fit the facts but break the ending. If one can, the logic is broken. Work on one file at a time and say your reasons aloud.
To stretch confident children
Write your own argument that is valid but false, and another that is broken but true. Use multiples or primes for the number facts. Swap with a partner and ask them to classify both, giving a reason for each mark.
Make it a game
Agents race to sort the files, then argue about any file where partners disagree. Each agent gets one minute to give a reason. The best reason wins the file. Keep a tally and see who wins the most.
Mistakes to watch for
Watch forA child marks Logic as V because the ending is true.
Try thisCover the ending and look only at the facts. A true ending can come from broken reasoning, so ask whether the facts force it.
Watch forA child marks Logic as B because the ending is false.
Try thisPretend the facts are true. If the ending then has to follow, the logic is V, even when the ending is false in real maths.
Watch forA child tries one number, finds it works, and decides the ending is always true.
Try thisOne example that works does not prove a claim about every number. Look for a number that fits the facts and breaks the ending.
Talk about it
- What is the difference between an argument being valid and an ending being true?
- Can an ending be true when the logic is broken? How would you show it?
- What does a counterexample do, and why is one enough?
- How did you decide whether a number was prime?
- Which file did you and your partner disagree on, and who changed their mind?
- Why might it matter in real life to check the reasoning as well as the answer?
Take it off the page
Spot the broken argument
Make up short everyday arguments, such as ones about sport or school rules. Take turns deciding whether the reasoning is valid or broken, then whether the ending is true.
Counterexample hunt
One person makes a claim about numbers, such as a pattern in a times table. Everyone else searches for a number that breaks it. Find out whether it can be broken.
Two column sort
Write short arguments on strips of paper. Sort them into four piles on the table: valid and true, valid and false, broken and true, broken and false.
Who it is for
Parents
Sit beside your child for the first file, then let them lead. Ask for the reason behind each mark rather than just the letter. If they get stuck, try a real number and see whether it fits.
Teachers
Use it as a starter, plenary, early finisher task or homework. It suits paired talk, because the best learning happens when partners disagree and have to justify a mark. Page 2 gives support and stretch ideas for mixed ability groups.
Home educators
Print it as part of a wider maths plan and pair it with work on multiples and primes. Talk through each reason aloud. The sheet is free to print again for brothers, sisters or revision a few weeks later.
Where this fits
Before this sheet, children meet multiples, factors and prime numbers in upper Key Stage 2. They learn to find them and to use times tables fluently. Here they use those number facts as evidence inside a reasoned argument.
After this sheet, Key Stage 3 moves towards algebra, generalising and proof. Children are asked to explain why a statement is always true, not just to show that it works once. Judging whether reasoning is valid, and finding counterexamples, are early steps towards that.
Questions parents and teachers ask
- What age is Valid or Just True? for?
It is written for Year 7 (ages 11 to 12), in Key Stage 3. It also suits confident Year 6 children and Year 8 children who want practice with logical reasoning.
- What do V, B, T and F mean?
V means the logic is valid and B means it is broken. T means the ending is true and F means it is false. The logic and the ending are marked separately.
- What is the difference between valid and true?
Valid means the facts force the ending. True means the ending is correct in real maths. An argument can be valid with a false ending, or broken with a true ending.
- What if it feels too hard?
Start by testing each ending with a real number. For Logic, ask whether another number could fit the facts but break the ending. Work on one file at a time and talk through the reasons.
- Is it free and screen free?
Yes. It is free to print for home and classroom use. It needs only paper and a pencil, so it works for quiet time, rainy days and school holidays.
- Can teachers use it in class?
Yes. It works as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing, and page 2 has support, stretch ideas and answers.
- Can I use it for home education?
Yes. Home educators and tutors can use it on its own or as part of a wider maths plan. It can be printed again for brothers, sisters or revision.
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.