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Thinking Skills Foundations

Drawing Valid Conclusions

This lesson teaches you to draw valid conclusions — statements the given facts guarantee to be true — by chaining the facts step by step, and to reject conclusions that reverse a rule or are merely possible.

  • Follow a chain of facts to a forced conclusion.
  • Reject a conclusion that reverses a rule.
  • Reject a conclusion that is only possible, not guaranteed.
Free sample lesson — reading only

Lesson overview

What this free sample teaches

Choose the conclusion the facts force and name the steps that prove it.

Focus

  • Valid conclusion: what the facts guarantee.
  • Deductive chain: steps each forced by a rule.
  • Direction: a rule runs only one way.

What gets tested

  • Following facts to a forced conclusion.
  • Rejecting a reversed rule.
  • Rejecting a merely-possible conclusion.

Quick guide

  • Chain the facts step by step.
  • Move along each rule the way it is stated.
  • Accept only what must be true, not what could be.

Success criteria

  • You can state the forced conclusion.
  • You can show the chain of steps.
  • You can explain why a tempting option is not guaranteed.

teach

Teach: accept only the conclusion the facts force

A valid conclusion must be true if the facts are true — not merely possible, likely, or word-matched.

Drawing-conclusions questions ask what must follow from given facts. The trap is to choose something that could be true or that reuses the same words. A valid conclusion is one the facts guarantee: if every fact is true, it cannot be false.

Deductive reasoning is a chain of forced steps. You start from the facts you are given and move only where a rule lets you. If 'all club members are in Year 6' and 'Priya is a club member', then 'Priya is in Year 6' is forced — it cannot be false while the facts are true. A valid conclusion is locked in by the facts.

Direction matters. A rule runs one way: 'all club members studied fractions' does not mean 'all who studied fractions are club members'. Swapping the two halves of a rule is the most common logic error, because the same words appear in both. Always move along a rule in the direction it is stated, never backwards.

Claim no more than the facts force. 'Must be true' is a high bar: an option that is merely possible, or true only sometimes, does not pass. If you can imagine the facts all being true while the option is false, then the option is not a valid conclusion. Test each option by trying to break it against the facts.

The most tempting wrong answer reuses the question's words in a new, unsupported way, or states something likely but not guaranteed. Both feel right because they sound related. Reject any option you cannot force from the facts step by step, and keep only the one that the facts make certain.

Valid conclusion

a statement the facts guarantee to be true.If the facts hold, it cannot be false.

Deductive chain

a series of steps each forced by a rule.Move only where a rule allows.

Reversal error

swapping the two halves of a rule.A rule runs one way; reversing it is invalid.

Possible vs forced

what could be true vs what must be true.'Must be true' rejects the merely possible.
Anatomy of a drawing-conclusions question
  1. Question cluewhich must be true, what follows, which conclusion is valid, or what can we be certain of
  2. Core evidencethe stated facts and rules, used only in the direction they run
  3. Reasoning movechain the facts step by step and accept only what they force to be true
  4. Trap checkan option that reverses a rule, or is only possible rather than guaranteed
  5. Answer shape... must be true, because ... so ...

The moveMove from the facts along the rules to the forced conclusion, then reject the reversed or merely-possible option.

  • You can follow a chain of facts to a forced conclusion.
  • You can reject a conclusion that reverses a rule.
  • You can reject a conclusion that is only possible, not guaranteed.

show

Show: a worked example

Watch a strong reasoner prove an answer, then lift it to scholarship level.

Read the problem and the question, then follow the worked thinking. The Selective answer proves the point efficiently; the Scholarship answer adds control while staying grounded in the facts.

Full problem: chain the facts

Question: Using only these facts, which statement must be true?

The Chess Club

Three facts are known about a school chess club:

  • Every member of the chess club is in Year 6.
  • Everyone in Year 6 has studied fractions.
  • Priya is a member of the chess club.

Using only these three facts, we want to know what must be true about Priya.

  1. Step 1 - Decode the question and name what to look for

    Name the exact thinking the question wants before you start.

    The phrase 'must be true' tells me this is a deductive question: I need the conclusion the facts force, not one that is merely possible or likely. So I will follow the facts step by step and accept only what they guarantee.

    • What the question is really askingThe student names what to look for first, so the search has a clear target.
    • What not to confuseNaming the question type heads off the nearest wrong move before it starts.

  2. Step 2 - Reasoning chain: clue -> rule -> step -> answer

    Follow the strong reasoner's path from the facts to the answer.

    Follow the chain the facts force.

    • Fact: Priya is in the chess club. Rule: every club member is in Year 6. So Priya is in Year 6.
    • Fact: Priya is in Year 6. Rule: everyone in Year 6 has studied fractions. So Priya has studied fractions.
    • Effect: Each step is forced by a stated fact, so the conclusion is guaranteed, not just likely.
    • Answer: Priya has studied fractions.
    • Clue to ruleThe proof step names the exact fact or rule, not a general impression.
    • Step and effectThe student shows what each step forces and how it decides the answer.

  3. Step 3 - Common wrong answer: spot the trap

    See why a tempting answer is wrong before choosing.

    Common wrong answer: Everyone who has studied fractions is in the chess club.

    Why students choose it: It reuses the same words — fractions and chess club — so it sounds connected.

    Why it is wrong: It reverses the logic. The facts say club members have studied fractions, not that fraction-studiers are club members. Many Year 6 students have studied fractions without being in the club. A conclusion must follow in the direction the facts run.

    Corrected reasoning: All the facts guarantee is that Priya, a club member, has studied fractions.

    • Why it tempts studentsA trap usually uses a real fact, which is why students choose it too quickly.
    • Corrected reasoningThe fix shows which fact or rule changes the answer, not just that it is wrong.

  4. Step 4 - The answer (Selective standard)

    Accurate, concise and proven from the facts.

    Priya has studied fractions. The facts chain together: Priya is in the chess club, every club member is in Year 6, so Priya is in Year 6; and everyone in Year 6 has studied fractions, so Priya has too. Each step is forced by a stated fact, so this conclusion must be true.

    • Direct answerThe first sentence answers the question instead of circling it.
    • Proof from the factsThe model ties each step back to a stated fact or rule.

  5. Step 5 - Aim higher: a Scholarship-level answer

    The same answer with more control and nuance.

    The only guaranteed conclusion is that Priya has studied fractions, and it follows by chaining the facts in one direction: club member -> Year 6 -> studied fractions. The reasoning is valid because each link is a stated rule, not a guess. The tempting errors all run the chain backwards or widen it: 'everyone who studied fractions is in the club' reverses a rule, and 'all Year 6 students are in the club' invents a link the facts never give. A valid conclusion uses the facts only in the direction they point, and claims no more than they force.

    • How the steps interactThe stronger answer connects the facts into a chain rather than listing them.
    • Controlled reasoningIt goes further than the Selective answer but keeps pointing at the facts.

  6. Step 6 - Why the Scholarship answer is stronger

    Compare the two model answers like a marker would.

    Selective AnswerScholarship AnswerWhy It Is Stronger
    States the forced conclusion with the chain.Shows the chain runs one way only.Stronger reasoning: it explains why the direction matters.
    Rejects the reversed statement.Names reversal and over-widening as the errors.Better exam control: the traps are understood, not just avoided.
    Stays accurate and concise.Adds why a valid conclusion claims no more than forced.Controlled answer: richer but still proof-based.
    • Selective vs ScholarshipThe comparison shows the upgrade in thinking, not just a longer answer.
    • What to imitateStudents can copy the move: connect the facts and explain why the trap fails.

compare

Compare: a word-matched guess vs a forced conclusion

The difference between sounding connected and being guaranteed.

Both students looked at the same problem. One stops at a first impression; the other proves the answer from the facts and rules. Markers reward the second.

A reversed rule

Everyone who has studied fractions is in the chess club.

The forced conclusion

Priya has studied fractions, because she is a club member, club members are in Year 6, and Year 6 students have studied fractions.

Reading the question

Weaker: Connects words that appear together.Stronger: Follows the facts in the direction they run.A valid conclusion moves the way the rules point.

Direction

Weaker: Reverses a rule (fractions to club).Stronger: Keeps the rule's direction (club to fractions).Reversing a rule is not a valid step.

How much it claims

Weaker: Claims more than the facts give.Stronger: Claims only what the facts force.A conclusion must be guaranteed, not just possible.

guide

Guide: student checkpoint

Do one small reasoning move before independent practice.

Reread the worked problem and question. Now pause like a strong reasoner: find the rule, name the trap, or upgrade a basic answer before you work on your own.

Two facts: 'All the red boxes are heavy.' and 'This box is red.' In one sentence, state what must be true and why.

Want feedback on your own answer? Get started to practise with instant marking.

  • State the conclusion the facts force.
  • Move along each rule in the right direction.
  • Reject a conclusion the facts only make possible.