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Logic & Puzzles · Grade 6

Logic, Counterexamples and Ambiguity

Learners test reasoning the way logicians do. They work with if-then statements and see why the converse does not automatically follow, use a single counterexample to defeat an “all” claim, sort with the quantifiers all, some and none using Venn-style regions, and spot ambiguity and vagueness that make claims slippery. An optional lesson for older learners introduces necessary and sufficient conditions and the contrapositive.

  • 5 lessons
  • About 120 minutes
  • Logic check: 9 questions
  • Ways to answer: fill in the blanks, choose an answer, highlight a text, match pairs, sort into groups and arrange tiles
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What learners will discover

  • Reason with if-then statements and explain why the converse does not automatically follow.
  • Use one counterexample to show that an “all” or “every” claim is false.
  • Use the quantifiers all, some and none correctly, including with Venn-style sorting.
  • Identify ambiguity (words or sentence structures with two meanings) and vagueness, and rewrite claims to be clear.

Lessons

  1. If-then and the converse 4 steps2 practiceabout 26 min
  2. One counterexample is enough 6 steps4 practiceabout 30 min
  3. All, some and none 5 steps3 practiceabout 28 min
  4. Ambiguity and vagueness 5 steps3 practiceabout 30 min
  5. Going further: necessary, sufficient and the contrapositive 5 steps2 practiceabout 25 min
  6. Logic check 9 questions at the end

Keep exploring

Games to practice with

  • Find OllyOlly is hiding! Spot him with clues about where things are.
  • Logic HotelCheck every guest into the right room using clues like "right above" and "between".
  • SwitchworksFlip switches to light the lamps in the target pattern — in as few presses as you can.

More 6th grade logic

Guide for grown-ups