A pile of sand... or not?
Put one grain of sand on a table. Is it a heap? Of course not! Add one more. Still not a heap. Add one more... and one more... and one more...
Adding just ONE grain never seems to turn a non-heap into a heap. But if you keep going, eventually you'll have a giant heap of sand! So when did it become a heap?
This puzzle is called the Sorites Paradox (soh-RYE-teez). "Sorites" comes from the Greek word soros, which means heap.
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The Sand Lab
Add or remove ONE object at a time. When does the definition change?
Choose an object. First, add one at a time and tell us when it becomes a heap (or crowd, or tall tower). Then, remove one at a time and tell us when it stops. Test at least 3 different objects!
What did you discover?
The Paradox
A tricky argument from ancient Greece.
Reading quiz
Big Words
The vocabulary of vagueness!
Tap each card to flip it.
Match each word to its meaning
Puzzles
Build the argument, then find the line in a rainbow.
Puzzle 1: Build the paradox
Put the steps of the Sorites argument in order.
Puzzle 2: Where does BLUE end?
These 11 colors slowly change from blue to green. Tap the last color you think is still BLUE.
Now look closely. Here's the last color you called BLUE, right next to the first color you called NOT blue:
Vague or Precise?
Sorites puzzles only happen with VAGUE words.
A vague word has fuzzy edges: people can disagree about where it starts and stops (like "tall" or "a lot"). A precise word or number has a sharp, exact edge (like "5 feet tall" or "exactly 12").
🌡️ Fuzzy thinking: HOW tall?
Some thinkers say vague words come in degrees. Instead of "tall or not tall," someone can be a little bit tall. Slide to show how "tall" you think each person is (from 0% to 100%).
The Grain Thief
A strategy game about taking a heap apart, one little bit at a time.
There are 21 grains of sand. You and Professor Pebble take turns taking away 1, 2, or 3 grains. Whoever takes the LAST grain wins! (Hint: there's a secret strategy. Can you find it?)
Drawing Lines in the Real World
When does a kid become old enough?
Is a person "old enough to drive" at 15 years and 364 days? What about one day later? Nothing magic happens overnight... but laws must draw a sharp line somewhere, so everyone knows the rule. Match each rule to its line (these are U.S. and Nevada rules).
4 ways to solve the paradox
Philosophers still argue about this! Tap the solution that makes the most sense to YOU.
The Big Question
Your final written response.
Locked!
Earn all 7 badges to unlock your final assignment.
Write a thoughtful response that connects your ideas (at least 3 paragraphs and 12 sentences).