Spot the Mistake: Math, Science & Arguments · Answer Key

Check the answers together. If an answer is different from yours, talk about how each of you got there. Both ways of thinking are worth hearing.

1. Solving equations
A kid asks the AI: “Can you check my equation answers?”
The AI answers: Sure! Here are four solved equations:
- Statement A: If 3x = 12, then x = 4.
- Statement B: If x + 7 = 15, then x = 8.
- Statement C: If 2x + 1 = 9, then x = 5. ← the mistake
- Statement D: If x/2 = 6, then x = 12.
Answer: C. Subtract 1 from both sides: 2x = 8. Then divide by 2: x = 4. Plugging x = 5 back in gives 11, not 9.
2. Fractions and percents
A kid asks the AI: “Tell me about fractions and percents!”
The AI answers: Here are four facts:
- Statement A: 25% of 80 is 20.
- Statement B: 1/4 is the same as 0.25.
- Statement C: 10% of 50 is 5.
- Statement D: 3/5 is bigger than 3/4. ← the mistake
Answer: D. With the same top number, the fraction with the bigger bottom number is smaller. 3/5 = 0.6 is less than 3/4 = 0.75.
3. Geometry
A kid asks the AI: “Give me some geometry facts.”
The AI answers: Here are four geometry facts:
- Statement A: The angles in a triangle add up to 180°.
- Statement B: A square has four equal sides and four right angles.
- Statement C: A circle's diameter is half its radius. ← the mistake
- Statement D: The area of a rectangle is length × width.
Answer: C. The diameter goes all the way across the circle, so it equals two radii. The radius is half the diameter, not the other way around.
4. Negative numbers
A kid asks the AI: “How do negative numbers work?”
The AI answers: Here are four rules:
- Statement A: −3 is less than −1.
- Statement B: The absolute value of −7 is 7.
- Statement C: A negative times a negative is negative. ← the mistake
- Statement D: Zero is neither positive nor negative.
Answer: C. Multiplying two negatives gives a positive: (−2) × (−3) = 6. A negative times a positive is negative.
5. Science claims
A kid asks the AI: “Tell me about physics and matter!”
The AI answers: Here are four science facts:
- Statement A: Plants make food using sunlight in photosynthesis.
- Statement B: In a vacuum, a hammer and a feather fall at the same rate.
- Statement C: Heavier objects always fall much faster than light ones, even with no air. ← the mistake
- Statement D: Atoms are the basic building blocks of matter.
Answer: C. Without air resistance, all objects fall at the same rate. A feather falls slowly in air only because of air resistance.
6. Arguments
A kid asks the AI: “Help me think about arguments.”
The AI answers: Here are four statements about reasoning:
- Statement A: If all cats are mammals and Tom is a cat, then Tom is a mammal.
- Statement B: An ad hominem argument attacks the person instead of their idea.
- Statement C: One example always proves a rule is true for everyone. ← the mistake
- Statement D: Two things happening together does not prove one caused the other.
Answer: C. A single example is not enough to prove a general rule. One counterexample, though, can disprove it.

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