One case that breaks the claim

Mathematics · Mathematical Thinking · ages 13-14

Name ______________________ Date ____________

What is the smallest odd composite number?
Answer: ______________
Which number disproves the claim that every number ending in 3 is prime?
- 13
- 33
- 23
- 3
What is the smallest odd composite number?
Answer: ______________
Which number disproves the claim that every odd number is prime?
- 9
- 7
- 5
Which number is a counterexample to the claim that every factor of 12 is even?
- 2
- 6
- 3
- 4
Zoe says one counterexample kills a claim, but a thousand supporting examples cannot prove it.
Circle one: True False
Give an even multiple of 3 below 10 to disprove the claim that all multiples of 3 are odd.
Answer: ______________
Which number is a counterexample to the claim that every factor of 12 is even?
- 2
- 6
- 3
Which of these claims is FALSE, meaning a counterexample exists?
- All primes are odd
- All multiples of 4 are even
- Squares of whole numbers are never negative
Every prime is odd, claims Ravi. The counterexample is the only even prime. What is it?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

9 · Odds run 1, 3, 5, 7, 9, and 9 is 3 times 3.
33 · 33 ends in 3 but equals 3 x 11, so it breaks the claim.
9 · Odd numbers start 1, 3, 5, 7, 9: 1 is neither prime nor composite, 3, 5, 7 are prime, and 9 = 3 x 3.
9 · 9 is odd but equals 3 times 3, so it breaks the claim.
3 · 3 divides 12 (12 = 3 x 4) and 3 is odd, so it breaks the claim.
True · A single break falsifies every, while support leaves cases untested.
6 · 6 is a multiple of 3 (3 x 2) and it is even, so the claim fails.
3 · 3 divides 12 and 3 is odd, so it breaks the claim.
All primes are odd · 2 is prime and even, so the first claim is false.
2 · 2 is prime (factors 1 and 2 only) and even, breaking Ravi's claim.