Download Conjecture Practice Sheet

Describe a pattern in the sequence of numbers. Predict the next number.
1. 1, 2, 6, 24, …
2. 0, 3, 8, 15, 24, …
Complete the conjecture based on the pattern you observe in the specific cases.
3. Conjecture: For any two numbers a and b, the product of (𝑎 + 𝑏) and (𝑎 − 𝑏) is always
equal to __?__.
2
4 −2
2
6 −3
(2 + 1) × (2 − 1) = 3 = 22 − 12
(4 + 2) × (4 − 2) = 12 =
(3 + 2) × (3 − 2) = 5 = 32 − 22
(6 + 3) × (6 − 3) = 27 =
2
2
Show the conjecture is false by finding a counterexample.
4. Conjecture: All odd numbers are prime.
5. Conjecture: The square of the sum of two numbers is equal to the sum of the squares
of the two numbers. That is, (𝑎 + 𝑏)2 = 𝑎2 + 𝑏 2
6. Define conjecture:
7. Define counterexample: