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Class 8
Chapter 5: Number Play
A conjecture is a guess based on patterns we see. We test it with examples; one counter-example is enough to disprove it.
Learning outcomes
- Investigate patterns in integers and primes
- Form and test conjectures with examples
Activities
- Conjecture-and-test number lab
Worked examples
Read through these first, then try the practice below.
Example 1 — Conjecture and test
Conjecture: 'The sum of two even numbers is always even.' Test with 6 and 10.
Solution: 6 + 10 = 16, which is even. Try more examples — they all work, so the conjecture seems true.
Example 2 — Find a counter-example
Conjecture: 'Every odd number greater than 1 is prime.' Find a counter-example.
Solution: 9 is odd and greater than 1, but 9 = 3 × 3, so it is not prime. The conjecture is false.
Self-do practice
Question 1 of 3 · Score 0/0True or False: One counter-example is enough to disprove a conjecture.
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