Conjectures and counterexamples worksheets 2025

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If we look at data over the precipitation in a city for 29 out of 30 days and see that it has been raining every single day it would be a good guess that it will be raining the 30th day as well. A conjecture is an educated guess that is based on known information.
Therefore, when you are writing a conjecture two things happen: You must notice some kind of pattern or make some kind of observation. For example, you noticed that the list is counting up by 2s. You form a conclusion based on the pattern that you observed, just like you concluded that 14 would be the next number.
If our conjecture would turn out to be false it is called a counterexample.

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If we look at data over the precipitation in a city for 29 out of 30 days and see that it has been raining every single day it would be a good guess that it will be raining the 30th day as well. A conjecture is an educated guess that is based on known information.
0:40 7:16 Inductive Reasoning - YouTube YouTube Start of suggested clip End of suggested clip Three two and one by following the given pattern. So the number of points in the fourth figure wouldMoreThree two and one by following the given pattern. So the number of points in the fourth figure would be four plus three plus two plus. One.
A conjecture is a good guess or an idea about a pattern. For example, make a conjecture about the next number in the pattern 2,6,11,15... The terms increase by 4, then 5, and then 6. Conjecture: the next term will increase by 7, so it will be 17+7=24.
Therefore, when you are writing a conjecture two things happen: You must notice some kind of pattern or make some kind of observation. For example, you noticed that the list is counting up by 2s. You form a conclusion based on the pattern that you observed, just like you concluded that 14 would be the next number.
To fully disprove a conjecture, one needs to find only ONE counterexample.

conjecture and counterexample worksheet