Imagine we are investigating what happens when you add even numbers. You might start with some examples e.g.
6 + 4 = 10 even + even = even
2 + 4 = 6 even + even = even
100 + 52 = 152 even + even = even
At this point you might begin to notice a pattern. You could therefore make a conjecture -
Conjecture: when you add two even numbers you always get an even answer
You have not tested every possible pair of even numbers to check this is correct - in fact it's not possible as there are an infinite number of possibilities. So a conjecture is a statement about what you think is happening. You might do more examples and find that the conjecture is not correct so have to make a new one, or the examples may fit the conjecture. However this has not proven that the conjecture is correct only that so far you haven't found any examples that contradict it. The are often ways to prove it is correct but we are not worried about proof at this stage!
