Skill: Make a reasonable conjecture

A conjecture is a careful prediction based on what you notice in examples. To make one:

1. Look closely at the examples.
2. Find what changes or stays the same.
3. Use that pattern to predict what comes next.
4. Check your prediction with another example.

Example:
What number comes next?

$$2,\ 4,\ 6,\ 8,\ \boxed{\ ?\ }$$

Step 1: Notice the pattern.
Each number is $2$ more than the number before it:

• $2+2=4$
• $4+2=6$
• $6+2=8$

Step 2: Make a conjecture.
If the pattern keeps adding $2$, the next number should be

$$8+2=10.$$

So, our conjecture is that the missing number is $\boxed{10}$.

Step 3: Check it.
The next number after $10$ would be $12$, and $10+2=12$. This fits the pattern, so our conjecture is reasonable.