Power is calculated based off a specific value of an alternative mean.  Pose an example to students where the null mean is 0.  Ask them if they are more likely to find statistically significant results if they have an alternative mean of 1 or 1000. They will of course say 1000. Explain how power is a probability of finding statistically significant results for a specific alternative, not just if the alternative hypothesis is true.

Require students to write the specific formula for calculating the t test statistic. It is harder to forget to divide by the square root of n then.