This is a bit subjective, but
I don't know exactly what your teacher is looking for, but here are some bullets:
Mean takes into account ALL of the data; therefore it can be skewed by outliers for small samples.
Mode describes what is the norm most of the time. In the case of children's weights, if the highest frequency are between 100-120 pounds use this rather than possibly skewing the data with the mean.
In the case of test scores you want to know what the middle point of your data set. So, median.