Seeing that 1/2 = 3/6 and 1/3 = 2/6, we see that the answer is 5/6, but why sixths? Why not some other fraction, like fourths or tenths? Real fractions show why.
What works is a magic show to the novice. The circles are put back together, and the first two are cut into sixths.
If one of the halves is placed next to one of the thirds (to indicate that they are being added) and compared to two of the fifths, then it is visually clear that the answer has to be bigger than 2/5, so adding across does not work.
The rules for working with fractions don’t make sense to elementary school students if they only work with the numbers. What the numbers prompt them to do is often wrong. Take 1/2 + 1/3, for example. What is wrong with just adding across and getting 2/5? Lots, but that isn't obvious unless real fractions are considered, like three circles—one cut into halves, one into thirds, and one into fifths.