In order to be able to perform arithmetic on fractions, students need to understand what fractions are and how they operate. Just teaching rules (e.g. "to add fractions you must have common denominators"), is not sufficient for developing an understanding why they work and for encouraging deeper conceptual thinking.
What big ideas lead to this understanding?
One example would be equivalence- that fractions can be written in different ways but represent the same proportion.
What does $\frac{3}{4}$ mean? Intuitively, you pick a pizza, cut it in $4$ pieces and take $3$ slices.
For any fraction: denominator means how small the slice is, the top how many slices. Fraction means intuitively the quantity of pizza.
Now fraction addition/subtraction
$$\frac{1}{2} +\frac{1}{3}=???$$
Problem: slices have different size.
Solution: make all slices same size. You split each of the half slices into 3 parts, each of the third slices in half, and you discover the idea of common denominator. A picture of the two pizza's before/after is very helpful.
Also, this last idea of cutting slices in mini-slices can be used to explain why fractions can be written in different way. Cut pizza in 2, shade 1 slice, and then cut each slice in 3 thirds. The shaded region was $\frac{1}{2}$ and now it is $\frac{3}{6}$. But the shaded region didn't change....