Like almost everything else we do in math, we learn how to add and subtract fractions first concretely with actual materials, then by drawing pictures, and finally by using abstract strategies. *Note: lessons on adding and subtracting fractions tend to merge with lessons on decomposing fractions and lessons on adding and subtracting mixed numbers. In other words, these three lessons of the unit tend to happen more or less simultaneously.
When students draw pictures of adding and subtracting fractions, it’s always a good idea to draw the whole first. This comes in especially handy when we start using mixed numbers.
Finally, students learn how to add and subtract fractions conceptually. Since the Common Core Standards only require that fourth grade students perform these operations on fractions with the same denominators, the only difficult part is changing improper fractions to mixed numbers and vice versa.
For example,
⅗ + ⅘ = ? By simply adding the numerators, student get a sum of 7/5 or 1 ⅖.
Another example,
1 4/7 - 5/7 would become 11/7 - 5/7. By subtracting the numerators, students get a difference of 6/7.