The term "mixed numbers" refers to fractions that are greater than a whole. 2 ⅓ therefore, means 2 wholes plus an extra third. We incorporate mixed numbers into problems in previous lessons on adding, subtracting, and decomposing fractions, but it does not hurt to teach mixed numbers again in their own formal lesson. The first objective is to make sure students are comfortable expressing fractions greater than 1 in both formats: as a “mixed number” and as an improper fraction. We practice concretely, pictorially, and abstractly.
When we practice adding and subtracting mixed numbers, we again work through the concrete stage, the pictorial stage, and finally, the abstract stage. The Common Core State Standards only require fourth grade students to manipulate mixed numbers with the same denominator.
Students can add the wholes first or the fractions first.
The following illustration is not the only way to subtract mixed numbers. Students could have changed both wholes into thirds, for example, instead of just changing one whole. Students may use any strategy that they can explain.
The following illustration is just one way to add and subtract mixed numbers. Students may use any strategy that they can explain.