Grade five is the last year where arithmetic is a focus, though in later grades there are many opportunities to continue practicing these skills — for example, dividing numbers when computing proportions.
This year students will learn to add fractions with unlike denominators. This is a complicated process, grounded in a firm understanding of the number line, in renaming fractions, and in adding fractions with the same denominator. All of this will make addition of fractions a process that makes sense, rather than something to remember without understanding.
This type of reasoning also helps to apply fraction arithmetic correctly. Many of us remember that you “multiply across” to multiply fractions, but struggle to know if one should multiply in a real world context. Students will use pictures to reason about the meaning of multiplying and dividing fractions. From these they will understand what is actually occurring in the operations and be able to know whether to multiply or divide, and have a sense for what they expect in a reasonable answer.
Students will use similar reasoning about whole numbers and decimals — using sketches, examples, and properties which have been carefully developed, so these arithmetic skills will provide a strong base for algebra.