Our Approach: Mathematical Language

The language used in this book is designed to help reveal mathematical structures to students and to be consistent with later mathematical usage.

For example, to help reveal mathematical structures we use "composing and decomposing" instead of "carrying and borrowing," or "regrouping." Their names suggest that each is the inverse of the other: composing is the inverse of decomposing and decomposing is the inverse of composing. Moreover, "composing and decomposing" can indicate what is composed and decomposed — a ten can be decomposed into 10 ones, a hundred can be decomposed into 10 tens, or 11 can be decomposed as 10 ones and 1 one.

We use "expressions" and "equations" rather than "number sentences." These are consistent with later usage. We talk about "using an expression to represent a mathematics problem" or "using a model to represent a problem." In some instances, we use "compute" and "calculate" rather than "add," "subtract," "multiply," and "divide," distinguishing between doing an operation and evaluating the result of the operation. For instance, we say, "calculate 2 + 4," rather than "add 2 + 4."4

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