• Math Tools and Models 3-6

Math Models and Tools

## Open Array with Multiplication and Division

An array is a rectangular arrangement of a set of objects or numbers often in rows or columns used to express multiplication and division situations. Real world examples of arrays are used to help introduce these concepts. Examples of arrays are found in everyday life such as a box of chocolates, a crate of oranges, rows of chairs in an auditorium. An open array, like the open number line, is a model for multiplication and division. Unlike the closed array, the open array does not explicitly show each object in the row or column but is a pictorial representation of larger numbers. It lends itself to modeling the partial product strategy and the distributive property of multiplication.

Multiply

Divide

Partial Product and Partial Quotient

Using partial products to multiply is a strategy that demonstrates an understanding of the Distributive Property. The array is a way to visually represent that strategy. The following is an example of how students would use partial quotients to solve a “long division” problem. The strategy relies on using multiples of ten to “partition” the number. It is the same as the "traditional" (using compatible numbers) with the quotient recorded on the right side rather than on top of the problem.

Product

Quotient

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