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Math Monthly

February 2022:

February’s Vocabulary: Partial Products

The partial products model is a model that breaks numbers down into their factors or place values to make multiplication easier. It is the basis for the area model of multiplication and long multiplication.

February’s Standard: Look for and make use of structure.

Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. 

Like tape diagrams, partial products help students bridge the gap from a concrete model to a representational or abstract model.  In third grade, partial products help students just learning about multiplication to use known multiplication facts to find larger products. As students move through elementary school, this gives meaning to the standard multiplication algorithm. As students are Introduced to algebraic expressions, the area model using partial products can help visualize how to multiply both numbers and variables.

See this strategy in action through a number talk with Jo Boaler here.