Using Partial Products

Using Partial Products: What is it?

Partial Products is a multiplication strategy in which numbers are decomposed in order to work with smaller portions.

Overview

When using partial products, one or both factors in a multiplication expression are decomposed into two or more numbers and these numbers are multiplied by the other factor. The partial products are then added to determine the product of the original multiplication expression. Partial product strategies are applications of the distributive property of multiplication.

For example, a student could solve 8x12 by decomposing 12 into 10+2.

8x10=80

8x2=16

So, (8x10) + (8x2) = 96

Supporting Students Using Partial Products

Using concrete materials and making models of the partial products is essential as you guide students to connect the different representations and make sense of abstract concepts.

In this example, students are using base ten materials to model 28 X 6. Students can also represent the multiplication on centimetre grid paper. When they count the material they automatically attend to the largest quantities of tens. By decomposing 28 into 20 and 8, the partial products become 20 X 6 and 8 X 6.

Using base ten materials to model a 2 digit by 2 digit multiplication question 23 X 14. Students model and then create the outline of this area using centimetre grid. Students can count quantity, however, they must also identify the partial product represented. Starting with questions that can fit on the grid will help scaffold the students’ understanding and visually cue them to identify the partial products.

As students build understanding of partial products using concrete materials, an open array can be valuable. An open array provides a model for demonstrating partial product strategies, and gives students a visual reference for keeping track of the numbers while performing the computations. The following example shows how 7× 42 might be represented using an open array.

Where to Next?

Once students are efficiently using partial products with larger numbers, they can be encouraged to begin representing this same thinking using alternative or standard algorithm.

Building Fact Fluency

Multiplication is the inverse operation and can be used to support division. Ensuring students are confident and have solid understanding of familiar facts, particularly x2, x5, and x10 will be beneficial for divisional thinking. Building arrays with square tiles will help students connect to the visual representation of an open array.

Array Work

Learning to create an array will help students see multiplication principles come to life. Extending this array work to visually represent partial products will support learners for deeper understanding. For more information, please see the array resource located on the Portal.

Looking to learn more? Check out the recorded session!

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