What is the math strategy, Using Partial Products, all about?
Math Strategy: Using Partial Products
Math Strand: Number Sense
Where is it on the Multiplication and Divison Continuum?
Overview:
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 added to determine the product of the original multiplication expression. Partial product strategies are applications of the distributive property of multiplication; for example, 5 ×19 = (5×10) + (5× 9).
Guide to Effective Instruction in Mathematics Grades 4 to 6 Volume 3 Multiplication page 19-23 http://www.eworkshop.on.ca/edu/resources/guides/NSN_vol_3_Multiplication.pdf
How to Support Student Learning:
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, above, 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.
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.
During mental math exercises perhaps during a number talk, using an open array to model student thinking when appropriate will strengthen this helpful representation of partial products.
Where to Next?
PARTIAL PRODUCT ALGORITHMS
Students benefit from working with a partial product algorithm before they are introduced
to the standard multiplication algorithm. Working with open arrays, helps students to understand how numbers can be decomposed in multiplication. The partial product algorithm provides an organizer in which students record partial products, and then add them to determine the final product. The algorithm helps students to think about place value and the position of numbers in their proper place-value columns.
STANDARD MULTIPLICATION ALGORITHM
When introducing the standard multiplication algorithm, it is helpful for students to connect
it to the partial product algorithm. Students can match the numbers in the standard algorithm to the partial products.
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