Using the Distributive Property for Partial Products
Using the Distributive Property for Partial Products is a Grade 5 math skill from Eureka Math that teaches students to break apart factors using the distributive property to find and add partial products. For example, 23 x 45 is decomposed into (20 + 3) x 45 = 20 x 45 + 3 x 45. Students calculate each partial product and add them together, building toward the standard multiplication algorithm.
Key Concepts
The distributive property allows us to multiply a sum by multiplying each addend separately and then adding the products. When we decompose factors by place value, the results of these smaller multiplications are called partial products. $$a \times (b + c) = (a \times b) + (a \times c)$$.
Common Questions
How does the distributive property produce partial products?
Break one factor into tens and ones, then multiply each part by the other factor. For example, 34 x 7 = (30 + 4) x 7 = 210 + 28 = 238. The 210 and 28 are the partial products.
What is a partial product in Grade 5 multiplication?
A partial product is the result of multiplying one part of a decomposed factor by the full other factor. All partial products are added to get the final product.
How does this skill connect to the area model?
The area model visually displays the same partial products as the distributive property. Each rectangle in the model represents one partial product (e.g., tens x tens, ones x tens).
What Eureka Math Grade 5 chapter covers the distributive property for partial products?
Eureka Math Grade 5 Chapter 7 covers using the distributive property for partial products as students develop multi-digit multiplication strategies.
Why does understanding partial products help with the standard algorithm?
The standard multiplication algorithm is an organized way to compute and record partial products. Students who understand partial products can interpret each line of the algorithm meaningfully.