Calculating Products Using the Partial Products Algorithm
This Grade 4 Eureka Math skill teaches the partial products algorithm, a method for multiplying multi-digit numbers by single digits using the distributive property. Students break the larger number into expanded form, multiply each place value separately, and sum the partial products. For example, 3 × 412 = (3×2) + (3×10) + (3×400) = 6 + 30 + 1200 = 1,236. This explicit, step-by-step approach from Chapter 11 of Eureka Math Grade 4 builds conceptual understanding before students use the condensed standard algorithm.
Key Concepts
The partial products algorithm uses the distributive property to solve multiplication. A multi digit number is broken into the sum of its place values (expanded form), and each part is multiplied separately before adding the results. $$a \times (b + c + d) = (a \times b) + (a \times c) + (a \times d)$$.
Common Questions
What is the partial products algorithm?
It is a multiplication method where you multiply the single-digit number by each place value of the larger number separately, then add all the results. It applies the distributive property of multiplication.
How do you use partial products to solve 3 × 412?
Break 412 into 400 + 10 + 2. Multiply: 3×2=6, 3×10=30, 3×400=1,200. Add: 6+30+1,200=1,236.
How do you use partial products to solve 4 × 2,153?
Break 2,153 into 2,000+100+50+3. Multiply each: 4×3=12, 4×50=200, 4×100=400, 4×2,000=8,000. Add: 12+200+400+8,000=8,612.
What property makes partial products work?
The distributive property: a×(b+c+d) = (a×b)+(a×c)+(a×d). Breaking the larger number into expanded form allows each part to be multiplied separately.
Why learn partial products before the standard algorithm?
Partial products make each step visible, building conceptual understanding of what multiplication means by place value. The standard algorithm compresses these steps using carrying (regrouping).