Concept: Decomposing into Partial Products
Grade 4 Eureka Math students learn to multiply two two-digit numbers by decomposing one factor into tens and ones, creating two partial products. For 26 × 35, decompose 26 as 20 + 6: compute 6 × 35 = 210 and 20 × 35 = 700, then add to get 910. This two-partial-product approach condenses the four-region area model into two calculations. Students bridge from the visual area model to an efficient numeric method, preparing them for the standard algorithm.
Key Concepts
To multiply two two digit numbers, you can decompose one number into its tens and ones. Multiply each part by the second number to get two partial products, then add them together. For two numbers $AB$ and $CD$, where $AB = 10A + B$: $$AB \times CD = (B \times CD) + (10A \times CD)$$.
Common Questions
What are partial products in multiplication?
Partial products are the results of multiplying one part of a factor at a time. They are then added together to find the total product.
How do you compute 26 times 35 using partial products?
Decompose 26 as 20 + 6. Multiply: 6 × 35 = 210 and 20 × 35 = 700. Add: 210 + 700 = 910.
How do you compute 48 times 19 using this method?
Decompose 48 as 40 + 8. Multiply: 8 × 19 = 152 and 40 × 19 = 760. Add: 152 + 760 = 912.
How does this method connect to the area model?
The area model shows four rectangles (tens × tens, tens × ones, ones × tens, ones × ones). Combining them into two partial products merges the tens-row and ones-row areas.
Why is the partial products method taught before the standard algorithm?
It keeps place value explicit, helping students understand that each step computes a meaningful portion of the total product.