Connection: Matching Partial Products to the Area Model
Connection: Matching Partial Products to the Area Model is a Grade 4 math skill in enVision Mathematics, Chapter 4: Use Strategies and Properties to Multiply by 2-Digit Numbers. Students see that each of the four partial products in 2-digit multiplication corresponds to the area of one rectangle in the area model.
Key Concepts
When you multiply two 2 digit numbers, the four partial products you calculate correspond to the areas of the four smaller rectangles in an area model. For factors decomposed as $(a+b)$ and $(c+d)$, the four partial products are $a \times c$, $a \times d$, $b \times c$, and $b \times d$.
Common Questions
How do partial products connect to the area model?
Each partial product you calculate when multiplying two 2-digit numbers equals the area of one of the four smaller rectangles in the corresponding area model.
Why are there exactly four partial products for two 2-digit numbers?
Two 2-digit numbers each have two parts (tens and ones). Multiplying (a+b) times (c+d) creates exactly four products: a times c, a times d, b times c, and b times d, matching four rectangles.
What is an example connecting partial products to an area model?
For 47 times 35, decompose as (40+7) times (30+5). The four partial products are 40 times 30 equals 1200, 40 times 5 equals 200, 7 times 30 equals 210, and 7 times 5 equals 35.
How does the area model ensure you multiply all factor parts?
Each rectangle in the area model represents one combination of the decomposed parts. If you fill in all four rectangles, you know you have not missed any multiplication step.
What chapter covers matching partial products to the area model in enVision Grade 4?
This connection is covered in Chapter 4: Use Strategies and Properties to Multiply by 2-Digit Numbers in enVision Mathematics Grade 4.