Area Model with Four Partial Products
Area Model with Four Partial Products is a Grade 4 math skill in enVision Mathematics, Chapter 4: Use Strategies and Properties to Multiply by 2-Digit Numbers. Students multiply two 2-digit numbers by decomposing each into tens and ones, computing four partial products, and summing them.
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 you use an area model with four partial products?
Decompose each 2-digit factor into tens and ones, then find four partial products by multiplying each part of one factor by each part of the other. Add all four products for the total.
Why are there four partial products when multiplying two 2-digit numbers?
Each 2-digit number has two parts (tens and ones), so when you multiply (a+b) times (c+d), you get four combinations: a times c, a times d, b times c, and b times d.
What is an example of an area model with four partial products?
For 46 times 23, decompose as (40+6) times (20+3). The four products are: 40 times 20 equals 800, 40 times 3 equals 120, 6 times 20 equals 120, 6 times 3 equals 18. Sum equals 1058.
How does the area model help with 2-digit multiplication?
The area model visually organizes all four partial products as rectangles, ensuring you multiply every part of one factor by every part of the other without missing any combinations.
What chapter covers area models with four partial products in enVision Grade 4?
The area model with four partial products is covered in Chapter 4: Use Strategies and Properties to Multiply by 2-Digit Numbers in enVision Mathematics Grade 4.