Find Partial Products from a Decomposed Array
Find Partial Products from a Decomposed Array (Chapter 3, second instance) is a Grade 4 math skill in enVision Mathematics. Students use a decomposed rectangular array to identify and compute partial products corresponding to each sub-array, then sum them for the total.
Key Concepts
The area of each smaller rectangle in a decomposed array represents a partial product. The total product is the sum of these partial products. For a problem like $a \times (b+c)$, the partial products are the areas of the two smaller rectangles: $(a \times b)$ and $(a \times c)$.
Common Questions
How do you find partial products from a decomposed array?
Break one side of the array by decomposing a factor into place value parts. Calculate the area of each resulting sub-array as a partial product, then add all partial products.
What does decomposing an array mean?
Decomposing an array means splitting the rectangular arrangement of rows and columns into smaller arrays by breaking apart one of the dimensions at a place value boundary.
Why use a decomposed array for multiplication?
A decomposed array makes the partial products visible and concrete, helping students see how the total product is built from smaller, manageable multiplication facts.
What is an example using a decomposed array?
An array of 7 rows by 38 columns can be split into 7 by 30 (210) plus 7 by 8 (56). The total product is 210 plus 56 equals 266.
What grade covers decomposed arrays for partial products?
Finding partial products from a decomposed array is a Grade 4 skill in enVision Mathematics, Chapter 3: Use Strategies and Properties to Multiply by 1-Digit Numbers.