Calculate Partial Products
Calculate Partial Products is a Grade 4 math skill in enVision Mathematics, Chapter 3: Use Strategies and Properties to Multiply by 1-Digit Numbers. Students use the distributive property to break a multi-digit number into expanded form and multiply each part by a single digit, adding results for the total product.
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. $$a \times (b + c + d) = (a \times b) + (a \times c) + (a \times d)$$ This can be visualized using an area model, where each partial product represents the area of a rectangle, and the total product is the sum of these areas.
Common Questions
How do partial products use the distributive property?
The distributive property lets you break a factor into place value parts and multiply each part separately: a times (b plus c plus d) equals (a times b) plus (a times c) plus (a times d).
What is the partial products algorithm?
Partial products is a multiplication algorithm where you multiply a single-digit number by each place value of the multi-digit number, record each product, and add them all for the final answer.
How is partial products related to the area model?
Each partial product represents the area of a rectangle in an area model. The sum of all partial products equals the total area, or total product.
What is an example of calculating partial products?
For 3 times 412: 3 times 2 equals 6, 3 times 10 equals 30, 3 times 400 equals 1200. Add: 6 plus 30 plus 1200 equals 1236.
What grade level uses partial products for multiplication?
Calculating partial products is a Grade 4 strategy in enVision Mathematics, Chapter 3: Use Strategies and Properties to Multiply by 1-Digit Numbers.