Recording Partial Products Vertically
Recording Partial Products Vertically is a Grade 4 math skill that organizes the distributive property multiplication calculation into a standard vertical format. Each partial product — computed by multiplying one digit of one factor by all the digits of the other factor — is written on its own line and aligned by place value. For 34 x 27: record 7 x 34 = 238 on the first line and 20 x 34 = 680 on the second line (with placeholder zero), then add. Covered in Chapter 16 of Eureka Math Grade 4, this organized vertical format bridges the area model and the compact standard algorithm.
Key Concepts
To find the total product, the four partial products are recorded vertically, aligned by place value, and then added together.
Common Questions
How do I record partial products vertically in multiplication?
Write the two factors. Multiply the ones digit of the bottom factor by the entire top factor and record the partial product on the first line. Multiply the tens digit of the bottom factor by the top factor (writing a 0 placeholder in the ones place first) and record on the second line. Add both partial products.
How do I solve 34 x 27 using partial products vertically?
Line 1: 7 x 34 = 238. Line 2: 20 x 34 = 680 (write 0 first, then 20 x 34 = 68 to the left: 680). Add: 238 + 680 = 918.
What is a partial product?
A partial product is the result of multiplying one digit of a factor (accounting for its place value) by the entire other factor. Two-digit by two-digit multiplication produces two partial products (one for the ones digit, one for the tens digit) which are added for the final product.
How does vertical partial products connect to the area model?
Each partial product in vertical form corresponds to a section of the area model rectangle. The ones digit row matches the bottom two sections, and the tens digit row matches the top two sections. Both methods compute the same four individual areas.
How does the vertical partial products method prepare for the compact standard algorithm?
The compact algorithm combines both partial products into one pass, using carry digits instead of writing separate lines. Students who understand partial products can interpret why the compact algorithm's carries occur and why the second partial product row is shifted left.
What chapter in Eureka Math Grade 4 introduces vertical partial products?
Chapter 16: Multiplication of Two-Digit by Two-Digit Numbers in Eureka Math Grade 4 introduces vertical partial products as the organized intermediate step between the area model and the compact standard multiplication algorithm.