If you teach multiplication with multi-digit numbers, it is helpful to keep a variety of strategies in your math toolbox. Using partial products to multiply is one long multiplication strategy that is essential for every upper elementary math classroom!
Let’s explore how you can multiply by using partial products!
Why Teach the Partial Products Strategy?
Multi-digit multiplication (also known as long multiplication) is a challenging math skill for most upper elementary students. Even with lots of practice, some students struggle to remember all of the steps and basic facts required for long multiplication.
Teaching more than one strategy to multiply bigger numbers is a good idea because all students learn information differently. A student may not understand using standard algorithm to multiply. But, show them a different strategy and it can click quickly.
You may be familiar with using partial quotients for long division. Like the division strategy, partial products uses fewer steps and breaks long multiplication into smaller parts that are easier for students to compute. Of all the multiplication models and methods that I have taught, using partial products to multiply is consistently a favorite for my students.
Using Partial Products to Multiply
The following step-by-step instructions show how to solve for 52 x 34 using partial products.
Step 1: Write the problem vertically. If your students are new to the partial products strategy, it can be helpful to have them write each digit in the bottom number a different color.
Step 2: Multiply the number in the ones place from the bottom number by the number in the ones place from the top number. Write the product below the line.
Step 3: Multiply the number in the ones place from the bottom number by the number in the tens place from the top number. Write the product below the line.
Step 4: Repeat the process for the number in the tens place from the bottom number. Write each product below the line.
Step 5: Add all of the products.
If the problem goes beyond the tens place, you will keep repeating the process. Multiply the next bottom digit (hundreds, thousands, etc.) by each of the top numbers individually, and write each product below the line.
More Long Multiplication Strategies
Using partial products to multiply is one of my favorite multiplication strategies that is not standard algorithm.
But, there are also many other long multiplication strategies you can use. My multiplication units teach students the following multi-digit multiplication methods in addition to standard algorithm:
- the box method
- factor multiplication
- the lattice method
All of my no-prep multiplication units come with step-by-step instructions for teaching each strategy and lesson. They also come with worksheets, games and centers, digital activities, and assessments to use when teaching long multiplication.
Because each grade level is required to use different number ranges when multiplying, four versions of the unit plans are available—
• Multiply up to 2-digits by 1-digit
• Multiply up to Two 2-digit numbers
• Multiply up to 3-digits by 2-digits
• Multiply up to Two 3-digit numbers
