Multiplication (Partial Products)
This Multiplication (Partial Products) is an interactive and engaging web-based application designed to help you practice your multiplication skills.
 
While the Area Model uses a grid, the Partial Products method uses a vertical stack, making it a perfect bridge between visual models and the Standard Algorithm. This Partial Products method is often considered the “stepping stone” to the standard way people usually learn in school. It keeps the place value clear so you don’t get lost in the steps. Scroll down the page if you need a more detailed explanation.
 
This Multiplication (Partial Products) Game has an option to give a guide for each partial products or you can put in the partial products in any order.
 

 

How to Play the Multiplication Game (Partial Products)
The game is designed to help you practice your Multiplication (Partial Products) skills in a fun environment.
Here’s how to play:

1. Step-by-step Guide: Check the Guide if you want a guide for each partial product. (If you did not select the Guide then you can enter the steps in any order). Click “Start Game”.
   
2. Look at the Problem: You’ll see two numbers at the top of the purple box. Your goal is to multiply them.
   
3. Enter the Partial Products: Type in the partial products. Add them up to get the total.
   
4. Check Your Work: Click the yellow Check button (or press the Enter key). The game will tell you if you’re correct. If you are wrong, you will be shown which of the answers are wrong.
   
5. Get a New Problem: Click the blue Next button (or press Enter again) for a new multiplication problem.
   Your score is tracked at the top, showing how many you’ve gotten right out of the total you’ve tried.
6. Back to Menu Click “Back to Menu” to restart the game.
    
   

Multiplication using Partial Products
Partial products is a multiplication method that breaks down a multi-digit multiplication problem into simpler, smaller parts based on the place value of each digit. It’s often taught to help students build a conceptual understanding of multiplication before learning the standard algorithm.
 
The core idea is to multiply each digit of one number by each digit of the other number, keeping their place values in mind. These individual results are called “partial products.” The final answer, or the “total product,” is then found by adding all the partial products together.
 
The Setup
Let’s use the example: 43 × 26
Stack the numbers vertically, just like you would for addition.
43
26
The Four Steps
Since we have two digits on top and two on the bottom, there are four specific multiplications to do. We always start with the ones place of the bottom number.

1. Ones × Ones
   Multiply the bottom ones digit (6) by the top ones digit (3).
   6 × 3 = 18
   
2. Ones × Tens
   Multiply the bottom ones digit (6) by the top tens digit (40). Remember: the 4 is in the tens place.
   6 × 40 = 240
   
3. Tens ×Ones
   Now move to the bottom tens digit (20). Multiply it by the top ones digit (3).
   20 × 3 = 60
   
4. Tens × Tens
   Multiply the bottom tens digit (20) by the top tens digit (40).
   20 × 40 = 800
   Bringing it All Together
   Write these four “partial products” under the line and add them up. Alignment is key—make sure your ones, tens, and hundreds are in straight columns.
    
   

The video gives a clear, step-by-step approach to walk through the process of multiplying a 2-digit number by 2-digit number using partial products.

• Show Video

 

Free Multiplication Games
Multiplication Tables Practice	Multiplication Tables	Multiply Tens & Hundreds
Find missing Factors	2-digit x 1-digit (no regrouping)	2-digit x 1-digit (with regrouping)
Multiplication (Partial Products)	2-digit x 2-digit

 

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