Vertical Multiplication Worksheets
You will traditionally find that in North America we approach multiplication from two aspects (horizontally and vertically). This are not the only two methods in the world. The Egyptian method breaks down values into a series of addition problems. You will also come across the Chinse method that creates a hybrid form that involves multiplying in horizontal and vertical orientation for the same product. We use the horizontal method for products that are part of the times tables and more math fact orientated values. The vertical multiplication is perfect for working with the product of very large values because it automatically lines up your place values for you. You will find it even more invaluable when working with decimal values because it keeps track of where the decimal point lies throughout the entire problem. These lessons and worksheets helps students practice completing single digit multiplication problems in a vertical alignment.
Aligned Standard: Grade 3 Operations - 3.OA.A.1
- Vertical Products Lesson - We work you through 2 problems. We use repeated addition for the lesson.
- Worksheet 1 - Twenty mixed problems for you. Remember that you can flip the values, if it easier for you.
- Worksheet 2 - A full rework of sheet 1. The values are a bit larger for you.
- Mad Minute Multiplication 1 - A great way to review your times tables. See if you can finish this in under a minute.
This should keep you pretty busy. There are a bunch of different strategies that you can use here.
- Practice 2 - Twenty up to down multiplication problems to complete.
- Practice 3 - You get three seconds a problem.
- Practice 4 - This is a nice practice page to get you ready for a minute.
- Practice 5 - I would suggest you have students complete one of these each day.
- Practice 6 - At first, students may be anxious when completing these, but they will get comfortable with it.
- Practice 7 - You can teach students to do all the zero and ones problems first.
- Practice 8 - Some students just like to go right down the page.
- Practice 9 - I like to get in the habit of posting fastest times with perfect scores.
- Practice 10 - This really motivates students to get better, quick!
Mad Minutes Multiplication
You should have students complete 1 of these a day for a week. That should help them master the skill.
- Mad Minute 2 - What might help you here is timing how long it takes and your accuracy.
- Mad Minute 3 - This where you really want to get the stopwatch ready.
- Mad Minute 4 - At this point, you need to insist that they only work for one minute.
- Mad Minute 5 - By now they should start to feel comfortable with this skill.
A quick way to check for understanding in your students.
Tips for Multiplying Vertically
Vertical multiplication or long multiplication is a method that is very common and taught in elementary school to students who are learning how to multiply larger values. It can help you organize yourself as you work with very large numbers because it creates a nice sense of columns and order. This method is used all over the world and can be used for multiplying numbers of arbitrarily large size and sometimes in decimal form. It is my recommended format for processing the products of decimals because it can really help you line up the decimal point throughout the procedure of finding the product.
Numbers that are multiplied are placed vertically on top of each other. The number at the top is called the multiplicand. The number that is placed directly below it is called the multiplier. The result that is achieved is called the product. These parts of multiplication can be diagramed as found to the right for the problem 18 x 5 = 90.
Multiplication is commutative. This means that we can choose which value is the multiplicand and multiplier and the value of the product will not change. In most cases, it is easier to have the large value serve as the multiplicand. This makes it easier to line things up. If you get a value that has many trailing zeroes (such as 4,000 or 800) it is often easier to process the problem when those values serve as the multiplier.
This multiplication starts with multiplying the multiplicand with the digit that is the least significant of the multiplier. This would mean to start with the lowest place value. The first step will be to generate a partial product. As you move on, the digits of the multiplicand multiply with the digits in the higher order of the multiplier. In the last step, all the partial products are then added together. The total sum is the value of the product. In our simple example there are only two partial products. As you scale up the value of the multiplicands and multipliers that you use, the number partial products go up as well. The vertical method can be extended to more than on multiplicand. The complexity of the problem increases with the number of multiplicands at hand.
It is often helpful to cross out or draw an X symbol over the numbers that you have used to form partial products. This helps you keep your place especially when working with multiplicands or multipliers that are composed of many different numbers.