# How to Complete a Division Table

Instructor: T.J. Hoogsteen

T.J. is currently a grade 5 teacher and Vice-Principal. He has a master's degree in Educational Administration and is working toward an Ed.D. in Educational Leadership.

In this lesson you will learn how to fill out a division chart by using the pattern in numbers. You will be able to use the patterns in the dividend, divisor, and quotient to help you solve division equations and fill in missing numbers.

## Patterns and Division

Patterns are everywhere. Humans love patterns. They are in the clothes we make and wear, the music we listen to (just listen to your favorite song and you will likely hear a repeating pattern), even how we behave. Patterning is one of the first skills taught in math classes with students learning to create something like this:

Later, that basic patterning helps people to learn about patterns found in numbers. Just like in our everyday lives, patterns are found everywhere in numbers. Look below for just a few examples.

Not only can patterns be found along the number line, they can also be found in mathematical operations like addition, subtraction, and multiplication. This lesson is about patterns in division, and how to use the patterns to help fill in a division table.

## Numbers Divided by 1

Division tables are a lot like tables for operations like addition or multiplication because they give the solution to a certain equation. But they are a bit different from multiplication tables because they are not set up in columns or rows. Division tables look like this:

While looking at the table, you may have noticed that the pattern in this division table shows numbers being divided by 1. Every quotient (the solution, or answer, to a division equation) increases by 1. Also, each dividend (the number being divided) increases by the same number as the divisor (in this case 1). Finally, each divisor (the number the dividend is being divided by) stays the same.

## Numbers Divided by 2

When looking at a division table for numbers being divided by 2, you'll see a similar pattern. Except this time, the dividend increases by 2 each time, the divisor stays the same, and the quotient increases by 1 each time. Here is what the division table for numbers being divided by 2 looks like:

## Numbers Divided by 3

So now that the pattern is becoming clear, we will use it to fill a division table for numbers divided by 3. The first dividend will be zero, the divisor will be 3, and the quotient will be 0.

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