Working with Division Input-Output Tables

Instructor: Jennifer Lowery

Jennifer has taught elementary levels K-3 and has master's degrees in elementary education and curriculum/instruction and educational leadership.

Division is a mathematical operation that can be used to solve different real world problems. Learn how to identify division equations from something called an input/output table.

The Operation of Division

If you have 10 brownies and you want to share them equally with 4 friends, you know that you need to divide the brownies equally among 5 people. This is one way people use division in everyday life. Division is often solved traditionally, and is used in other math concepts like simplifying fractions. The operation of division can also be found in input-output tables.

Traditionally division is presented in this way.
Traditional Division

Input-Output Tables

An input-output table is a table that has one column of numbers ''coming in'' and another column of numbers ''going out.'' Think of it as a machine that performs a specific operation to the numbers coming in, and produces numbers going out using that operation. The key to understanding these tables is to find the same operation rule that works for each set of numbers.

Is the Output Getting Bigger or Smaller?

To solve an input-output table, we first need to determine the operation. Keep in mind that the operations of addition and multiplication will result in a number going out that is larger than the number coming in. The operations of subtraction and division will result in a number going out that is smaller than the number coming in. Identifying the changes in the numbers going out can help us eliminate addition and multiplication.

Notice the numbers in the output column are smaller than the numbers going in.
Division Table

Subtract or Divide?

Now that you have figured out that the machine is not adding or multiplying, is it subtracting or dividing? We can check by subtracting first. Look at the top number going in. How much would you need to subtract in order to create the number going out? In the input-output table shown, 72 minus 66 equals 6. So, you might think that minus 66 is the rule for this table. However, this will not work for the next set of numbers because 60 minus 66 is not 5.

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