Odd and Even Numbers

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The models developed in the first page of this lesson are very useful for looking at how odd and even numbers behave when we perform basic operations with them. For example, what happens when we add two odd numbers together? The models can make it quite clear:

We can show other situations as well:

• What is the result of subtracting an even number from an odd number?

• How about adding an odd and even number together?

• What if we multiply an odd and even number?

The model is simple if we think of the grouping idea. We can combine an odd number of even groups or an even number of odd groups:

Here are some other questions you can try to answer using the odd and even models:

• What is the outcome of adding three odd numbers together?
• How about addition of five odd numbers and one even number?
• What is the result of multiplying an odd number with an odd number?
• What happens when an odd number is subtracted from an even number? What about subtracting an odd number from an odd number?

We can use these models and the ideas they represent to quickly check of the results of our computations as well as explore number theory. They are just an example of the power of visual models used in mathematics. Here's one last challenge on which to try out the models:

Which group of numbers can be divided into two equal odd numbers? Why is this so?