Recognizing and Solving Mathematical Patterns

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  • 0:03 Mathematical Patterns
  • 1:01 Recognizing…
  • 2:20 Solving Mathematical Patterns
  • 3:59 Lesson Summary
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Lesson Transcript
Instructor: Laura Pennington

Laura received her Master's degree in Pure Mathematics from Michigan State University. She has 15 years of experience teaching collegiate mathematics at various institutions.

Patterns show up in the world around us on a daily basis. In this lesson, we will define mathematical patterns and look at recognizing and solving these patterns. We will examine examples to solidify our understanding of this process.

Mathematical Patterns

Imagine it's a New Year, and one of your New Year's resolutions is to save $100 per month. The following chart shows how much money you will have saved after each month for the first four months:

Month Total Amount Saved
1 $100
2 $200
3 $300
4 $400

Take a good look at this chart. Based on the data shown, can you predict how much money you will have saved after five months? If you are thinking $500, then you are correct! There are a number of ways you may have come to that conclusion.

Regardless of how you came to it, the process you used is an example of recognizing and solving mathematical patterns. A mathematical pattern is something that follows a particular rule. For instance, the savings example is a pattern that follows the rule that the total amount saved goes up by $100 each month. Who knew that your New Year's resolution would involve math? Let's talk a bit more about recognizing and solving patterns.

Recognizing Mathematical Patterns

As we said, in the savings example, there are a number of ways that you could figure out that you would have saved $500 after five months. You may have noticed that, each month, the total amount saved goes up by $100. You also may have taken it a step further and recognized that the total amount saved follows the rule that it is equal to 100x, where x is the number of months you've been saving.

Both of these are examples of recognizing patterns. Recognizing mathematical patterns is exactly as the name implies. It consists of observing (or recognizing) patterns within the given data. Because a pattern is something that follows a specific rule, recognizing a pattern involves figuring out what that rule is.

Let's consider another example. In this image, observe the squares made up of dots:


recsolpat3


What types of patterns can you recognize in this sequence of squares? There are quite a few! Let's name some of them.

  • The number of dots in each square goes up by odd consecutive numbers, starting at 3, for each square.
  • The number of dots in the nth square represents the area of the square, with side length n.
  • The number of dots in the nth square in the sequence is equal to n2.

And that's just to name a few! Based on these patterns that we've recognized, can you determine how many dots will be in the next square in the sequence? Doing so is actually an example of solving a pattern, so let's talk a bit about solving mathematical patterns.

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