Recognizing and Writing Equations for Patterns

In this lesson, you will learn how to recognize patterns and find equations to describe them. You will also learn how to predict future terms in a sequence based on your equation. Through various examples, you will see how to identify patterns and write rules to describe them. These examples include toothpick squares, algebra tiles, and dot patterns. By the end of this lesson, you will have a better understanding of how to recognize and write equations for patterns.

Learn how to recognize patterns and how to find an equation to describe the pattern. Also, you will learn how to predict future terms in a sequence based on your equation.

• What is the perimeter of toothpick square shape 29?
• How do you recognize patterns?
• What are the next four terms in the pattern / sequence 4, 11, 25, 53, 109?
• What are some different ways of finding successive terms in sequences?
• How do you draw the next figure in a sequence of figures of dots?
• How do you explain or describe the pattern in a relationship?
• How do you write a rule for drawing figure n in a series of figures?
• How do you make up a rule using a variable for a pattern?
• How do you make a rule or expression that gives the number of dots in figure n for a pattern?
• Why does having a 0 case or base case of a pattern help you find the pattern or equation for the nth figure?
• How do you figure out how many dots are in figure 42 in a series of figures of dots?
• What is the pattern for toothpick squares?
• How can you figure out the perimeter of shape n in a pattern of toothpick squares?
• What is the rule of shape n of toothpick squares?
• What are the problem solving steps for finding rules for patterns in shapes and equations for sequences?
• How can you find the perimeter of algebra tiles that are stacked on top of each other or next to each other using an equation or rule?
• What is the perimeter of a long rectangle made up of 5 algebra tiles if the length (x) of each tile is 7cm?