# Growing Patterns

• Do you recall what a pattern is?
• A pattern is an arrangement or sequence that follows a certain order. In the last lesson, you learned about repeating patterns, patterns that repeat themselves. But there are other types of patterns, too.

## Related Topics

In this lesson, let’s explore a different category of patterns – called growing patterns!

• Patterns that increase (or grow) according to a certain rule, are called increasing patterns, or growing patterns.
• you can find a growing pattern with pictures shapes, objects, numbers, etc.
• A growing pattern has $$2$$ important parts- the terms and the rule.
• Each step of a growing pattern is a term.
• The fixed order in which a growing pattern increases is called its rule.
• To work with a growing pattern, we need to be able to find its rule.
• To find the rule of a pattern, observe how the pattern increases as it moves from one sequence to the next.

## Finding Unknown Terms of a Growing Pattern

Sometimes, we may need to find unknown terms in a growing pattern.

To find unknown terms of a growing pattern, first, find its rule and then use it to find the unknown terms.

## Growing Patterns – Example 1:

Draw the picture that comes next in the growing pattern.

Solution:

This is a growing pattern. In the second step, two circles are added to the initial single circle, one on the right and the other at the top. In the third step, the same thing happened again, that is, two new circles were added to the previous three circles, one on the right and the other on top of the previous circles. So in the next step, we add two circles again to the previous five circles: one on the right and the other on top of the circles.

## Growing Patterns – Example 2:

Draw the picture that comes next in the growing pattern.

Solution:

This is a growing pattern. In the second step, two triangles are added to the initial single triangle, on the bottom of the first one. In the third step, three new triangles were added to the bottom of the three previous triangles. So in the next step, we add four triangles to the bottom of the six previous triangles.

## Exercises for Growing Patterns

Draw the picture that comes next in each growing pattern.

1)

2)

1)

2)

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