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Growing Patterns

A kindergarten introduction to growing patterns: sequences of shapes, objects, or numbers that get bigger following a rule. Learn how growing patterns differ from repeating patterns, how to find the rule, and how to extend the pattern with simple step-by-step examples using blocks and numbers.

What Is a Growing Pattern?

A growing pattern is a sequence of shapes, objects, or numbers that changes by following a rule, with each step becoming bigger than the one before it. Instead of showing the same small group over and over, a growing pattern adds something new every single time. For example, a tower with 1 block, then 2 blocks, then 3 blocks, then 4 blocks is a growing pattern because it keeps getting taller by the same amount at each step.

Growing Patterns vs Repeating Patterns

Many of the first patterns kindergarteners learn about, like color patterns or shape patterns, repeat the same small group again and again, such as red, blue, red, blue, or circle, square, circle, square. A growing pattern works differently. Nothing repeats exactly the same way twice. Instead, each new step grows by a set amount, so the pattern keeps getting bigger and bigger as it continues.

How to Find the Rule in a Growing Pattern

Every growing pattern follows a rule that tells you exactly how much bigger each step gets. Finding that rule is the key to understanding, and later extending, the pattern.

Look at the first step and count how many objects, shapes, or units it has.
Look at the next step and count again.
Find the difference between the two steps. This difference is the rule.
Check that the same rule works between every pair of steps in the pattern.
Use the rule to figure out what the next step should look like.

Example: A Growing Block Pattern

Look at the towers of blocks below. The first tower has 1 block, the second has 2 blocks, the third has 3 blocks, and the fourth has 4 blocks.

Each tower has one more block than the tower before it.

Counting the blocks gives the numbers 1, 2, 3, 4. Between each step, exactly 1 block is added. That means the rule for this pattern is "add 1 block each time." Following that rule, the next tower should have 5 blocks, then the one after that should have 6 blocks.

Example: A Growing Number Pattern

Growing patterns can also appear as lists of numbers without any pictures at all. Consider the numbers 2, 4, 6, 8. Checking the gap between each pair of numbers shows that every step adds 2. So the rule is "add 2 each time," and the pattern should continue with 10, then 12, then 14.

Extending a Growing Pattern

Once the rule is known, extending a growing pattern is simply a matter of applying that rule one more time. If a pattern of stars grows as 1, 3, 5, and the rule is "add 2 each time," the next group should have 7 stars, and the group after that should have 9 stars. Practicing this skill alongside completing a pattern helps build confidence in predicting what comes next in any sequence.

Tips for Spotting Growing Patterns

Count carefully at each step before comparing it to the next one.
Ask "how much bigger is this step than the last one?" every time.
Check that the same amount is added between every pair of steps, not just the first two.
Remember that growing patterns can use blocks, shapes, dots, or plain numbers, the rule works the same way in every case.

Related lessons

Kindergarten