Understanding Number and Shape Patterns

Patterns are everywhere in math! A pattern is a sequence of numbers or shapes that follows a specific rule. If you know the rule, you can easily figure out what comes next, or even create your own patterns.

Repeating Shape Patterns

Shape patterns often repeat in a specific order. To find what comes next, look for the "core" of the pattern—the exact group of shapes that repeats over and over.

Example: Look at this pattern: Triangle, Square, Circle, Triangle, Square, Circle...

• The Core: The repeating group is "Triangle, Square, Circle".
• What comes next? After the second Circle, the pattern starts over. The next two shapes will be a Triangle, then a Square.

Growing Number Patterns

Number patterns usually grow or shrink by following a math rule. This rule might involve adding, subtracting, multiplying, or dividing.

Example: Finding the rule Look at the sequence: $2, 6, 18, 54, \dots$ How do we get from one number to the next?

• $2 + 4 = 6$, but $6 + 4$ does not equal $18$. So, addition isn't the rule.
• Let's try multiplication: $2 \times 3 = 6$.
• Does it work for the next numbers? $6 \times 3 = 18$, and $18 \times 3 = 54$.
• The Rule: Multiply by $3$.

Generating a Pattern from a Rule

Sometimes you are given a starting number and a rule, and you need to build the pattern yourself.

Example: Start with $3$, add $5$ each time. Let's find the first 5 numbers in this pattern:

1. Start: $3$
2. Add $5$: $3 + 5 = 8$
3. Add $5$: $8 + 5 = 13$
4. Add $5$: $13 + 5 = 18$
5. Add $5$: $18 + 5 = 23$

The pattern is: $3, 8, 13, 18, 23$.

A Quick Tip: When trying to find a rule for a number pattern, always test your rule on at least three numbers in the sequence to make sure it works every time!