Patterns - Number Patterns

A Number Pattern is a sequence of numbers that follow a specific rule to find the next number in the series. Imagine a set of stairs where each step is the same height; this represents a consistent increase in value.

The Rule of a pattern is the logical link that tells us how to get from one number to the next. To identify it, we look at the difference between two consecutive numbers. If the numbers are growing, we look for addition; if they are shrinking, we look for subtraction.

Increasing Patterns occur when each term is larger than the previous one, usually by adding a fixed number. For example, in $4, 8, 12, 16$, the rule is to add $4$. Visually, this looks like a bar graph where each bar is taller than the one to its left by an equal amount.

Decreasing Patterns occur when each term is smaller than the previous one, usually by subtracting a fixed number. In the sequence $50, 45, 40, 35$, the rule is to subtract $5$. This can be visualized as a countdown or a set of blocks being removed one by one.

Skip Counting is a pattern where we count by jumping over numbers by a fixed interval, such as $2s, 5s, 10s,$ or $100s$. On a number line, this is represented by equal-sized 'hops' from one number to the next.

Even and Odd Patterns follow specific sequences. Even numbers always end in $0, 2, 4, 6,$ or $8$ and follow the pattern $+2$. Odd numbers end in $1, 3, 5, 7,$ or $9$ and also follow a $+2$ pattern but start from an odd digit. Even numbers can be visualized as pairs of dots with no single dot left alone.

Repeating vs. Growing Patterns: A repeating pattern has a core sequence that stays the same (e.g., $1, 0, 1, 0$). A growing pattern changes in a predictable way (e.g., $1, 11, 111$). A repeating pattern looks like a decorative border on a wall, while a growing pattern looks like a pyramid being built layer by layer.