Pattern and Function - Rules for Patterns

A Pattern is a set of numbers, shapes, or objects that follow a specific, predictable rule. For example, a visual pattern might look like a row of alternating colored blocks: Red, Blue, Red, Blue.

A Repeating Pattern has a 'core' or a unit that repeats over and over again. If you see a sequence like $\triangle, \square, \triangle, \square$, the repeating core is $\triangle, \square$.

A Growing Pattern is a sequence where each term increases by a specific amount or follows a rule that makes it larger. Imagine a staircase made of blocks where the first step has $1$ block, the second has $2$ blocks, and the third has $3$ blocks; this is a growing pattern where we add $1$ each time.

A Shrinking Pattern is a sequence where each term decreases. Visually, this looks like a stack of coins getting shorter, such as starting with $10$ coins, then $8$, then $6$. The rule here is to subtract $2$ from the previous number.

The Rule is the mathematical instruction that tells us how to get from one number to the next in a sequence. If a sequence is $5, 10, 15, 20$, the rule is $+5$.

A Number Sequence is a list of numbers arranged in a specific order according to a rule. For example, $2, 4, 6, 8, 10$ is a sequence of even numbers.

An Input-Output Table (or Function Machine) shows how a rule is applied to a set of numbers. Imagine a machine where you drop in the number $3$ (Input), the machine adds $4$ (Rule), and out pops $7$ (Output). This can be visualized as a two-column table where every number in the left column is changed the same way to get the number in the right column.

Predicting Patterns involves using the identified rule to find missing terms or future terms. If the rule is $+10$ and the last number you see is $40$, you can predict the next number will be $50$.