Algebra - Matchstick Patterns

Algebraic patterns use variables to represent a rule that applies to any number of shapes. In matchstick patterns, we observe how the number of sticks grows as we increase the number of figures (like letters or polygons) being formed.

A variable is a letter, such as $n$, $x$, or $l$, used to represent an unknown or changing quantity. In the context of matchstick patterns, the variable usually represents the number of shapes or figures you want to create.

The rule for the letter 'L' involves two matchsticks—one vertical and one horizontal. To make one 'L', we need $2 \times 1 = 2$ sticks; for two 'L's, we need $2 \times 2 = 4$ sticks. The general rule is $2n$, where $n$ is the number of 'L's.

The rule for the letter 'C' consists of three matchsticks forming a 'U' shape rotated sideways. One 'C' needs 3 sticks, two 'C's need 6 sticks, and so on. Visually, each new 'C' adds a group of 3 sticks, leading to the algebraic rule $3n$.

The rule for a square formed separately involves four matchsticks. One square looks like a box made of 4 sticks, two separate squares use 8 sticks. The pattern follows the rule $4n$, where $n$ is the number of squares.

Constants and Variables: In the rule $5n$, the number $5$ is a constant because the number of sticks per figure remains fixed, while $n$ is a variable because the number of figures can change (1, 2, 3, etc.).

Pattern recognition involves looking at a sequence of figures and determining how many matchsticks are added for each new step. If the first figure has 3 sticks and each subsequent figure adds 2 more (forming a connected chain), the rule is derived by seeing the growth as $2n + 1$.