Play with Patterns - Shape Patterns

Understanding Patterns: A pattern is a sequence where shapes, colors, or designs repeat in a specific order. For example, a sequence showing a red circle followed by a blue square, then repeating that same pair, forms a basic repeating pattern.

Repeating Patterns: These are patterns where the core unit stays exactly the same as it repeats. In a visual sequence like $\bigtriangleup, \square, \bigcirc, \bigtriangleup, \square, \bigcirc$, the core unit is $\bigtriangleup, \square, \bigcirc$. To find the next shape, you identify where the sequence starts over.

Growing Patterns: In these patterns, the elements change according to a rule, usually getting larger or adding more parts. For example, if the first step is a single dot $\cdot$, the second is a $2 \times 2$ square of dots, and the third is a $3 \times 3$ square of dots, the pattern is growing by increasing the side length of the square by $1$ each time.

Rotational Patterns (Turns): Shapes often change their orientation using turns. A $\frac{1}{4}$ turn rotates a shape by $90^{\circ}$ clockwise (like a clock hand moving from 12 to 3). A $\frac{1}{2}$ turn rotates it by $180^{\circ}$, making it appear upside down compared to its original position.

Mirror Symmetry in Patterns: Some patterns are created by reflecting a shape across a line of symmetry. If you see a shape like the letter 'E' and the next shape is its mirror image '彐', they form a symmetrical pattern. The line of symmetry acts like a mirror placed vertically or horizontally.

Tiling and Tessellations: This is a type of shape pattern that covers a flat surface completely without any gaps or overlaps. Think of a bathroom floor with hexagonal tiles or a brick wall; the shapes fit together perfectly to create a continuous pattern.

Identifying the Pattern Rule: To solve any pattern problem, you must find the 'rule'. This is done by comparing the first term to the second term and checking if that same change applies to the third term. The rule could be 'Rotate $90^{\circ}$ clockwise' or 'Add one more side to the polygon'.