Patterns - Shape and Geometrical Patterns

Understanding Patterns: A pattern is a sequence of shapes, objects, or numbers that are arranged according to a specific rule. For example, a string of beads alternating between a round red bead and a square blue bead forms a geometric pattern.

Repeating Patterns and Pattern Units: A repeating pattern is one where a specific group of shapes repeats itself exactly. The smallest part of the pattern that repeats is called the 'Pattern Unit'. In a sequence like $\triangle, \square, \bigcirc, \triangle, \square, \bigcirc$, the unit is the group of three shapes: $\triangle, \square, \bigcirc$.

Growing Patterns: In a growing pattern, the number of shapes or the size of the shapes increases at each step according to a rule. For example, Step 1 might have $1$ triangle $\triangle$, Step 2 has $2$ triangles $\triangle\triangle$, and Step 3 has $3$ triangles $\triangle\triangle\triangle$. The rule here is to add $1$ triangle at each step.

Reducing or Shrinking Patterns: These patterns decrease in size or quantity at each step. If a pattern starts with $6$ circles $\bigcirc\bigcirc\bigcirc\bigcirc\bigcirc\bigcirc$, then $4$ circles $\bigcirc\bigcirc\bigcirc\bigcirc$, then $2$ circles $\bigcirc\bigcirc$, the rule is to subtract $2$ circles each time.

Rotational Patterns: Shapes in a pattern can change their orientation by turning. Imagine a heart shape $\heartsuit$ that points up, then points right, then points down, then points left. This is a pattern based on a $90^{\circ}$ clockwise rotation at each step.

Tessellations: This is a special type of geometric pattern where shapes fit together perfectly without any gaps or overlaps, like the hexagonal patterns found in a honeycomb or square tiles on a floor.

Symmetry in Patterns: Many geometrical patterns use symmetry. If you place a line through the center of a shape or pattern and both sides look like mirror images of each other, the pattern is symmetrical. For example, a pattern of butterflies uses the central body as a line of symmetry for the wing designs.