Patterns - Number Patterns

Growing Patterns: These are sequences where each number increases by a fixed rule. For example, in $4, 8, 12, 16$, each term increases by $4$. Visually, imagine a staircase where each step is $4$ units higher than the previous one.

Square Numbers: A square number is the result of multiplying a whole number by itself (e.g., $3 \times 3 = 9$). Visually, these numbers can be arranged as dots in a perfect square grid with an equal number of rows and columns, such as a $4 \times 4$ grid representing $16$.

Triangular Numbers: These are numbers that can form an equilateral triangle. The sequence is $1, 3, 6, 10, 15, \dots$. Visually, you can build this by starting with $1$ dot, then adding a row of $2$ dots underneath, then a row of $3$, and so on ($1, 1+2, 1+2+3$, etc.).

Magic Squares: A magic square is a $3 \times 3$ grid of numbers where the sum of each row, each column, and both diagonals is the same constant value. Visually, it looks like a sudoku-style grid where every direction adds up to the same 'Magic Sum'.

Number Towers/Pyramids: In this pattern, numbers are stacked in blocks. The value of any block is equal to the sum of the two blocks directly underneath it. Visually, it looks like a brick wall where each brick rests on two bricks from the row below.

Fibonacci-like Patterns: This is a sequence where each number is the sum of the two numbers before it. For example, in $2, 3, 5, 8, 13$, we see $2+3=5$ and $5+8=13$. Visually, this pattern is often seen in the growth of flower petals or spiral shells.

Patterns in Odd and Even Numbers: There are specific rules for sums: $Even + Even = Even$, $Odd + Odd = Even$, and $Odd + Even = Odd$. For example, $3 (Odd) + 5 (Odd) = 8 (Even)$.

Coding and Decoding: Patterns can be used to hide messages by assigning numbers to letters (e.g., $A=1, B=2, C=3$). A pattern like 'Add 2' would change 'A' into $3$ (C). Visually, this is like a translation table where one set of symbols maps to another.