Play with Patterns - Number Patterns

Number Patterns: A number pattern is a sequence of numbers that follows a specific rule. For example, in the pattern $2, 4, 6, 8, 10$, each number increases by $2$. Visualizing this on a number line, you would see equal-sized 'jumps' of $2$ units between each number to reach the next term.

Increasing Patterns: These are patterns where the numbers grow larger by adding or multiplying a specific value. For instance, in $3, 6, 12, 24$, each number is multiplied by $2$. Visually, this looks like a staircase where each step gets significantly taller than the previous one as you move from left to right.

Decreasing Patterns: These patterns show numbers getting smaller through subtraction or division. For example, in $100, 90, 80, 70$, we subtract $10$ each time. On a graph or chart, this would be represented by a series of points or bars that slope downwards in a straight line.

Growing Patterns: In these patterns, the amount being added or subtracted changes in a predictable sequence. For instance, in $1, 2, 4, 7, 11$, the jumps are $+1, +2, +3, +4$. Visually, if you represented these numbers with dots, you would see a shape (like a triangle) that expands by adding a longer row at the bottom each time.

Number Towers: A number tower is a pyramid-shaped arrangement of boxes. The rule is that the number in any box is the sum of the two numbers in the boxes directly below it. If you look at a tower with three levels, the single box at the very top is the final sum of the values layered beneath it.

Magic Squares: A magic square is a grid (often $3 \times 3$) where the sum of numbers in every horizontal row, every vertical column, and both diagonals is exactly the same. Visually, no matter which straight line you draw through the grid, the numbers on that line will add up to a 'Magic Sum.'

Coding and Decoding: Number patterns are used in secret messages by assigning each letter of the alphabet a specific number (e.g., $A=1, B=2, \dots, Z=26$). This creates a pattern where words like 'BAG' are converted into the sequence $2, 1, 7$. Decoding involves reversing this pattern to find the original words.