Visual Number Patterns

Summing Patterns

Consider a square grid of numbers where the outer layer is all 40s, the next is 50s, etc. Instead of adding one by one, use multiplication.

Example: The “40-50” Square

Imagine a grid:

• 4 corners are 40.
• Edges between corners have 40.
• Center has 50s.

Method: Count how many 40s and how many 50s. $\text{Total} = (\text{Count of 40} \times 40) + (\text{Count of 50} \times 50)$

Hexagonal Patterns

Look at this hexagonal expansion.

The numbers often follow a rule:

• Sum of vertices?
• Difference between layers?

In the textbook example (Page 14), we see $35$ surrounded by $25$s, surrounded by $15$s. The rule might be $15 \times 6$ (outer) $+ 25 \times 6$ (inner) $+ 35$ (center).