Shape, matchstick & figure-counting patterns

Patterns with shapes ask you to count sticks, dots, corners, or squares. Strategy:

1. Count for the first few figures.
2. Look at the difference — is it arithmetic?
3. Write a formula in n.

Matchstick patterns:

• Row of linked triangles: 1→3, 2→5, 3→7 sticks → 2n + 1.
• Row of linked squares: 1→4, 2→7, 3→10 sticks → 3n + 1.
• Row of hexagons joined side-by-side: 1→6, 2→11, 3→16 → 5n + 1.