Pictorial Representations
Many number sequences can be understood better by visualizing them as shapes made of dots. This connects Arithmetic (numbers) with Geometry (shapes).
Triangular Numbers
Numbers that can be arranged in a perfect triangle. Sequence: 1, 3, 6, 10, 15…
Square Numbers
Numbers that can be arranged in a perfect square grid. Sequence: 1, 4, 9, 16, 25…
Hexagonal Numbers
A Hexagonal Number represents the number of distinct dots in a pattern of hexagons consisting of a central point and successive hexagonal layers. Sequence: 1, 7, 19, 37…
The rule for generating hexagonal numbers involves adding multiples of 6:
Tip
Connection: Notice that 36 is both a triangular number and a square number (). This means 36 dots can be arranged perfectly into a triangle AND a square.