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Cubic and Square Numbers and Multiples of 9 — Four in a Row Game and Sum of Cubes = Triangular Squares

After studying square and cubic numbers, to bring it all together, I created a game that combines these two sequences of numbers and introduces a third sequence of numbers: multiples of 9.

Cubes, Jackson Origami — First 12 Cubic Numbers — Midpoints

After spending weeks exploring the wonders of squares and square numbers, the natural extension from two dimensional figures is the study of cubes. 

Estimating Square Roots—Kramer Method

When I was in fifth grade I was fascinated with square roots. The square root of perfect squares are easy if you know your squares such as 1x1=1, 2x2=4, 3x3=9 and so on. Since the square of 3 is 9, the square root of 9 is 3. They are opposites: square roots are the opposite of squares; addition is the opposite of subtraction; multiplication is the opposite of division.

Square + its Root + Next Root = Next Square; Product of 4 Consecutive Integers + 1 = Square

Square + its Root + Next Root = Next Square