Odd Numbers and Square Numbers

cults3d

Odd Numbers and Square Numbers Odd numbers {2n - 1, where n is a natural number} are not "odd" at all; they're actually very interesting and geometrically beautiful. One activity suitable for students of all levels involves the sum of the first M odd numbers, which equals M^2. For example, the sum of the first five odd numbers (1, 3, 5, 7, 9) is 25 = 5^2. Without 3D models, one can simply use a square grid and have students color the odd numbers while discussing the progression of sums. Using 3D models allows reaching out to more students and enabling them to see, feel, and play with multiple connections between number concepts and their geometric implications. There are many ways to create squares or other shapes! It can be proven by induction: (1) When M = 1, Sum = 1^2; the sum of the first odd number is just 1. (2) Assuming the sum of the first M odd numbers equals M^2, the sum of the first (M + 1) odd numbers equals *M^2 + 2M + 1*, which can be written as (M + 1)^2. (3) QED. This is nice, but I still prefer the geometric aspect of the story. Among the Files 1. A set of odd numbers (1, 3, 5, 7, 9, 11) with a height of 20mm. 2. A set of odd numbers (1, 3, 5, 7, 9, 11) with varying heights (step = 5mm). 3. The odd numbers can be printed all at once or one by one. Reference Conway, J. H., & Guy, R. (1995). The book of numbers. New York, NY: Copernicus.