Grade 6-8: Trigonometric Sine Function

Visualization of the trigonometric sine function

Grade 6-8: The Fibonacci's Sequence

The Fibonacci's Sequence is a series of numbers in which each number ( Fibonacci number ) is the sum of the two preceding numbers. 
The simplest is the series 1, 1, 2, 3, 5, 8, etc. The next number is found by adding up the two numbers before it.

1. • The 2 is determined by adding the two numbers before it (1+1)
   • Similarly, the 3 is determined by adding the two numbers before it (1+2),
   • And the 5 is (2+3),
   • and so on!

   (The Fibonacci sequence is defined by the property that each number in the sequence is the sum of the previous two numbers; to get started, the first two numbers must be specified, and these are usually taken to be 1 and 1. In mathematical notation, if the sequence is written  then the defining relationship is

with starting conditions .)

Math Games: Fractals

According to Merriam Webster, a fractal is a curve or geometric figure, each part of which has the same statistical character as the whole. Fractals are useful in modeling structures (such as eroded coastlines or snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth, fluid turbulence, and galaxy formation.

The term fractal was coined by Benoit Mandelbrot in 1975 in his book Fractals: Form, Chance, and Dimension.

In 1979, while studying the Julia set, Mandelbrot discovered what is now called the Mandelbrot set and inspired a generation of mathematicians and computer programmers in the study of fractals and fractal geometry.

Fractals involve numbers and equations, like other mathematician ideas. The difference is that fractals can be used to generate complex, beautiful images. 

Here is a gallery of computer-generated fractals. 

Square Root