Room 215

On the FIRST day of math class, Mrs.McManus gave to me...

a book titled Geometry!

This geometry book is very useful! Geometry is the branch of mathematics that studies size, shape, and position of shapes and figures. It is very important to visualize and apply higher-order thinking skills! 

On the SECOND day of math class, Mrs.McManus gave to me...

TWO SPIRALS OF ARCHIMEDES!

The spiral of Archimedes is a plane curve made by a line turning itself uniformly around one of its points(origin). Invented by Greek mathematician Archimedes, the length of the curve's radius r from its center is always a constant ratio of the angle that the radius forms with a fixed axis. The equation is  r = aθ.

and a book titled Geometry!

The beauty of the Euler Circuit! A Euler Circuit is a circuit that utilizes every edge inside a graph without repeating any edge. It begins and ends at the same vertex. 

On the THIRD day of math class, Mrs.McManus gave to me...

THREE EULER CIRCUITS! 

two spirals of Archimedes, and and a book titled Geometry!

On the FOURTH day of math class, Mrs.McManus gave to me...

FOUR DETERMINANTS!

The determinant is a scalar value that can computed from the elements of a square matrix. Using geometry, it can also be a "volume scaling factor" of the linear transformation described by the matrix. It can be positive or negative. Below is an example of a 2 x 2 matrix with the determinant ad-bc. 

       three euler circuits, two spirals of Archimedes, and a book titled Geometry!

On the FIFTH day of math class, Mrs.McManus gave to me...

five fascinating fractals!

Take a good look at these! A fractal is a complex pattern created by repeating a simple process in a continuous "feedback loop". Fractals exist in nature, geometry(Sierpinski Triangle and Koch Curve), algebra(Mandelbrot set). They are infinitely COMPLEX.

On the SIXTH day of math class, Mrs.McManus gave to me...

six combinations!

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter, and you can select items in any order you want! The formula for a combination is

How many pairs can be made from a group of 6 people?

EXAMPLE:

On the SEVENTH day of math class, Mrs.McManus gave to me...

         SEVEN SIERPINSKI TRIANGLES!

A type of geometric fractal, a Sierpinski triangle is a fractal attractive fixed set with the shape of an equilateral triangle. It is continuously subdivided into smaller equilateral triangles.

On the EIGHTH day of math class, Mrs.McManus gave to me...

   EIGHT GEOMETRIC SEQUENCES!

A geometric sequence is a sequence of numbers in which each term is found by multiplying the previous term by a certain factor, called the common ratio r.

1, 2, 4, 8 , 16....

1, 2, 4, 8 , 16....

1, 2, 4, 8 , 16....

1, 2, 4, 8 , 16....

1, 2, 4, 8 , 16....

1, 2, 4, 8 , 16....

1, 2, 4, 8 , 16....

1, 2, 4, 8 , 16....

   NINE PERMUTATIONS!

On the NINTH day of math class, Mrs.McManus gave to me...

A permutation is a mathematical technique that determines the possible arrangement in a set when the order of the arrangement matters.

6 people are in a contest. How many ways can first and second place be awarded?

EXAMPLE:

   TEN DERIVATIVES!

On the TENTH day of math class, Mrs.McManus gave to me...

A little taste of calculus! A derivative is the instantaneous rate of change or the slope at a specific point of a function. It is also known as the slope of a tangent line. It is a fundamental tool in calculus!