Definition of Mathematics
The four most central things that math studies are: Numbers and Equations; measurements; properties; and shapes.
Examples:
Numbers and Equations- In math classes when we solve equations such as 4x+2=10 , we are evaluating how the numbers relate to eachother. In Algebra we do a lot of graphing, which is taking numbers and equations and plotting them onto a graph, this shows the relationships of numbers and equations. Algebra can be used as a tool for representing and solving a varitey of practical everyday problems. We can use addition, subtraction, multiplication, division and exponentiation to form algebraic expressions. Concepts such as prime numbers and relatively prime numbers, factorization, divisor, multiple, and divisibility can help further our understanding of solving problems involving intergers.
Measurements- Various types of systems and methods are used in math class to measure certain areas, lengths, volume, etc. In geometry for example, measurements are one of the main focuses. Comparing rise over run (slope) measures steepness. Problems involving a scale such as in maps and diagrams involves measuring. Measurements can be used to represent graphs of functions in standard coordinate systems. Measurements are a main constituent of variables and integers in basic algebra problems.
Properties- Different properties such as the associative, distributive, symmetric, and more, are often applied to numbers and equations. They are applied to functions such as logarithms to help solve them. Properties are very useful to help you solve equations because they will give a a layout of what to do and then you must finish solving them. Properties are used in every math equation as a step in solving it.
Shapes- In math class we study various shapes. In geometry for example, we apply algebra to different shapes and figures in order to find out more about the relationships of numbers and shapes. The example below shows how shapes can be used to figure out algebra problems, this could also be written into algebraic form and vice versa to help solve practical problems. If the trapezoid equals 1 then the triangle equals 1/3 and from there the end result can be answered.
If 
+ 
= 2/3, what is 1? 
Paragraph 1- http://www.odedodea.edu/instruction/curriculum/math/pdf/algebra1.pdf
Paragraph 2- http://www.odedodea.edu/instruction/curriculum/math/pdf/algebra1.pdf
Paragraph 3- homepages.ius.edu/DTRAUGHB/ bertrand.htm
Paragraph 4- math.rice.edu/~lanius/ Patterns/
Picture 1- scnc.mcs.k12.mi.us/~mhspage/ clubs/equations/
Picture 2- math.rice.edu/~lanius/ Patterns/
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