Basic equations are the most straight-forward type of math problem; numbers and operations are presented, and you must figure out the answer. "3 • 4 = " is a number sentence, as is 78(3^4/14) + -16.6 - 9 =". The point is that you are solving only for the answer, not part of the question, and as such, you can solve the problem as it is written without having to invert anything or cancel anything out.
Algebraic equations are like basic equations except you already have at least part of the answer and are instead solving for part of the problem, usually represented by variables.
"x • 4 = 12" is an algebraic equation, as is 2x^2 -45z + 28 = y. Knowing how to solve algebraic equations is the foundation for all higher forms of math including trigonometry and calculus.
Word problems are math problems written like stories to show their real-world application. For example, 3 • 4 = as a word problem would read something like "Oranges come in bags of three. Chen buys four bags. How many oranges did Chen buy?" Word problems can also be used in algebra. "A motor boat maintained speed of 27 miles per hour relative to the water going 20 miles upstream and returning. The total time of the trip was 1.5 hours. What is the speed of the current?"
Graphs are visual representations of equations or relationships between numbers, pictures of simple and algebraic equations. A graph can be converted into an equation and vice-versa if you know the correct formulas. The graph of a basic equation is a straight line and called a linear graph. Algebraic equations can form different types of graphs, the most common being a function: the graph of an equation with one output value for each input.
Shapes can be mathematical problems when you must figure out their dimensions. Geometry is the study of shapes, and trigonometry the study of triangles. Problems involving area, volume, perimeter and pi are all shape problems. Shape problems often relate to algebra, for example, if you are given 130m as the perimeter of a quadrilateral, and three sides with lengths of 20m, 50m and 40m and must find the length of the missing side.