| uses Algebra or Geometry to REPRESENT an IDEA or CONCEPT in the real world.
The form that the models can take are varied and can include: figures and diagrams as in Geometry; tables, graphs, and equations as in Algebra; and computer programs as simulations. Models help us understand things too large, too small, or too complicated to study directly. Scatter plots are graphs of (x,y) ordered pairs used to determine any association between two variables, (ie. how the outside temperature is related to the calendar month.) Within the ordered pair the first coordinate is called the "independent variable" and the second coordinate is called the "dependent variable".
 ???What would you expect the graph to look like if you compare the number of letters in a person's name and their shoe size???...... We call this example "no association". Communication of information is the underlying theme of mathematics. There are basically three ways to communicate: Words, Pictures, or Symbols. Words have limitations and require the receiver of the infomation to be able to translate and give meaning to the data. Pictures (graphs, tables, diagrams) are somewhat more readily understood by interpreters. Symbols (equations), however, provide the most universally understood form of communication. In studying Algebra we learn how to convert from one form of communication to another, ie, picture to symbol, words to pictures, tables to equations, with the ultimate goal of being able to take any worded scenario and convert the relationship into equation form.
More complicated relationships require a little more analysis before the relationship becomes obvious. Try this one!
Using your knowledge of the slope-intercept form (y=mx + b) for the equation of a line you could derive the same equation using a minimum of any two of the data points. |
Recall that variables are quantities which change depending on the situation
while constants are quantities with a fixed value like $1.00 = 100 cents