Methods of instruction, demonstration and presentation vary according to the mathematical background, age group and level of students. As is common sense, many variables must be considered when teaching and attempting to reach multiple intelligences when presenting abstract material or mathematics. For a brief thought, one may consider presenting graphs of single varible fuctions to a typical 8th grade group of students (which is anything from typical).

Two methods for demonstrating graphs may be helpful suggestions to instruction.

Method 1 (early in day, mature students, advanced students)

Demonstrate what you are doing with fucntions and show graphs of the family of curves/lines together. Then procduce the sequence slowly one at a time illustrating what causes them to be geometrically different. You may close or refine lesson by again showing all the functions graphed together.

Step 1

Step 2

Step 3

Step 4

Step 5

Method 2 (late in the day, students who get overwelmed/frustrated easily, very advanced students)

Set a stage for what you are doing by graphing a function. Proceed by graphing a logical sequence of a family of curves/lines illustrating how you can change the curve by manipulating the formula for the functions. For enrichment, all the curves can be presented together. For gifted students the lesson may begin by presenting one function and allowing them to take over and go with it in as many directions as possible.