Ratios, Proportions, Variation - A Lesson
by
Jackie Ruff

Discuss everyday use of word "directly proportional" - as one quantity increases/decreases the other quantity increases/decreases.

Ad Happiness directly proportional to public despair
Survey response directly proportional strength of relationship
Direct Proportions in Chemistry

Teacher note:  Good definition for students to work toward:  Two quantities, A and B, are in inverse proportion if by whatever factor A changes, B changes by the reciprocal or multiplicative inverse of that factor.  Definition from http://id.mind.net/~zona/mstm/physics/mechanics/forces/inverseProportion/inverseProportion.html
.

Funny photos for everyday use of term, "inversely proportional"

Inversely Proportional Photo

Inversely Proportional Photo 2

Complete this investigation by solving a few problems using what you have learned.

1.  According to Boyle's Law, the pressure P of a compressed gas is inversely proportional to the volume, V.  Click here to see an animation, Boyle's Law .  Suppose that fifty pounds per square inch is the pressure exerted by 150 cubic inches of a gas.  Find the pressure if the gas is compressed to 100 cubic inches.

2.   Click here to read about Ohm's Law.  After reading and solving the problem given on that page, find the amps of current if we change the resistor to a 50-Ohm resistor.

3.  Suppose that y varies inversely with x and y = 3 when x = 5.  Find y when x = 3.

Use the rabbit problem found here, RABBITS.

Find ratios of each term to preceding term and graph.
GoldenRatio.xls.
Construct golden rectangle, a rectangle where the length of the longer side to the shorter side is the golden ratio.

Link for students to investigate further:  Fibonacci

Student investigation using GSP file - GSP file reviews ratio for pi and leads students through construction of golden ratio and investigation of golden ratio in a regular pentagon:  ParticularRatios.gsp