Ratios, Proportions, Variation - A Lesson
Discuss everyday use of word "directly proportional" - as one quantity increases/decreases the other quantity increases/decreases.Ad Happiness directly proportional to public despairSurvey response directly proportional strength of relationshipDirect Proportions in Chemistry 5) Solve the three illustrated problems on this page, Solution Problems.
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 PhotoInversely Proportional Photo 2
Complete this investigation by solving a few problems using what you have learned.
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
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