Monthly Archives: May 2011

Real-World Math

Students always ask, “When am I ever going to use this?” The following is a list of a few common math function types and associated real-world math contexts.

Linear functions

Anything that has a constant rate of change is a linear function.

The total cost of bowling n games at a price of $5.00 per game when the shoe rental is $4.00:
linear function example

A cell phone plan costs $59.99 for 1000 minutes. Additional minutes are $0.45 each. The monthly cost of the plan when you go over by x minutes:
linear function example
Gasoline currently costs $3.799 per gallon. The cost of buying g gallons:
linear function example
Degrees Fahrenheit and degrees Celsius are both used to measure temperature. Water freezes at 32 degrees Fahrenheit or 0 degrees Celsius. Water boils at 212 degrees Fahrenheit or 100 degrees Celsius. The temperature in degrees Fahrenheit when the temperature is c degrees Celsius:
linear function example


Exponential functions

Anything with a constant percentage change is an exponential function.

According to the Central Intelligence Agency, Argentina had a population of 41.8 million people in 2011 and was growing at a rate of 1.017% per year. The population of Argentina (in millions) t years since 2011:
exponential function example
According to the Central Intelligence Agency, Japan had a population of 126.4 million people in 2011 and was declining at a rate of 0.278% per year. The population of Japan (in millions) t years since 2011:
exponential function example
The future value of a $1000 investment earning 3.21% interest compounded monthly after t years:
exponential function example


Piecewise functions

Anything where different rules apply in different situations.

The monthly cost of a cell phone plan with 1000 included minutes for $59.99 and extra minutes costing $0.45 when m total minutes are used:
exponential function example
The cost of n greeting cards when cards cost $1.29 each when 10 or less cards are ordered and cost $0.99 each when more than 10 cards are ordered:
exponential function example

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Arithmetic activity cover photo.

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Rule of 4

The Rule of 4 refers to representing mathematical functions with graphs, tables, equations, and words. As learners discover how to represent functions in each of these ways, the mathematics becomes more meaningful. For example, consider the following cell phone plan offered by T-Mobile in 2011, represented using the Rule of 4.

Words Representation (from website)
Even More 1000 Talk + Unlimited Text
$59.99 includes 1000 whenever minutes
Additional minutes $0.45 per minute

Table Representation
Table of minutes vs cost

Graph Representation
Graph of cost vs minutes used

Equation Representation
Equation representing cost vs minutes used

Despite the fact that each of these representations of the cell phone cost function looks different, the same function is represented in each representation. All learners should practice to increase their ability to “see” the other forms mentally even when only one form is given.