Fawn Nguyen, a creative and inspiring teacher, had a great idea for Math Taboo on her blog. What a great way to teach math vocabulary with a fun diversion. Check it out!

Math Taboo

One important component of the Make It Real Learning approach is making sense of mathematics and mathematical models of real-world contexts. For example, consider the following sample exam question for an algebra class and its corresponding solution.

Based on data from 1985 - 2004, the difference between US oil field production and net oil imports may be modeled by million barrels where t is the number of years since 1985 (Source: Modeled from Statistical Abstract of the United States 2007, Table 881). When the value of the function is negative, the US is importing more oil than it is producing. What is the practical meaning of the 2251 and the -278.3 in the equation?

This question doesn’t require any computations but it does require an understanding of quadratic function models.

The 2251 is the initial value of the function. Since 1985 is the initial year (t = 0) for the model, US oil field production exceeded net oil imports by 2251 million barrels in 1985.

The -278.3 is the initial rate of change of the function. In 1985, the difference between US oil field production and net oil imports was decreasing at a rate of 278.3 million barrels per year. According to the model, the difference in 1986 was predicted to be about 278 million barrels less than the difference in 1985.

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:

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:

Gasoline currently costs $3.799 per gallon. The cost of buying g gallons:

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:

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:

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:

The future value of a $1000 investment earning 3.21% interest compounded monthly after t years:

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:

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:

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

Graph Representation

Equation Representation

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.