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.