Reasoning Using Mathematical Models Module Overview

Mathematics is about the patterns that arise in the world about us. Good mathematical models are often versatile and flexible, and the models of this unit apply to problems of life. Growth of money at interest is like growth of biological populations. Inflation of a currency or depreciation of an assets is like decay of radioactive substance. In this unit, you will consider models that change over time: bank accounts, the amount due on a loan, temperature effects and the size of a population. You will see how mathematics can be applied to your life in interesting, enjoyable, and meaningful ways.

Essential Questions

What might we mean by bivariate data? How long will it take to save $2000?
How can money earned be thought of as a sequence of values?
How do we determine the rate of change in an earnings model?
Why do you think the prices of goods change over time?
Will the temperature of a hot cup of coffee change at a constant rate?
Are there patterns observed in functions without a constant rate of change?
What types of models are used for investigating events involving time?
What significant differences in time/seasons exist between the Southern and Northern Hemisphere?
How do hurricanes affect the weather of Florida?
What mathematics can be observed in a Ferris Wheel?
What do you think the rebound percentage is for a tennis ball? A basketball? A racquetball?
When taking medication, is it important to take the same amount each day?

Key Terms

The following key terms will help you understand the content in this module.

arithmetic sequence - a pattern of numbers that have constant differences between consecutive terms.
bivariate data - data that involves two different variables whose values can change
exponential function - a function with a constant multiplier
function rule - defines a term in a sequence using the term number and is based on an input-output model
geometric sequence - a pattern of numbers that has a constant ratio between consecutive terms
linear function - a function with a constant rate of change
periodic function - functions that repeat over and over, or cycle on a specific period
recursive rule - defines a term in a sequence using the previous term and is based on an iterative process
step function - special piecewise function with a series of segments

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