This year, we will focus our study of algebra on the creation of mathematical models--that is math that we can use to predict and describe the world around us.
Sometimes, mathematicians, scientists, or engineers create models to try to predict what will happen. Other times, they create models using math, because to build a physical model of something is too expensive, or dangerous.
You can create a mathematical model of a disease travelling through a population to try to predict who will become infected.
You can create a mathematical model of a farm, to figure out what the best crops to plant are, in order to maximize profit.
You can create a mathematical model of yearly temperatures in Danvers, to predict how hot it will be on graduation day.
You can create a mathematical model of the population of the world, to predict when our population will pass 8 billion people.
Mathematical modeling is a growing field of employment, and a great way for us to apply math in a more useful way than traditional word problems.
The process of modeling goes something like this:
You notice a pattern, or something interesting that you'd like to know more about.
You collect data to better understand the patterns you're interested in.
You analyze the data to see if you can make an equation that will help you predict future data.
You compare your predictions with what actually happens to see how good your model is.
You tweak your model to make it more accurate.
You make lots of money! Well, wouldn't it be nice if that were always the case.