Mathematical Modelling and Earth Day
Earth Day is April 22nd each year. To celebrate we made a few resources for you and your students to explore the world around us using mathematical models.
Scatterplots
We can use scatterplot graphs to create our mathematical models using a linear equation. Here’s a short video explaining what these graphs are and how we use them. Including how to calculate slope, yintercept, and the equation of the line.
Variables
In order to answer our question we need to collect data, and that data comes in the form of variables. But what are the different types of variables and what do they mean?
Calculating the Slope of a Linear Model
In order to be able to use our mathematical model we need to be able to create an equation.
For a linear graph this is y = mx + b.


 y: what we are looking for (response variable)
 x: what we are looking at to find y (explanatory variable)
 m: the slope of the line, where m = (y2 – y1)/(x2x1); two points on our line of best fit (not two of our data points)
 b: the yintercept, or what y equals when x = 0 (need to find slope first to find this value)

We first start with the line of best fit (a line we either draw or use a program like Excel to help us find) that is as close to as many points as possible. We then choose our two points (x1, y1) and (x2, y2) from this line in order to find our slope (and equation) of our line.
You can also use Excel to find this equation as well if you ask Excel to show the equation of the line as a label.
Your Turn
Now it’s your turn! Go out in your community or search national databases to come up with a question that you can model and make predictions about our world and our impact on it!
Remember the 6 steps:

 Think of a topic
 Turn it into a question
 Gather data
 Build your model
 Explore results/make predictions
 Present your results
And then think of something you’d like to investigate. Here are some ideas:


 Water usage vs # of household members
 Neighbourhood greenspaces vs average building height
 Changes in temperature vs time

If you find a good one to explore please share it with us on Twitter @FieldsInstitute and @DrPamB