Linear functions are the most important family of functions. They pervade our everyday lives and our work. Their graph is a line, and their general form is f(x)=mx+b where m is the slope of the function and b is the y-intercept, the value where the line crosses the y-axis. This Lab is designed to give you a picture of a linear function based on its formula. So play with it until you can picture the function from its formula and its formula from its graph.
Author: Ryan McQuade
Rate of Growth
We look at world population over the past 60+ years and ask whether the earth’s population is growing faster or slower today. Is it out of control and something we should all worry about or are we getting it under control? This is another problem directly related to climate change and one that students can argue with each other about. We use this opportunity to ask students about which kind of graph or chart would best convey the issue to other people. The type of graph or chart to be used to convey data is of great importance in business and industry today and one that requires students to creatively ask What if… about.
CO2 Growth
Spreadsheets offer us a nearly unlimited ability to develop and learn from case studies using real world data. We will focus mainly on climate change which is an area rich in possibilities and of great interest to students. In this case study we look at the production of carbon dioxide per person in the United States over the past 200 years. We take this opportunity to introduce students to the difference between quantity and growth, between the amount of CO2 produced and the year-to-year growth in production. We challenge students to consider whether this growth is an increasing problem.
Sierpinski Fractals
Fractals are a new 21st century mathematics. They are patterns that repeat themselves at various scales. This one is based on the odd numbers in Pascal’s triangle. We learn to create it easily by using Conditional Formatting which enables us to color cells or text based on a quantitative relationship. To turn Pascal’s triangle into a Sierpinski fractal all we have to do is color cells that are odd numbers. Here again is an amazing pattern involving odds and evens. There are a wide number of other Sierpinski fractal patterns.
Normal Distribution
Most museums with math exhibits have a Pascal’s triangle made up of pegs with balls falling down between them and bouncing off of them. One of the things they want to show is probability and the Normal or Bell curve produced by these balls as they fall down most of us are familiar with. This is the curve produced if we flip a honest coin a large number of times and ask what are the chances of getting all heads, of all heads but one and one tail, of getting all but 2 heads etc. We ask what does a Normal distribution look like and why does this extremely simple pattern produce it?