Y=mx+c

Linear functions have been a difficult topic for me in the past but I think I´ve finally nailed it.

It was the first time my year 8 class had encountered linear functions so we started with real world situations.  I know it sounds ridiculous, and it´s a bit embarrassing, but I´ve never started with a real life situations when previously teaching this topic.  I know.  Terrible maths teacher mistake!  The lesson went as such:

• The students started to understand the concept of gradient and how each point increases by the same amount before I even hit them with all of the different variable in the standard equation.  One example we worked with was wages. 

• The wage per hour was $12.50 and we started by calculating how much an individual would earn as their hours increased. 

• Next, we pretended to be business owners and we needed to calculate our employee's wages quickly and efficiently since we are Mathematicians and that´s how we work.  We created an equation so that we could calculate any amount of wages when there is a starting amount and then wages increase with every hour worked.  For example, C=12.50x+50 where someone receives $50 plus $12.50 for every hour that they work.  Since we had just completed real-life graphs it was easy for students to plot a graph to illustrate their calculations with hours on the x-axis and total wages on the y-axis. 

• We then started to consider how the points increase consistently and discuss the concept of gradient or slope.  Also we use the starting point to learn about the y-intercept and how these aspects of the graph connect to the equation.  They got.  They finally got why the gradient is useful, how the equation connects to the graph and how we can take information like the y-intercept and gradient from the equation in slope-intercept form.  PHEW!

Another nice part of this lesson is the way I got students to take notes.  I used an interactive notebook where they created a foldable and we discussed important parts of y=mx+c.  My students enjoyed the alternative method of note taking and I enjoy looking through their books much more!