Setup Costs and Linear Equations

I am heading into linear equations in my Algebra I class.  As part of it, I include the usual business equations in the book.  Unfortunately, they assume that students will do the problems without understanding what the m and b are about or the students already have the knowledge.

Unfortunately, my students do not understand the basic premise enough to understand what the equation is about.  I do not want them to blindly plug in numbers because they don't understand the results.

So I have to include a lesson on what the slope and the y intercept represents within a business context.  I take time to establish  a scenario that they are soon to be business owners who have to determine the cost of making an item. 

This is fun because they have to determine the setup cost before they even start making the item.  Then they have to figure out the cost of making that item. The second step is to determine the revenue of the same item.  Finally they determine the the break even point.  This activity puts it more into a real world situation.

The one thing I have not been doing but will start this year (Thanks, Adam Liss) is having them use a spread sheet to see how adjustments in cost and setup can effect the final amount made and the breakeven points.  How does one penny more or less change everything.  They need to see this through the use of spread sheets.

The nice thing about spread sheets is they automatically change the graphs for you, all you do is change the amounts.  The visual graphs can make a greater impact on students than just the numbers because they see the changes by looking at just the slopes.

To prepare students for this, I found Khan Academy has a great section of instruction focused on linear function word problems that are actually decent as far as real world goes.  Fuel consumed, gym memberships, icebergs, etc. 

I think too often we teach linear functions with just the equations. We should take time to discuss the possible meanings behind the equations to give students a chance to see there is meaning.  I just had the students do a performance task involving two different linear equations and one student realized the slope was different. (Yeah.)

As I've said before, we need to add context to the equations so they understand the concepts better.

Let me know what you think.  Have a great day.