Linear Equations Applications

Kids have trouble with algebra.  Like big trouble.  Many of them suck at it...big time.  I think that a lot of that comes from the fact that all of a sudden math gets really abstract and a lot more complicated than it was before.  Take linear equations for example.  In pre-algebra (where I taught at least) they learned about slope-intercept form.  And we did tons of applications with it.  Tons of scenarios that for the most part made sense to them.  So they were for the most part comfortable with writing equations.

All of a sudden in algebra though, we have standard form and even more abstract point-slope form.  And they all kinda represent the same thing (a line).  Take a kid for whom math doesn't come naturally and they're going to have no idea what's going on.

I tried for this unit to focus on some of the applications of these equations.  Especially so for standard form.  I actually feel pretty strongly about starting standard form off with an application.  I have always felt like standard form equations come naturally to many kids.  Before mentioning anything about standard form, or even being linear, I had kids do this activity.


Disclaimer: I did not make this up and take no credit for it whatsover.  It is a lesson from Connected Mathematics 2.

So without mentioning anything about Ax+By=C, kids are able to

• write and graph an equation
• find points
• determine that the relationship is linear
• find x and y intercepts

This is the part of CMP2 that I really liked, so I like to be able to infuse the investigation type model into a more traditional textbook curriculum.  I think that a mix of the two is ideal.

I'd love to have something similar for point-slope but I don't.  Maybe someday I will.

After teaching all three forms, I had kids do this station activity.


Another disclaimer: I didn't make up any of these problems.  I stole them all..just like I steal pretty much everything else.

They had to look at each problem and first determine what information was being given.  Some kids tried to read the problem and guess which form to use right away but I would stop them.  I had them first write down what information they were being given.

For example:

Marty is spending money at the average rate of $3 per day.  After 14 days he has $68 left.  The amount left depends on the number of days that have passed.

First I had them list the information out that they were being given:

• $3 per day - RATE
• 14 days, $68 left - PAIR OF VALUES

Then from there they could choose an appropriate form and write an equation.  They had to also be sure to define their variables.

Overall they did well and I enjoyed watching them actually have to think.  They couldn't just plug numbers into spots, they had to first make sense of the information which is often the most difficult part.

For homework that night I had them complete the same type of thing individually



My main reason for giving this homework was because the activity during class was done in groups so I wanted to check what they were able to do on their own.