## 3.09.2011

### Systems of Equations: Substitution

I spent one day on solving systems by graphing which is exactly what I wanted since I know I will need much more time for substitution and elimination.

Before jumping into it, I wanted to review testing ordered pairs to see if they were solutions or not. Here was my thought: I would take four systems from our graphing investigation that weren't parallel and had simple ordered pairs for solutions. I made up a similar worksheet so that students could write the solutions in. Then in the middle box, we substituted the solution into the equation to algebraically prove why the ordered pair was a solution. I wanted to spend the rest of the class period reviewing this concept. So at home I had made up these index cards (I know, I'm obsessed!) of equations and their solutions.

And I said to myself, "Kyle, (That's what I call myself. Just kidding, that's a reference to a Boy Meets World episode. Eric is ridiculous!) how can I use these cards?" My first thought was a scavenger hunt where solutions would be hidden around the room and students would have to search for the correct one. Ok, so that was my only thought. But then what to do with the equations? Well why not hide them too? I had one of my geometry classes hide the cards and they were super sneaky. I should have taken pictures of all the places they hid them. It was insane. So students happily searched high and low, writing down equations and solutions in their nice, neat rows. And then suddenly it dawned on me...everything was written down randomly. We had no idea which solution went with which each equation. It would take forever to plug in every solution to every equation. What to do? Luckily, that was the end of class so I had plenty of time to ponder.

The next day I created another sheet, very similar to the past two. I laid out all of the index cards (there were 9) and had each student (luckily there are 9 of them too- what a coinky dink) take one. They wrote this at the top of the paper. Then, I gave them the first ordered pair which they wrote in the left column. In the middle column, they plugged the ordered pair into their equation. If it worked, they wrote 'yes' in the right column. If not, they wrote 'no'. The beauty of this was that there would only be one yes each time. But since you never know who will be yes, every person has to do every problem. Well technically after you get a yes, you don't need to do anymore, but I wanted them to practice.

This turned out to be a long, drawn out activity to practice nine problems. And they only used one equation! Next year I suppose I should give them one ordered pair and have them test several equations? Or maybe just scrap this entire activity and find something that gives practice with a variety of ordered pairs and equations.

I am proud of myself for making this activity work, even though it floundered on day one.

The students asked me if they could have a quiz over solving systems by graphing and proving solutions of equations because it was so easy, so I take that as a positive sign.

And I might just take them up on that offer.