Introduction to Systems of Equations

My Algebra 1A students are just starting the systems of equations unit, and what better way than a TrashketBall competition. I’ve seen a few people use Trashketball as a fun review game, but Mr. Orr shared an awesome three day lesson on his blog. I borrowed Day 2 and 3, adjusted them a bit and made it an introduction to systems of equations.

Students played 4 rounds of 1 minute each to find their average make rate per minute, converted that to makes per second and came up with an equation using that rate. Then they graphed their lines. With a partner, students discussed what their graphs meant and compared and contrasted the lines. (All start at 0, but all different rates etc). A few pairs shared out insights.

IMG_0051 IMG_0054  IMG_0053 IMG_0058

We then graphed all the lines on a projected Desmos graph. I asked who would win a basketball competition and how they knew. Then I asked how to make the game more fair. Eventually they settled on giving the slower rate a head start. They jumped back with their partner and overlaid their original graphs using patty paper on one graph. They had to decide who should get the advantage and how many balls that advantage should be. One group wanted to give the ‘better’ player a late start (moving the x-intercept instead of the y) which I said was fine. They graphed the new line on the same graph as the line that wasn’t changing.

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Up to this point we had just thought about how to make the game more fair. I asked them to make observations about the new set of lines. The first observation was that they intersected. Another student pointed out the the originals intersected too, but that the intersection was no longer at (0,0). We ran with that and talked about what the intersection would mean and why did we want to move it away from the origin. That intersection point became new time length for each partner to compete against each other. I had them write down the intersection point and decide what each value meant (time of game, # of makes expected)

Almost all of these games were quicker than the original one minute, but one generous competitor gave a bigger advantage had an almost 2 minute game. New partnerships were formed and they played one more time.

Closing as a whole group discussion about the game. We had a few ties and most were fairly close to the predicted make values. A few were outliers so we talked about those as well. I then introduced the term “systems of equations” and “solution to a system of equations” and the students contented them to the context of the trashketball game.

Tomorrow, we’ll move into solving systems graphically more formally, with lots of in class practice time. Then we’ll move into pictorial puzzles to lead into the substitution method. Elimination/Combination will round out the introduction to systems – still looking for the best hook for that one.

I really encourage you to try out Trashketball. Every single student was engaged and doing lots of great math. I will definitely be refining it for next year, maybe even extending as a unit long project. I did also promise a trashketball performance task on the unit final….

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Author:

I am a math teacher at a public, alternative high school school. I’m the only math teacher at my site, so I get to teach it all. This is good. The bad? I have 7 different preps! Twitter: @altmath

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