Systems of Equations Unit Plan

During this years MTBoS blogging initiative, I used the share the love prompt to capture some of the things I wanted to use and remember for teaching the quadratics unit. I am going to try to continue doing something similar to keep links and ideas for other units as well. I am really terrible about keeping all the activities I have used in the past or new things I want to try so this way I have an electronic record and I can share idea with other math people:

We are knee deep into a systems of equations unit in one of my Algebra classes. So far we’ve done the Systems of Equations Launch which I wrote about here. Which led into graphing systems. At the bottom of that post I wrote how I would adapt it next year by adding in some lines that never cross or end up being the same. Since I hadn’t done that with the launch, I used that idea for the warm-up the next day.

I projected a Desmos graph with a few different lines and told them that the battleship path was the red line. They were tasked with estimating mine placement for the other 4 lines.

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This quickly brought up the “missing” orange line and the inability to lay a mine on the green path. We discussed possible numbers of solutions to a linear system then I had them sketch ideas for a system that could have two solutions.  Afterwards they did some more practice with graphing to find solutions. And ended by having the students create scenarios were you’d care about the intersection and then write up a problem which would fit that story. I collected them. Some will turn into warm ups or lagged review and some will end up  on quizzes or the end of unit assessment.  I’ve been working over the last few years to incorporate student generated problems. They seem to get excited about the possibility and its improved their problem writing because they want me to use theirs. Continue reading “Systems of Equations Unit Plan”

Systems of Equations Launch

After wrapping up our linear functions unit, the students had one day off. When they returned to class on Thursday, each table had been turned into a mini command center. Big sheets of graphing paper were stuck down to the table and an assortment of string, scissors, tape, rulers and three colored dots were at each table.

When students were sorted into teams, they were handed the mission sheet:

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I told them they could only use the supplies on the table and at the end of the activity, I’d need a report on where the mines should be laid in the form of coordinates.  And they were off! (Side note, the original question had more information, basically telling them how to solve, so I just erased it which is way the type is a bit crazy. I’ll type up a nicer version for next time with the additions I add at the end of this post).

After we stopped, I took the coordinates and posted each teams on the board. No groups had the exact same answers. They wanted to know if they “won” but I told them they’d have to wait. Continue reading “Systems of Equations Launch”

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.

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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….