Reflection: Relevance Creating your own Systems of Equations - Section 3: Closure

In this lesson, my students chose the first three scenarios far more than the others. No one chose the Grass Eaters scenario. The Bake Sale, Nickels and Dimes, and Cell Phone problems were modeled and solved quite well. In the cell phone problem, some students did not really state which was the better plan. They simply solved their system and wrote the coordinates of the solution. A couple of groups did not interpret the meaning of the solution with respect to the problem, which was required (see student work phone plan).

The Nickels and Dimes coin problem was set up and solved well. At the end, the students wrote the coordinate pairs and what coin each variable represents, but many added a solution with variables switched (see student work nickels dimes). I asked the students why they did this, and one of them said that it did not matter what variable came first here because their is no x and y.

So, I need to make things clearer to this group without getting too deep in theory. I indicated that the common definition of an ordered pair, which is generally accepted, satisfies the property (a, b) = (x, y) if a = x and b = y, and that we could state the order of the coordinates, at the beginning so that we remain consistent until the end. I talked with the students about the fact that in this case they began and should continue with the model (n, d).

Teacher:  Can you tell me when could it be important to state the variables in a particular order?

Teacher: Well, you solved this system by what method?

Students: Substitution, Oh….when I have to graph.

Teacher: Yes, why would the order matter then?

Students: Because the first variable is like the x and the second the y and they fall in different places on the graph.

Teacher: Yep, we generally use the first coordinates as our x, indicating horizontal movement, and the second as our y for vertical  movement.

I believe that the reason for these scenarios being chosen most was the relevance aspect they have. Personal and real-world relevance is motivating to students because they relate the subject matter to the world around them. The scenarios like the Cell Phone Plan and the Bake Sale are topics that students not only had previously encountered in other lessons, but probably have had personal experiences with.

In the classroom I find it very important to link material to the real world. I can usually tell when too much time is being spent on abstract ideas by observing student behavior. Many students become unmotivated and start to daze off, or just stop participating. Any time you stop and tell a story, or ask a question involving a real-world situation, students become more attentive.

Through listening to students' comments and discussions as they went around the scenarios, I quickly found that they identified with these cases and were more willing to come up with a situation involving a system of equations. Besides, similar situations to these particular scenarios had been modeled before. Students did not even try the Grass Eaters problem. Maybe this scenario could be replaced, or the idea could be portrayed better by adding signs near the animals indicating what they are eating or how much food the buckets contain. This may trigger some "equation" ideas in students' minds. Replacing it by a more relevant situation to the students is probably better.

Another reason why students may have chosen these cases is that they lend themselves to the use of equations in Standard form. Students have seen some of these types of problems before and these may have seemed familiar to them. In the phone problem, students wrote equations in slope intercept form easily, indicating the cost per minute as slope and a fixed fee as the y intercept but failed to interpret the solution. The coin problem was the next best. Most students obtained both equations correctly and performed the solving quite well.

Relevance: Successful Scenarios in the lesson

Creating your own Systems of Equations

Unit 6: Systems of Linear Equations
Lesson 10 of 13

Big Idea: Designing problems and applying learned skills in different real world contexts fosters higher order thinking.

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Subject(s):
Math, Algebra, Systems of Equations and Inequalities, systems of equations, Math 8, Systems of, linear modeling
65 minutes

Mauricio Beltre

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