4-way Representation - Trig System of Equations

I will take some time at the start of class today to review the 3-2-1 Assessment from yesterday's closing segment. Today, I will address only the questions. If I don’t find time to address all of these today, I will keep them up and come back to them at the beginning/end of class throughout the next week. I only remove a Sticky Note once I have answered the question, and then I know which questions have not been answered.

These assessments shed light on the ways that some of my students are struggling. I had a couple of comments like “Can you start over? I am so lost.” Being that these were anonymous, I encouraged kids that wrote these things to see me for help outside of class.  It is a nice formative assessment of the class as a whole. Are they ready to move on? If not, you may want to back it up and take a day to review. These next few days students will be modeling with real world data, so it may be too challenging if they don’t have the pre-requisite skills from the beginning of this unit. 

After reviewing some questions from yesterday, I will begin students work today by asking them to complete the problem on Page 2 of  the 4-way Representation Flipchart. This problem requires students to recall how to solve a system of equations. Depending on a student’s solution methods, it may also require a student to review solving a quadratic equation. 

I expect my students will solve the problem in many different ways:

1. Graphing – putting in both equations and finding where the two functions intersect
2. Graphing – setting the two equations equal to each other and graphing in standard form, found x-intercepts
3. Table – put in both equations and find where the table values say they are equal
4. Table – using standard form of combined equations and finding where equal to zero
5. Algebraically – substitution method and then used quadratic formula or factor
6. Algebraically – elimination method and then used quadratic formula or factor

It would be awesome for students to present all these different methods to help remind their peers of them, but I tend to think that would take too long. Instead, I plan to remind students by identifying all of the solution methods I am seeing. I will most likely encourage students to use Methods 3 and 4 above to check their answers, but not to solve the system. It is an inefficient method when working in the set of real numbers.

If I model the solution, I will use Method #5. I think that this will be most helpful in scaffolding the remainder of the lesson. 

For the last 10 minutes of class, have students complete the Yo-Yo Problem on the back side of the Student Worksheet: 4-way representation. This problem guides students through writing a function to model the motion of a yo-yo. So, it is not necessarily closing out the learning from today’s lesson, but reviewing past concepts from the last unit in context. Students can text in their answers (see Page 4 of Flipchart). I will use the information they text in to judge what they remember from the last unit about writing trig functions.

Teacher's Note: If my students need more time on the 4-way model, I will assign this closure problem as homework and address it at the start of class tomorrow.