Station Learning Activity – Asymptotes

I wanted to try a station learning activity that was inquiry based. Too often asymptotes are taught to students without much consideration for how or why the functions behave in this particular way. Personally, I think asymptotes are interesting, but to students they are a strange phenomena that have no application. The approach with the inquiry is to help students find interest in an abstract learning segment. This lesson comes near the end of a unit about polynomials and we have just covered polynomial long division. This activity is geared to help students learn through the various aspects of polynomial division and what could happen. Since slant asymptotes are unique, we will cover these the next day of class.

Pre-Lesson:

Students have been studying polynomials for about a month and we are just exiting a section about the Fundamental Theorem of Algebra and complex roots. It is clear that students are weak in factoring polynomials, but I cannot afford to stop all learning to generate mastery. So, I have designed a 2.5 day mini-unit in which students will have lots of practice in factoring polynomials, reviewing polynomial division while exploring asymptotic functions. This mini-unit will hopefully tie a lot of somewhat random ideas together and help loop some previous learning so that students can practice skills they should already know and continue to learn new ideas.

On my website (link below, date Feb. 24) I have posted 4 worksheet activities for the day (I created these by the way). As students walk in, they will be divided into 1 of 4 groups. They will read start the entry task which should require them to access prior knowledge. Students will have about 30 minutes at each station to complete a short worksheet. Since the period is 100 minutes long, I expect that all students will get through about 3 stations.

I will be walking around to each group during the class to ensure students are grasping the important concepts at each station and catching some misconceptions along the way.

My personal goal in creating this station learning activity is to: 1) Get students moving in the classroom during a long period. 2) Engage student in an exploratory, inquiry based activity. 3) Differentiate instruction so that struggling students can achieve new skills. 4) Fold in prior learning (factoring, finding roots, polynomial division) so we can move forward in content and review prior knowledge.

http://www.mrgermanis.com/precalculus/3PolynomialModels/index.html

 

2/24
(Block Day)
Entry TaskFor the function f(x) = (x + 2) ÷ (x – 1), describe as many of the following features as possible. DO NOT GRAPH!

  • x-intercept
  • y-intercept
  • end behavior of f (x) as x approaches positive infinity.
  • end behavior of f (x) as x approaches negative infinity.
  • function behavior when the input is close to 1.
Activity“Be Rational!” (Station Learning Activity)

See THESE notes to clarify information from stations.

Journal Reflection: Complete the JR for each associated station you visited today. Build a rational polynomial that:

  1. Has a hole at x = -10
  2. Has a horizontal asymptote at y = -5
  3. Has a vertical asymptote at x = 3
  4. Intersects the x-axis at (3, 0) and the y-axis at (0, -5)
HomeworkThis homework is due on 3/2.
Note: Some problems may cover concepts NOT at your station. During class, we will continue the activity. All problems should be solvable by the due date.Pg. 229-233 # 1, 2, 3, 4a, 7

Lesson Goals: Students will learn about basic asymptotic behavior that results from polynomial division including domain and range of asymptotic functions. Additionally, students will recognize a polynomial which results in a curve with a hole.

Post-Lesson Reflection

My lesson today went well! There are a lot of opportunities to observe students understanding (or not understanding) the ideas of the lesson. I noticed some problems in the wording of some of my activities which was challenging since I needed to talk individually with each group to clarify my writing.

I created groups of 4-5 students and strategically selected different ability levels in each group. Roles per group were also assigned to bring out the qualities of each student that I needed. For instance one group contained a student who generally asks good questions in class and another student who generally has a difficult time engaging in lessons and a third student who has a difficult time asking questions. In this group, I assigned the unengaged student the role of reader, the curious students the role of checker/questioner and the quiet student an arbitrary roll. With these students and roles in the group the quiet student and the unengaged student became members of a group and engaged in the lesson well attaining significant new knowledge. Overall, this strategy worked very well, only one group of higher level students complained about the group roles and didn’t follow the structure. As a result this group was unsatisfied and felt lost during critical parts of the activity.

Thinking about pacing, I am realizing that these activities require a lot of thinking and within a single 100 minute period, students may have a difficult time accomplishing even just three of these activities (the intent was for students to complete 3 of the 4 lessons). If I were to do this activity again, I would divide the problem into two days of station learning and have only two worksheets per day (even during a block day). This will allow me to debrief more quickly to ensure students are getting at the heart and the objective of each station.

Additionally, if I do this activity in the future, I will provide check in point where the document controller will report their groups finding to the teacher to ensure connections are being made and the objective is being met.

One task that should be shared with the teacher in particular are the generalizations of the findings of the activity. Many parts of the activity were examples where students were to uncover HOW asymptotes, holes or intercepts worked. Making generalizations will solidify these ideas and prepare students to apply this knowledge to new situations.

 

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2 thoughts on “Station Learning Activity – Asymptotes

  1. Pingback: Riley Germanis | P4 – Differentiated Teaching

  2. Pingback: Riley Germanis | P2 – Differentiated Instruction

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