Reflection: Advanced Students More Applications of Rational Functions - Section 2: Investigation


I ended making a ton of different resources for the lesson today, because with each class period, I realized that there were a wide range of needs in my class. I always have a few students who fully understand a new problem on the very first day, while other students need up to a week to reach the same level of understanding. 

For this lesson, I am providing a wide variety of resources, because I ended up teaching this lesson differently with each class period. By my third try, I came up with the mixture problems, because I realized that some of my students needed even more of a challenge.

The way that I handle this type of highly differentiated lesson, is by trying to assess students (informally) during the warm-up. I try to ask a lot of questions and circulate several times to get a sense of how thoroughly each student understands the concepts from yesterday. 

Then, I try to communicate to students either individually or in groups what I want them to work on. One way to do this is to assign pairs (homogeneously) by listing pairs of students and listing the level that I want them to work on next to each pair, either on a white-board or a projector. Once students are in their pairs, I can circulate again to make sure that they are working on problems that are at the right level. I often ask them: "Do these problems seem too easy or too hard?" 

Like many aspects of my teaching, this may seem a bit sloppy--and sometimes teachers wonder, "Do students feel okay about different people doing different problems?" or even, "Is it equitable to give different tasks to different students?" I think these are valid questions and every teacher needs to develop their own belief about what is equitable. I believe that equity means that every students is given tasks that are both accessible and challenging to them--right in their Zone of Proximal Development. This is pretty hard to pull off gracefully--so it involves many conversations with students, because they need to be involved in the process. So this process is not top-down; I don't have enough information to make all the decisions about what students should be working on, the only way to get this information is to help coach them and teach them to give it to me. I have found that students are really cooperative with this, and I have never had a single student say, "This is not fair--why do I have to do this hard problem when she has an easy problem?" I think because I am very explicit about the purpose, and because I involve them in the process, they feel that it is fair and equitable.

  Flexible, Continuous Assessment and Differentiation
  Advanced Students: Flexible, Continuous Assessment and Differentiation
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More Applications of Rational Functions

Unit 6: Rational Functions
Lesson 2 of 10

Objective: SWBAT write rational functions to describe real-world situations and choose inputs that will enable them to graph these functions.

Big Idea: How can we create functions to describe these real world situations? Students explore the behavior of rational functions that they generate.

  Print Lesson
Math, Precalculus and Calculus, Graphing (Algebra), asymptotes, rational function
  70 minutes
student work
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