While teaching at Freedom I taught a unit in my pre-calculus class that was very interdisciplinary. Although I had not started out with the plan that it would be my interdisciplinary unit for my intern teaching, it quickly became this. I soon discovered while planning my lessons for the next unit that the topics we would be covering crossed many areas of study. Please take the time to look through the unit that I have created. Not all of the lessons are included, but I have chosen to share the lessons that I feel would interest you most.

I. Content Outline

A. Focus: In this unit my students will gain knowledge on how to use trigonometric functions to solve realistic problems.

B. Conceptual Outcomes: Upon completion of this unit my students will be able to define the six trigonometric functions and their properties. They will understand the parts of an equation that represent transformations of a curve, and then apply this to solve realistic problems. Students will recognize that their is a strong relationship between math, the sciences and even English.

C. Related Standards: Throughout this unit my students will be meeting several of the standards set forth by the National Education Standards. They are as follows -

M3k - Makes predictions by interpolating or extrapolating from given data or a given graph.

M3n - Uses technology such as graphics calculators to represent and analyze functions and their graphs.

M5d - Mathematical Reasoning - The student demonstrates mathematical reasoning by using logic to prove specific conjectures, by explaining the logic inherent in a solution process, by making generalizations and showing that they are valid, and by revealing mathematical patters inherent in a situation. The student not only makes observations and states results but also justifies or proves why the results hold in general.

M7d - Communicates logical arguments clearly, showing why a result makes sense and why the reasoning is valid.

D. Objectives:

The students will be able to-

* Define the 6 trigonometric functions.

* State the properties of the 6 trigonometric functions.

* Find the harmonic equation of a slinky using rules of trigonometric functions.

* Explain and prove a realistic problem using trigonometric equations.

E. Materials and Resources: For this unit there are a variety of materials that will be needed. They include the following things. Explanations will be provided when needed.

* Textbook - Advanced Mathematics - a precalculus approach

* NCTM journal - used for warm-ups

* TI-83 graphing calculators with links for transmitting programs

* Motion Detector

* Science Lab book - for lab write-up guidelines

* Measuring tools ( yardsticks, meter roller, rulers)

* Overheads with graphs of functions

F. Integrated Activities: Although the focus of this lesson is on math and making sure that my students understand the basic concepts about trigonometric functions, it is also possible for me to incorporate other subject areas into this unit. My students will be using their writing skills that they have learned in English class to write and prove a word problem. They will have to explain in great detail the thought processes that they used to solve the problem and also provide support and analyze why they feel the way they do. My students will also be required to write a lab-write up for this unit, incorporating what they have learned in their science classes. They will be doing an experiment with finding the equation of a slinky in motion, and they will need to write their results using a form they learned in science.

Both of these tasks are generals ways that my students will be incorporating what they have learned in other classes to enhance what we are doing in math class. It makes math realistic, and also more fun.

II. Activity Center

During the this unit my students were also learning how to apply the trigonometric functions to solving right triangles. Most days my students are very curious as to how all of this applies to them, and when are they ever going to use this information. This activity center allowed my students to experience hands on ways of using trigonometric functions in everyday life.

1. The students discovered how many different ways they could measure the height of objects and buildings, using trigonometric functions and other means they created.

2. The materials needed for this activity included yardsticks, meter roller, and hypsometers.

3. The students were required in their groups of four to rotate to four different locations on the school property. They were required to measure the height of the flag pole, main entrance, tallest point of the building, and our new science wing. At each location they were required to measure the height of the object using one of four methods. This worksheet allows you to see exactly what the students were required to do at each location. The students then determined which method of measurement was the easiest, most difficult, least accurate, and most accurate. We then compared our answers as a class and discussed difficulties they had with each method. The students quickly learned that using the properties they learned of trigonometric functions, they could measure the height of almost any object.

III. Lesson Plans

To begin this unit I started with a lesson that allowed the students to explore on their own what sine and cosine functions look like. They were broken into groups, and they were required to complete the following tasks with their group members. They had no prior background knowledge of trigonometric functions before they began lesson 1. The students were scored using this rubric. They were assessed individually rather than as a group.

Lesson 2 was intended to provide students with the concepts that they needed to study trigonometric functions and their graphs. This lesson was necessary to work on the skills that the students would need so they could apply the concepts to future problems. View this lesson here.

Lesson 3 was partially a group activity, and partially an individual activity. The students are required to do writing activities to meet the standard goals, so each marking period they are given a problem relating to a topic we are covering. The student is required to analyze the problem, solve it, and explain it in detail in report form. This lesson introduces this new writing activity to the students. The rubric on how the students are assessed follow at the end of the lesson. This rubric is consistent throughout all of the writing activities that they do. This way they can see what areas they need to improve upon for next time.

Lesson 4 is another informative lesson where I am trying to relay concepts and ideas to my students about trigonometric functions. In this lesson we begin looking at real life situations where we can use these functions.

Lesson 5 was a fun way for the students to see the relationship between trigonometric functions and their realistic uses. This activity relates directly to lesson 4. The students were required with a partner to find the equation that represent the motion of a slinky. The rubric that assessed their assignment can be viewed at the bottom of the lesson.

Reflection: I think this interdisciplinary unit was very useful for myself and my students. It was a great way for them to see how math can actually be related to real life situations. Especially once the concepts start becoming more abstract and difficult, I have found that students have less and less interest. I think that the students really enjoyed many of these lessons because they required group work, higher thinking skills, and it was not me lecturing to them. If I were to do this unit again I would try to incorporate a video explaining trig. functions or find a piece of literature that would be another resource.

Click here to see my Classroom Management Plan.