Exploration+of+Angles+with+iMovie

Class: Algebra-Trig Grade: 10th-12th Unit: Solving Triangles
 * Solving for triangles in real life **  **(Law of Cosines, Law of Sines) **

__Standards Addressed: __ A2.8.A Analyze a problem situation and represent it mathematically. A2.8.B Select and apply strategies to solve problems. A2.8.C Evaluate a solution for reasonableness, verify its accuracy, and interpret the solution in the context of the original problem.

__Materials Needed: __
 * Student Computers
 * Handout of grading checklist
 * Map of US as a reference for students
 * iMovie software or other movie making software
 * Calculators
 * Paper
 * <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">Pencils

__<span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">Grouping: __ <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">As the teacher explains the grading procedures, the class will be together as a whole. Once the main idea is communicated and all questions are clarifyied, students should break into groups of three to begin the project. Depending on the class, groups can be teacher selected or group selected.

__<span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">Timeline: __<span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;"> This project could take from one to three days depending on length of classes, and whatever extra expectations teachers may have. Included below is a sample timeline for the project.

<span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">Teacher Preparation:
 * <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">Setting up Movie Software - The teacher should look into what kind of movie making software is available and become familiar with it.

<span style="font-family: 'Times New Roman',serif; font-size: 16px; line-height: 24px;">Day 1:
 * <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">(10 Minutes) Teacher should explain the project, including how the students will be graded.
 * <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">(15 Minutes) Students break into groups and decide which three cities they want to investigate. Students should mark the location of their cities on a map.
 * <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">(10 minutes) Students should find the distances between their three cities.
 * <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">(20 minutes) Students analyze their triangles to determine the measure of each of the angles (using the law of sines and the law of cosines). Students should classify their triangles as acute, obtuse, or right.
 * <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">If students finish the above with extra time, they should start making their iMovie.

__<span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">Day 2 & 3: __
 * <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">Students create their iMovie in class. It would be helpful to print out a copy of the user’s manual.
 * <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">If students need extra time, they can come in after school to finish up.

__<span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">Assessment: __<span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;"> Students can be assessed in a variety of ways including a rubric, checklist, etc, depending on teacher preference. Included below is a checklist that will be used for grading students' iMovie and project reflection.

<span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">iMovie (35 points) <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">You will receive 5 points for including each of the following: <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">1. Introduction – Introduce the members of your group and the purpose of your video 2. The cities you chose to investigate – explain why you chose them! <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">3. A map – your map should include the location of your three cities 4. The distances between the each of the three cities <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">5. How you solved for each of the angles 6. Classification of your triangle <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">__7. A resources page (title and link to webpages)

<span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">Reflection (10 points):
 * <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">Do your routes accurately model the three sides of a triangle?
 * <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">How is it different?
 * <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">Is the triangle segment longer or shorter than the route between the two cities?
 * <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">How would this effect your angles?
 * <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">How did you find the angles of your triangle? Did you use a special Theorem or Law? If so, explain why you used it.

<span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">**For each mathematical, spelling, or grammatical error, 1 point will be deducted from your total score

<span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">Total Score: _/45

__<span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;">Reflection: __ <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;"> It is important for teachers to find fun ways to increase student engagement and motivation by increasing the relevance and rigor in mathematics. Though this lesson may not focus on extremely difficult mathematical concepts, it is the manner in which the project is created that can increase rigor and relevance. There are a couple main components if this lesson that increase mathematical rigor and relevance in the classroom. <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;"> First, I think adding any sort of technology into a lesson increases the relevance for students because technology is becoming a huge part of how we live. I think it is important that students are forced to become familiar with different computer programs, including a movie making software, whether it is Windows Movie Maker or iMovie. Though students may not build a career around understanding how to make an iMovie, learning the process can be both fun and educational. <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;"> Also, this lesson makes students think about how mathematical concepts and ideas can be used in a real world setting. Often times, it is easier for teachers to simply teach the theorems and procedures, without making students really think about how the mathematical concepts can be made relevant to the students’ lives. <span style="color: black; font-family: 'Times New Roman',serif; font-size: 12pt;"> Finally, I think it is really important for students to be able to evaluate and analyze their work and once their project is all done find a couple key ideas that could have made it better. This can make students look back on what they accomplished and think about how they performed and in what ways they can improve for the future. I think one of the most important steps in the problem solving process is for students to “look back” (the step that I would argue is most often skipped) and check to see if their answer or project really makes sense. This reflection process is important for students to learn because it really makes them think and it is a great life skill to have.