John+Edmonds

Right Triangle Trigonometry Application & Problem-Based Learning Right Triangle Trigonometry Application & Online Collaboration  Apply trigonometric functions and inverse trigonometric functions in problem solving (OLSD, 2009). Use radian and degree angle measurement in conversions and angle measurement (OLSD, 2009). || 2. Communication and Collaboration 3. Research and Information Fluency 4. Critical Thinking, Problem Solving and Decision Making
 * = Daily Lesson GAME Plan = ||
 * Lesson Title: Right Triangle Trigonometry Application |||| Related Lessons: Right Triangle Trigonometric Ratios ||
 * Grade Level: Pre-Calculus |||| Unit: Right Triangle Trig ||
 * ==GOALS== ||
 * Content Standards:
 * ISTE NETS-S

Instructional Objectives: Students will apply their knowledge of right triangle trigonometry ratios to real world situations. || In order to have my students ready to apply their knowledge of right triangle trigonometry, I will have spent two days in class instructing my students how to find the missing information from a right triangle. I will make sure that each student has a graphing calculator that they can use to solve the real world application questions with and have a few extra for any students that forget to being their own.
 * ==ACTION== ||
 * Before-Class Preparation:

I will also be showing a youtube.com video to introduce this lesson, so I will need to request a filter bypass for my teacher computer for the lesson. ||
 * During Class ||
 * Time |||| Instructional Activities || Materials and Resources ||
 * 5 - 10 minutes

8 - 10 minutes

25 - 35 minutes

(Next 3 Days of Class) 45 minutes |||| Review one question from basic right triangle trig that has no application. This will help me gain an understanding of whether or not I can move quickly through a few application examples or if I will need to go slowly to accommodate the students that are still confused.

In order to increase the intrigue of my students and to show them that right triangle trigonometry is used beyond the classroom, I will be showing a youtube.com video. This video discusses how to set and solve trigonometry application problems.

Show students two to three examples of increasingly difficult word problems that require critical thinking and analysis to solve. I will walk them through these examples so that they can see what questions I am asking myself as I solve. They will help me with all the math that is required and help come up with ideas to try as I solve the questions. During this portion of the lesson, I am showing them the level of work that I require to see in their final product of solved questions.

Each day I am going to have the students group themselves into groups of two or three. They will be working together to solve right triangle trigonometry applications of various types. The reasoning for workdays are to get my students to work passed the difficult questions that are seemingly impossible to solve. || LCD Projector Class Example Graphing Calculator

LCD Projector www.youtube.com Video

LCD Projector Graphing Calculator

Application Worksheet Trig Applications ||
 * Note student groupings, environmental modifications needed, etc:

Students will be self-selecting groups of two or three. They will be changing groups throughout this unit so I will be recording who is working with who and on which day. || After the first work day and during each subsequent work day, I will be conferencing with each group to see how their progress is going. Depending upon where they are, I will be giving added direction, challenging their thinking further, or regrouping them with other students.
 * ==MONITOR== ||
 * Ongoing Assessment(s):

I also will attach the answers to each question to my teacher website so that my students will be able to self assess if they are able to accurately solve each question. My students understand that the process of solving is more important than the solution.

Accommodations and Extensions: I only have one Pre-Calculus class this year. I have one student in this class that has an IEP with a behavior plan. He gets very frustrated when he cannot get the answer and will be pushed to his limit during these questions. With this in mind, I am going to be watching him closely so that I can try to diffuse the situation as quickly as possible and encourage him to come back to any question that he has trouble with the first time.

I have built the extension into my assignment by making each question more difficult than the one before it. I am expecting most of my students to not be able to solve all of the questions that I am assigning for the unit. I have also included a challenge question (#17) that will require a thorough understanding of Geometry and the properties of parallelograms.

Back-Up Plan: My back-up plan will be to continue to help the whole class construct the necessary thinking framework they need to solve these questions. I do not anticipate having to move quicker than I have planned. || The evaluation for this part of the unit will be through the Application Worksheet that is attached above. I will collect each student's work at the end of the week of work and give them both quantitative and qualitative feedback. I am fortunate to only have one section of Pre-Calculus, so it does not take long to give written feedback to each student on their work.
 * ==EVALUATE AND EXTEND== ||
 * Be specific and include the evaluation that you will use for this lesson:

I will be grading these applications with a rubric. See Below: A : Shows a thought process and work on **all** of the problems. All answers are correct. Shows understanding of **every** concept including drawing a picture, using inverse trig functions, using right triangle trig ratios, and labeling each answer with a unit.

A- : Shows a thought process and work on **all** of the problems. Has a strong understanding of **all** concepts including drawing a picture, using inverse trig functions, using right triangle trig ratios, and labeling each answer with a unit. Mistakes are minor errors, not misconceptions.

B : Shows a good thought process on **most** of the problems. Only one or two problems are left blank. Has a good understanding of **almost all** concepts including drawing a picture, using inverse trig functions, using right triangle trig ratios, and labeling each answer with a unit. Mistakes show a misunderstanding or misconception of one concept, however all parts after the mistake are correct OR numerous minor mistakes affect the correct answer.

C : Shows a thought process on **most** of the basic and middle level concepts. Has an average understanding of the concepts including drawing a picture, using inverse trig functions, using right triangle trig ratios, and labeling each answer with a unit OR several problems were left blank or not supported with work.

D : Shows a thought problems on **some** of the questions. Many problems were left blank or not supported with work. Does not show understanding on multiple concepts including drawing a picture, using inverse trig functions, using right triangle trig ratios, and labeling each answer with a unit.

F : Is not able to show an adequate level of understanding of right triangle trig.

I am building towards my students coming up the answer to a difficult question about the ability to see the Sears Tower from an island in Lake Erie. This will require a great deal of critical thinking and application of radians and trigonometry.

LESSON REFLECTIONS AND NOTES: ||
 * || I under estimating the amount of time that my students would need to complete the assigned work. I needed to extend it for 2 additional days. I also used direct instruction to work through an example every day that I extended this lesson. Other than the length of this lesson, I was pleased with how well my students were able to grasp the material. ||  ||   ||

 Apply trigonometric functions and inverse trigonometric functions in problem solving (OLSD, 2009). Use radian and degree angle measurement in conversions and angle measurement (OLSD, 2009). || 2. Communication and Collaboration 3. Research and Information Fluency 4. Critical Thinking, Problem Solving and Decision Making Instructional Objectives: Students will apply their knowledge of right triangle trigonometry ratios and the radian measure of an angle to real world situations. || I will need to make copies of the worksheet that I am giving to my students to explain the very difficult am mentally challenging problem. My district just came out with a student and teacher only blogging site. I am going to do research on how this website works, but I already know that each student already has a login and is loaded into my blog by class. ||
 * = Daily Lesson GAME Plan = ||
 * Lesson Title: Right Triangle Trigonometry Application with the Radian Measure of an Angle - Mountains |||| Related Lessons: Right Triangle Trigonometric Ratios ||
 * Grade Level: Pre-Calculus |||| Unit: Right Triangle Trig ||
 * == GOALS == ||
 * Content Standards:
 * ISTE NETS-S
 * == ACTION == ||
 * Before-Class Preparation:
 * During Class ||
 * Time |||| Instructional Activities || Materials and Resources ||
 * up to 10 minutes

10 - 15 minutes

Finish out period (20 mins) and blog that night so that the solution can be found during the next class period (45 minutes). |||| Review any questions from the previous application problems that we have worked through.

Introduce my students to the school's blogging website. Show them how to post their own question and reply to another person's post. I will also spend time explaining how I will be logging on to this site each night to help answer questions. I am going to encourage my students to both ask and answer questions.

My goal in this lesson is to really challenge my students to think beyond what they have thought in the past. As a way to stretch them, I will be giving little instruction during this lesson. I want them to think through that they have learned and find a way to answer the questions being posed to them. They will need to pull together the ideas of arc length, the radian measure of an angle, and all of the right triangle ratios. My students will be answering a challenging question about whether or not a mountain is visible from a different island in Hawaii. With the curve of the Earth, this is a very applied question and takes a lot of thought about how to deal with the curve of the Earth. || Graphing Calculator LCD Projector || Students will be self-selecting groups of two or three. They will be changing groups throughout this unit so I will be recording who is working with who and on which day. || During this portion of the unit, I am going to be gathering teacher observations of which students are really working hard to problem solve. I will be keeping track of which students work through errors and have quality ideas of how to get started. I will also be taking note of students that are not adding to the problem solving process. The goal is to make them think, so I will be keep track of who has good thinking. Back-Up Plan: My back-up plan will not be needed until the second period of this lesson. If half way through the second day of this lesson, I will begin to give assistance to any groups that have not gotten started in the right direction. || My evaluation for this lesson will come in the next lesson when they have to answer a similar question with even less information. I will also be reading the blogs that students posted to see who is using it to their benefit as well as helping others find answers to other's questions.
 * Note student groupings, environmental modifications needed, etc:
 * == MONITOR == ||
 * Ongoing Assessment(s):
 * == EVALUATE AND EXTEND == ||
 * Be specific and include the evaluation that you will use for this lesson:

LESSON REFLECTIONS AND NOTES: ||
 * || As expected, my students really struggled through this lesson. The class blogging website Schoology was a good way to get students to communicate about math. I will be using this website again in the next lesson because it worked so well and the students really used to to further the conversations that began in class. ||  ||   ||

Apply trigonometric functions and inverse trigonometric functions in problem solving (OLSD, 2009). Use radian and degree angle measurement in conversions and angle measurement (OLSD, 2009). || 2. Communication and Collaboration 3. Research and Information Fluency 4. Critical Thinking, Problem Solving and Decision Making
 * = Daily Lesson GAME Plan = ||
 * Lesson Title: Problem-Based Trigonometry Application Lesson |||| Related Lessons: Right Triangle Trigonometric Ratios ||
 * Grade Level: Pre-Calculus |||| Unit: Right Triangle Trig ||
 * == GOALS == ||
 * Content Standards:
 * ISTE NETS-S

Instructional Objectives: Students will apply their knowledge of right triangle trigonometry ratios to real world situations. Students will research two real structures that are approximately 50 to 300 miles apart to see if they are visible for each other. ||
 * == ACTION == ||
 * Before-Class Preparation:

I will need to gain access to google maps which requires an internet filter bypass on our school computers. I am going to have my students use Jing or iMovie to make a digital storytelling of what they researched and found out. I will need to reserve the library Mac lab so that my students will have access to both programs. ||
 * During Class ||
 * Time |||| Instructional Activities || Materials and Resources ||
 * 5 - 15 minutes

30 - 40 minutes

45 - 90 minutes

45 minutes |||| I need to be very clear about exactly what I am expecting from my students. I am going to spend the time the first day explaining the requirements of the assignment.

The assessment details are: 1. Students will research and choose two structures that are approximately 50 to 300 miles apart. An example is the Sears Tower and Perry Peace Monument. 2. Students will research the highest point of each of these structures and how their height relates to sea level. 3. Students will then need to either find or calculate the exact distance between the two structures. They can use latitude and longitude or find the information online as long as they understand that the driving distance is not the correct measurement. 4. Students will then apply the same ideas that they used when solving the Hawaii Mountains Problem to see if these two structures can be seen from each other.

Students will do the needed research and choose their two structures. They will then post those two structures on the class' Schoology blog so that I can check to see what each group has chosen. Overnight, I will have them post a short description of what information they have already found about the two structures. I would be looking for structure height, height above sea level, and approximate distance between the two structures.

I do not really know how familiar my students are with iMovie or Jing, so I want to give plenty of time to allow them to work on both the math calculation and the digital storytelling of their findings.

Finally, I will spend one class period showing what each student found. In order to help other students learn from each other and to give meaning to making the digital storytelling of their work, I will show as many projects to the class as possible. || LCD Projector

School Library Student computer for each group

School Library Student computer for each group

LCD Projector and speakers ||
 * Note student groupings, environmental modifications needed, etc:

Students will be self-selecting groups of two or three. They will be changing groups throughout this unit so I will be recording who is working with who and on which day. || I am going to use the Schoology blog to assess that my students are finding the material that they will need to answer the question of whether the two structures can been seen from each other. This assessment form will be formative and I will be giving suggestions and encouragements through the blog to help guide them in their thinking.
 * == MONITOR == ||
 * Ongoing Assessment(s):

Accommodations and Extensions: The accommodations that I foresee using for this lesson would be class-wide. As I have never done digital storytelling in class, I do now know how long it will take them to complete and finalize the video. I may have to extend the deadline for the final due date of the project.

Back-Up Plan: My back-up would be to have the student groups pair-up and share with each other what they found. I would have to do this if the digital storytelling was not cooperating or useful for showing the math that needs to be communicated. Pairing up groups would allow my students to practice communicating their thoughts with others in a organized and informative way so that I can still work on mastering the standards that I would like to through this lesson. ||
 * == EVALUATE AND EXTEND == ||
 * Be specific and include the evaluation that you will use for this lesson:

The final assessment of this unit will be the digital storytelling of their situation. I will be collecting the videos and showing them to the class when they are completed and will be grading them using the rubric seen below. I am going to collect these using a shared folder on our school's network. As I become more comfortable with Jing and iMovie, I may begin to have them submit their video on youtube.com.

Grading Rubric: A : The digital storytelling is thorough and shows thought and work on **all** areas. Shows understanding of **every math** concept including drawing a picture, using inverse trig functions, using right triangle trig ratios, applying the radian measure of and angle, and labeling each answer with a unit. Storytelling is descriptive and creatively presented.

A- : The digital storytelling is thorough and shows thought and work on **most** areas. Shows understanding of **every math** concept including drawing a picture, using inverse trig functions, using right triangle trig ratios, applying the radian measure of and angle, and labeling each answer with a unit. Storytelling is descriptive and creatively presented. **Minor** mistakes are present.

B : The digital storytelling is thorough and shows thought and work on **a majority** of the areas. Shows understanding of **most math** concepts including drawing a picture, using inverse trig functions, using right triangle trig ratios, applying the radian measure of and angle, and labeling each answer with a unit. Storytelling is descriptive but **not creatively** presented. **Minor** mistakes are present.

C : The digital storytelling shows thought and work on **some** areas. Shows understanding of **some math** concepts including drawing a picture, using inverse trig functions, using right triangle trig ratios, applying the radian measure of and angle, and labeling each answer with a unit. Storytelling is descriptive but not creatively presented. **Major** mistakes are present.

D : The digital storytelling is thorough and shows thought and work on **some** areas. Shows understanding of **some math** concepts including drawing a picture, using inverse trig functions, using right triangle trig ratios, applying the radian measure of and angle, and labeling each answer with a unit. Storytelling is **not descriptive** but is presented. **Major** mistakes are present.

F : No work is presented.

LESSON REFLECTIONS AND NOTES: ||
 * || I am not sure that the digital storytelling software that I chose to have my students work with was best. I did not receive the level of material from my students that I expected. Maybe with more practice, my students will generate a better final product. I am going to use the best project from this year and show my students next year, so they have a better understanding of what is expected. ||  ||   ||