Course: Analytic Geometry

Title of Lesson: Trigonometric Ratios (Lesson Plan 1)

Date: October 7th, 2014

Learning Objectives: By the end of the lesson, students should be able to know the definitions of sine cosine and tangent. This includes knowing what each trig ratio means (e.g.

sine= oppositehypotenuse

, cosine= adjacenthypotenuse

,t angent=oppositeadjacent ) and also knowing how to

calculate them.

Essential Question: How are trigonometric ratios related to one another?

Standards:MM2G2 Students will define and apply sine, cosine, and tangent ratios of complementary angles.

Practice Standards: (1) Make sense of problems and persevere in solving them(2) Reason abstractly and quantitatively(5) Use tools appropriately(6) Attend to precision(7) Look for and make use of structure

Materials: Pencil or Pen Ruler Trig Ratios Learning Task worksheet

Vocabulary: Adjacent Side Angle Cosine Hypotenuse Complementary Angles Opposite Side Ratio Right Triangle

Sine Special Right Triangles Tangent Theta (θ) Trigonometric Ratios

Learning Task: The activity will be completed in one 70-minute class period depending on how long the students spend on the lesson. For this lesson we will spend 10 minutes the introduction where students will work on the warm-up. For the warm-up, students are provided with cut outs of various similar triangles on them where they need to measure certain sides of the triangles that will be specified via the SMART board. We did this so that later on in the lesson (the closer) they will be able to quickly calculate the sine, cosine, and tangent values. All in all this should take about 10 minutes to complete. After this, we will dive right into the main activity. With this students will be exploring the trigonometric ratios. They will have to first measure the sides of a group of triangles; then they will have to categorize them as either the opposite side, adjacent side, or the hypotenuse; then they will have to calculate the trigonometric ratios; then lastly they will need to investigate if these values will be the same for all right triangles with congruent angles. This activity will take about 30 to 40 minutes to complete. Basically it will last the rest of the class period. During this time, we will move around each table monitoring and helping in what ever way we can. For the closing part of the classroom, if time permits, they will have to answer the wrap-up problem. Hopefully students will realize that the wrap-up looks familiar since it is exactly the same as the warm-up. The only difference is that instead of measuring the lengths of the triangles form the warm-up, they will now use those measurements to calculate the sine, cosine, and tangent values. We did this to gauge if students learned the main topics of the lesson. With this, we will have them write their answer on a separate sheet of paper, which we will take up as a quick classwork grade. Again if time permits, this should take around 10 minutes. While they are completing the wrap-up, we will discuss what the homework will be for the night and make any announcements that are needed in order to prepare for the next class.

Handouts for students:

Extensions of task/lesson:Some extensions of this task could be to add some application problems. This will include calculating the sine, cosine, and tangent values of triangles. Since this is an introductory lesson, I do not want to go to crazy on extensions since students will already be struggling with the new concept. These extensions will be provided to the students if needed.

Instructional Strategies: Since this is an introductory lesson into the trigonometric ratios, the only thing I can think about as a way to differentiate the task is through the use of technology. Since this task touches on how the trigonometric ratios change over an interval, this applet will mainly be used for trying to make comparisons between the sine, cosine, and tangent measures of similar triangles. Through the use of the applet, we can have the calculations for each trigonometric ratio shown on screen and from there we can have a slider that controls the size of the triangle. This will allow the students to see that now matter what the size of the triangle, as long as the triangles are similar the sine, cosine, and tangent values amongst them will be the same.

Ways to assess student progress: Since there are three of us in the classroom, we will each monitor two to three groups during the activity. With this, we are able to go back and forth between each group and help them with any questions/concerns they may have with the activity. If we see that some groups are not completing the activity with the time we allotted, we can either add more time or decrease the amount of time needed for this investigation. Also by monitoring the progress of each group we will have a better understanding of where the students are struggling with the most while working on this assignment. This will allow us to get a better idea of the questions they may ask at the end of the class during the full class discussion.

Course: Analytic Geometry

Title of Lesson: Trigonometric Word Problems (Lesson Plan 3)

Date: October 14th, 2014

Learning Objectives: By the end of the lesson, students should be able to use the definitions of the trigonometric ratios in order to solve problems. Students will have to be able to solve for the missing sides of a triangle, the missing angles of triangles, and also various application/“real world” problems.

Essential Question: How can use the trigonometric functions to solve problems?

Standards:MM2G1: Students will define and apply sine, cosine, and tangent ratios of complementary angles.b) Explain the relationships between the trigonometric ratios of complementary angles.

Practice Standards: (1) Make sense of problems and persevere in solving them(2) Reason abstractly and quantitatively(4) Model with mathematics(6) Attend to precision(7) Look for and make use of structure

Materials: Pencil or Pen Paper Notebook

Vocabulary: Adjacent Side Angle Angle of Depression Angle of Elevation Cosine Hypotenuse

Complementary Angles Opposite Side Ratio Right Triangle Sine Special Right Triangles Tangent Theta (θ) Trigonometric Ratios Vertices

Learning Task: The activity will be completed in one 70-minute class period depending on how long the students spend on the lesson. For this lesson we will spend 10 minutes the introduction where students will work on the warm-up. With this, students are to use the knowledge that they have learned about the trigonometric functions in order to determine how they might be able to find the missing side length of a triangle. Since they do not yet know how to do this, this question is mainly for discussion. We did this in order to have students start thinking about how they can use the trigonometric ratios to solve various problems. This will help smooth out the lesson since students will have to be able to think about the ratios and also how to manipulate them in order to solve various application problems. All in all this should take about 10 minutes to complete. After this, we will hold a quick lecture that reviews the trigonometric ratios and also work some guided application problems. Once the lecture is done, we will dive right into the main activity. With this students will be exploring application problems of the trigonometric ratios. The actual task will be given via the SMART board so there will not be a handout given to the students. With this, students will have to solve various application problems including finding missing side lengths and also finding missing angle measures. Even though this activity is given through the SMART board this task is still group based. The students will have to copy down the problem and in their groups they will have to figure out first what the problem is asking, how to use the information given, then actually solve the problem. Thus the first few problems will be guided in order for students to see the process behind these application/word problems. All in all, this activity will take about 30 to 40 minutes to complete. In other words, this activity will last the rest of the class period. During this time, we will move around each table monitoring and helping in what ever way we can. For the closing part of the classroom, if time permits, they will have to answer the wrap-up problem. For this portion of this class, we will come together as a class and discuss the wrap-up problem at the end of the slides. Instead of now finding the missing side, students

will need to use the knowledge they learned from the activity in order to find the missing angles of a triangle. We did this to gauge if students learned the main topics of the lesson. Also this will give the students a foundation for them when they start practicing more with finding the missing angles and sides of triangles by using the trigonometric ratios. With this, we will have them write their answer on a separate sheet of paper, which we will take up as a quick classwork grade. Again if time permits, this should take around 10 minutes. While they are completing the wrap-up, we will discuss what the homework will be for the night and make any announcements that are needed in order to prepare for the next class.

Instructional Strategies:One way to differentiate the class would be make the task a white board activity or a stations activity. For the whiteboard activity, we would give each student a whiteboard and a marker to write their work on. With this, we would have each student work the problem on the whiteboard and then once tie is allotted we will ask the class to raise up their boards. Then if we need we will go over the problem as a class. With this, it will be a quick and easy way to gauge if the class understands how to solve these types of problems. For the stations activity, we would use the same problems as the slides, but instead they will be spread out across the room. That way, students will be able to move around and have some activity rather than sitting at their desk taking notes. This will allow us as teachers to walk around and monitor students more one-on-one allowing for more in depth and personalized instruction. I do believe that these methods are great for working on application problems, but since this task is mostly used as an introductory lesson I believe students will need guided instruction.

Handouts for students: Since the task will be given via the SMART notebook, there will be no handouts given to the students, but the students will have a copy of the slides in order to complete them for homework.

Extensions of task/lesson:Since the task is being provided via the SMART notebook file, there will be no extensions given with this task. This is because I believe that students will struggle enough with the problems that are provided to them. This is because the students have a hard time looking and also utilizing information given to them whether it is in a word problem or proof.

Ways to assess student progress:

Since there are three of us in the classroom, we will each monitor two to three groups during the activity. With this, we are able to go back and forth between each group and help them with any questions/concerns they may have with the activity. If we see that some groups are not completing the activity with the time we allotted, we can either add more time or decrease the amount of time needed for this investigation. Also by monitoring the progress of each group we will have a better understanding of where the students are struggling with the most while working on this assignment. This will allow us to get a better idea of the questions they may ask at the end of the class during the full class discussion.