Subject/Grade: Grade 11 Lesson Title: Exploring Primary Trig Ratios of Obtuse Angles Teacher: Miss Oesch

Stage 1: Identify Desired ResultsObjectives/Outcome(s)/Indicator(s):

FM20.5: Demonstrate understanding of the cosine law and sine law (including the ambiguous case).

(a) Identify and describe situations relevant to self, family, or community that involve triangles without a right angle.

Key Understandings: (‘I Can’ statements)

I can identify triangles without a right angle.

I can make connections between acute angles and obtuse angles.

I can use trigonometric ratios based on right triangles to understand acute angles and obtuse angles.

I can transfer my knowledge of triangles that have acute angles towards triangles with obtuse angles.

I can recognize the relationship between trigonometric ratios of acute angles and obtuse angles.

Essential Questions:

What type of relationship does acute angles and obtuse angles have?

What type of relationship does trigonometric ratios of acute angles have with trigonometric ratios of obtuse angles?

How can you find equal trigonometric ratios using two different angles?

How can you find opposite trigonometric ratios using two different angles?

Prerequisite Learning:Students have a good understanding of using primary trigonometric ratios and angle measurements to find the value of specific trig ratios. Students know how to use their calculator to solve for the value and understand using angles in degrees. They are familiar with variables and terminology such as theta for angle variables, sine, cosine, and tangent as the primary trigonometric ratios, and solving for the value to certain decimal places/degrees. Students do have an understanding of angle definitions from previous math courses, which will be reviewed so that they continue to use proper terminology during the activity and exit slip. Students understand that 180-degrees in a straight line and 90-degrees is a right angle. During the activity and handout students are accustomed to working on examples as a class and understand the necessity of filling in the blanks/activity table. During both they are also capable of asking questions and actively participating.

Instructional Strategy:Visual Diagram Classroom Discussion Math Activity

Handout/Examples Pair Work Exit Slip

Stage 2: Determine Evidence for Assessing LearningFormative Assessment- During the lesson students have the opportunity to do exploring of the trigonometric ratios with obtuse angles. Students will work in pairs to split the work and recognize the relationship between the values. During the activity I will be checking in with students to see if they are understanding the calculations and recognizing the pattern/relationship that is shown in the table. While students are filling in

section 2 of the handout which is a reflection/noticing piece they will have to demonstrate what they noticed, during that time I will gauge whether students notice the pattern and while sharing the answer students’ misunderstandings will be addressed. During the example’s students will also be given time to think of processes and I will watch for students participating, attempting to engage the students who may not share their thoughts to make sure everyone is getting an understanding. The final formative assessment for this concept is an exit slip that requires the students to demonstrate an understanding of what was taught in the class and a reflective question about whether students feel prepared to continue on or whether they have any questions about the topic. I decided this was a formative assessment as I want to give students feedback on their process and be able to tackle any questions or concerns the students may have about this topic so that in the next lesson, they are prepared to apply the knowledge.

Stage 3: Build Learning PlanSet (Engagement): Length of Time: 10 minutes

1. Engage students in the prerequisite knowledge that they have so that they are thinking about ways they can use their information towards this task and their assignment. Have students recall SOH CAH TOA, by having them demonstrate through a conversation that:

sin x=opphyp

cos x= adjhyp

tan x=oppadj

2. Ask students discussion questions that encourage new thinking about angle sizes and definitions. Questions that will be asked include:

a. What is an acute angle? (an acute angle is an angle whose measure is between 0° and 90°)

b. What is an obtuse angle? (an obtuse angle is more than 90° but less than 180°)

c. Are there any connections we know of between acute and obtuse angles? (possible connections can be made that if we add certain acute angles to an obtuse angle, we can create 180° angles.

3. Show students’ different options in a circle that represent acute angles and obtuse angles as well to give students an angle within a circle to give students a visual representation from this website: https://www.mathsisfun.com/definitions/obtuse-angle.html

Materials/Resources:

Computer Projector Exploring Primary

Trigonometric Ratios of Obtuse Angles Handout (x15)

Calculator Box Primary Trigonometric Ratios

of Obtuse Angles Exit Slip (x15)

Possible Adaptations/

Differentiation:

During the circle angle demonstration if students are not understanding then more explanations would be needed-hence we would go through definitions and do more examples of angles

If students are not wanting to participate and come up to the board- I will ask students to participate from their desk by explaining the angle instead of showing

Students will be doing the activities in pairs to split to work; if students want to work independently, I will have half the class fill in the top 5 and the other half do the bottom 5 and then fill the table together giving students time to fill in

I will ask the students to share angle sizes that they want to explore by having each one come up with an angle size greater than 90 and less than 180 in their head and then each of them comes up and predicts where they think their angle will be in the circle. Once the student makes their prediction by showing us where they believe the line for the angle lies with their finger, we will move the mouse and compare where the angle is. This activity will encourage students to recognize when specific angles may be obtuse.

Development: Time: 45 minutes

4. Introduce 4.1: Exploring Primary Trigonometric Ratios of Obtuse Angles Handout. Explain to the students that we will now be applying obtuse angles to the primary trigonometric ratios that we have been doing with acute angles. Introduce the activity by explaining: In the table there is a list of theta angles that range from 90 to 180 degrees which are all obtuse angles. On the empty sides of the table there is space to find the solution to the trigonometric ratios using theta or 180-theta: which you can solve for the angle then use the specific number in the trig functions on the calculator. Remind students that they can use their calculators to solve for the trigonometric ratios of the angle stated in the left column. Look at the first example on the handout and ask students:

a. What do you think of this example?

b. What types of predictions can you make from this first example?

Pair students up with one another by table groups and have them split the calculations to fill in both of their tables. Encourage students to split the work with one another so that they can finish the entire table and better recognize possible relationships between the solutions in the table.

Remind the students that their calculators need to be in degrees and they need to record their answers to two decimal places. Give students time to work on Exploring Primary Trigonometric handout section 1: which is the table. If students finish up section 1 earlier then the class, they can begin the bottom section of reflection with their partner. (20 minutes)

5. After students are wrapping up their table as a class, we will go over the reflection bottom to make sure all the students have the correct concept moving forward. I will encourage students to share their thoughts and why the blanks were found from the table and

their table to recognize the relationship

During the examples if students are struggling to understand I will find further examples and go over them as a class. The exit slip would also be simplified so that students explain what is most important to understand and sorting out misconceptions

Management Strategies:

Cold-call of student strategies Phones Away during pair work Encouragement statements:

recognize good work ethics during activity and thank students for answers to encourage further participation

Physical Movement to represent where students are (put your hand-up if you have this written down, etc.)

If students become restless with the activity brain break: (5-4-3-2-1 Activity: 5 jumping jacks, spin around 4 times, hop on one foot 3 times, walk the entire classroom 2 times, and then give 1 person a high-five find your seats.

Safety Considerations:

Students are working with one another for the beginning activity- I want to make sure that students feel comfortable with their partner and are able to contribute to one another in a healthy and appropriate way. I want to encourage them to work well together to create a table that they both understand. If pairs are not working well then pairs will need to be changed.During the exit slip students are asked to write about what they felt about the

then fill in the answers on the projected handout on the board. Students will have to check their answers and then we will move on to examples.

6. On the back of the handout there are four examples that we will go over as a class to demonstrate the usage of trigonometric ratios in obtuse angles and showing that there is a relationship between the value of trigonometric ratio for an acute angle and the value of trigonometric ratio for the supplementary angle (obtuse). During the examples I want students to engage in the process of finding the answer by asking them questions that create student conversation including:

a. How do we know that this relationship exists?

b. How can we use this relationship to understand using trigonometric ratios in obtuse angles versus acute angles?

c. What types of considerations did we use when deciding on our predictions?

d. What can we use to check our predictions?

During the example’s students will be asked to give process and answers, which we will fill in on the board within the projected handout. Students will use this example page to reference while solving future oblique triangles; triangles that do not contain a 90-degree angle. We will finish the examples together.

Learning Closure: Time: 5 minutes

7. To wrap up the class I will have students complete an exit slip: Primary Trigonometric Ratios of Obtuse Angles Exit Slip that shows their understanding of the primary trigonometric ratios of obtuse angles from the examples as well as a question regarding how they feel about their understanding of obtuse/acute angles in triangles and using trigonometric ratios with both types of angles for feedback. As I hand out the exit slip, I will tell students: Please answer both the questions to the best of your ability as I will be reading and giving you feedback on your answers and we will be looking at any questions or problems that you have in tomorrow's class, so please take them seriously! The exit slip will not be for a mark, but instead students will be given written feedback about the mathematical process question so that they can use it on their quiz and then I will take the second question as room for possible confusions to address in the following class so that students are comfortable in using obtuse angles in future sine and cosine law questions.

lesson and if they have an understanding of the concept taught today. Students may not feel comfortable sharing or share ideas that are very personal so I want the exit slip to be independent and unique to each student.

Stage 4: Reflection

4.1 Exploring the Primary Trigonometric Ratios of Obtuse Angles

Until now you have always used the primary trigonometric ratios only with acute angles. Here we will investigate the values of the primary trigonometric ratios for obtuse angles.

Definitions: Acute Angle- an acute angle is an angle whose measure is between 0° and 90°

Obtuse Angles- an obtuse angle is more than 90° but less than 180°

Activity: Using your calculator, you will go through and find the results of calculating the trigonometric function at each angle. While you are filling in the chart watch for patterns or relationships!

90°

100°

110°

120°

130°

140°

150°

160°

170°

180°

What relationships do you observe when comparing the trigonometric ratios for obtuse angles with the trigonometric ratios for the related supplementary acute angles?

Obtuse Angle = Related Angle = 180° -

Sine: The obtuse angle and the related acute angle have the _________________ sine ratio.

Cosine & Tangent: The obtuse angle and the related angle have the ______________ numerical value, but the ____________________ sign.

Trigonometric Ratios of Obtuse Angles

Example 1: Which of the following equations are valid? Give reasons for your choices.

a) c)

b) d)

Example 2: Calculate each ratio to four decimal places. Predict another angle that will have an

opposite trigonometric ratio. Check your prediction.

a) = Opposite Ratio Prediction:Check Your Prediction:

b) = Opposite Ratio Prediction:Check Your Prediction:

Example 3: Calculate each ratio to four decimal places. Predict another angle that will have an equal trigonometric ratio. Check your prediction.

a) = Equal Ratio Prediction:Check Your Prediction:

b) = Equal Ratio Prediction:Check Your Prediction:

Example 4: Determine two angles between 0° and 180° that have each sine ratio.

Acute: Obtuse:

a) 0.95

b)

Primary Trigonometric Ratios of Obtuse Angles Exit SlipName: Date:

1. Determine the measures of two angles between 0° and 180° that have this sine ratio. Round each answer to the nearest degree.

Acute: Obtuse:

a.

2. During the lesson today…

a. What did you learn about trigonometric ratios and obtuse angles?

b. What did you find difficult about what we are learning or about how it was taught?

c. Do you have any burning questions that you didn’t ask Miss Oesch today that you would like answered next class?

Feedback:

Professional Development Plan

Topic: Exploring Primary Trig Ratios of Obtuse Angles

Date: March 14th 2019

Teacher: Miss Cassidy Oesch Observer: Tera Lynn & Jannae Bridgeman

1. Professional Target: Avoid using the saying guys or boys & girls.

During the lesson I want to avoid using the slang names for my students by calling them guys as well I don’t want to offend students who may get offended by the statements boys & girls which is something that I have a habit of stating. I also want to start getting use to using the student’s names within my lessons and learning.

Students should feel comfortable in the classroom and I want to continue growing my relationship with the students by using their names and not referring to them as generic boys & girls which can be offensive to students who struggle with gender.

2. Steps to Achieve Target I will use more sayings towards

the class that encompass such things as everyone, friends, or students

While I am discussing with students directly, I will call them by name or speak to pairs by addressing them with their table number

3. Instructions to observer (be specific):During my lesson I would like you to mark down anytime I use the sayings guys or boys & girls during the teaching of the topic and then when I am speaking to the pairs or students when they are engaged in the task or the examples. Please checkmark under which one I say during my teaching.

4. Data Collection:Guys Boys & Girls

Reflection:

This lesson was the beginning lesson in the unit and was interrupted by our students participating in creating their video for Scott’s Got Talent, which was relationship building but took a lot of the middle section of the lesson. Overall during the time that I taught it was useful for students to see examples of the rows filled in to the trigonometric function values because they commonly went through the columns not finishing the rows which made it difficult for students to see the relationship without being told by me as the teacher or a friend who has completed parts of the table or recognized values. During the calculator activity I found that some of the students had difficulties finding the referent acute angles value because students were plugging into their calculator incorrectly. If I did this activity again, I would specifically assign parts of the table to each person and then have them fill in a larger table which we would work on together to recognize the patterns and relationship between sine values and cosine and tangent values. Even in the short time period that we had to teach and learn students had a good understanding of what is expected of chapter 4.1. The exit slip and examples were not completed the day of the lesson but instead I had the students work on it the following day which filled the beginning of the lesson with previous knowledge so that students were prepared for the 4.2-chapter information. This lesson definitely showed the inconsistency of the High School classroom with school activities and demonstrating student’s ability to work on examples or activities together before or after exciting activities.

My PDP for this lesson was working on saying proper names for students and not using slang sayings that refer to students that may offend students such as boys and girls or the saying guys. I wanted to adjust to saying things such as everyone and grade 11’s to describe the entire class or ask for everyone to do something together. I wanted to also focus on using the student’s names and getting to know more about each of the students individually. Overall my PDP goals were met closely although I still have a habit of referring to groups of students as guys because I speak to them as a whole. It is important to recognize when I am referring to students to make them feel as included as possible through proper pronouns and not using statements that don’t personalize information to the students specifically. For the following lesson I want to work on asking questions to the students that get them involved in the lesson because I felt that students were cut off from the information and not engaged in the activity the entire time. I want to question the student’s knowledge and get them involved in the learning to make it easier for students to succeed.

PDP SHEETS: Tera Lynn & Jannae Bridgeman