Purpose: In order for students to be successful with trigonometry, they first need to be able to use and solve problems involving the Pythagorean Theorem. If they are not proficient with this, they will quickly fall behind for the learning objectives involved in this module. This section should be used as a pre-assessment or warm-up to understand the students' level of understanding thus far.

Method: The students will complete section Q.1 Pythagorean Theorem at IXL.com under the Geometry tab. Students will complete this on their own device (either a tablet or laptop). IXL provides instant feedback and step-by-step instructions on how to correctly solve if and when students miss the problem posed. Because of this, the teacher should monitor student progress through the teacher mode of IXL and assist students that are struggling as needed. From this feedback on student progress, the teacher should make small groups for the students. For example, pair students that are not as strong in this topic with students that have mastered it to help foster their growth.

Tips: If you notice one student is quickly finished with the IXL task, have them partnered with another student that may be struggling with this concept. This way, the student gets the help needed while the other student is solidifying their understanding of the Pythagorean Theorem by helping explain it to another student.

Purpose: To allow students to get a general understanding of what trigonometry is, how it differs from problems solvable by the Pythagorean Theorem, and how it can be used in an application setting. The comments student make are to get them communicating their own interpretations of what trigonometry is. By sharing their ideas, students will see different explanations from their peers that could help them better understand their own thoughts. 

Method: Introduce the construction problem with the whole class first. Hold a brief whole class discussion on how to solve the problem. Project the image of the building problem for students to visualize. Questions to ask: Can we use the Pythagorean Theorem, why or why not? What pieces of information do we need in order to use the Pythagorean Theorem? And is measuring the missing piece a legitimate option to complete in the real world situation? Be sure to close the discussion by stating the Pythagorean Theorem is definitely not an option, so we must find a new one. Use this to transition to Trigonometry. Have the students independently watch both videos and take notes from them to form their own definitions and understanding of trigonometry. 

Tips: Once the students have finished watching the videos, allow them to collaborate through their comments. Try not to give them any hints or help on this. It should not be biased by what we as teachers already know about trigonometry. 

Purpose: Allow students to use the resources available to them to figure out the correct way to solve a trigonometric problem. By letting students struggle (a little) to come up with their own solutions, they will retain this knowledge further on. 

Method: Instruct students to watch and take notes on the Khan Academy videos. Then pass out their note pages. Complete the first page as a whole class. Then, have the students figure out the method to solve the remaining examples through their own conclusions first. This will help them solidify the concept as opposed to you simply giving them answers. Complete the note pages with the students as a guided practice. However, place it on them to do the work, do not simply give them answers to copy down. Give them time to productively struggle on the examples in their small groups. Provide support as needed, but encourage students to collaborate and use the resources (videos, PDF's of worked out examples) before turning to you as the solution. Give students the opportunity to share their solutions and methods with the entire class. Allow them to be the teacher for this concept and have them verbally walk through and explain their solutions. 

A copy of the completed notes is provided in the PDF below.

Trig_20SOHCAHTOA_20notes.pdf

Tips: If and when students become frustrated with the struggle, lead them in the right direction without giving them the step-by-step instructions. Ask prompting questions that will tap into their prior knowledge like: what information do we need to use sine, cosine, or tangent? what information does the problem already provide us? 

Purpose: The students up until this point think trigonometry can only be used on right triangles. Having them work through the proof of the Law of Sines shows them there are more possibilities. Thus, leading them to exploring into the Law of Cosines as well. 

Method: Allow small groups to read through the proof of the Law of Sines provided. Be walking amongst the student groups to give support and extra explanations for this proof as the students need clarification. As the students work through the video example, make sure they are not simply copying down the work, but trying to solve it themselves first. The goal here is for the students to collaborate and come up with correct methods to solve first. 

Tips: Since the students are working in groups, take time to check in with students one-on-one for short comprehension checks. There are often students at this point that are not fully engaged in Law of Sines and will simply "follow along" with their group instead of learning it for themselves. 

Purpose: This module is to clarify any confusion from the previous module on Law of Sines where students explore the same concept for cosine and tangent. Students should be able to understand these two Laws and know why this is not possible or useful for the tangent ratio by the end of the module. 

Method: Allow students to work in their small groups to productively struggle in solving the inital problem solved. Be walking amongst student groups to ensure all group members are participating and engaged in the discourse. Provide assistance in the form of small hints. Remember, the goal should be for the students to discover the formula on their own terms; not simply given it to memorize. This being said, make sure all student groups are grasping the concept. There should be a productive struggle, not just a struggle. As students complete the IXL assignment, monitor their comprehension levels through the teacher interface. An example of what this looks like live is shown below:

Image retrieved from: IXL.com

In this mode, you are able to see, specifically, which students need your assistance. This is also a great way to partner students together. For example, partnering a student that has mastered the skill with one who needs clarification would benefit both students. 

Tips: Take advantage of the IXL Real-Time Center to help students as they need it. This is a great way to provide individualized assistance without every student knowing which student (or students) is struggling with the concept. 

Purpose: Now that students understand the mathematical procedure of trigonometry, it is vital for students to see and understand how this concept applies to their lives outside of the classroom. This module's focus is to help students solve application problems involving trigonometry. 

Method: Monitor student groups as they work through the website. Be looking for misconceptions related to angles of elevation and depression. Students often mix these up and struggle to correctly draw them in their diagrams. Just as before, provide helpful hints and assistance as needed, but let the students productively struggle in their exploration of this concept. The students should be proficient in the mathematical procedure of solving for missing sides and angles at this point. Their focus should be on how to correctly draw and interpret the image of the situation explained in a word problem. Be looking for incorrect diagrams. Take time at the end of this lesson to explain how trigonometry is used in some of the jobs listed as relevant. Then pose the assignment for students to create an update of their own research relating to jobs using trigonometry. Encourage them to engage in this discourse with their fellow students through their comments as well. The answer key for their practice set of word problems is provided in the PDF below.

practice_20word_20problems_20solved.pdf

Tips: If students are struggling to comprehend how an angle of depression is at the top of a triangle, review the concepts of angles created by two parallel lines being cut by a transversal, specifically alternate interior angles being congruent.  

Purpose: This module's goal is to allow students to be creative and explore how trigonometry is relevant to their lives. This project allows students to research topics that interest them and make connections to how it relates to trigonometry. By successfully completing this project, the students are showing mastery of the concept by applying and creating thier own trigonometric problem. 

Method: Take time to explicitly explain the expectations of the project. Go over the grading procedure of the rubric and ensure that every student has a copy to reference as they work as well. As the students are researching topics, walk amongst them and check in with students' topics to make sure they are relevant and appropriate for the project. Give students plenty of time to fully peer edit each others' work and time to revise their own after receiving peer feedback. The rubric for the project is shown below:

​Tips: Allow students to be creative with this project, but monitor progress to ensure they are staying focused on the task at hand and not straying from the learning objective. As students are making their own trigonometry problem, pose questions like: what do we need to include in a trigonometry problem? what pieces of information do they give us and which do they expect us to find mathematically? Help students, but do not create their projects for them. 

This survey can be used as both a pre- and post-assessment. Its purpose is to collect data on what students comprehend and are still unsure about in relation to the topics covered in this module, based on self-reflection. From the results, you can determine which instructional methods were successful, and which to modify for future use. 

Use the data from the survey to modify future lessons as needed. Find areas of common misconceptions and be proactive in preparing for them for future lessons. In the same sense, find areas where students were not challenged enough and supplement those modules to challenge and enhance student learning.

A link of the survey can be found here.