Trigonometric Functions in Right Triangles: An Interactive Nearpod Lesson

Author:

Jamie Wolverton-Van Vlymen

How can we use trigonometry as a tool to solve real world problems around us?
What patterns or relationships do we see in trigonometry?

Grade Level

10th-12th

Subjects

Mathematics

Duration

2 Hours

Mode

Asynchronous Online Face-to-Face Hybrid Synchronous Online

Learning Objectives

Students will find the values of trigonometric functions for acute angles in a right triangle.
Students will use trigonometric functions to calculate values for missing side lengths and angle measures of right triangles.

Instructional Rationale

How will you access students’ prior knowledge and incorporate that into the lesson?

This lesson begins by engaging students in a quick brainstorming session to contemplate methods of finding the height of a well known, local landmark such as a bridge, building, water tower, statue or other structure without being able to measure the structure directly. Allow students choose the landmark to bring relevancy to the process and share their ideas devised in the brainstorming activity.

By the end of the lesson students will able to:

Find all six trigonometric ratios for angles in a right triangle given triangle side lengths.
Find the remaining five trigonometric ratios for an acute angle in a right triangle given one trigonometric ratio.
Use trigonometric ratios to solve for missing side lengths of right triangles.
Use trigonometric ratios and inverse trigonometric functions to solve for missing angle measures in a right triangle given at least two side lengths.

How are you integrating UDL (multiple means of engagement, representation, and action & expression) into your lesson?

Information is presented in several different manners such as text, visual imagery and audio recordings.
Students can engage both independently or collaboratively based on need.
Students can engage both live (in person and synchronously) or asynchronously which allows the student to revisit the material at their own pace.
Students can provide responses to independent practice and assessments in a variety of ways such as: typing, drawing, writing, uploading images, or through voice recording. Both multiple choice and open ended response questions are utilized and scaffolded with fading response stems.

What evidence do you have that you are connecting teaching to the CRP tenets (academic success, cultural competence and critical consciousness)?

Lesson material is both rigorous and scaffolded including guided procedures to promote academic success.
Cultural competence and critical consciousness are considered during the introduction or hook to the lesson. Choosing a familiar landmark to spark the brainstorming session can create a safe, comfortable environment for learning. In addition, images and examples used throughout the lesson are not culturally biased.
To enrich the cultural relevance, an extension project could be created at the end of this lesson. Students could be assigned different architectural elements to measure and present to the class as a cross curricular project. A deeper dive into the methods and materials of construction could lead to a discussion of equity or lack of across various cultures.

Assessments

Formative – Problem Set: Evaluating Trigonometric Functions.

These practice problems are embedded within the lesson and require students to draw (or type) the answer on the Nearpod slide. Students can also upload a drawing or file from their computer and even record their voice, allowing them more flexibility in their methods for answering each question. Students will be finding the values for all six trigonometric functions for various angles, given the length of each side of a triangle.

Formative – Problem Set: Finding Trigonometric Ratios.

These practice problems are embedded within the lesson and require students to draw (or type) the answer on the Nearpod slide. Students can also upload a drawing or file from their computer, allowing them more flexibility in their methods for answering each question. Students will find the remaining five trigonometric functions, given the value of one trigonometric function.

Formative – Problem Set: Finding a Missing Side Length.

These practice problems are embedded within the lesson and require students to draw (or type) the answer on the Nearpod slide. Students can also record their voice explaining the solutions, allowing them more flexibility in their methods for answering each question. Students will calculate the missing side length of a right triangle, given an angle measure and one side length.

Formative – Problem Set: Finding a Missing Angle Measure.

These practice problems are embedded within the lesson and require students to draw (or type) the answer on the Nearpod slide. Students can also upload a drawing or file from their computer or record their voice allowing them more flexibility in their methods for answering each question. Students will calculate the missing angle measure of a right triangle, given the length of two sides.

Summative – Multiple Choice / Short Answer Quiz.

This quiz is positioned at the end of the lesson and intended to be a summative assessment. The problems will be a mixture of short answer or open ended questions, and multiple choice. For the open ended questions, students will be able to type, draw, upload an image, or record their voices to provide solutions for the problems. Students will demonstrate the four skills practiced throughout the lesson as well as apply them to real-world problems. Teachers should request photos of each student’s work to be emailed to them for the quiz portion of the lesson to hold the student accountable for their work.

Materials & Resources

Time Requirements:

This lesson should encompass approximately two 60-minute class periods to allow time for both presentation of material within the Nearpod, and time for independent practice/formative assessments (Practice Problems), and the seven question quiz intended for formative assessment.

Technology Requirements:

Teachers and students will need a device with internet connection to access the Nearpod presentation.

All materials have been inserted into a Nearpod lesson. All assessments, both formative and summative, are located within the presentation. Basic Nearpod accounts are free for teachers. I have attached a link below that will allow you to make an editable copy of the Nearpod presentation. Once you have clicked the link and made a copy, you can edit any slide. You can also record your own voice reading directions or explanations.

This lesson can be utilized for in-person, remote, or hybrid learning. Teachers can access reports to collect data on the students’ answers in real time, so this lesson works just as well live as asynchronous. Teachers can choose to launch the lesson live or in student-paced mode for remote learning.

https://np1.nearpod.com/sharePresentation.php?code=7ce08d3361c53b6d36657f7c3c43f9f6-1

Procedures & Implementation

Introducing and Facilitating the Lesson

In your introduction, choose a hook that will be relevant to your student population, such as calculating the height of a nearby structure, water tower, or building. Allow the students to choose the landmark to bring more relevancy into the activity. Ask the students how they would find the height of the structure without being able to measure it outright. You can have the students write their methods down, or share them orally.

Since this lesson is designed to work both synchronously, asynchronously and in person, you will choose to launch the lesson live or student-paced, based on your class needs. A code and/or link will be generated for student entry into the lesson.

This lesson works well with Zoom or Google Meet when your screen is shared. You can share the link in the chat for students to join the Nearpod for live lessons. Students can pull up the presentation on another tab while in the Meet and toggle back and forth for instruction and independent work.

Sequence of Events (Total Time: 120 Minutes)

Introduction/Hook – 5 minutes
Review of Vocabulary, Standards, and Objectives – 5 minutes
Explanation of Trigonometric Ratios – 10 minutes
Example #1 – 5 minutes
Problem Set #1- 10 minutes
Example #2 – 10 minutes
Problem Set #2 – 10 minutes
Example #3 (sway) – 10 minutes
Problem Set #3 – 15 minutes
Example #4 (sway) – 10 minutes
Problem Set #4 – 10 minutes
Quiz – 20 minutes

Tying This Lesson to Assessment and Expected Outcomes

The problem sets and quiz built into the Nearpod presentation directly ask students to demonstrate skills and expected outcomes that are in line with Indiana Geometry standard G.T.10 and the given objectives.

Modifications Based on Student Needs

Student responses can be collected in a variety of ways such as through voice recordings, drawings, images, typing, and writing. Responses can also be resubmitted for students whose performances are not at proficiency .
The Microsoft Immersion Reader can be enabled in the lesson settings. The immersion reader can allow text to speech, read aloud, and translation support for EL students.
Teachers can modify the Nearpod presentation to add voice recordings for directions and explanations in addition to the visual images and text already incorporated into the presentation.
The lesson can be launched both live and student-paced to suit synchronous, asynchronous and in-person teaching methods.
Additional cultural relevance can be added by using a structure in the hook that is well known and meaningful in the local area.
Teachers can replace the images within the Nearpod presentation with images from within their own community to foster the sense of connection between the students and the learning material.

Standards & Indicators

Indiana State Geometry Standard:

G.T.10 Use trigonometric ratios (sine, cosine and tangent) and the Pythagorean Theorem to solve real-world and other mathematical problems.

Indiana State Process Standards:

PS.4 Model with mathematics. Mathematically proficient students apply the mathematics they know to solve problems arising in everyday life, society, and the workplace using a variety of appropriate strategies. They create and use a variety of representations to solve problems and to organize and communicate mathematical ideas. Mathematically proficient students apply what they know and are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

PS.5 Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Mathematically proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. Mathematically proficient students identify relevant external mathematical resources, such as digital content, and use them to pose or solve problems. They use technological tools to explore and deepen their understanding of concepts and to support the development of learning mathematics. They use technology to contribute to concept development, simulation, representation, reasoning, communication and problem solving.

Trajectory

Acknowledged

Engages in discussions and activities around representative diversity and individual differences without grappling with structural oppressions. Culture is externalized and the focus is on the abstract. Minor discomfort may be felt and tensions are largely avoided.

Throughlines

Multiple Ways of Knowing and Doing

The knowledge and wisdom of the students, families, and communities are centered in content and materials to promote equitable and inclusive learning experiences.

Intentional Use of Technology

Technology is used in a purposeful manner that is informed by context and is oriented towards building equitable and inclusive learning environments.

Deep and Transformational Learning

The promotion of academic success and transformational ends through a rigorous and integrated process that honors learners and communities as cultural entities and works to change the world to be a more equitable and inclusive place.

Standards

Social Justice

Diversity 6 - Students will express comfort with people who are both similar to and different from them and engage respectfully with all people.

ISTE NETS

Empowered Learner 1c - Students use technology to seek feedback that informs and improves their practice and to demonstrate their learning in a variety of ways.

Innovative Designer 4a - Students know and use a deliberate design process for generating ideas, testing theories, creating innovative artifacts or solving authentic problems.

Creative Communicator 6c - Students communicate complex ideas clearly and effectively by creating or using a variety of digital objects such as visualizations, models or simulations.