Week 13: Mobile Device Learning Lesson for Math Content Area
Background:
Content Area: Trigonometry (usually within the Algebra or PreCalculus curriculum)
Title: Mastering the Unit Circle with Apps
Grade Level or Target Group: High School Math Students Grades 10-12
Title: Mastering the Unit Circle with Apps
Grade Level or Target Group: High School Math Students Grades 10-12
Pre-Planning:
Big Idea(s): Often times, trigonometry students learn how to use the unit circle without understanding why this tool is so important or how it is constructed. When I teach my students the unit circle, I make sure to emphasize the relationship that the circle has with angle measurement, Cartesian coordinates, trigonometric function values and trigonometric graphs. Students often make the mistake of thinking that they have to memorize the unit circle when in fact they just need a solid understanding of it. If a student understands the unit circle, where the values come from and what they represent, then he/she will never have to memorize a thing.
Essential Questions:
Objectives:
Summative Assessment:
Students will be quizzed following this lesson on their proficiency in solving trigonometric function using only the use of a blank unit circle.
Students will also submit their picture project displaying their knowledge of unit circle trigonometry.
Essential Questions:
- What is the unit circle?
- How is the unit circle used to solve trig functions?
- How is the unit circle related to the graph of a trig function?
Objectives:
- Explore the properties of the Unit Circle.
- Exhibits knowledge to solve trig functions using the Unit Circle
- Discover the relationships between the Unit Circle and graphing trig functions.
- Understand how the Unit Circle is constructed.
Summative Assessment:
Students will be quizzed following this lesson on their proficiency in solving trigonometric function using only the use of a blank unit circle.
Students will also submit their picture project displaying their knowledge of unit circle trigonometry.
Lesson Opening:
Lesson Opening (The Hook): Trig Func – Check the Visual Trig Functions! (Free)
This app provides a great visual interpretation of the unit circle. Students can use this app to explore and discover the development of the unit circle. Some students only learn how to memorize and use the unit circle but they often struggle to interpret and truly understand the concepts behind the using the unit circle. This application is a wonderful example of how technology can emphasize important concepts and make learning a hands-on activity.
At the beginning of the lesson, students will be asked to download this app and explore its functions for a few minutes. Once everyone has access to the technology, students will be directed to make observations using the following questions as a guide.
This app provides a great visual interpretation of the unit circle. Students can use this app to explore and discover the development of the unit circle. Some students only learn how to memorize and use the unit circle but they often struggle to interpret and truly understand the concepts behind the using the unit circle. This application is a wonderful example of how technology can emphasize important concepts and make learning a hands-on activity.
At the beginning of the lesson, students will be asked to download this app and explore its functions for a few minutes. Once everyone has access to the technology, students will be directed to make observations using the following questions as a guide.
- What is the largest (and smallest) x-value that you observe in both the Calc and
List screens? What is the largest (and smallest) y-value that you observe? - What do you notice about the value of the hypotenuse?
- Can you write equations to represent the sine and cosine functions of this triangle
using the x, y and r values? What can you conclude about these equations
given your answer to #2? - While observing the list screen, what do you notice
about the table of values? Please write any and all observances you may see. - How does the table of values in the list mode relate to the graphs
seen on the waves screen? - Can you draw any conclusions about the
relationship between the calc screen and the wave screen? - Explore the inverse function table of values and graphs and make observations of the
relationship and behavior of these functions.
Lesson Body:
Explanation
Fun Trig (Free)
This unit circle is animated and color coded so that students can see the angle location and the reference angle used to evaluate it trig function values. A right triangle is drawn to the location of any angle on the unit circle. The orange side of the triangle correlates to the length of y-value and the sine value of that angle while the green side of the triangle corresponds to the x-value and the cosine value of that angle. This visual is helpful for students to ‘see’ that answers to common questions when using the unit circle such as understanding that relationship between the coordinate plane and the function values. This app also has a great graphing feature where students can see how the x-values of the unit circle are plotted to create the cosine wave and the y-values create the sine wave. This app will be used to not only teach students how use the unit circle but also to introduce the graphs of trigonometric functions.
This unit circle is animated and color coded so that students can see the angle location and the reference angle used to evaluate it trig function values. A right triangle is drawn to the location of any angle on the unit circle. The orange side of the triangle correlates to the length of y-value and the sine value of that angle while the green side of the triangle corresponds to the x-value and the cosine value of that angle. This visual is helpful for students to ‘see’ that answers to common questions when using the unit circle such as understanding that relationship between the coordinate plane and the function values. This app also has a great graphing feature where students can see how the x-values of the unit circle are plotted to create the cosine wave and the y-values create the sine wave. This app will be used to not only teach students how use the unit circle but also to introduce the graphs of trigonometric functions.
iUnit Circle (Free)
This is a very simple but straightforward and easy to use application for trig students. During this lesson, I will show this app to my students and have them download it as a reference tool. This interactive Unit Circle allows you to tap any of the 16 major angles to reference any of the six trig function values. The option to view angles in degree or radian is useful as well as the ability to see the function values in radical or decimal form.
This is a very simple but straightforward and easy to use application for trig students. During this lesson, I will show this app to my students and have them download it as a reference tool. This interactive Unit Circle allows you to tap any of the 16 major angles to reference any of the six trig function values. The option to view angles in degree or radian is useful as well as the ability to see the function values in radical or decimal form.
Following the use of these apps by students, the instructor will provide notes and a variety of practice problems will be modeled and practiced by students.
Check for Understanding
Brain Builder Trig (Free)
This is a good app for students to use when practicing independently. The BrainBuilder app offers the ability to customize the questions asked during the game. Students are asked to solve a trig function and they are offered multiple choice options for the solution. Students can choose to be quizzed on particular trig functions, specific angles or angle measurement. This game is perfect for a student trying to master his/her trig skills using the unit circle. This app will be shown to students to use independently while practicing their new skills in the
lesson.
This is a good app for students to use when practicing independently. The BrainBuilder app offers the ability to customize the questions asked during the game. Students are asked to solve a trig function and they are offered multiple choice options for the solution. Students can choose to be quizzed on particular trig functions, specific angles or angle measurement. This game is perfect for a student trying to master his/her trig skills using the unit circle. This app will be shown to students to use independently while practicing their new skills in the
lesson.
Trig Tester (Free)
After students have had time to practice their skills with the Brain Builder game, they will be “put to the test”. Students will use this Trig Tester app. This app adds an element of competition to the task of learning how to do unit circle trigonometry. There are several options and game modes available to use this app. The app supports radian and degree measure as well as all six trig functions. First, students will do play the game using the points mode. Everyone in the class will be given 3 minutes to play and the faster a student answers, the more points he/she gets. At the end of the time, the student with the highest score will be given praise and a small prize (candy). After playing the points mode, we will play the timed version of the game. Students will be asked to complete as many points as possible in 120 seconds. The student with the most correct answers will be rewarded.
After students have had time to practice their skills with the Brain Builder game, they will be “put to the test”. Students will use this Trig Tester app. This app adds an element of competition to the task of learning how to do unit circle trigonometry. There are several options and game modes available to use this app. The app supports radian and degree measure as well as all six trig functions. First, students will do play the game using the points mode. Everyone in the class will be given 3 minutes to play and the faster a student answers, the more points he/she gets. At the end of the time, the student with the highest score will be given praise and a small prize (candy). After playing the points mode, we will play the timed version of the game. Students will be asked to complete as many points as possible in 120 seconds. The student with the most correct answers will be rewarded.
Extended Practice
Trig Pro (Free)
This app will be shown to students at the end of the lesson because it provides a great collection of instructional resources covering more than just the unit circle. The information and tools provided for graphing trig functions, which is the subsequent lesson to this lesson, are particularly helpful. This app provides not only the graph of any trig function but it also lists its attributes such as amplitude, period, phase shift and vertical shift. Another helpful tool in the app is the reference angle finder, which is a great extension to the unit circle lesson. In addition, there is a triangle solver and an angle measurement converter.
This app will be shown to students at the end of the lesson because it provides a great collection of instructional resources covering more than just the unit circle. The information and tools provided for graphing trig functions, which is the subsequent lesson to this lesson, are particularly helpful. This app provides not only the graph of any trig function but it also lists its attributes such as amplitude, period, phase shift and vertical shift. Another helpful tool in the app is the reference angle finder, which is a great extension to the unit circle lesson. In addition, there is a triangle solver and an angle measurement converter.
Closing:
Lesson Closing: Easy Angle & You Doodle (Free)
I want you to carefully examine the world around you to search for ordinary objects and surroundings that you can demonstrate your knowledge of trigonometry and unit circle trig. You are to use the Easy Angle app to measure an angle that you see, it can be in nature, around the house, or be within a circle to parallel the unit circle idea. Please be creative and have fun searching. Once you take the picture, save it to your camera roll and use the You Doodle app to highlight the measurements. You should use your unit circle apps to find the measurement of the sine and cosine functions. You should label your photo with these measurements (x, y, and r). Save your photo and upload it to the class blog along with a paragraph reflecting on this project.
I want you to carefully examine the world around you to search for ordinary objects and surroundings that you can demonstrate your knowledge of trigonometry and unit circle trig. You are to use the Easy Angle app to measure an angle that you see, it can be in nature, around the house, or be within a circle to parallel the unit circle idea. Please be creative and have fun searching. Once you take the picture, save it to your camera roll and use the You Doodle app to highlight the measurements. You should use your unit circle apps to find the measurement of the sine and cosine functions. You should label your photo with these measurements (x, y, and r). Save your photo and upload it to the class blog along with a paragraph reflecting on this project.
Materials:
This lesson will require the use of personal mobile devices. For students without access to a smartphone, a set of classroom iPads are available for use. These mobile devices will need to have the ability to connect to the internet as well as take pictures.
AECT Standards achieved: 1.2 Message Design, 1.3 Instructional Strategies, 2.2 Audiovisual
Technologies, 2.4 Integrated Technologies, 3.1 Media Utilization, 3.2 Diffusion of Innovations
Technologies, 2.4 Integrated Technologies, 3.1 Media Utilization, 3.2 Diffusion of Innovations