Coloring With the Unit Circle

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

Coloring With the Unit Circle is a Google Doc tool that allows the student to study the Unit Circle and the different parts that make up the Unit Circle such as reference angles, radian measure, trigonometric ratios, and angle measurements. The student will find and color the reference angles on the unit circle.

This activity was created as a result of the ALEX Resource Development Summit.

Phase

Before/Engage

Mathematics (2019) Grade(s): 09-12 - Algebra II with Statistics

MA19.A2.21
Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle, building on work with non-right triangle trigonometry.

Vocabulary

Unit circle
Radian measure
Quadrantal
Traversed

Knowledge

Students know:

Trigonometric ratios for right triangles.
The appropriate sign for coordinate values in each quadrant of a coordinate graph.

Skills

Students are able to:

Accurately find relationships of trigonometric functions for an acute angle of a right triangle to measures within the unit circle.
Justify triangle similarity.
Find the reference angle for any angle found by a revolution on a ray in the coordinate plane.
Relate the trigonometric ratios for the reference angle to those of the original angle.
Determine the appropriate sign for trigonometric functions of angles of any given size.

Understanding

Students understand that:

Trigonometric functions may be extended to all real numbers from being defined only for acute angles in right triangles by using the unit circle, reflections, and logical reasoning.

Learning Objectives

Students will use the definition of one radian is the measure of the central angle of a unit circle which subtends (cuts off) an arc of length one to determine measures of other central angles as a fraction of a complete revolution (2π for the unit circle).

Students will use radian measure as a ratio of the arc length to the radius.

Students will be able to accurately find relationships of trigonometric functions for an acute angle of a right triangle to measure within the unit circle.

Students will be able to justify triangle similarity.

Students will be able to find the reference angle for any angle found by a revolution on a ray in the coordinate plane.

Students will be able to relate the trigonometric ratios for the reference angle to those of the original angle.

Students will be able to determine the appropriate sign for trigonometric functions of angles of any given size.

Students will be able to determine the amplitude, frequency, and midline of a trigonometric function.

Students will be able to develop a trigonometric function to model periodic phenomena.

Activity Details

Before a lesson on the Sine Curve using right triangles, the teacher will use the Google Doc, Coloring With the Unit Circle, to spark interest and encourage thinking.

The teacher will need to put the students into groups of two.
Each group will need to have the following supplies:

-Four copies of the blank Unit Circle

-A fine point Sharpie or black pen

-Four different colored highlighters

The teacher will review the reference angles with the students.
The teacher will demonstrate on the board as he/she instructs the students to use the yellow highlighter to color in the segment that contains the reference angles for π/6, 5/6, 7/6, and 11/6 (see example).
The teacher will demonstrate on the board as he/she instructs the students to use the green highlighter to color in the segment that contains the reference angles for π/4, 3/4, 5/4, and 7/4 (see example).
The teacher will instruct the students to use the blue highlighter to color in the segment that contains the reference angles for π/3, 2/3, 4/3, and 5/3 (see example).
The teacher will demonstrate on the board as he/she instructs the students to use the pink highlighter to color in the segment that contains the reference angles for π/2, 3/2 (see example).
The teacher will need to have a discussion with the class about the reference angles for π and 2π being 0.
Once the angles have been highlighted the teacher will instruct the students to use the sharpie to label each angle and to draw a dotted line showing the reference triangle inside each segment.
Tell the students to keep their unit circles because they will need them later in the lesson.

Assessment Strategies

The teacher would assess the students by observing the Coloring With the Unit Circle activity while walking around the room.

Variation Tips

Colored pencils could be used instead of highlighters.

Instead of putting the students into groups, the activity could be completed by every student.

Background / Preparation

The teacher would need to make four copies of the blank Unit Circle.
The teacher will need the following supplies for each group: a fine point Sharpie or black pen and four different colored highlighters

Coloring With the Unit Circle Google Doc Activity

https://docs.google.com/document/d/1qJY7xFY7-sQ0C8NRN9uNW3P9cD_3dSwZ3wKi-hqnj2Q…

Approved Date

2020-07-16

Owner (Author)

kristylacks