DEPARTMENT OF EDUCATION AND TEACHER DEVELOPMENT
DIRECT INSTRUCTION
ED 467: INTERN TEACHING: ______
Candidate: John Fort
Date: Thursday, March
24, 2016
Content Area:
Math
Subject Matter:
Calculus
Lesson Content Description:
Having established the concept of the unit circle we need to
delve into what it can do for us. What are Sine and Cosine? What
are their connections to the unit circle? How can we use these to
solve problems of importance?
Grade Level:
11-12
Instructional Strategies/Method of Delivery:
Direct Instruction; Query of class and table groups; Reflection on homework
Common Core Standard:
CCSS.Math.Content.HSF.TF.A.1
Understand radian measure of an angle as the length of the arc on the unit circle
subtended by the angle.
CCSS.Math.Content.HSF.TF.A.2
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.
CCSS.Math.Content.HSF.TF.A.3
(+) Use special triangles to determine geometrically the values of sine, cosine, tangent for
π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent
for x, π + x, and 2π - x in terms of their values for x, where x is any real number.
ELD Standard:
Use written and spoken communication to work together with groups solving problems
Common Core Lesson Objective:
Understand that sine and cosine are features of an angle that tell us about the relationship
between the sides of the right triangle created by that angle. Use this knowledge to describe
and solve problems of importance.
Assessment:
Formative:
Ask table groups to write out the answer to Cosϴ for ϴ = π/2 Radians
Ask table groups to write out the answer to Sinϴ for ϴ = π Radians
Ask table groups to write out the answer to Cosϴ for ϴ =3π/2 Radians
Ask table groups to create challenge problems for each other around the unit circle.
Summative:
Give students take home quiz on unit circle that ties together the concepts of Sine, Cosine,
and Radians.
Lesson/Assessment Modifications: ELL: Special Needs
Group Work. Emphasis on graphics
Technology: Describe the types of technology you will be utilizing in your lesson to create
and enhance instruction
Writing on Whiteboard. Overhead projection

LESSON PREVIEW PRIOR TO TEACHING
Prior knowledge required for this lesson/objective success
 Special Triangles, Radians
Review sub-skills required for this lesson/objective

June 2014
LESSON PRESENTATION
INTO
Students will
Understand radian measure of an angle as the length of the arc on the unit circle
subtended by the angle, 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, and Use special triangles to
determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use
the unit circle to express the values of sine, cosine, and tangent for x, π + x, and 2π - x in
terms of their values for x, where x is any real number.
Understand that sine and cosine are features of an angle that tell us about the relationship
between the sides of the right triangle created by that angle.
We will assess this through looking at their written responses to inclass querries.
Show students powerpoint from precalc classes and ask them if they need review on any of
the topics. If so, complete the review. If not continue to move forward by talking about
FUNCTIONS and how those might apply to what we’ve doing with the unit Circle.
THROUGH
Step-by-Step Modeling/Presentation of the Objective

What are Functions?
Functions are a special kind of relation in which each elements of one set maps onto a
unique element of another set.
(Domain and Range)
Step-by-Step Guided/Structured Practice of the Objective: Gradual Release of
Instruction

Call students to board to demonstrate their skills at solving Function Identification
Problems.
Checking for Understanding/Formative Assessment of Each Student’s
Performance/Closure of Instruction

Check understanding base on student performance calculations and function
identification.
BEYOND
Independent Practice/Summative Assessment of Each Student’s Performance
Ask students to complete a final problem set on their own. Evaluate individual
performance on the problem set.
June 2014