DEPARTMENT OF EDUCATION AND TEACHER DEVELOPMENT
DIRECT INSTRUCTION
ED 467: INTERN TEACHING: ______
Candidate: John Fort
Date:Friday, Sept 5,
2014
Content Area:
Math
Subject Matter:
Calculus
Lesson Content Description:
What are Sine and Cosine? Connection to the unit circle.
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. Extend the understanding to
the π/6 points around the circle. Begin to explore sine and cosine as functions of ϴ and then
of x.
Assessment:
Formative:
Ask table groups to write out the answer to Sinϴ for ϴ = π/6 Radians
Ask table groups to create challenge problems for each other
Summative:
Give students take home worksheet 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
Kickstarter:
1. On your own piece of Paper, silently draw 5 unit circles. On each circle draw a
different angle and write down the exact measure of that angle in radians.
Here is an example:
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 in class queries.
Add on the additional feature of π/6 points.
Begin to discuss the sine of the angles involved.
THROUGH
Step-by-Step Modeling/Presentation of the Objective

Announce that there will be a prize for the group who comes up with a correct answer
that no other group has given. Let the groups whiteboard and then have them hold up
their boards for each other to see.
Step-by-Step Guided/Structured Practice of the Objective: Gradual Release of
Instruction

Technology used to create and enhance Guided Practice examples:
Interactive whiteboarding (student groups have whiteboards on desks)
Rolling and unrolling the unit circle.
Checking for Understanding/Formative Assessment of Each Student’s
Performance/Closure of Instruction

Walk around to check students progress
EL: Special Needs Adaptations:
BEYOND
Independent Practice/Summative Assessment of Each Student’s Performance
Final Closure of Lesson: Closure question to reinforce instruction learned
Assign Weekend Homework:
π/6 worksheet and worksheet to tie together special triangles with unit circle
sine/cosine.
June 2014