Download arc length, coterminal angles, radian, unit circle, odd function, even

WOODLAND HILLS HIGH SCHOOL LESSON PLAN
SAS and Understanding By Design Template
Name Melissa Broadwater
Date 1/28/13
Edline was updated this week:
Length of Lesson 29 days
Content Area Intro to Calculus
My Class website was updated this week:
STAGE I – DESIRED RESULTS
LESSON TOPIC:
Trigonometry
BIG IDEAS:
(Content standards, assessment anchors, eligible content) objectives, and skill
focus)
M11.A.1.1
Represent and/or use numbers in equivalent forms (e.g.,
integers, fractions, decimals, percents, square roots, exponents and scientific
notation).
M11.A.2.1 Apply ratio and/or proportion in problem-solving situations.
M11.A.2.2 Use exponents, roots and/or absolute value to solve problems.
M11.B.2.1
Use and/or compare measurements of angles.
M11.C.1.2
Recognize and/or apply properties of angles, triangles and
quadrilaterals.
M11.C.1.3
Use properties of congruence, correspondence and
similarity in problem-solving settings involving two- and three- dimensional
figures
M11.C.1.4
Solve problems involving right triangles using the
Pythagorean Theorem.
M11.D.1.1
Analyze and/or use patterns or relations.
UNDERSTANDING GOALS (CONCEPTS):
Students will understand: Use operations (e.g., opposite, reciprocal, absolute
value, raising to a power, finding roots, finding logarithms).
Develop and use computation concepts, operations and procedures with real
numbers in problem-solving situations. Select and use appropriate units and tools
to measure to the degree of accuracy required in particular measurement
situations. Measure and compare angles in degrees and radians
Demonstrate mathematical solutions to problems (e.g., in the physical sciences).
Select and use appropriate mathematical concepts and techniques from different
areas of mathematics and apply them to solving non-routine and multi-step
problems. Use symbols, mathematical terminology, standard notation,
mathematical rules, graphing and other types of mathematical representations to
communicate observations, predictions, concepts, procedures, generalizations,
ideas and results. Present mathematical procedures and results clearly,
systematically, succinctly and correctly. Conclude a solution process with a
summary of results and evaluate the degree to which the results obtained
represent an acceptable response to the initial problem and why the reasoning is
valid. Represent functional relationships in tables, charts and graphs
Analyze properties and relationships of functions (e.g., linear, polynomial,
rational, trigonometric, exponential, logarithmic). Model situations
geometrically to formulate and solve problems. Use graphing calculators to
display periodic and circular functions; describe properties of the graphs.
Identify, create and solve practical problems involving right triangles using the
trigonometric functions and the Pythagorean Theorem.
ESSENTIAL QUESTIONS:
How do you cChange from radian to degree measures and vice
versa.
What is meant by coterminal angles?
In what ways can the unit circle be used?
How do you determine the domain, range, and period of the
sine and cosine functions using the unit circle?
How do you sketch a graph of a sin, cos, tan, cot, sec, or csc?
VOCABULARY: arc length, coterminal angles, radian, unit
circle, odd function, even function, trigonometric identities
STUDENT OBJECTIVES (COMPETENCIES/OUTCOMES):
Students will be able to:
1 Change from radian to degree measures and vice versa.
2.
Sketch and find coterminal angles.
3.
Find arc length with degree and radian measures.
4.
Use the unit circle to evaluate the 6 trig functions and
their inverses.
5.
Determine the domain, range, and period of the sine
and cosine functions using the unit circle.
6.
Define odd and even functions and relate them to trig
functions (using unit circle).
7.
Define the six trig functions using right triangle trig.
Evaluate trig functions of special angles without a calculator.
Evaluate trig functions using a calculator.
8.
Understand and apply trig identities to solve
problems.
9.
Find the trig function of any angle using definitions,
reference angles, trig identities and calculators.
10.
Construct basic sin and cos curves.
11.
Identify period, amplitude, shifts, and translations
from a sin or cos equation. Use identified information to
graph functions.
12.
Determine an equation of a function given its graph.
13.
Sketch basic tan, cot, sec, and csc curves.
14.
Define, evaluate and sketch inverse trig functions.
15.
Apply trig functions to solve problems.How do you
use operations involving logarithms?
STAGE II – ASSESSMENT EVIDENCE
PERFORMANCE TASK:
Students will actively
participate in class examples, discussion, and group work.
FORMATIVE ASSESSMENTS:
#1. Exit Tickets
#2. Pre-Assessment
#3. Graphic Organizers
Others: Summarizing Main Idea
STAGE III: LEARNING PLAN
INSTRUCTIONAL
PROCEDURES:
MATERIALS AND
RESOURCES:
Active Engagements used:
#1. Note-Taking
#2. Compare Contrast
Others: Graphic Organziers,
Summarizing, Cooperative
Education, Partnering
Chapter 3 (Precalculus
text and supplementals)
Describe usage: See below for
Compare/Contrast, Graphic
Organizers, Cooperative
Education, Partnering, NoteTaking. Check for understanding
and summarizing using warm
up, homework, formative
assessment questioning or exit
tickets to determine whether to
continue lesson or do
interventions as needed. (model,
spiral scaffolding, instruct/
reteach as needed)
Warm ups (daily)
Homework (daily)
worksheets/ activities
Unit Test
Additional materials as
needed (rulers, compass,
grid paper, etc)
CONTENT AREA
READING:
Guided Notes
INTERVENTIONS:
ASSIGNMENTS:
Struggling students will be
referred to RTII
Small group/flexible
grouping will occur.
Various computer programs.
•Complete Chapter 4 Note
Sheets
Text Problems
Pg. 367: 1-14
Pg. 367: 15-61 eoo
Pg. 367: 71-81 odd
Pg. 377: 1-16
Pg. 377: 17-30
Pg. 378: 25-53 odd
Pg. 387: 1-21 odd
Pg. 388: 23-55 odd
Pg. 389: 57-67 odd
Pg. 399: 1-21 odd
Pg. 400: 43-67 odd
Pg. 401: 75-80
Scaffolding used:
#1. Guided Notes
#2 . Build on Prior Knowledge
Others: Graphic Organizers,
Build Vocabulary
Describe usage: Warm up to
include spiraling review of prior
knowledge to include upcoming
lesson. All notes are guided notes
to build vocabulary, interspersed
with group activities. Graphic
organizers utilized when
appropriate to compare/contrast
vocabulary.
Other techniques used:
MINI LESSON:
Based on daily assessments
(formative and summative),
additional modeling, instruction,
homework, review, interventions,
group work, computer or teacher
guided practice will be done.