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WOODLAND HILLS HIGH SCHOOL LESSON PLAN
SAS and Understanding By Design Template
Name Melissa Broadwater Date 10/01/14
Calculus
Length of Lesson 29 days
Content Area Intro to
STAGE I – DESIRED RESULTS
LESSON TOPIC:
Trigonometry
BIG IDEAS:
UNDERSTANDING GOALS (CONCEPTS):
Students will understand how to 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?
.
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.
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 and OTHER EVIDENCE:
Students will actively participate in class examples,
discussion, class work, whiteboards, open ended
assessments, graphic organizers, exit tickets, daily
warm ups, homework, unit tests, quizzes, and other
formative assessments.
STAGE III: LEARNING PLAN
INSTRUCTIONAL
PROCEDURES:
MATERIALS AND
RESOURCES:
DO NOW:
DO NOW will include a spiraling
review of prior knowledge as well as
the upcoming lesson. We will use
Collins writing 1 and 2 daily
Chapter 4 (Precalculus text
and supplementals)
Mini Lesson:
Mini lessons will vary daily based
upon student needs and informal
assessments. We will use Active
Engagement and
Scaffolding within each lesson.
Examples:
Radian and Degree Measures
Coterminal Angles
The Unit Circle
Right Triangle Trigonometry
Trigonometric Functions
Graphs of Sin, Cos, Tan
Warm ups (daily)
Homework (daily)
worksheets/ activities
Unit Test
Additional materials as
needed (rulers, compass,
grid paper, etc)
INTERVENTIONS:
Think Through Mass
Peer Tutoring
A+ Math (if available)
Math Lab
Online Self Check
Quizzes and Tests
ASSIGNMENTS:
Note: Assignments may be
altered based on student need
for practice and drill.
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
Review
Test
Applications of Trig Curves
Inverse Trig Functions
Guided Practice:
Note Taking, Modeling, Whole Class
Response, Partnering, Higher Level
Thinking Skills
Guided Notes, Chunking, Build on
prior Knowledge, Teacher Prompting,
Visual Support
Independence Practice:
Check for understanding using
practice pages and text as well as
school/SAS developed activities.
Summative/Formative Assessments:
Quizzes as needed for understanding.
Unit test is summative as well as
cumulative for constant knowledge
retention. Students will actively
participate in class examples,
discussion, class work, whiteboards,
open ended assessments, graphic
organizers, exit tickets, daily warm
ups, homework, Study Island and, unit
tests, quizzes, and other formative
assessments.
Reflections:
Check for understanding using do
now, homework, or formative
assessment questioning to determine
whether to continue as needed or do
interventions as needed. (Model, spiral
scaffolding, instruct/reteach as needed)
Teacher reflection: