WOODLAND HILLS HIGH SCHOOL LESSON PLAN
SAS and Understanding By Design Template
Name _ Irene M Runco Date 5.4.15_
Length of Lesson _15 days_
Ed line was updated this week X
My class webpage was updated this week. X
Content Area Algebra 2
STAGE I – DESIRED RESULTS
LESSON TOPIC: CHAPTER 9
BIG IDEAS:
Rational Expressions and Equations
There are some mathematical relationships that
are always true and these relationships are used
as the rules of arithmetic and algebra and are
useful for writing equivalent forms of
expressions and solving equations and
inequalities.
UNDERSTANDING GOALS (CONCEPTS):
ESSENTIAL QUESTIONS:
Operations:
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Add, subtract,
multiply, divide and simplify rational expressions
complex fractions with fractional numerators and
denominators.
Graph rational functions with no more than 1 vertical
asymptote or point of discontinuity.
Identify domain and range of rational functions
Solve problems involving direct and inverse variation.
Identify graphs of different types of functions (linear,
quadratic, cubic, absolute value, radical, rational).
Solve rational equations
How can you extend algebraic properties
and processes to quadratic, exponential and
polynomial expressions and equations and
then apply them to solve real world
problems??
VOCABULARY
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Rational expression,
complex fraction
*Asymptote
rational function
continuity,
*Direct variation
constant of variation
joint variation
inverse varation
Rational equation
STUDENT OBJECTIVES
(COMPETENCIES/OUTCOMES):
Students will be able to:
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Add, subtract,
multiply, divide and simplify rational
expressions
complex fractions with fractional numerators
and denominators.
Graph rational functions with no more than
1 vertical asymptote or point of
discontinuity.
Identify domain and range of rational
functions
Solve problems involving direct and inverse
variation.
Identify graphs of different types of
functions (linear, quadratic, cubic, absolute
value, radical, rational).
Solve rational equations
STAGE II – COMMON CORE STANDARDS ADDRESSED
CC.9-12.A.CED.1Create equations and inequalities in one variable and use them to solve problems.
Include equations arising from linear and quadratic functions, and simple rational and exponential
functions.
CC.9-12.A.CED.2 Create equations in two or more variables to represent relationships between
quantities; graph equations on coordinate axes with labels and scales.
CC.9-12.A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or
inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example,
represent inequalities describing nutritional and cost constraints on combinations of different foods.
CC.9-12.A.APR.7 Understand that rational expressions form a system analogous to the rational
numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational
expression; add, subtract, multiply, and divide rational expressions.
CC.9-12.A.REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x)
and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g.,
using technology to graph the functions, make tables of values, or find successive approximations.
Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and
logarithmic functions.★
CC.9-12.F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative
relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to
assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.★
CC.9-12.F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in
simple cases and using technology for more complicated cases.★
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CCSS.Math.Content.HSF-IF.C.7a Graph linear and quadratic functions and show intercepts, maxima,
and minima.
CCSS.Math.Content.HSF-IF.C.7b Graph square root, cube root, and piecewise-defined functions,
including step functions and absolute value functions.
CCSS.Math.Content.HSF-IF.C.7c Graph polynomial functions, identifying zeros when suitable
factorizations are available, and showing end behavior.
CCSS.Math.Content.HSF-IF.C.7d (+) Graph rational functions, identifying zeros and asymptotes when
suitable factorizations are available, and showing end behavior.
CCSS.Math.Content.HSF-IF.C.7e Graph exponential and logarithmic functions, showing intercepts and
end behavior, and trigonometric functions, showing period, midline, and amplitude.
STAGE III – ASSESSMENT EVIDENCE
OTHER EVIDENCE:
 Daily warm up or exit polls ,
 homework,
 Keystone Diagnostic Tool,
 Study Island and Glencoe.unit tests,
 quizzes,
 formative assessments.
 Student work in portfolio
PERFORMANCE TASK:
Students will participate in
1. class discussions,
2. guided notes & practice,
3. computer work,
4. whiteboard activities
STAGE IV: LEARNING PLAN
INSTRUCTIONAL
PROCEDURES:
(Active Engagement, Explicit
Instruction, Metacognition, Modeling,
Scaffolding)
ACTIVE
ENGAGEMENT USED:
 Cooperative
learning
 Think pair share
 Notetaking
 Higher level
thinking
DESCRIBE USAGE
Students will work from
basic procedures to solve
equations
Solving world problems
Solving real world
applications
Proving properties of
algeb
SCAFFOLDING USED
MATERIALS AND
RESOURCES:
Unit 1 Chapter : Systems of
Equations and Inequalities
( Glencoe Text )
Warm ups & Exit
polls(daily)
Homework (daily)
Guided practice and
Enrichment from Glencoe
Grab & Go workbooks
Glencoe teacher
works…chalkboard is
Good for Promethean
Board use. Use end of
powerpoint for extra
examples and practice.
Use 5 minute check as
exit slip.
INTERVENTIONS:
Study Island
A+ Math
Math Lab
Khan Academy
Videos
Keystone Diagnostic
Tool
National Library of
Virtual Manipulatives
is an excellent site for
use with promethean
boards for this unit.
On line activities are
very good in this
chapter for finding a
pattern and making
predictions based on
your observations.
ASSIGNMENTS:
Note: all assignment
are from the same
page, but different
questions are assigned
based on grouping by
teacher.
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Weekly blogs
Word problem
practice from
2008 copy of
Algebra 2 (on
line form
Glencoe.com)
Enrichment
from 2008
Glencoe (
advanced)
Khan Academy
videos
Truly struggling
students will be
referred to
guidance/SAP (RTI)
:
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Chunking
Building on Prior
knowledge
Providing Visual
Support
•
Small group/
flexible grouping will
occur if necessary.
MINI LESSONS:
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Polynomial
denominators
Use a complex
fraction to solve a
problem
Vertical
asymptotes and
point discontinuity
Graph with a
vertical asymptote
Graph with point
discontinuity
Use graphs of
rational functions
Direct variation
Joint variation
Inverse variation
Use inverse
variation
Identify a function
given the graph
Match equation
with graph
Identify a function
given its equation
Solve a rational
equation
Elimination of a
possible solution
Work problem
Rate problem
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Monday 155B
Complete guided
notes from section
9-2
Special attention
to changing
expressions to
higher terms
Complete all of 9-
Tuesday 156 A
Guided notes on
graphing a
rational function
 Finding
asymptotes
 Choosing
values on
either side
HW from guided
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Students will
be encouraged to stay
for or find help with a
math teacher during
free time, after school,
or lunch.
Wednesday 157 B
Direct, Joint, and
inverse variation
 Setting up
problems
with correct
fractions
First ½ of 9-4
§ 9-1p. 476-478
§9-2 p. 481-484
§9-3p. 488-490
§9-4p. 495-498
§9-5p. 501-504
Note: Reading with
Mathematics pages
from Grab & Go are
especially good for
standard classes.
Thursday 158 A
Finding joint
variation
 How these
relate to
gas laws
and
formulas in
math
Finish section 9- 4
Friday 159 B
Cooperative
learning activity
with rational
functions
 Walk
around
Complete activity
2 homework
notes packet
Math Lab – Tuesday, Thursdays
Wednesday- ?????
in
homework
homework