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MIFFLIN COUNTY SCHOOL DISTRICT
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MCSD Mathematics Curriculum
Algebra III
Planned Instruction
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Title of Planned Instruction:
Algebra III |
| Subject Area: Mathematics Grade Level:
Grades 11-12 |
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Prerequisites: Algebra II and
Geometry
Course Description: This course builds
on the concepts and skills learned in algebra and geometry.
It focuses on graphing more advanced functions and solving the
related equations. Exponential functions, series, and
sequences are some specific topics that will be examined.
Higher order thinking skills will be strengthened during this
time.
Required Time: 90 days
Major Text(s) and Resources: |
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Advanced Mathematical Concepts:
Precalculus with Applications,
Copyright 1999 by Glencoe/McGraw-Hill |
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Names of District Subject Area Curriculum Writing Committee: |
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Daniel F. Bartos -- Lewistown High School
Allen C. Muir -- Lewistown High School |
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Date of Board Approval: July 24, 2003 |
Major Topics
- Nature of graphs
- Quadratics
- Polynomial and rational functions
- Exponential and logarithmic functions
- Series and sequences
Course Objectives and Performance Indicators
Strand: 2.1
Standard: Numbers, Number Systems and Number Relationships
Course: Algebra III |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.1.11A |
Use operations. |
Add, subtract, multiply,
and divide functions. Find composite functions and inverse functions.
Use the properties of exponents to evaluate and simplify expressions.
Use logarithms to solve exponential equations. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.2
Standard: Computation and Estimation
Course: Algebra III |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.2.11A |
Develop and use computation
concepts, operations and procedures with real numbers in problem-solving
situations. |
Perform calculations
involving polynomial, rational, exponential or logarithmic, and any other
previously learned functions or their inverses. Evaluate expressions
involving logarithms with and without a calculator |
7 Observation 8 Evaluate
written work
9 Performance assessments
10 Tests, quizzes
11 Problem solving journal/activity
12 Evaluate oral response |
| 2.2.11B |
Use estimation to solve
problems for which an exact answer is not needed. |
Use a calculator to find
estimated answers to problems that involve any of the functions studied in
this course. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.2.11C |
Construct and apply
mathematical models, including lines and curves of best fit, to estimate
values of related quantities. |
Estimate values of related
quantities by constructing and applying mathematical models including:
a) polynomial functions
b) rational functions
c) exponential/logarithmic functions
d) arithmetic/geometric/other sequences or series
e) other curves of best fit. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.2.11D |
Describe and explain the
amount of error that may exist in a computation using estimates. |
Identify and explain the
amount of error that may exist in a computation using estimates when a
real life answer is also known. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.2.11E |
Recognize that the degree
of precision needed in calculating a number depends on how the results
will be used and the instruments used to generate the measure. |
Compare and contrast the
solution(s) of an equation solved by graphing (hand and graphing
calculator) the related function with solutions found using other
techniques. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.2.11F |
Demonstrate skills for
using scientific and graphing calculators. |
Using a calculator: a)
graph the functions studied in this course
b) evaluate expressions involving logarithms and anti logarithms
c) solve problems involving sequences and series
d) find regression equations (exponential, power, and quadratic)
e) solve problems involving various functions. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.3
Standard: Measurement and Estimation
Course: Algebra III |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.3.11A |
Select and use appropriate
units to the degree of accuracy required in particular measurement
situations. |
Select and use appropriate
units in all measurement situations. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.4
Standard: Mathematical Reasoning and Connections
Course: Algebra III |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.4.11A |
Use direct proofs, indirect
proofs or proof by contradiction to validate conjectures. |
Make conjectures about
graphical transformations and use a graphing calculator to validate or
contradict (e.g., given parent graph f(x) = |x|, guess how graph would
change for 3f(x), f(3x), f(x+3), and f(x)+3). |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.4.11B |
Construct valid arguments
from stated facts. |
Solve algebraic equations
using correct techniques. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.4.11C |
Determine the validity of
an argument. |
Given a proof’s steps and
reasons, determine if the steps and reasons are valid. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.4.11E |
Demonstrate mathematical
solutions to problems. |
Use algebraic techniques to
solve problem situations involving formulas used in science (e.g., volume,
distance, business). |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.5
Standard: Mathematical Problem Solving and Communication
Course: Algebra III |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.5.11A |
Select and use appropriate
mathematical concepts and techniques from different areas of mathematics
and apply them to solving non-routine and multi-step problems. |
Select, use, and display
all of the mathematical procedures that are necessary to the solution of a
problem situation and achieve the correct answer. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.5.11B |
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. |
Communicate all of the
mathematical procedures concepts, conclusions, etc. necessary to the
solution of a problem situation using correct and appropriate mathematical
representations. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.5.11C |
Present mathematical
procedures and results clearly, systematically, succinctly and correctly. |
Present all of the
procedures important to the solution of a problem in ways that are
understandable. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.5.11D |
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. |
Explain how a problem was
solved and why the chosen procedures were used. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.6
Standard: Statistics and Data Analysis
Course: Algebra III |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.6.11D |
Make predictions using
interpolation, extrapolation, regression and estimation using technology
to verify them. |
Make predictions using
interpolation, extrapolation, regression and estimation using technology
to verify them. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.8
Standard: Algebra and Functions
Course: Algebra III |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.8.11A |
Analyze a given set of data
for the existence of a pattern and represent the pattern algebraically and
graphically. |
Given a table of values,
find a nonlinear relationship between two variables. Represent the
nonlinear relationship between two variables by graphing and by equation. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11B |
Give examples of patterns
that occur in data from other disciplines. |
Find examples of patterns
that occur in data from science, business, or other areas. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11C |
Use patterns, sequences and
series to solve routine and non-routine problems. |
Use patterns, sequences and
series to solve routine and non-routine problems involving any of the
functions studied in this course. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11D |
Formulate expressions,
equations, inequalities, systems of equations, systems of inequalities and
matrices to model routine and non-routine problem situations. |
Formulate expressions,
equations, inequalities, systems of equations, systems of inequalities and
matrices to model routine and non-routine problem situations. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11E |
Use equations to represent
curves (e.g., lines or parabolas). |
Given the graph of a
parabola, write the equation. Given the graph of a linear function,
write the equation.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11J |
Demonstrate the connections
between algebraic equations and inequalities and the geometry of relations
in the coordinate plane. |
Given an algebraic equation
or inequality, draw the graph on the coordinate plane. Determine the
algebraic equation or inequality from its graph on the coordinate plane. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11N |
Solve quadratic and
exponential equations both symbolically and graphically. |
Solve quadratic equations
by graphing the related functions. Solve quadratic equations by using
algebraic techniques or the quadratic formula.
Solve exponential equations by using logarithms. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11O |
Determine the domain and
range of a relation, given a graph or set of ordered pairs. |
Determine the domain and
range of all the relations and functions studied in this course, given a
graph or set of ordered pairs. Determine horizontal, vertical, and slant
asymptotes. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11Q |
Represent functional
relationships in tables, charts and graphs. |
Represent all functional
relationships studied in this course in tables, charts and graphs. Find
inverses for all studied relations and graph them.
Determine roots of polynomial equations to help graph.
Apply the Fundamental Theorem of Algebra to help graph.
Use the discriminant to describe the roots of quadratic equations. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11R |
Create and interpret
functional models. |
Create and interpret
functional models for the various functions studied in this course. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11S |
Analyze properties and
relationships of functions (e.g., linear, polynomial, rational,
exponential, logarithmic) |
Use transformations to
"parent" functions to determine properties and relationships of functions.
Identify graphs of the following:
a) simple polynomial functions
b) absolute value functions
c) step functions
d) rational functions
e) exponential and logarithmic functions
f) inverses for relations and functions. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.8.11T |
Analyze and categorize
functions by their characteristics. |
Given a graph of a
function, identify it using algebraic equations to describe the function.
Given an algebraic equation for a function, determine the type of function
the equation represents.
Determine continuity or discontinuity of functions.
Identify the end behavior of graphs.
Find the factors of polynomials using the remainder and factor
theorems.
Identify all possible rational roots of a polynomial equation by using
the rational root theorem.
Determine the number of positive and negative real zeros a polynomial
function has.
Approximate the real zeros of a polynomial function. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.9
Standard: Geometry
Course: Algebra III |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.9.11J |
Analyze figures in terms of
the kinds of symmetries they have. |
Identify symmetrical
graphs. Use symmetry to complete a graph. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.11
Standard: Concepts of Calculus
Course: Algebra III |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
| 2.11.11A |
Determine maximum and
minimum values of a function over a specified interval. |
Determine maximum and
minimum values of a function over a specified interval. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.11.11B |
Interpret maximum and
minimum values in problem situations. |
Interpret maximum and
minimum values in problem situations. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.11.11C |
Graph and interpret rates
of growth/decay. |
Use properties of exponents
to simplify expressions. Evaluate and simplify expressions containing
rational exponents.
Evaluate expressions with irrational exponents.
Graph exponential and logarithmic functions and inequalities with and
without a graphing calculator.
Graph the exponential function that contains the natural number as a
base.
Use the natural logarithm when the natural number is involved in the
problem.
Solve equations involving logarithms without the use of a calculator by
applying the properties of logarithms.
Find common logarithms and antilogarithms of numbers.
Solve exponential and logarithmic equations and inequalities.
Solve equations using natural logarithms.
Find answers to growth/decay problem situations.
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- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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| 2.11.11D |
Determine sums of finite
sequences of numbers and infinite geometric series. |
Find the nth term and
arithmetic means of an arithmetic sequence. Find the sum of n terms of
an arithmetic series.
Find the nth term and geometric means of a geometric sequence.
Find the sum of n terms of a geometric series.
Find the sum of an infinite geometric series. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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District Recommended Instructional Approaches For
the Course
To Drive Teacher’s Instructional Activities |
- Whole group instruction
- Small group instruction
- Projects
- Class discussion
- Peer evaluation
- Teacher and peer conferencing
- Oral presentations
- Individual instruction
- Research
- Dramatization
- Role playing
- Independent reading
- Read aloud
- Directed reading-thinking activities
- Modeling process
- Games
- Self-reflection
- Self-evaluation
- Independent study
- Guest speaker
- Guest reading
- Writing activities
- Thematic units
- Notebooks
- Study guides
- Computer technology
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