Download Standards-Based Mathematics 12 is a 12th grade course that has

STANDARDS-BASED MATHEMATICS
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COURSE SYLLABUS
Standards-Based Mathematics 12 is a 12th grade course that has been specially designed to enable students to
demonstrate proficiency in the PA Mathematics Standards. These standards address mathematics topics from Algebra 1,
Geometry, and Algebra 2, plus topics in statistics and probability.
Demonstrating proficiency in the PA Mathematics Standards is now a graduation requirement of the State of
Pennsylvania. If students do not demonstrate such proficiency, they will not receive a high school diploma.
Students are enrolled in this course because they have not demonstrated proficiency in the mathematics standards via
other means:

Scoring at a “Meet the Standard” or “Meet the Standard with Honors” level on the Grade 10 New Standards
Mathematics Reference Exam;

Scoring at the Proficient or Advanced level on the Grade 11 PSSA Mathematics test. (You will have another
opportunity to score at these levels on the fall Grade 12 retest.):

Achieving a grade of C or better in both semesters of Elementary Functions.
Standards-Based Mathematics gives students another way to demonstrate proficiency in the PA Mathematics Standards.
In Standards-Based Mathematics, they will learn and/or review the mathematics in the standards, with emphasis on how
this mathematics is used in everyday life, in various careers, and in other disciplines. They will be able to demonstrate
proficiency in the standards through regular assessments: in-class tests (2 per marking period). Students will have several
opportunities to pass each assessment. Successfully passing the course assessments will demonstrate proficiency in the
mathematics standards, i.e., that this state graduation requirement has been achieved.
If students fail to pass the assessments in this course, they will not have demonstrated proficiency in the standards.
Unless students demonstrate this proficiency through one of the other ways listed above, they will not have met this PA
graduation requirement.
COURSE MATERIALS
Basic Texts
Gold, David, PSSA Mathematics Coach Grade 11 (WAA – 508), published by Educational Design / Triumph Learning Inc.
Copyright 2001. (one per student)
Burrill, Gail F. and Patrick Hopfensperger, Data-Driven Mathematics: Exploring Linear Relations (1-57232-210-1),
published by Dale Seymour Publications/Pearson. Copyright 1998. (for use in class)
Hopfensperger, Patrick, Henry Kranendonk, and R. Scheaffer, Data-Driven Mathematics: Probability Through Data (157232-225-X), published by Dale Seymour Publications/Pearson. Copyright 1999.x (for use in class)
Tools
TI-83 Plus Graphing Calculator (for use in class)
Useful Websites
www.pde.state.pa.us/ - This is the website for the Pennsylvania Department of Education. It explains the graduation
requirements, posts test scores by school, and provides sample assessment problems.
STUDENT REQUIREMENTS AND EXPECTED LEVELS OF ACHIEVEMENT
Students will be expected to:

attend class daily and participate in class discussions and activities.

complete all homework assignments.

study materials presented in class and in the textbook.

pass quizzes and tests.
John W. Thompson, Ph.D.
Superintendent of Schools
Copyright 2003
CONTENT PERFORMANCE BENCHMARKS
These are the PA Grade 11 Mathematics Standards that are addressed in this course.
Academic
Standard
Performance Benchmarks
2.1.11
Numbers, Number
Systems, and Number
Relationships
2.2.11
Computation and
Estimation
2.3.11
Measurement and
Estimation
2.4.11
Mathematical
Reasoning and
Connections
2.5.11
Mathematical
Problem Solving
and Communication
2.6.11
Statistics and
Data Analysis
A. Use operations (e.g., opposite, reciprocal, absolute value, raising to a power, finding roots, finding logarithms.)
A.
B.
C.
F.
Develop and use computation concepts, operations, and procedures with real numbers in problem solving situations.
Use estimation to solve problems for which an exact answer is not needed.
Construct and apply mathematical models, including lines and curves of best fit, to estimate values of related quantities.
Demonstrate skills for using computer spreadsheets and scientific and graphing calculators.
A. Select and use appropriate units and tools to measure to the degree of accuracy required in particular measurement situations.
C. Demonstrate the ability to produce measures with specified levels of precision.
A. Use direct proofs, indirect proofs, or proof by contradiction to validate conjectures.
E. Demonstrate mathematical solutions to problems (e.g., in the physical sciences).
A. Select and use appropriate mathematical concepts and techniques from different areas of mathematics and apply them to solving
non-routine and multi-step problems.
B. 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.
C. Present mathematical procedures and results clearly, systematically, succinctly and correctly.
D. 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.
B. Use appropriate technology to organize and analyze data taken from the local community.
C. Determine the regression equation of best fit (e.g., linear, quadratic, exponential).
D. Make predictions using interpolation, extrapolation, regression, and estimation using technology to verify them.
A. Compare odds and probability.
2.7.11
Probability and
Predictions
2.8.11
Algebra and
Functions
2.9.11
Geometry
2.10.11
Trigonometry
2.11.11
Calculus
B. Apply probability and statistics to perform an experiment involving a sample and generalize its results to the entire population.
C. Draw and justify a conclusion regarding the validity of a probability or statistical argument.
D. Use experimental and theoretical probability distributions to make judgments about the likelihood of various outcomes in uncertain
situations.
E. Solve problems involving independent, simple and compound events.
A. Analyze a given set of data for the existence of a pattern and represent the pattern algebraically and graphically.
C. Use patterns, sequences and series to solve routine and non-routine problems.
D. Formulate expressions, equations, inequalities, systems of equations, systems of inequalities and matrices to model routine and
non-routine problem situations.
F. Identify whether systems of equations and inequalities are consistent or inconsistent.
G. Analyze and explain systems of equations, systems of inequalities, and matrices.
H. Select and use an appropriate strategy to solve systems of equations and inequalities using graphing calculators, symbol
manipulators, spreadsheets and other software.
J. Demonstrate the connection between algebraic equations and inequalities and the geometry of relations in the coordinate plane.
K. Select, justify and apply an appropriate technique to graph a linear function in two variables, including slope
intercept, x- and y- intercepts, graphing by transformations and the use of a graphing calculator.
L. Write the equation of a line when given the graph of the line, two points on the line, or the slope of the line and a
point on the line.
M. Given a set of data points, write an equation for the line of best fit.
N. Solve linear, quadratic and exponential equations both symbolically and graphically.
O. Determine the domain and range of a relation, given a graph or set of ordered pairs.
P. Analyze a relation to determine whether a direct or inverse variation exists and represent it algebraically and graphically.
Q. Represent functional relationships in tables, charts, and graphs.
B.
D.
E.
F.
H.
I.
J.
Prove that two triangles or two polygons are congruent or similar using algebraic, coordinate and deductive proofs.
Identify corresponding parts in congruent triangles to solve problems.
Solve problems involving inscribed and circumscribed polygons.
Use the properties of angles, arcs, chords, tangents and secants to solve problems involving circles.
Construct a geometric figure and its image using various transformations.
Model situations geometrically to formulate and solve problems.
Analyze figures in terms of the kind of symmetries they have.
B. Identify, create and solve practical problems involving right triangles using the trigonometric functions and the
Pythagorean Theorem.
A. Determine maximum and minimum values of a function over a specified interval.
B. Interpret maximum and minimum values in problem situations.
C. Graph and interpret rates of growth/decay.
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CONTENT PACING GUIDE
FIRST SEMESTER
SECOND SEMESTER
Unit One: Algebra
 Order of operations
 Fractions, decimals, percents,
proportions
 Patterns – specific term, nth term
 Solving linear equations
 Graphing linear equations
 Writing the equation from the graph of a
line
 Converting between slope-intercept and
standard form
Unit Five: Geometry
 Solve problems involving polygons
 Solve problems involving angles
and segments of circles
 Symmetry
 Transformations
Unit Six: Similarity, Congruence, etc.
 Write and solve proportions
 Solve for measures of similar
figures
 Prove triangles congruent
 Calculate measures of parts of
congruent triangles using CPCTC
 Indirect reasoning and Venn
diagrams
Unit Two: Linear Regression and Geometry
 Calculate a linear regression equation
for given data
 Interpret the meaning of linear
regression equations, i.e., slope,
intercepts
 Angle Relationships and Parallel Lines
 Pythagorean Theorem
 Use of formulas – area, volume, etc
 Mini unit – PSSA Prep, Sample Items
Unit Seven : Probability
 Odds vs probability
 Analyze data samples to make
generalizations
 Probability of simple events with
and without replacement.
 Experimental vs. theoretical
probability
Unit Three: Systems of Equations, etc.
 Write, analyze and explain systems of
equations
 Determine solutions of graphed systems
 Domain and range
 Indirect and direct variation
Unit Eight : Nonlinear Equations
 Calculate quadratic or exponential
regression equation for given data
 Interpret the meaning of quadratic
regression equations, i.e., intercepts,
max and min points
 Interpret the meaning of exponential
regression equations, i.e., rate of
change
 Make predictions using data and
technology
Unit Four: Measurement
 Measure with a specified level of
precision
 Determine reasonableness of estimates
 Solve problems using geometric
modeling
Process Standards
Throughout the year, students will address Standards 2.5.11A, B, C, and D. These standards involve
problem solving and communication.
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SAMPLE ASSESSMENT
Below is the data showing the relationship between the selling price of a graphing calculator
and the daily profit earned from the sale of all calculators sold that day at that selling price.
Selling price of a
Graphing Calculator
Daily
Profit
$65
$15,950
$70
$17,600
$75
$18,760
$80
$19,320
$85
$19,600
$90
$19,240
$95
$100
$18,000
$17,150
$105
$15,300
Interpreting Data and Predictions:
1. What is the quadratic regression equation?
2. What is the maximum value for y in this quadratic regression equation?
3. What does the maximum value for y mean in the problem situation?
4. When y reaches its maximum value, what is the value of x?
5. What does this x value mean in the problem situation?
6. “The more we charge for calculators, the higher our daily profit!”
Do you agree or disagree with this claim? Justify your conclusion
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