Math 3 Syllabus
Mrs. Sarah Rayski
773-534-8600 ext.26118
skrayski@cps.edu
Welcome to the wonderful world of mathematics and to the 2012-2013 school year at Jones College Prep! It is my
goal that you will be able to use what you have learned in previous math courses and continue to work to improve
your math skills while in this class. If you choose to be a responsible, organized, and motivated student, you will
succeed in this class and be well prepared for your future math courses and life in general! I am looking forward
to an exciting and successful year in Math 3. I would like all students and parents/guardians to be familiar with
our classroom procedures and expectations so please take some time to read the information below. Afterwards,
please sign and return the last page of this syllabus. If you have any questions about my policies or the course,
please do not hesitate to contact me. I am looking forward to working with you this year.
Needed materials and supplies:
Students should bring the following to class each day:
IMP Year 3 Textbook (if lost, there is a mandatory replacement fee)
Graph paper (used for math class only)
Pencil/pen
TI-83 or TI-84 Graphing Calculator
3 Ring Binder (used for math class only)
Positive attitude and willingness to participate and learn everyday
Course Description:
This year’s Math 3 class will be using a curriculum that meets college entrance requirements and prepares
students to use problem-solving skills in further education and in the work place. The Interactive Mathematics
Program (IMP) curriculum looks and feels dramatically different from a traditional math curriculum. Jones
College Prep’s goal is to provide the mathematics needed to succeed in this changing world. We want to present
mathematics in a manner that reflects how mathematics is used and reflects the different ways people work and
learn together.
The IMP curriculum is
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Problem centered
Integrated
More rigorous than the traditional scope of high school mathematics
Focused on developing understanding
Rooted in long-term open-ended investigations
Accessible to students from various mathematical backgrounds in heterogeneous classrooms
Jones College Prep’s instructional goal is to lead students toward becoming more accomplished critical thinkers.
We define critical thinking as the well-reasoned problem-solving process where one examines evidence and
decides what to believe, communicate, or do. The IMP curriculum is the math department’s vehicle for such
student development.
The following units will be covered during the Year 3 Course:
Class Topic Schedule (subject to change)
Semester 1
Orchard Hideout
Meadows or Malls
Semester 2
Small World
Math Review
Statistics
September-November
November-February
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February-March
April
May-June
Orchard Hideout
The central problem of this unit concerns two people who have planted an orchard on a circular lot. They want to
know how long it will take before the trees grow so large that someone outside the orchard cannot see into the
center of the orchard. Answering this question requires students to study circles and coordinate geometry. They
develop the formulas for the circumference and the area of a circle, as well as the distance and midpoint formulas,
and learn to find the distance from a point to a line. Another theme of the unit is geometric proof. Throughout this
unit, students are applying knowledge they acquired in earlier units about similar triangles, trigonometry, and the
Pythagorean Theorem.
Meadows or Malls?
The title problem of this unit concerns a decision that must be made about land use. This problem can be
expressed using a system of linear inequalities, which lends itself to a solution by means of linear programming, a
topic introduced in the Year 2 unit Cookies. Building on their work in that unit, students see that a key step in
solving the system of linear inequalities is to find various points of intersection of the graphs of the corresponding
equations. This, in turn, leads to the need to solve systems of linear equations. Along the way, students learn
about graphing equations in three variables, see that the graph of a linear equation in three variables is a plane,
and study the possible intersections of planes in space. Because graphing calculators allow students to find
inverses of square matrices (when the inverses exist), matrices are a good tool for solving systems of linear
equations with several variables. So, in addition to strengthening their skills with traditional methods, students
learn to express linear systems in terms of matrices and develop the matrix operations required to understand
the role of matrices in the solution process.
Small World, Isn't It?
This unit opens with a table of world-population data over the last thousand years; it asks the following rather
facetious question: If population growth continues to follow this pattern, how long will it be until people are
squashed up against each other? In order to attack this problem, students study a variety of situations involving
rates of growth. Based on these examples, they develop the concept of slope, and then generalize this to the idea
of the derivative, the instantaneous rate of growth. In studying derivatives numerically, they discover that an
exponential function has the special property that its derivative is proportional to the value of the function, and
see that, intuitively, population growth functions ought to have a similar property. This, together with simplified
growth models, suggests that an exponential function is a reasonable choice to use to approximate their
population data. They also learn that every exponential function can be expressed in terms of any positive base
(except 1) and that scientists use as a standard basis the number for which the derivative of the exponential
function equals the value of the function. They find this base, e, experimentally. Along the route of their study of
exponential functions, they review logarithms, are introduced to the natural log function, and see that logarithms
are a useful tool for answering questions raised by exponential functions.
Pennant Fever
One team has a three-game lead over its closest rival for the baseball pennant. Each team has seven games to go in
the season (none of which are between these two teams). The central problem of the unit is to find the probability
that the team that is leading will win the pennant. Students use the teams’ current records to set up a probability
model for the problem. Their analysis of that model requires an understanding of combinatorial coefficients and
uses probability tree diagrams as a tool. In the process of their analysis, students work through the general topic
of permutations and combinations, and develop the binomial theorem and properties of Pascal’s triangle. They
also apply their general understanding of the binomial distribution to several decision-making problems
involving statistical reasoning.
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Course Objectives:
The following list gives a general idea of the topics that will be covered throughout the year. Mastery of these
topics will prepare students to continue in additional mathematics courses at Jones College Prep and at the
collegiate level.
The topics listed above will focus on the following skills outlined in the ACT College Readiness Standards:
Equations and Inequalities
Score Range 20 – 23
- Apply and use number properties to model and solve problems that involve reasoning with proportions.
- Select and use appropriate units when solving problems that involve one or more units of measure.
- Solve literal equations for any variable.
- Represent and interpret relationships defined by equations and formulas; translate between representations as
ordered pairs, graphs, and equations; and investigate symmetry and transformations.
Score Range 24 – 27
- Apply and use elementary number concepts and number properties to model and solve nonroutine problems
that involve new ideas.
- Graph linear equations and inequalities, determine slopes of lines, identify parallel and perpendicular lines, and
find distances.
Score Range 28 – 32
- Solve problems that require combining multiple concepts.
- Explain, solve, and/or draw conclusions for complex problems using relationships and number concepts.
Score Range 33– 36
- Draw conclusions based on number concepts, algebraic properties, and/or relationships between expressions
and numbers.
- Write equations and inequalities that require planning, manipulating, and/or solving.
- Solve simple absolute value inequalities.
- Solve problems integrating multiple algebraic and/or geometric concepts.
Linear Equations and Functions
Score Range 20 – 23
- Identify, interpret, and generate symbolic representations that model the context of a problem.
Score Range 24 – 27
- Identify characteristics of figures from a general equation.
Score Range 33– 36
- Solve complex arithmetic problems involving percent of increase or decrease and problems requiring
integration of several concepts from pre-algebra and/or pre-geometry.
Systems of Linear Equations and Inequalities
Score Range 20 – 23
- Create and solve linear equations and inequalities that model real-world situations.
Score Range 24 – 27
- Explore and use different methods to solve systems of equations.
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Score Range 28 – 32
- Find solutions to systems of linear equations.
- Formulate expressions, equations, and inequalities that require planning to accurately model real-world
problems (e.g., direct and inverse variation)
Score Range 33 – 36
- Analyze and draw conclusions based on information from figures, tables, and graphs.
- Write expressions that require planning and/or manipulating to accurately model a situation.
Quadratic Functions
Score Range 24 – 27
- Create and use basic families of functions (which include linear, absolute value, and quadratic) to model and
solve problems in common settings.
- Factor simple quadratics (e.g., the difference of squares and perfect square trinomials).
Score Range 28 – 32
- Solve quadratic equations.
- Recognize special characteristics of parabolas and circles (e.g., the vertex of a parabola and the center or radius
of a circle.)
- Solve and graph quadratic inequalities.
Score Range 33 – 36
- Match number line graphs with solution sets of simple quadratic inequalities.
Polynomials and Polynomial Functions
Score Range 20 – 23
- Factor and perform the basic operations on polynomials.
Score Range 24 – 27
- Write an expression for and evaluate composite functions.
- Evaluate polynomial functions, expressed in function notation, at integer values.
Score Range 33 – 36
- Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax 2 + c.
- Write an expression for the composite of two simple functions.
Score Range 20 – 23
Trigonometric Ratios and Functions
- Identify the basic trigonometric ratios.
- Recognize when to apply geometric properties and relationships of triangles to find unknown angle measures.
Score Range 24 – 27
- Apply special right-triangle properties and the Pythagorean Theorem to solve congruent and similar shape
problems.
- Use basic trigonometric ratios to solve problems involving indirect measurement.
- Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths.
Score Range 28 – 32
- Explore geometric models where unit circle trigonometry and basic identities can be used to solve problems.
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Trigonometric Graphs, Identities, and Equations
Score Range 20 – 23
- Apply a variety of strategies to determine the circumference or perimeter and the area for circles, triangles,
rectangles, and composite geometric figures.
Score Range 28 – 32
- Investigate angle and arc relationships for circles.
Score Range 33 – 36
- Exhibit knowledge of unit circle trigonometry.
- Match graphs of basic trigonometric functions with their equations.
Powers, Roots and Radicals
Score Range 20 – 23
- Use the inverse relationships for the four basic operations, exponentiation, and root extractions to determine
unknown quantities.
- Perform basic operations with complex numbers.
Score Range 24 – 27
- Manipulate radical expressions (e.g., rationalize denominators).
- Apply rules of exponents.
Score Range 33– 36
- Apply properties of complex numbers.
Exponential and Logarithmic Functions
Score Range 24 – 27
- Model and solve real-world problems that involve a combination of rates, proportions, and/or percents.
Score Range 33 – 36
- Exhibit knowledge of logarithms and geometric sequences.
Course Expectations:
All Jones College Prep expectations outlined in the Student-Parent Handbook will be in place in our classroom so
that we can create a positive and respectful learning environment. In addition to these expectations, below you
can read about performance expectations and grading policies.
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You are expected to be IN your seat when the bell rings, NO EXCEPTIONS!!! Pencils should be
sharpened ahead of time. You will be marked tardy if you are not sitting when the bell rings. Each
tardy is a detention.
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You are expected to come prepared to class everyday with all necessary materials. You are expected
to use the entire class time for learning math. Do not pack up early or you will not be dismissed.
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You are expected to participate in group work. You are expected to engage in class discussions. Ask
questions that are appropriate and at the right time, present ideas to the class, and actively listen.
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You are expected to RESPECT yourself, your classmates, your teacher, and your school. This includes
respecting the rights and properties of others.
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No food, candy, or drinks (other than water) are allowed. If you bring them to class they will be
thrown away immediately and without warning.
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Cell phones and other electronic devices are also not allowed. Consider this your warning, if I see it, I
will take it and you will receive up to 5 detentions. If I see or hear a phone during a test or quiz,
you will receive a zero.
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You are expected to be a responsible student and do your best to succeed in this class.
In-Class Performance:
Your involvement in class is essential to your success and the success of your peers. We all have strengths to
share and it is important that everyone can work together in positive, cooperative groups. Nothing makes us
happier than hearing students question each other and then work through an explanation! Please be open to
sharing ideas, questioning yourself and others, and making mistakes. This is what real mathematicians do!
Homework:
Homework will be assigned on a daily basis and will be checked at the beginning of the next class unless
otherwise noted. If you cannot arrive at a solution to the homework problems, you must provide a written
explanation detailing your trials, thoughts, and areas of confusion. If you complete the whole assignment (attempt
all problems and SHOW ALL WORK) you will receive two points for that day. If you did some of the homework
(more than half) you will receive one point. If you did nothing or less than half, then you will receive zero points.
At the end of the week I will input a homework grade into gradebook. If you are absent the homework will be due
the day you return to class.
Quizzes and Tests:
You will have quizzes throughout the semester. Most quizzes will be announced in advance, but some may be a
surprise at the beginning of class.
You will have up to three tests each semester. Each test will cover material from the latest unit with specific topics
and format outlined a reasonable amount of time prior to the day of the test. In addition, there will be an extended
test portion given after each test.
The extended test could include a challenge problem (a problem that asks students to extend on their knowledge
from the unit) or a demonstration of what they have learned during the unit. The specific format will be outlined a
reasonable amount of time prior to the day of the test.
Students will be given the opportunity to retake up to 5 quizzes per semester to improve their grades. In order
to do so, students must meet with Mrs. Rayski outside of class to go over the material that they struggled with.
Then they may be assigned additional practice problems to work on before retaking the quiz. The purpose of this
is to encourage students to continue developing their skills even after a grade has been assigned. The retake quiz
score will be averaged with the old quiz to form the new score. The “quiz retake” policy can be found as a separate
file, in its entirety, on the class homework website. Students will not have the opportunity to retake tests.
If a student is absent during a quiz or test, it is important that he or she speaks with Mrs. Rayski as soon as
possible (either by email during the day that you are absent or at school on the day you return) to set up a time to
make up the test or quiz. Given the block schedule to be followed this school year, students should not wait until
the next class meeting. Typically, students can make up tests and quizzes before school, after school, or during a
lunch period. If you have an unexcused absence on the day of a quiz or test you will receive a zero.
Projects:
Projects will be assigned periodically throughout the year. These may be assigned to individuals or to groups, as
in class or out of class work, and in written or multi-media formats. A Service-learning project is also a required
component of the Math 3 curriculum. Further details will be made available later in the semester.
Final Exams:
The semester final exams will include all material covered during the respective semester (i.e. the semester 2
exam will only contain semester 2 material.) They may contain a variety of question styles (short answer,
multiple choice, free response, etc.).
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Grading information:
Homework /Classwork
Projects
Quizzes
Tests
Extended Tests
Final Exam
10%
10%
25%
20%
15%
20%
92%-100%
83%-91%
74%-82%
65%-73%
64% and below
A
B
C
D
F
Academic Dishonesty
Academic dishonesty is detrimental to the educational progress of all students and is not tolerated. Any student
caught copying homework or cheating in a test or quiz will receive a zero for that assignment and they will face
any additional consequences described in the Student and Parent Handbook.
Most importantly, I am here to help. If anything is unclear, please ask. If something is bothering you, please talk
to me. I am here for you. I will be available before school or after school in room 500. I want to do whatever I
can to help you be successful in my class! Parents, please feel free to call or email me throughout the year with
any questions or concerns. I believe that it is crucial that we work together to achieve our common goal of your
child’s success.
Email is the fastest form of communication for me but you may also reach me through voicemail. I look forward
to meeting you all!
Sincerely,
Mrs. Sarah Rayski
773-534-8600 ext.26118
skrayski@cps.edu
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Please fill in the following information and return this page of the syllabus.
Name: ___________________________________________________________ Period: __________ Grade:_________________
Last year’s math class and teacher:_________________________________________________________________________
Parent/Guardian: ___________________________________________________________________________________________
Cell phone:______________________________________ Work phone: ________________________________________
Home phone :_______________________________________
Email:_________________________________________
Preferred method of contact (please circle): cell
work
home
email
Comments/Concerns:
__________________________________________________________________________________________________________________
__________________________________________________________________________________________________________________
__________________________________________________________________________________________________________________
__________________________________________________________________________________________________________________
__________________________________________________________________________________________________________________
Please sign below indicating that you have read and understand Mrs. Rayski’s Expectations.
Student signature: __________________________________________________________________________________________
Parent/Guardian signature:________________________________________________________________________________
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