MATHEMATICS 6
The sixth grade math classroom is a space for students to exchange ideas, build
skills, deepen their understandings and find their best practice as mathematicians.
Sixth grade level math is a comprehensive review of elementary concepts and
skills involving natural numbers, fractions, and decimals, and is an exploration
of extensions of these areas in preparation for higher math. We strive to improve
com putation, to develop logical reasoning and problem solving skills, and ultimately,
to build confidence and flexibility of thinking. Students leaving sixth grade
should have a strong understanding of how to be an efficient and effective mathematician.
Some topics include reading and creating graphs, understanding and applying
proportion (rate, ratio, proportions and percent), analyzing data, calculating
simple statistics, using scientific notation, investigat ing variables and linear
equations, introducing integers, geometry, creating and using formu las. Both
computation (including mental math) and application are emphasized in each unit.
Students have only limited access to calcula tors. The class uses manipulatives,
drawings and discussion, which often ask students to explain their thinking.
Text: Sadlier-Oxford Progress in Mathematics - Grade 6
(2008) with teacher supplements
PROBLEM SOLVING (7th Grade)
The 7th grade Problem Solving course is designed to prepare students for success
in Algebra and Geometry. The main goal is to allow students to learn and think
mathematically, to make the transition from the computation and mechanics of
arithmetic to the abstract reasoning of higher mathematics, and to become problem
solvers and critical thinkers. Through a series of different units, we begin
to explore proportions and proportional reasoning, how we compare things and
what those comparisons mean, what big numbers look like and how we understand
them, measurement and counting, understanding volume and surface area, graphing
linear functions, probability (theoretical, experimental, “what is fair?”),
equations, and geometry. Through all of these topics, we focus on communicating
mathematics, and looking at the subject matter in depth.
These topics are presented with an emphasis on the formal strategies of Problem
Solving: Guess & Check, Working Backwards,. Finding a Pattern, Making a
Table, Drawing a Diagram, Making it Simpler, Using a Model, Writing Mathematical
Expressions and others. Extensive use of project based assessments and writing
assignments are included in addition to class group work.
Prerequisite: Completion of 6th Grade Mathematics or equivalent
Text: Connected Mathematics, Ed. Lappan, Fey, Fitzgerald,
Friel, & Phillips
Calculator Requirement: Scientific calculator (TI - 30X or
equivalent – no graphing calculators)
ALGEBRA I (8th Grade)
This course covers all of the topics of first year algebra. It begins with a
review of using mathematical properties to solve for an unknown variable. Algebra
I also includes the study of operations with polynomials and radicals. Additionally,
there is significant time dedicated to work with algebraic functions (linear,
exponential and quadratic), linear equations, and inequalities. The course is
tied together by having students develop the ability to move fluidly between
the three representations of a function: the graph, the equation, and the table.
Algebra I builds on the problem solving and reasoning from 7th grade Problem
Solving. The students apply their newly acquired algebraic skills to a wide
assortment of problems. Successful completion of Algebra I fully prepares the
student for either Geometry or Honors Geometry in the 9th grade.
Prerequisite: Problem Solving
Text: Algebra I (McDougall, Littlell, & Co., 2000)
Calculator Requirement: Scientific Calculator (TI-30X or equivalent)
GEOMETRY (Regular and Honors)
Geometry: The course covers traditional Euclidian topics of plane and solid
geometry. Units include lines and angles, triangles, polygons, congruence, similarity,
circles, Pythagoras, area, and volume. Students quickly learn how to define
new terms and also to think inductively. Unlike many “traditional”
courses, they are asked to examine geometric situations and make their own conjectures.
In late fall, students are exposed to the ideas and logic behind deductive proof.
They then practice turning their conjectures into theorems. Mixed into the curriculum
are algebra review, coordinate geometry, right triangle trigonometry, and some
transformational geometry.
Honors Geometry covers the same topics as Geometry with more advanced problems
and at a considerably faster pace. Topics are covered in more depth and intensive
problem solving is required of the students. Students enrolled in the honors
sections are expected to have an inherent love of mathematics and possess superior
numerical skills. Throughout the course, students work with The Geometer’s
Sketchpad software with which they perform constructions, transformations and
investigations. Special topics include construction, coordinate geometry, trisection,
networks, transformations, tessellations, and fractals.
Prerequisite: Algebra I
Text: Discovering Geometry, 4th ed., Michael Serra
(2008), Key Curriculum Press
Calculator Requirement: A scientific calculator is required
(no graphing technology needed).
Note: Ninth grade students with no previous Algebra experience
are expected to complete Algebra I through private tutoring or equivalent summer
school course before enrollment in Geometry. Please speak to the Department
Chair to receive confirmation for the student’s plan of action.
ALGEBRA II (Regular and Honors)
Algebra II is a course that studies a number of the major families of mathematical
functions including linear, quadratic, polynomial, exponential, logarithmic,
absolute value and variation. Throughout the study of each function family,
students work with tables, graphs and equations, and they strive to model real-world
phenomena using these functions. Students also solve in-depth problems requiring
them to connect different ideas. Beyond the study of functions, students are
exposed to topics
such as sequences, dynamical systems, series, counting, and probability. Lastly,
a significant portion of time in Algebra II
is dedicated to learning the many functions of the TI-83+, including programming.
The honors course covers the same topics as Algebra II in more depth and at
a faster pace. Students are asked to do a fair amount of independent learning
and are expected to have a desire to put in extra time as well as possess superior
skills of symbolic manipulation. Additionally, topics such as matrices, complex
numbers, Euler’s number e, the natural number phi, conic sections, polynomial
functions, rational functions, and radical functions are studied in Honors Algebra
II.
Prerequisite: Geometry (Regular or Honors)
Text (for Algebra II Regular): Algebra II, Holt, Reinhart,
Winston (2004)
Calculator Requirement: TI-83+ or TI-84
Note: TI-89, TI-92s and all calculators that perform symbolic
manipulation are allowed in Head-Royce mathematics classes but are not usually
admitted on exams administered by ETS and the College Board.
PRECALCULUS
Precalculus is a regular level course designed to give students exposure to
all the basic functions ordinarily studied in high school mathematics. There
is a systematic review of functions first encountered in Algebra II (exponential
and logarithmic functions, in particular), with an added emphasis on func tion
transformations and the use of graphing calculator technology. Then, students
briefly review conic sections. Trigonometric functions are studied thoroughly,
beginning with a review of right triangle trigonometry and continuing with a
discussion of trigonometric graphs and equations. The course concludes with
discrete mathematics and a preview of statistics. Spring topics include sequences
and series, sigma notation, combinatorics, probability theory, and random variables.
Honors Precalculus covers the Precalculus curriculum and more. Students are
expected to have mastered basic algebra skills, and will be asked to solve non-routine
problems on a regular basis. Trigonometry, in particular, is studied at a more
advanced level, with the addition of the double and half angle formulas, and
the study of polar coordinates. Moving beyond Precalculus, the course ends with
the study of limits and the derivative at a level of sophistication close to
what students will see in AP Calculus the following year.
Note: Students interested in taking AP Calculus must take Honors
Precalculus.
Prerequisite: Algebra II (Regular or Honors)
Text: Advanced Mathematics: Precalculus with Discrete Mathematics
and Data Analysis (Richard Brown, Houghton Mifflin 2003)
Calculator requirement: TI-83+ or TI-84
CALCULUS ( Advanced Placement AB and BC)
Calculus AB is a college level course in dif ferential and integral calculus
of one variable. Considerable time is spent devoted to under standing the major
concepts of the derivative and the integral and applying them to a variety of
problems. The Advanced Placement syllabus is followed closely and the last month
of the class is spent reviewing for the AP exam.
In addition, sample problems from old AP tests are given as an exposure to the
test throughout the year. Students who are enrolled in Calculus are required
to take the AP exam in May. Whether or not college credit is granted is determined
by the policies of the various col leges and universities each student will
attend.
Calculus BC covers the same topics as AB with additional topics of sequences
and series and further techniques of integration. In addition, some topics have
additional sub-topics. In some years, AB and BC are taught together.
Prerequisite: Precalculus Honors
Text: Calculus, Rogawski, 2008
Calculator requirement: TI-83+ or TI-84
ADVANCED PLACEMENT STATISTICS
AP Statistics is a college level course. It begins with a study of descriptive
statistics, normal distributions and regression analysis. Then, experimental
design and data gathering methods are extensively studied culminating in each
class producing a study on a question or issue relevant to the Head-Royce community.
Students will then examine probability and random variables. The course concludes
with several units on statistical inference (the logic and mathematics behind
confidence intervals, hypothesis testing, and decision making). The Advanced
Placement syllabus is followed closely and the last weeks of the class are spent
reviewing for the AP exam. Students who are enrolled in Statistics are asked
to take the AP exam in May. There are no exceptions. Whether or not college
credit is granted is determined by the policies of the various colleges and
universities each student will attend.
Prerequisite: Algebra II Honors or FTS. NOTE: Due to scheduling
constraints, AP Statistics is reserved almost exclusively for seniors. It may
be taken simultaneously with another mathematics course.
Text: The Practice of Statistics, Moore, Yates, and
Starnes (3rd Edition, 2008)
Calculator Requirement: TI-83+ or TI-84
INTRODUCTION TO CALCULUS AND STATISTICS
This course is intended as a non-AP option for senior year, for students who
want to continue their mathematical studies. It will work on mastery of certain
topics from Precalculus (Algerbraic simplification, log and exponent rules,
trig identities and relationships) in the context of an introduction to topics
in Calculus. We will specifcally focus on Limits and derivatives. The statistics
portions will contains much of the content of other Statistics classes but with
a more hands-on, project based approach to accommodate a variety of learning
styles. This content will be interwoven with the Calculus ideas throughout the
course of the year. The statistics content will include three main strands:
(1) Probability and Sampling; (2) Data Analysis/Mathematical Modeling and (3)
Visual Design. In each strand, there is an approach in which students can do
interesting work with a fairly low level of math. But at the same time, there
is a wealth of deep mathematics available for the stronger students.
For the calculus topics, we will look at a variety of real
world problems, and seek multiple approaches to solving them (analytical, graphical,
algebraic). These units will have standard assessments (homework, tests and
quizzes). We will refer to the texts used in other courses (Precalculus and
Calculus).
For the statitsics topics, work will include a Horoscope survey
(connection to random sampling, double-blind surveys, 90% confidence intervals);
a Data Analysis project (collection of two forms of data – numerical and
categorical – and analyzing the data. Will also include a visual design
element.); a Survey project (this is a major project in which students will
pick a relevant topic and conduct a school-wide survey using the principles
we’ve dis cussed – random sampling, bias, survey design, visual
design, analysis and the 90% confidence intervals.) and a Visual design project
We will also do reading from several different sources, including: Edward Tufte’s
books, the Gallup organization (How We Conduct Polls), and The
Universe and the Teacup by K.C. Cole.
THREE-DIMENSIONAL GEOMETRY AND MULTIVARIABLE CALCULUS
Multivariable Calculus is a second-year college level mathematics course, designed
for students who have already taken AB or BC Calculus and desire an even more
advanced mathematical experience. Considerable time will be spent at the start
of the year study ing three-dimensional analytic geometry (3D graphing, equations
of lines and planes, vectors), and then we will proceed to study the standard
topics of multivariable calculus (partial derivatives, multiple integration,
vector calculus). As only strong students with serious interest in science and
mathematics should be enrolled in this course, it is likely that at least some
class time will be devoted to prepara tion for national mathematics contests.
Other advanced mathematical topics outside of the normal syllabus for this particular
course are likely to be touched on as well.
Prerequisite: Calculus AB or BC
Text: Calculus, Rogawski, 2008
Calculator Requirement: TI-83+ or TI-84
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Updated January 31, 2011