Download Euclidean Geometry

Accelerated Math 1
Mr. Billy Singletary
Billy.singletary@barrow.k12.ga.us
Mrsingletary.com
Room 9265
Syllabus
Course Description: This is the first in a sequence of mathematics courses designed to prepare
students to take AB or BC Advanced Placement Calculus. It includes radical, polynomial and rational
expressions; functions and their graphs; quadratic and radical equations; fundamentals of proof;
properties of polygons, circles and spheres; coordinate geometry; sample statistics and curve fitting.
Standards may be downloaded at
http://www.barrow.k12.ga.us/wbhs/student28/SingletaryB/teacher/BillySingletary.html
Or www.mrsinlgetary.com
Textbook: McDougal-Littell Mathematics 1; McDougal-Littell Mathematics 2
On-line Textbook:
WEBSITE: activate.classzone.com
ACTIVATION CODE: 2418112-390
PRODUCT NAME: Mathematics 1 - eEdition - GA
ISBN #: 9780618920204
INSTITUTION: Winder Barrow High School
WEBSITE: activate.classzone.com
ACTIVATION CODE: 2418112-710
PRODUCT NAME: Mathematics 2 - eEdition - GA
ISBN #: 9780618920259
INSTITUTION: Winder Barrow High School
Unit Overviews
Unit 1: Characteristics of Functions
In seventh and eighth grade, students learned about functions generally and about linear functions
specifically. This unit explores properties of basic quadratic, cubic, absolute value, square root, and
rational functions and new language and notation for talking about functions. The discussion of
function characteristics includes further development of the language of mathematical reasoning to
include formal discussion of the logical relationships between an implication and its converse,
inverse, and contrapositive.
Unit 2: Polygons in the Plane
Through the study of topics in the geometry strand for grades K – 8, students have acquired an extensive
vocabulary of describing geometric figures in the plane, a deep understanding of the concepts of
congruence and similarity for plane figures, and broad experience in using the concepts of symmetry
and transformations to identify properties of geometric figures. In Grade 7, they used standard ruler and
compass constructions to understand properties of lines, angles, and figures and justified these
constructions. In this unit, students will apply their geometric knowledge and skills to explore angles in
polygons, congruence and points of concurrency for triangles, and properties of special quadrilaterals.
Students will make conjectures based on their explorations and then prove their conjectures through
multiple forms of justification. In addition students will begin their study of coordinate geometry by
developing the formulas for the distance between two points, the distance between a point and a line,
and the midpoint of a segment and then using these formulas as they revisit quadrilaterals in the context
of the coordinate plane.
Unit 3: Circles and Spheres
In this unit students will explore the properties of circles and use these properties to solve problems
involving arcs, angles, sectors, chords, tangent lines and secant lines. Students will continue their study
of measurement geometry in a study of the surface area and volume of a sphere.
Unit 4: The Chance of Winning
In this unit, students will calculate probabilities based on angles and area models, compute simple
permutations and combinations, calculate and display summary statistics, and calculate expected values.
They should also be able to use simulations and statistics as tools to answering difficult theoretical
probability questions.
Unit 5: Algebraic Investigations – Quadratics and More
The focus of the unit is developing basic algebra skills and using these in a concentrated study of
quadratic functions, equations, and inequalities. Students first develop skill in adding, subtracting,
multiplying, and dividing elementary polynomial, rational, and radical expressions and apply these skills
in working with functional models and in solving elementary quadratic, rational, and radical equations.
Then, they extend and apply this basic algebraic knowledge during an in-depth study of quadratics.
Through exploration of many real world situations which are represented by quadratic functions,
students are introduced to general quadratic functions in both standard form and vertex form. Students
learn to solve any quadratic equation by applying additional factoring techniques, converting the
quadratic expression to vertex form and then extracting square roots, or using the quadratic formula.
Study of the quadratic formula introduces the complex numbers so students learn the basic arithmetic of
complex numbers. Students make connections between algebraic results and characteristics of the
graphs of quadratic function and apply this understanding in solving quadratic inequalities. They
conclude the unit with an exploration of arithmetic series; this work provides a foundation for modeling
data with quadratic functions, a topic that will be explored in Unit 6.
Unit 6: Putting the Pieces Together
In Unit 1, students built on their knowledge of functions by exploring quadratic, cubic, absolute value,
and rational functions. They also developed ways of discussing and notation for functions. Unit 5
deepened students’ knowledge of quadratic functions. This unit wraps up the study of basic functions
with piecewise and step functions. Discontinuous and continuous piecewise functions, and their utility,
are discussed. Unit 4 introduced students to data through the study of summary statistics. This unit
builds on that knowledge and extends it to linear and quadratic regression. Regression and different
basic functions are combined as further illustration of the utility of these mathematical ideas.
This syllabus is subject to change with proper notification
Our goal at Winder Barrow High School is to promote the
academic success of each student. Students are expected to take
advantage of all opportunities for success, which are made
available to them by all teachers.