COURSE TITLE: Accelerated Algebra I/Geometry Honors
COURSE DESCRIPTION: Students are selected for this course through the Advanced Algebra Placement Test administered in April. Those enrolled complete both Geometry and Algebra I. Students complete six extensive assignments in algebra during the summer before their freshman year. The geometry portion of the course covers the traditional topics offered in the sophomore year. The algebra portion completes the student's study of algebra begun in junior high school. This is a college preparatory course.
Prerequisite: Placement based on Entrance Test, Algebra Placement Test, Junior High teacher and Math Department Chairperson recommendation.
COURSE REQUIREMENTS/REQUIRED MATERIALS:
A. Algebra 1 textbook/Geomerty textbook
B. Spiral Notebook.
C. Pencils.
D. Scientific calculator.
E. One pocket folder to be used only for math.
COURSE OBJECTIVES/STUDENT OUTCOMES:
1) Students will become familiar with the Real Number System.
Upon completing this goal the student will be able to:
• evaluate algebraic and numerical expressions using the rules
for order of operations
• identify the subsets of real numbers and relationships among them
• add, subtract, multiply and divide using real numbers
2) Students will learn the methods for solving equations and
inequalities in one variable.
Upon completing this goal the student will be able to:
• solve a linear equation in one variable
• solve equations that involve absolute value and graph their
• solution sets
• solve quadratic equations by factoring
• solve fractional equations
• solve radical equations
• solve inequalities and graph their solution sets
• solve and graph inequalities that involve absolute value
• solve word problems that involve equations and inequalities in
one variable
3) Students will acquire an understanding of the nature of polynomials.
Upon completing this goal the student will be able to:
• add, subtract, multiply and divide polynomials
• simplify expressions with positive and negative exponents
• express numbers in scientific notation
• find the products and quotients of numbers expressed in
scientific notation
• identify the degree of a polynomial
• arrange the terms of a polynomial in ascending and descending order
• factor monomials into prime factors
• factor binomials and trinomials either by extracting common factors
or by using FOIL
• use grouping techniques to factor polynomials with four or more terms
4) Students will gain an understanding of the techniques for working
with rational expressions.
Upon completing this goal, the student will be able to:
• simplify rational expressions
• multiply and divide rational expressions
• add and subtract rational expressions
5) Students will discern the differences and similarities among
functions and relations.
Upon completing this goal, the student will be able to:
• show relations as sets of ordered pairs, mappings, tables,
graphs and equations
• identify the domain and range of a relation
• determine whether a given relation is a function
• calculate functional values for a given function
• write an equation to represent a relation, given a chart of values
6) Students will experience graphing linear equations and inequalities
with two variables.
Upon completing this goal, the student will be able to:
• graph linear equations
-by making a table and plotting points
-by using x- and y-intercepts
-by using the slope and y-intercept
• find the slope of a line
-when given two points
-when given the equation of a linear relation
• write a linear equation in standard and slope-intercept form given
-the coordinates of two points on the line
-the slope and the y-intercept
-the coordinates of a point on the line and the slope of the line
• determine whether two lines are parallel or perpendicular
• find the coordinates of the midpoint of a line segment
• graph lines using the graphing calculator
• graph linear inequalities
7) Students will develop the methods for solving systems of equations
and inequalities.
Upon completing this goal, the student will be able to:
• solve a system of linear equations
-by graphing by hand and using a graphing calculator
-by the substitution method
-by the elimination method
• determine whether a system of equations has one solution,
no solution or infinitely many solutions algebraically and graphically
• solve a system of inequalities by graphing
• use a system of two linear equations in two variables to
solve word problems
8) Students will gain an understanding of the properties of radicals.
Upon completing this goal, the student will be able to:
• simplify square roots
• find approximate value for square roots
• simplify radical expressions
• use the Pythagorean Theorem
• distinguish rational and irrational numbers
• add, subtract, multiply and divide radical expressions
• solve radical equations
• use the distance formula
9) Students will become familiar with the language of geometry.
Upon completing this goal, the student will be able to
• graph ordered pairs on a coordinate plane
• identify collinear and coplanar points and intersecting lines and planes
• find the distance between points on a number line, find the
distance between points in the coordinate plane
• find the midpoint of a segment
• identify angles and parts of angles
• classify angles as acute, obtuse, right and straight
• identify and use adjacent angles, vertical angles,
complementary angles, supplementary angles,
and linear pairs of angles.
10) Students will experience the elements of deductive reasoning.
Upon completing this goal the student will be able to:
• identify the hypothesis and conclusion of an if-then statement
• write the converse of an if-then statement
• identify and use basic postulates about points, lines, and planes
• use the laws of deductive reasoning
• properly write a proof
11) Students will develop an understanding of the relationship between
angles formed by a transversal intersection parallel line.
Upon completing this goal the student will be able to:
• identify the relationships between pairs of angles formed by
pairs of lines and transversals
• recognize angle conditions that produce parallel lines
• prove two lines are parallel based on given angle relationships
• find the slope of a line
• use slope to identify parallel and perpendicular lines
12) Students will acquire an understanding of congruent triangles and
their corresponding parts.
Upon completing this goal the student will be able to:
• identify the parts of a triangle
• classify triangles
• identify congruent triangles
• name and label corresponding parts of congruent triangles
• use postulates SSS, etc. to test for triangle congruence
13) Students will recognize the applications of congruent triangles.
Upon completing this goal the student will be able to:
• identify and use medians, altitudes, angle bisectors and
perpendicular bisectors in a triangle
• recognize and apply relationships between the sides and
angles in a triangle
14) Students will gain an understanding of the properties of
quadrilaterals and the relationship that exists between
quadrilaterals.
Upon completing this goal the student will be able to:
• recognize and define a parallelogram
• use the properties of a parallelogram
• recognize and define a rectangle
• use the properties of a rectangle
• recognize and define the properties of squares and rhombi
• use the properties of squares and rhombi
• recognize and define the properties of trapezoids
• use the properties of trapezoids
15) Students will develop a familiarity with the properties and
applications of similarity.
Upon completing this goal the student will be able to:
• recognize and use ratios and proportions
• identify similar figures
• solve problems involving similar figures
16) Students will experience an introduction to right triangle
trigonometry.
Upon completing this goal the student will be able to:
• find the geometric mean between two numbers
• use the Pythagorean theorem
• recognize and use trigonometric relationships from right triangles
• solve triangles using the law of sines and the law of cosines
17) Students will gain familiarity with the properties of a circle and
the relationship of circles to special lines, i.e. chords, secants,
tangents.
Upon completing this goal the student will be able to:
• name parts of a circle
• write an equation of a circle in the plane
• recognize major and minor arcs of circles
• find the measures of arcs and central angles
• find the measures of inscribed angles
• find the measures of angles formed by intersecting chords,
secants and tangents in relation to intercepted arcs
• find the measures of segments formed by intersecting chords,
secants and tangents in relation to intercepted arcs
18) Students will develop a conceptual understanding of the area of a
plane figure.
Upon completing this goal the student will be able to:
• identify and name polygons
• identify faces, edges and vertices of a polyhedron
• find the sum of the measures of the interior and exterior
angles of a convex polygon
• find the measure of each interior and exterior angle of a
regular polygon
• find the area of all standard quadrilaterals
• find the area of regular polygons
• find the area of a circle
19) Students will acquire an understanding of the surface area and
volume of three dimensional figures
Upon completing this goal the student will be able to:
• draw three dimensional figures
• identify the parts of prisms and cylinders
• find the volumes and surface area of standard three dimensional
objects: cylinders, prisms, pyramids, cones, and spheres
COURSE OUTLINE:
A. Simplify
1) Order of operations
2) Combine like terms
3) Polynomials - multiply and divide
4) Rational expressions - factoring
a) Monomials
b) Binomials
c) Trinomials
d) Four terms
B. Graphing
1) On a number line
a) sets of numbers
b) inequalities
2) On a coordinate plane
a) points
b) Functions and relations
1. linear equations
2. linear inequalities
C. Linear equations
1) slope
a) given the graph
b) given two points
c) given the equation
2) write linear equation in the form y = mx + b
a) given slope and y-intercept
b) given slope and point on the line
c) given y-intercept and point on the line
d) given two points
e) given parallel to other line through point
f) given perpendicular to other line through point
D. Solve
1) One variable
a) linear equation
b) proportion
c) quadratic equation
d) absolute value
e) rational - fractional equation
f) radical equation
2) More than one variable
a) literal equations
b) systems of linear equations
1. solve graphically
2. solve by substitution
3. solve by elimination (addition)
3) Inequalities
a) single variable
b) compound
c) absolute value
E. Verbal Expressions and sentences
1) one variable
a) linear
1. consecutive integers
2. proportions
b) inequalities
c) quadratic
2) two variables - systems of equations
F. The Language of Geometry
1) The coordinate plane
2) Points, lines, planes
3) Problem-solving strategies
4) The measure of a segment
5) Segment relationships
6) Rays and angles
7) Classifying angles
8) Pairs of angles
G. Reasoning and Introduction to Proofs
1) Inductive reasoning and conjecturing
2) If-then statements, converses
3) Deductive reasoning
4) Properties from algebra
5) Problem-solving strategies
6) Two column proofs with segments
7) Two column proofs with angles
H. Parallels
1) Problem solving strategies
2) Parallels and transversals
3) Using parallel lines
4) Proving lines parallel
5) Slopes and lines
6) Parallels and distance
I. Congruent triangles
1) Classifying triangles
2) Angle measure in triangles
3) Congruent triangles
4) Tests for congruent triangles
5) Another test for congruent triangles
6) Problem solving strategies
7) Isosceles triangles
J. Applying Congruent Triangles
1) Special segments in triangles
2) Right triangles
3) Problem solving strategies
4) Indirect proof and inequalities
5) Inequalities for sides and angles of a triangle
6) The triangle inequality
7) Inequalities involving two triangles
K. Quadrilaterals
1) Parallelograms
2) Problem solving strategies
3) Tests for parallelograms
4) Rectangles 5) Squares and rhombi
6) Trapezoids
L. Similarity
1) Properties of proportions
2) Applications of proportions
3) Similar polygons
4) Similar triangles
5) Proportional parts
6) Parts of similar triangles
7) Problem solving strategies
M. Right Triangles and Trigonometry
1) The geometric mean
2) The Pythagorean theorem
3) Special right triangles
4) Trigonometry
5) Applications: using trigonometry
6) Law of sines
7) Law of cosines
8) Problem solving strategies
N. Circles
1) Parts of circles
2) Angles and arcs
3) Arcs and chords
4) Inscribed angles
5) Tangents
6) More angle measure
7) Special segments in a circle
8) Problem solving strategies
O. Polygons and Areas
1) Polygons and polyhedra
2) Angles of Polygons
3) Problem solving strategies
4) Area of Parallelograms
5) Area of triangles, rhombi, and trapezoids
6) Area of regular polygons
7) Area and circumference of a circle
8) Geometric probability
9) Polygons as networks
P. Surface Area and Volume
1) Problems solving strategies
2) Exploring surface area
3) Surface area of prisms and cylinders
4) Surface area of pyramids and cones
5) Volume of prisms and cylinders
6) Volume of pyramids and cones
7) Surface area and volume of spheres
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