Download O`Neill`s Math

2009-2010 11th Grade Client-based Project: Phase I & Phase II
ROP Graphic Design/Multimedia Production: making W.A.V.E.S
School of Digital Media & Design
Inter Algebra/Pre Calculus – O’Neill
1st SEMESTER
Timeline
Units of Study
Essential
Questions?
Applied Learning
Projects
September
October
November
December
January
Chapter 5
Quadratic Functions
5.1 Introduction to
Quadratic Functions
5.2 Introduction to
Solving Quadratic
Equations
5.3 Factoring Quadratic
Expressions
5.4 Completing the
Square
5.5 The Quadratic Formula
5.6 Quadratic Equations
and Complex Numbers
5,7 Curve Fitting with
Quadratic Models
5.8 Solving Quadratic
Inequalities
What is a system of linear
equations, and what do
they represent?
Out of This World
After completing the
Chapter Project, the
student will be able to do
the following:
 Use the function to
model the vertical
motion of a
basketball.
 Compare and contract
algebraic models of
Chapter 6
Chapter 1
Data and Linear
Representations
1.1 Tables and Graphs of
Linear Equations
1.2 Slopes and Intercepts
1.3 Direct Variation
1.4 Scatter Plots and
Least-Squares Lines
1.5 Intro to Solving
Equations
1.6 Intro to Solving
Inequalities
1.7 Solving Absolute Value
Chapter 2
Numbers and Functions
2.1 Operations with
numbers
2.2 Properties of
exponents
2.3 Introduction to
functions
2.4 Operations with
functions
2.5 Inverses of Functions
2.6 Special Functions
2.7 A Preview of
Transformations
Chapter 3
Systems of Linear
Equations and Inequalities
3.1 Solving Systems by
Graphing or Substitution
3.2 Solving Systems by
Elimination
3.3 Linear Inequalities in
Two variables
3.4 Systems of Linear
Equations
3.5 Linear Programming
3.6 Parametric Equations
What are the different
ways linear data can be
represented?
Correlation Exploration
After completing the
Chapter Project, the
student will be able to do
the following:
What are the operations
that can be performed on
numbers and functions?
Space Trash
After completing the
Chapter Project, the
student will be able to do
the following:
 Use a table to
represent the
relationship between
time in years and the
number of space
debris objects, and
What is a system of linear
equations, and what do
they represent?
Maximum Profit/Minimum
Cost
After completing the
Chapter Project, the
student will be able to do
the following:
 Represent real-world
data by using scatter
plots.
 Find and use linear
models to predict
 Set up and solve linearprogramming
problems that involve
finding maximums
Exponential and
Logarithmic Functions
6.1 Exponential Growth
and Decay
6.2 Exponential Functions
6.3 Logarithmic Functions
6.4 Properties of
Logarithmic Functions
6.5 Applications of
Common Logarithmic
6.6 The Natural Base, e
6.7 Solving Equations and
Modeling
What are exponential and
logarithmic functions and
what do they represent?
Warmups
After completing the
Chapter Project, the
student will be able to do
the following:
 Collect real-world data
on the heating and
cooling of an object,
and determine an
appropriate
other possible data
values.
Making W.A.V.E.S.
Project Integration
Resources
Assessment
Content Standards
Students introduced to
client *understand
project scope *begin
research
EQ: How can students
develop professional
work for an authentic
client?
Identification of the roles,
processes, and
documentation that are
inherent in the production
of client based media
projects
*Graphing data - linear
using data from WAVES
Textbooks:
Algebra 2 - Holt 2004
PreCalculus -Pearson
2004
Class work
Homework
Quizzes
Tests
Chapter Projects
1.0, 9.0, 21.0,24.0, 25.0
show that an
appropriate function
models this
relationship.
 Find and discuss
models for
accumulation of
space debris.
 Determine the
piecewise function
that describes the
relationship between
altitude and number
of orbital objects.
Production research:
Research current
solutions and problems
vs. proposed solutions
WS 1.7; WA 2.4
EQ: How do graphic
designers communicate a
written idea visually?
*Graphing using
transformations
*Inductive & Deductive
Reasoning using data
from WAVES
Digital Portfolio upload
Textbooks:
Algebra 2 - Holt 2004
PreCalculus -Pearson
2004
Class work
Homework
Quizzes
Tests
Chapter Projects
Benchmark
11.1, 12.0, 21.0, 24.0, 25.0
and minimums.
Investigate how
changes in the
objective function or
in the constraint
inequalities affect the
outcome.
the form for the
vertical motion of the
basketball on
different planets.
exponential function
to model the heating
and cooling of an
object.
 Make predictions
about the
temperature of an
object that is heating
or cooling to a
constant surrounding
temperature.
 Verify Newton’s law of
cooling.
Production assimilation
and Video Production:
EQ: What elements
contribute to a wellorganized media project?
Synthesize what has been
learned in production
applications to support a
production process.
Digital Portfolio upload
*Graphing System of
Equations using data from
WAVES
EQ: How does one
determine the
effectiveness of a
product?
Fine tuning oratory skills
for media presentation SA
2.4
Digital Portfolio upload
*Graph data - quadratics
Final Media Package
Showcase to client
EQ: In what ways has the
research and production
process influenced the
final Media Package?
Developing an
understanding of the
production process and
its relationship to a future
project
*Graphing Exponential
Functions using data from
WAVES
Digital Portfolio upload
Textbooks:
Algebra 2 - Holt 2004
PreCalculus -Pearson
2004
Class work
Homework
Quizzes
Tests
Chapter Projects
Textbooks:
Algebra 2 - Holt 2004
PreCalculus -Pearson
2004
Class work
Homework
Quizzes
Tests
Chapter Projects
Textbooks:
Algebra 2 - Holt 2004
PreCalculus -Pearson
2004
Class work
Homework
Quizzes
Tests
Chapter Projects
2.0, 21.0
8.0, 9.0, 10.0, 16.0, 21.0
11.1, 11.2, 15.0, 21.0

2nd SEMESTER
Timeline
Units of Study
Essential Question
Applied Learning
February
Chapter 7
Polynomial Functions
7.1 An Introduction to
Polynomials
7.2 Polynomial Functions
and Their Graphs
7.3 Products and Factors
of Polynomials
7.4 Solving Polynomial
Equations
7.5 Zeros of Polynomials
Functions
What are polynomial
functions and what do
they represent?
Fill It Up!
After completing the
Chapter Project, the
student will be able to do
the following:
 Collect and organize
data.
March
April
May
June
Chapter 8
Rational Functions and
Radical Functions:
8.1 Inverse, Joint, and
Combined Variation
8.2 Rational Functions
and Their Graphs
8.3 Multiplying and
Dividing Rational
Expressions
8.4 Adding and
Subtracting Rational
Expressions
8.5 Solving Rational
expressions and
Inequalities
8.6 Radical Expressions
and Radical Functions
8.7 Simplifying Radical
Expressions
8.8 Solving Radical
Equations and
Inequalities
What are rational and
radical functions and
what do they represent?
Chapter 10
Counting Principles and
Probability
10.1 Introduction to
Probability
10.2 Permutations
10.3 Combinations
10.4 Using Addition with
Probability
10.5 Independent Events
10.6 Dependent Events
and Conditional
Probability
10.7 Experimental
Probability and Simulation
Chapter 9
Conic Sections
9.1 Introduction to Conic
Sections
9.2 Parabolas
9.3 Circles
9.4 Ellipses
9.5 Hyperbolas
9.6 Solving Nonlinear
Systems
Chapter 11 & Chapter 12
Sequences and Series
11.1 Sequences and Series
11.2 Arithmetic Series
11.3 Arithmetic Sequences
11.4 Geometric Sequences
11.5 Geometric Series and
Mathematical Induction
12.4 Measures of
Dispersion
What are permutations
and combination and
what do they represent?
What are conic sections
and what do they
represent?
Means to an End
After completing the
Chapter Project, the
student will be able to do
the following:
 Find the arithmetic
mean and the
harmonic mean of a
“Next, Please…”
After completing the
Chapter Project, the
student will be able to do
the following:
Focus on This!
What is the difference
between an Arithmetic
and Geometric series or
sequence and what can
they represent?
Over the Edge
After completing the
Chapter Project, the
student will be able to do
the following:
 Set up models that
simulate random
After completing the
Chapter Project, the
student will be able to do
the following:
 Describe the properties
 Experimentally
determine the center
 Determine a
polynomial model
that best fits a data
set.
 Test your polynomials
model.
Making
W.A.V.E.S.English/Language
Arts Phase II
Project
Integration
Resources
Assessment
Content Standards
EQ: What elements are
necessary to produce a
countywide youth event?
Advertising Campaign
production-print
materials, website, email
communications psa
production to expand the
client’s market Students
are grouped according to
career pathway interestdivided into pre-, during,
and post-production
components
Digital Portfolio upload
*Graph polynomials using
data from WAVES
Textbooks:
Algebra 2 - Holt 2004
Pr Calculus -Pearson 2004
Class work
Homework
Quizzes
Tests
Chapter Projects
Benchmark
5.0, 6.0, 21.0, 25.0
set of data.
 Determine the
relationship between
the arithmetic and
harmonic mean.
 Determine which of the
averages - arithmetic
mean, harmonic
mean, or weighted
harmonic mean - best
represents a data set.
EQ: What elements are
necessary to produce a
countywide youth event?
Advertising Campaign
production-print
materials, website, email
communications psa
production to expand the
client’s market Students
are grouped according to
career pathway interestdivided into pre-, during,
and post-production
components
Digital Portfolio upload
*Explore geometric
representation using data
from WAVES
Textbooks:
Algebra 2 - Holt 2004
PreCalculus -Pearson 2004
Class work
Homework
Quizzes
Tests
Chapter Projects
7.0, 21.0, 25.0
events.
 Use data from
simulations to
estimate
probabilities.
of ellipses, parabolas,
and hyperbolas.
 Create ellipses,
parabolas, and
hyperbolas by using
an alternative
method of graphing.
of gravity of an
object.
 Model data from our
experiments with
sequence and series
 Determine whether
your model gives
predictions that are
consistent with
observations.
EQ: What actions can
students take to affect
change in their
community?
Finalize production
process
SDGS Forum last week of
April
Student presentations at
forum which include light
presentation materials
Day of forum photo and
video documentation
Digital Portfolio upload
* Determine probability
of events using data from
WAVES
EQ: How can a political
message be effectively
communicated through
the combination of text,
images, sound and
rhetorical strategies?
DMD Earth Day-student
presentations of research
Post-production of forum
video
Digital Portfolio Upload
and finalized
* Graph using data from
WAVES
EQ: How can a political
message be effectively
communicated through
the combination of text,
images, sound and
rhetorical strategies?
DMD Earth Day-student
presentations of research
Post-production of forum
video
Digital Portfolio Upload
and finalized
* Graph using data from
WAVES
Textbooks:
Algebra 2 - Holt 2004
PreCalculus -Pearson 2004
Class work
Homework
Quizzes
Tests
Chapter Projects
Textbooks:
Algebra 2 - Holt 2004
PreCalculus -Pearson 2004
Class work
Homework
Quizzes
Tests
Chapter Projects
18.0, 19.0, 20.0, 21.0, 24.0,
25.0, PS1, PS2
16.0, 17.0
Textbooks:
Algebra 2 - Holt 2004
PreCalculus -Pearson 2004
Class work
Homework
Quizzes
Tests
Chapter Projects
Benchmark
21.0, 22.0, PS3
Geometry
Standards Correlation to Chapter and Section
Section
Chapter 1- Foundations for Geometry
 Understanding Points, Lines, and Planes
 Measuring and Constructing Segments
 Measuring and Constructing Angles
 Pairs of Angles
 Using Formulas in Geometry
 Midpoint and Distance in the Coordinate Plane
 Transformations in the Coordinate Plane
Content Standard
Vocabulary
1.0 Demonstrate understanding by identifying and giving
examples of undefined terms, axioms, theorems, and inductive
and deductive reasoning.
8.0 Know, derive, and solve problems involving perimeter,
circumference, area, volume, lateral area, and surface area of
common geometric figures.
16.0 Perform basic constructions with a straightedge and
compass, such as angle bisectors, perpendicular bisectors, and
the line parallel to a given line through a point off the line.
22.0 Know the effects of rigid motion on figures in the
coordinate plane and space, including rotations, translations,
and reflections.
1.0 Demonstrate understanding by identifying and giving
examples of undefined terms, axioms.
Academic Vocabulary
demonstrate show
identifying seeing and being able to name
what something is
solve find the value of a variable that makes the
left side of an equation equal to the right side of
the equation
basic most important pr fundamental; used as a
starting point
effect outcome
rigid motion movements of a figure that do
not change its shape
undefined terms
segment
point
endpoint
line
ray
plane
opposite rays
collinear
postulate
coplanar
1.2 Measuring and Constructing Segments
 Use length and midpoint of a segment
 Construct midpoints and congruent segments
16.0 Perform basic constructions with a straightedge and
compass.
1.3 Measuring and Constructing Angles
 Name and classify angles
 Measure and construct angles and angle bisectors
16.0 Perform basic constructions with a straightedge and
compass, such as angle bisectors.
1.4 Pairs of Angles
 Identify adjacent, vertical, complementary, and
supplementary angles
 Find measures of pairs of angles
1.5 Using Formulas in Geometry
 Apply formulas for perimeter, area, and
circumference
Preparation for 13.0 Prove relationships between angles in
polygons by using properties of complementary, supplementary
and vertical angles.
coordinate
distance
length
congruent segments
construction
angle
vertex
interior of an angle
exterior of an angle
measure
degree
adjacent angles
linear pair
vertical angles
1.1 Understanding Points, Lines, and Planes
 Identify, name and draw points, lines, segments, rays,
and planes
 Apply basic facts about points, lines, and planes
8.0 Know and solve problems involving perimeter,
circumference, area of common geometric figures.
perimeter
area
base
height
between
midpoint
bisect
segment bisector
acute angle
right angle
obtuse angle
straight angle
congruent angles
angle bisector
complementary angles
supplementary angle
diameter
radius
circumference
pi
1.6 Midpoint and Distance Formula in the Coordinate Plane
 Develop and apply the formula for a midpoint
 Use the distance formula and the Pythagorean
Theorem to find the distance between two points
Preparation for 17.0 Prove theorems by using coordinate
geometry, including the midpoint of a line segment and the
distance formula
coordinate plane
leg
hypotenuse
1.7 Transformations in the Coordinate Plane
 Identify reflections, rotations, and translations
 Graph transformations in the coordinate plane
Chapter 2 Geometric Reasoning
 Using Inductive Reasoning to Make Conjectures
 Conditional Statements
 Using Deductive Reasoning to Verify Conjectures
 Biconditional Statements and Definitions
 Algebraic Proof
 Geometric Proof
 Flowchart and Paragraph Proofs
22.0 Know the effects of rigid motion on figures in the
coordinate plane, including rotations, translations, and
reflections.
1.0 Demonstrate understanding by identifying and giving
examples of undefined terms, axioms, theorems, and inductive
and deductive reasoning.
2.0 Write geometric proofs, including proofs by contradiction.
3.0 Construct and judge the validity of a logical argument and
give counterexamples to disprove a statement.
transformation
reflection
preimage
rotation
image
translation
Academic Vocabulary
inductive reach a conclusion based on
examples
deductive reach a conclusion based on laws
geometric relating to the laws and methods of
geometry
valid(ity) legal
argument statements that support or are
against something
2.1 Using Inductive Reasoning to Make Conjectures
 Use inductive reasoning to identify patterns and
make conjectures
 Find counterexamples to disprove conjectures
1.0 Demonstrate understanding by identifying and giving
examples of inductive reasoning.
Also covered: 3.0 Construct and judge the validity of a logical
argument and give counterexamples to disprove a statement.
inductive reasoning
conjecture
counterexample
2.2 Conditional Statements
 Identify, write and analyze the truth value of
conditional statements
 Write the inverse, converse and contrapositive of a
conditional statement
3.0 Construct and judge the validity of a logical argument and
give counterexamples to disprove a statement.
conditional statement
hypothesis
conclusion
truth value
negation
converse
inverse
contrapositive
logically equivalent statements
2.3 Using Deductive Reasoning to Verify Conjectures
 App;y the Law of Detachment and the Law of
Syllogism in Logical Reasoning
1.0 Demonstrate understanding by identifying and giving
examples of inductive and deductive reasoning.
deductive reasoning
2.4 Biconditional Statements and Definitions
 Write and analyze biconditional statements
3.0 Construct and judge the validity of a logical argument and
give counterexamples to disprove a statement.
biconditional statement
polygon
quadrilateral
2.5 Algebraic Proofs
 Review properties of equality and use them to write
algebraic proofs
 Identify properties of equality and congruence
Preparation for 2.0 Write geometric proofs, including proofs
by contradiction
Proof
Also covered 15.0
definition
triangle
2.6 Geometric Proof
 Write two-column proofs
 Prove geometric theorems by using deductive
reasoning
2.0 Write geometric proofs
theorem
two-column proof
2.7 Flow Chart and Paragraph Proofs
 Write flowchart and paragraph proofs
 Prove geometric theorems by using deductive
reasoning
2.0 Write geometric proofs
flow chart proofs
paragraph proofs
Chapter 3 Parallel and Perpendicular Lines
 Lines and Angles
 Angles Formed by Parallel Lines and Transversals
 Proving Lines Parallel
 Perpendicular Lines
 Slopes of Lines
 Lines in the Coordinate Plane
1.0 Demonstrate understanding by identifying and giving
examples of undefined terms, axioms, theorems, and inductive
and deductive reasoning.
2.0 Write geometric proofs, including proofs by contradiction.
7.0 Prove and use theorems involving the properties of parallel
lines cut by a transversal, the properties of quadrilaterals, and
the properties of circles.
16.0 Perform basic constructions with a straight edge and
compass, such as angle bisector, perpendicular bisectors, and
the line parallel to a given line through a point off the line.
Academic Vocabulary
demonstrate show
identifying seeing and beong able to name
what something is
geometric relating to the laws and methods of
geometry
properties unique features
cut to go across or through something
basic most important or fundamental: used as a
starting point
bisector(s)a line that devidess and angle or
another line into two equal parts
3.1 Lines and Angles
 Identify parallel, perpendicular and skew lines
 Identify the angles formed by two lines and a
transversal
Preparation for 7.0 Prove and use theorems involving the
properties of parallel lines cut by a transversal
parallel lines
perpendicular lines
skew lines
parallel planes
transversal
corresponding angles
alternate interior angles
alternate exterior angles
same-side interior angles
3.2 Angles Formed by Parallel Lines and Transversals
 Prove and use theorems about the angles formed by
parallel lines and a transversal
3.3 Proving Lines Parallel
 Use the angles formed by a transversal to prove two
lines are parallel
3.4 Perpendicular Lines
 Prove and apply theorems about perpendicular lines
3.5 Slopes of Lines
 Find slopes of lines
 Use slopes to identify parallel and perpendicular
lines
3.6 Lines in the Coordinate Plane
 Graph lines and write their equations in slopeintercept and point-slope form
7.0 Prove and use theorems involving the properties of parallel
lines cut by a transversal
7.0 Prove and use theorems involving the properties of parallel
lines cut by a transversal
Also covered 16.0
2.0 Write geometric proofs
Preparation for 17.0 Prove theorems by using coordinate
geometry
Preparation for 17.0 Prove theorems by using coordinate
geometry
perpendicular bisector
distance from a point to a line
rise
run
slope
point-slope form
slope-intercept form

Classify lines as parallel, intersecting, or coinciding
Chapter 4 Triangle Congruence
 Classifying Triangles
 Angle Relationships in Triangles
 Congruent Triangles
 Triangle Congruence: SSS and SAS
 Triangle Congruence: ASA, AAS, and HL
 Triangle Congruence: CPCTC
 Introduction to Coordinate Proof
 Isosceles and Equilateral Triangles
4.0 Prove basic theorems involving congruence
5.0 Prove that triangles are congruent and use concept of
corresponding parts of congruent triangles
12.0 Find and use measures of sides and of interior and
exterior angles of triangles to classify figures and solve
problems
13.0 Prove relationships between angles in polygons by using
properties of complementary and exterior angles
17.0 Prove theorems by using coordinate geometry
Academic Vocabulary
involving relating to
concept idea
corresponding matching
interior inside
exterior outside
relationships links
coordinate geometry a form of geometry
that uses a set of numbers to describe the exact
position of a figure with reference to the x- and
y-axes
4.1 Classifying Triangles
 Classify triangles by their angle measures and side
lengths
 Use triangle classification to find angle measures and
side lengths
4.2 Angle Relationships in Triangles

Find the measures of interior and exterior angles of
triangles
 Apply theorems about the interior and exterior
angles of triangles
12.0 Find and use measures of sides and of interior angles of
triangles to classify figures and solve problems
4.3 Congruent Triangles
 Use properties of congruent triangles
 Prove triangles congruent by using the definition of
congruence
4.4 Triangle Congruence: SSS and SAS
 Apply SSS and SAS to construct triangles and solve
problems
 Prove triangles congruent by using SSS and SAS
5.0 Prove that triangles are congruent and use concept of
corresponding parts of congruent triangles
acute triangle
equiangular triangle
right triangle
obtuse triangle
equilateral triangle
auxiliary line
corollary
interior
exterior
interior angle
exterior angle
corresponding angles
corresponding sides
congruent polygons
5.0 Prove that triangles are congruent and use concept of
corresponding parts of congruent triangles
triangle rigidity
included angle
4.5 Triangle Congruence: ASA, AAS, and HL
 Apply ASA, AAS, and HL to construct triangles and
to solve problems
 Prove triangles congruent by using ASA, AAS, and
HL
4.6 Triangle Congruence: CPCTC
 Use CPCTC to prove parts of triangles are
congruent
4.7 Introduction to Coordinate Proof
 Position figures in the coordinate plane for use in
5.0 Prove that triangles are congruent and use concept of
corresponding parts of congruent triangles
included side
5.0 Prove that triangles are congruent and use concept of
corresponding parts of congruent triangles
CPCTC
17.0 Prove theorems by using coordinate geometry
coordinate proof
12.0 Find and use measures of interior and exterior angles of
triangles to solve problems
13.0 Prove relationships between angles in polygons by using
properties of complementary and exterior angles
isosceles triangle
scalene triangle
remote interior angle
coordinate proof
 Prove geometric concepts by using coordinate proof
4.8 Isosceles and Equilateral Triangles
 Prove Theorems about isosceles and equilateral
triangles
 Apply properties of isosceles and equilateral
triangles
Chapter 5 Properties and Attributes of Triangles
 Perpendicular and Angle Bisectors
 Bisectors of Triangles
 Medians and Altitudes of Triangles
 The Triangle Midsegment Theorem
 Indirect Proof and Inequalities in One Triangle
 Inequalities in Two Triangles
 The Pythagorean Theorem
 Applying Special Right Triangles
5.1 Perpendicular and Angle Bisectors
 Prove and apply theorems about perpendicular
bisectors
 Prove and apply theorems about angle bisectors
5.2 Bisectors of Angles
 Prove and apply properties of perpendicular
bisectors of a triangle
 Prove and apply properties of angle bisectors of a
triangle
12.0 Find and use measures of sides and of interior angles of
triangles to classify figures and solve problems
legs of an isosceles triangle
vertex angle
base
base angles
2.0 Write geometric proofs, including proofs by contradiction
6.0 Know and be able to use the triangle inequality theorem
14.0 Prove the Pythagorean theorem
15.0 Use Pythagorean theorem to determine distance and find
missing lengths of sides of right triangles
16.0 Perform basic constructions with a straight edge and a
compass
17.0 Prove theorems by using coordinate geometry
20.0 Know and be able to use angle and side relationships in
problems with special right triangles, such as 30, 60, 90
triangles and 45, 45, 90 triangles
2.0 Write geometric proofs
Academic Vocabulary
contradiction a statement that disagrees or
conflicts with a know fact
able to use have the skills you need
prove explain why something is true
determine find
relationships connections
special particular
2.0 Write geometric proofs
concurrent
point of concurrency
circumcenter of a triangle
circumscribed
incenter of a triangle
inscribed
median of a triangle
centroid of a triangle
altitude of a triangle
orthocenter of a triangle
midsegment of a triangle
5.3 Medians and Altitudes of Triangles
 Apply properties of medians of a triangle
 Apply properties of altitudes of a triangle
16.0 Perform basic constructions with a straight edge and a
compass
5.4 The Triangle Midsegment Theorem
 Prove and use properties of triangle midsegments
5.5 Indirect Proof and Inequalities in One Triangle
 Write indirect proofs
 Apply inequalities in one triangle
5.6 Inequalities in Two Triangles
 Apply inequalities in two triangles
5.7 Pythagorean Theorem
 Use Pythagorean Theorem and its converse to solve
problems
 Use Pythagorean inequalities to classify triangles
5.8 Applying Special Right Triangles
17.0 Prove theorems by using coordinate geometry
2.0 Write geometric proofs, including proofs by contradiction
6.0 Know and be able to use the triangle inequality theorem
equidistant
locus
indirect proof
2.0 Write geometric proofs, including proofs by contradiction
14.0 Prove the Pythagorean theorem
15.0 Use Pythagorean theorem to determine distance and find
missing lengths of sides of right triangles
Also covered 6.0 and 12.0
20.0 Know and be able to use angle and side relationships in
Pythagorean triple
 Justify and apply properties of 45-45-90 triangles
 Justify and apply properties of 30-60-90 triangles
Chapter 6 Polygons and Quadrilaterals
 Properties and Attributes of Polygons
 Properties of Parallelograms
 Conditions of Parallelograms
 Properties for Special Parallelograms
 Conditions for Special Parallelograms
 Properties of Kites and Trapezoids
problems with special right triangles, such as 30, 60, 90
triangles and 45, 45, 90 triangles
2.0 Write geometric proofs, including proofs by contradiction.
7.0 Prove and use theorems involving the properties of
quadrilaterals
12.0 Find and use measures of sides and of interior and
exterior angles of triangles and polygons to classify figures and
solve problems
15.0 Use the Pythagorean theorem to determine distance and
find missing lengths of sides of right triangles
17.0 Prove theorems by using coordinate geometry
6.1 Properties and Attributes of Polygons
 Classify polygons based on their sides and angles
 Find and use the measures of interior and exterior
angles of polygons
6.2 Properties of Parallelograms
 Prove and apply properties of parallelograms
 Use properties of parallelograms to solve problems
12.0 Find and use measures of sides and of interior and
exterior angles of triangles and polygons to classify figures and
solve problems
6.3 Conditions for Parallelograms
 Prove that a given quadrilateral is a parallelogram
7.0 Prove and use theorems involving the properties of
quadrilaterals
17.0 Prove theorems by using coordinate geometry
7.0 Prove and use theorems involving the properties of
quadrilaterals
12.0 Find and use measures of sides and of interior angles of
polygons to solve problems
17.0 Prove theorems by using coordinate geometry
7.0 Prove and use theorems involving the properties of
quadrilaterals
12.0 Find and use measures of sides and of interior angles of
polygons to solve problems
also covered 17.0
2.0 Write geometric proofs, including proofs by contradiction.
7.0 Prove and use theorems involving the properties of
quadrilaterals
12.0 Find and use measures of sides and of interior and
exterior angles of triangles and polygons to classify figures and
solve problems
also covered 15.0
5.0 Prove that triangles are similar
7.0 Use theorems involving the properties of parallel lines cut
6.4 Properties of Special Parallelograms
 Prove and apply properties of rectangles,
rhombuses, and squares
 Use properties of rectangles, rhombuses, and
squares to solve problems
6.5 Conditions for Special Parallelograms
 Prove that a given quadrilateral is a rectangle,
rhombus, or square
6.6 Properties of Kites and Trapezoid
 Use properties of kites to solve problems
 Use properties of trapezoids to solve problems
Chapter 7 Similarity
 Ratio and Proportions
7.0 Prove and use theorems involving the properties of
quadrilaterals
12.0 Find and use measures of sides and of interior angles of
polygons to solve problems
Academic Vocabulary
involving relating to
properties unique features
interior inside
exterior outside
determine find
length(s) distance from end to end
coordinate geometry a form geometry that
uses a set of numbers to describe the exact
position of a figure with reference to the x- and
y- axes
side of a polygon
concave
vertex of a polygon
convex
diagonal
regular polygon
parallelogram
rectangle
rhombus
square
kite
trapezoid
base of a trapezoid
leg of a trapezoid
base angle of a trapezoid
isosceles trapezoid
midsegment of a trapezoid
Academic Vocabulary
similar alike





by a transversal
11.0 Determine how changes in dimensions affect the
perimeter and area of common geometric figures
12.0 Find and use measures of sides and of interior angles of
triangles and polygons to solve problems
17.0 Prove theorems by using coordinate geometry
determine find out
dimensions size of objects
interior inside
coordinate geometry a form of geometry
that uses a set of numbers to describe the exact
position of a figure with reference to the x- and
y-axes
7.1 Ratio and Proportions
 Write and simplify ratios
 Use proportions to solve problems
Preparation for 5.0 Prove that triangles are similar
ratio
proportion
extremes
7.2 Ratios in Similar Polygons
 Identify similar polygons
 Apply properties of similar polygons to solve
problems
7.3 Triangle Similarity: AA, SSS, and SAS
 Prove certain triangles are similar by using AA, SSS,
and SAS
 Use triangle similarity to solve problems
7.4 Applying Properties of Similar Triangles
 Use properties of similar triangles to find segment
length
 Apply proportionality and triangle angle bisector
theorems
5.0 Prove that triangles are similar
similar
similar polygons
similarity ratio
7.5 Using Proportional Relationships
 Use ratios to make indirect measurements
 Use scale drawings to solve problems
11.0 Determine how changes in dimensions affect the
perimeter and area of common geometric figures
12.0 Find and use measures of sides of triangles and polygons
to solve problems
5.0 Prove that triangles are similar
17.0 Prove theorems by using coordinate geometry
indirect measurement
scale drawing
scale
4.0 Prove basic theorems involving similarity
15.0 Use the Pythagorean theorem to find missing lengths of
sides of right triangles
18.0 Know the definitions of the basic trigonometric functions
defined by the angles of a right triangle
19.0 Use trigonometric functions to solve for an unknown
length of a side of a right triangle, given an angle and a length of
a side
Academic Vocabulary
involving relating to
Pythagorean mathematics that relate to
ancient Greek mathematician, Pythagoras
lengths distances along the side of a right
triangle form end to end
trigonometric mathematics that uses the
proportional relationships between the sides
and angles of right triangles
functions quantities used to show the
relationship between the parts of a triangle
Ratios in Similar Polygons
Triangles Similarity: AA, SSS, and SAS
Applying Properties of Similar Triangles
Using Proportional Relationships
Dilations and Similarity in the Coordinate Plane
7.6 Dilations and Similarity in the Coordinate Plane
 Apply similarity properties in the coordinate plane
 Use coordinate proof to prove figures similar
Chapter 8 Right Triangles and Trigonometry
 Similarity in Right Triangles
 Trigonometric Ratios
 Solving Right Triangles
 Angles of Elevation and Depression
 Law of sines and law of cosines
 Vectors
means
cross products
5.0 Prove that triangles are similar
7.0 Use theorems involving the properties of parallel lines cut
by a transversal
12.0 Find and use measures of sides and of interior angles of
triangles to solve problems
dilation
scale factor
8.1 Similarity in Right Triangles
 Use geometric mean to find segment lengths in right
triangles
 Apply similarity relationships in right triangles to
solve problems
8.2 Trigonometric Ratios
 Find the sine, cosine, and tangent of an acute angle
 Use trigonometric ratios to find side lengths in right
triangles and to solve real-world problems
4.0 Prove basic theorems involving similarity
geometric mean
18.0 Know the definitions of the basic trigonometric functions
defined by the angles of a right triangle
19.0 Use trigonometric functions to solve for an unknown
length of a side of a right triangle, given an angle and a length of
a side
trigonometric ratio
sine
cosine
tangent
8.3 Solving Right Triangles
 Use trigonometric ratios to find angle measures in
right triangles and to solve real-world problems
19.0 Use trigonometric functions to solve for an unknown
length of a side of a right triangle, given an angle and a length of
a side
Also covered:15.0 18.0
8.4 Angles of Elevation and Depression
 Solve problems involving angles of elevation and
angles of depression
19.0 Use trigonometric functions to solve for an unknown
length of a side of a right triangle, given an angle and a length of
a side
8.5 Law of Sines and Law of Cosines
 Use the Law of Sines and the Law of Cosines to
solve triangles
19.0 Use trigonometric functions to solve for an unknown
length of a side of a right triangle
8.6 Vectors
 Find the magnitude and direction of a vector
 Use vectors and vector addition to solve real-world
problems
19.0 Use trigonometric functions to solve for an unknown
length of a side of a right triangle
vector
component form
magnitude
direction
Chapter 9 Extending Perimeter, Circumference, and Area
 Developing Formulas for Triangles and
Quadrilaterals
 Developing Formulas for Circles and Regular
Polygons
 Composite Figures
 Perimeter and Area in the Coordinate Plane
 Effects of Changing Dimensions Proportionality
 Geometric Probability
8.0 Know, derive, and solve problems involving the perimeter,
circumference, and area of common geometric figures
10.0 Compute area of polygons, including rectangles, scalene
triangles, equilateral triangles, rhombi, parallelograms, and
trapezoids
11.0 determine how changes in dimensions affect the
perimeter and area of common geometric figures
12.0 Find and use measures of sides of triangles and polygons
to classify figures and solve problems
Academic Vocabulary
derive develop a conclusion about something
using a different method
solve find the value of a variable that makes
the left side of the equation equal to the right
side of the equation
compute calculate of work out a problem
rhombi plural of rhombus, a parallelogram
with four sides of equal length
determine find out
dimensions sizes of objects
classify assign polygons to groups according to
their features
9.1 Developing Formulas for Triangles and Quadrilaterals
8.0 Know, derive, and solve problems involving the area of
angle of elevation
angle of depression
equal vectors
parallel vectors
resultant vectors

Develop and apply the formulas for the areas of
triangles and special quadrilaterals
 Solve problems involving perimeters and areas of
triangles and special quadrilaterals
9.2 Developing Formulas for Circles and Regular Polygons
 Develop and apply the formulas for the area and
circumference of a circle
 Develop and apply the formula for the area of a
regular polygon
9.3 Composite Figures
 Use the Area Addition Postulate to find the areas of
composite figures
 Use composite figures to estimate the area of
irregular shapes

9.4 Perimeter and Area in the Coordinate Plane
 Find the perimeters and areas if figures in a
coordinate plane
common geometric figures
10.0 Compute area of polygons, including rectangles, scalene
triangles, rhombi, parallelograms, and trapezoids
9.5
Effects of Changing Dimensions Proportionally
Describe the effect on perimeter and area when one
or more dimensions of a figure are changed
 Apply the relationship between perimeter and area
in problem solving
8.0 Know and solve problems involving the perimeter,
circumference, and area of common geometric figures
10.0 Compute area of polygons, including rectangles, scalene
triangles, and parallelograms
11.0 determine how changes in dimensions affect the
perimeter and area of common geometric figures
Geometric Probability
Calculate geometric probability
Use geometric probability to predict results in realworld situations
8.0 Know and solve problems involving the area of common
geometric figures
10.0 Compute area of polygons, including rectangles,
equilateral triangles, and trapezoids
geometric probability
1.0 Demonstrate understanding by identifying and giving
examples of inductive reasoning
8.0 Know and solve problems involving perimeter,
circumference, area, volume, lateral area, and surface area of
common geometric figures
9.0 Compute the volumes and surface area of prisms,
pyramids, cylinders, cones, and spheres; and commit to
memory the formulas for prisms, pyramids, and cylinders
11.0 Determine how changes in dimensions affect the area and
volume of solids
Academic Vocabulary
demonstrate show
identifying seeing and being able to name
what something is
common geometric figures figures formed
with straight lines and/or simple shapes, for
example, rectangles, squares, and circles
commit keep in mind information so it can be
recalled later
determine find out

9.6


Chapter 10 Spatial Reasoning
 Solid Geometry
 Representation of Three-Dimensional Figures
 Formulas in Three Dimensions
 Surface Area of Pyramids and Cones
 Volume of Prisms and Cylinders
 Volume of Pyramids and Cones
 Spheres
8.0 Know, derive, and solve problems involving the
circumference, and area of common geometric figures
10.0 Compute area of polygons, equilateral triangles
8.0 Know and solve problems involving area of common
geometric figures
10.0 Compute area of polygons, including rectangles, scalene
triangles, parallelograms, and trapezoids
circle
center of a circle
center of a regular polygon
apothem
central angle of a regular polygon
composite figure
8.0 Know and solve problems involving the perimeter and area
of common geometric figures
10.0 Compute area of polygons, including rectangles, scalene
triangles
12.0 Find and use measures of sides of polygons to classify
figures and solve problems
dimensions size of objects
face
cone
edge
cube
vertex
net
prism
cross section
cylinder
pyramid
orthographic drawing
isometric drawing
perspective drawing
vanishing point
horizon
10.1 Solid Geometry
 Classify three-dimensional figures according to their
properties
 Use nets and cross sections to analyze threedimensional figures
Preparation for 9.0 Compute the volumes and surface area of
prisms, pyramids, cylinders, cones,
10.2 Representations of Three-Dimensional Figures
 Draw representations of three-dimensional figures
 Recognize a three-dimensional figure from a given
representation
Preparation for 9.0 Compute the volumes and surface area of
prisms, pyramids,
10.3 Formulas in Three Dimensions
 Apply Euler’s formula to find the number of vertices,
edges, and faces of a polyhedron
 Develop and apply the distance and midpoint
formulas in three dimensions
Preparation for 9.0 Compute the volumes and surface area of
prisms, pyramids, cylinders, cones and spheres
polyhedron
space
10.4 Surface Area of Prisms and Cylinders
 Learn and apply the formula foe the surface area of
a prism
 Learn and apply the formula foe the surface area of
a cylinder
9.0 Compute surface area of prisms, cylinders, commit to
memory the formulas for prisms and cylinders
11.0 Determine how changes in dimensions affect the area of
solids
lateral face
lateral edge
right prism
oblique prism
altitude
10.5 Surface Area of Pyramid and Cones
 Learn and apply the formula for the surface area of a
pyramid
 Learn and apply the formula for the surface area of a
cone
9.0 Compute the surface area of pyramids, cones, and commit
to memory the formulas for pyramids
vertex of a pyramid
axis of a cone
regular pyramid
right cone
altitude of a pyramid
oblique cone
vertex of a cone
altitude of a cone
slant height of a regular pyramid
slant height of a right cone
10.6 Volume of Prisms and Cylinders
 Learn and apply the formula foe the volume of a
prism
 Learn and apply the formula for the volume of a
cylinder

10.7 Volume of Pyramids and Cones
 Learn and apply the formula for the volume of a
pyramid
 Learn and apply the formula for the volume of a
cone
10.8 Spheres
9.0 Compute the volumes of prisms, cylinders, and commit to
memory the formulas for prisms, and cylinders
11.0 Determine how changes in dimensions affect the area and
volume of solids
Also covered: 8.0, 11.0
volume
9.0 Compute the volumes of pyramids, cones and commit to
memory the formulas for pyramids
11.0 Determine how changes in dimensions affect the volume
of solids
9.0 Compute the volumes and surface area spheres
sphere
surface area
lateral surface
axis of a cylinder
right cylinder
oblique cylinder

Learn and apply the formula for the volume of a
sphere
 Learn and apply the formula for the surface area of a
sphere
Chapter 11 Circles
 Lines That Intersect Circles
 Arcs and Chords
 Sector Area and Arc Length
 Inscribed Angles
 Angle Relationships in Circles
 Segment Relationships in Circles
 Circles in the Coordinate Plane
11.1 Lines That Intersect Circles
 Identify tangents, secants, and chords
 Use properties of tangents to solve problems
11.0 Determine how changes in dimensions affect the area and
volume of solids
7.0 Prove and use theorems involving the properties of circles
21.0 Solve problems regarding relationships among chords,
secants, tangents of circles
interior of circle
exterior of a circle
chord
secant
tangent of a circle
point of tangency
congruent circles
concentric circles
tangent circles
common tangent
11.2 Arcs and Chords
 Apply properties of arcs
 Apply properties of chords
7.0 Prove and use theorems involving the properties of circles
21.0 Solve problems regarding relationships among chords of
circles
central angle
arc
minor arc
major arc
semicircle
adjacent arcs
congruent arcs
11.3 Sector Area and Arc Length
 Find the area of sectors
 Find arc lengths
8.0 Know and solve problems involving the circumference and
area of common geometric figures
21.0 Solve problems regarding relationships among chords of
circles
sector of a circle
segment of a circle
arc length
11.4 Inscribed Angles
 Find the measure of an inscribed angles
 Use inscribed angles and their properties to solve
problems

11.5 Angle Relationships in Circles
 Find the measures of angles formed by lines that
intersect circles
 Use angle measures to solve problems
7.0 Prove and use theorems involving the properties of circles
21.0 Prove and solve problems regarding relationships among
inscribed angles, and inscribed polygons of circles
inscribed angle
intercepted arc
subtend
11.6 Segment Relationships in Circles
 Find the lengths of segments formed by lines that
intersect circles
 Use lengths of segments in circles to solve problems
11.7 Circles in the Coordinate Plane
7.0 Prove and use theorems involving the properties of circles
21.0 Prove and solve problems regarding relationships among
chords, secants, tangents of circles
7.0 Prove and use theorems involving the properties of circles
8.0 Know and solve problems involving the circumference and
area of common geometric figures
16.0 Perform basic constructions with a straightedge and
compass
21.0 Prove and solve problems regarding relationships among
chords, secants, tangents, inscribed angles, and inscribed
polygons of circles
center of a sphere
radius of a sphere
hemisphere
great circle
Academic Vocabulary
involving relating to
properties unique features
basic most important or fundamental; used as
a starting point
regarding about
relationships connections
7.0 Prove and use theorems involving the properties of circles
21.0 Prove and solve problems regarding relationships among
chords, secants, tangents, inscribed angles of circles
7.0 Prove and use theorems involving the properties of circles
secant segment
external secant segment
tangent segment

Write equations and graph circles in the coordinate
plane
 Use the equation and graph of a circle to solve
problems
Chapter 12 Extending Transformational Geometry
 Reflections
 Translations
 Rotations
 Compositions of Transformations
 Symmetry
 Tessellations
 Dilations
8.0 Know and solve problems involving the perimeter and area
of common geometric figures
11.0 Determine how changes in dimensions affect the
perimeter and area of common geometric figures
22.0 Know the effect of rigid motions on figures in the
coordinate plane and space, including rotations, translations,
and reflections
12.1 Reflections
 Identify and draw reflections
12.2 Translations
 Identify and draw translations
12.3 Rotations
 Identify and draw rotations
12.4 Compositions of Transformations
 Apply theorems about isometries
 Identify and draw compositions of transformations,
such as glide reflections
12.5 Symmetry
 Identify and describe symmetry in geometric figures
22.0 Know the effect of rigid motions on figures in the
coordinate plane, including reflections
22.0 Know the effect of rigid motions on figures in the
coordinate plane including translations
22.0 Know the effect of rigid motions on figures in the
coordinate plane, including rotations
22.0 Know the effect of rigid motions on figures in the
coordinate plane including rotations, translations, and
reflections
12.6 Tessellations
 Use transformations to draw tessellations
 Identify regular and semiregular tessellations and
figures that will tessellate
22.0 Know the effect of rigid motions on figures in space,
including rotations, translations, and reflections
12.7 Dilations
 Identify and draw dilations
8.0 Know and solve problems involving the perimeter and area
of common geometric figures
11.0 Determine how changes in dimensions affect the
perimeter and area of common geometric figures
22.0 Know the effect of rigid motions on figures in space,
including rotations and reflections
Academic Language
common geometric figures figures formed
with straight lines and/or simple shapes, fro
example, rectangles, squares, and circles
determine find out
dimensions sizes of objects
effect outcome
rigid motion movements of a figure that do
not change its shape or size
isometry
composition of transformations
glide reflection
symmetry
line symmetry
line of symmetry
rotational symmetry
translation symmetry
frieze pattern
glide reflection symmetry
tessellation
regular tessellation
semiregular tessellation
center of dilation
enlargement
reduction