Download Correlation to Alaska Standards - Alaska Independent Distance

Page 1
Preparation for the AGS Geometry
(Distance Delivery Course)
Course Syllabus and Correlation to Alaska Performance Standards
Course Title
Grade Levels
Offered
Credit Awarded
Content Area
of Study
Prerequisites
Geometry
9-12
1 Credit/SY
Mathematics
Pre-Algebra (required)
Algebra 1 (suggested)
Required or
Elective
Elective
Course Description
This course is the study of lines, angles, and basic shapes and figures in one, two, and three dimensions.
Topics covered include the properties of geometric shapes; symmetry; calculations and measurements of
angles, lengths, areas, and volumes; geometric postulates and theorems; linear and quadratic equations, and
the use of algebra to solve geometric problems. Skills covered include the transformations of figures,
graphing on a coordinate plane, geometric proofs and constructions, creating and solving algebraic
equations, and deductive and inductive reasoning; AGS Geometry will be used as the text. This course is
designed to meet the Yukon-Koyukuk School District Curriculum, State of Alaska Performance Standards,
and National Council of Teachers of Mathematics Standards.
Alaska Performance Standards Note:
Performance standards this course primarily supports include Geometry, Functions and Relationships,
and Numeration. Process Skills (including Problem Solving, Communication, Reasoning, and
Connections) and Measurements are covered adequately as these topics relate to Geometry. Estimation
and Computation, and Statistics and Probability are nominally covered in this course, but not
emphasized.
Textbook(s) and/or Materials
Geometry
 2005 AGS Publishing
ISBN 0-7854-3830-0
Student Progress Evaluations
Students will complete 104 lessons and 11 chapter tests.
Quarter Progress Evaluations
First Quarter
25 lesson quizzes
3 chapter tests
Joe Marley, Geoff Johnson
Second Quarter
30 lesson quizzes
3 chapter tests
AGS Geometry
Third Quarter
25 lesson quizzes
3 chapter tests
Fourth Quarter
24 lesson quizzes
2 chapter tests
Page 2
COURSE OUTLINE
Semester One
Quarter One:
Performance
Standards
Focus:
Chapter 1
“Exploring Geometry: Points, Lines and
Angles in the Plane”
Performance
Standards
Focus:
Quarter Two:
Chapter 4
“Using Algebra: Lines in the
Coordinate Plane”
1-1 Points and Lines in the Plane
M5.2.7
4-1 Naming Points
1-2 Ruler Postulates
M1.4.1
4-2 Horizontal Lines
1-3 Copying and Bisecting Angles
M5.3.7
M2.3.3
4-3 Vertical Lines
1-4 Angle Measurement
M5.3.7
M2.3.1
M2.3.3
4-4 Slope of a Line
1-5 Complementary and Supplementary Angles
4-4 Calculator Practice
1-5 Calculator Practice
M5.4.6
M4.3.5
M4.4.3
1-6 Algebra and Angles
M4.3.5
4-6 Writing the Equation of a Line
1-7 Algebra Connection: Positive Exponents
M1.4.4
M1.4.5
4-6 Calculator Practice
M4.4.1
M4.4.3
Application: Drawing Networks
M5.4.6
M7.4.1
M10.3.2
M10.4.2
4-7 Finding the Midpoint of a Segment
M4.4.5
M5.3.7
4-8 Algebra Connection: Rate and
Mixture Problems
M2.4.3
M8.3.1
M8.3.2
M6.4.1
M9.3.1
M10.3.2
4-5 Using Algebra: y = mx
M1.4.1
M4.3.4
M5.4.5
M4.4.1
M4.3.4
M5.4.5
M10.3.2
M4.4.1
M4.3.4
M5.4.5
M4.4.1
M4.3.4
M5.4.5
M10.4.2
M4.4.1
+b
Application: Screaming Slopes
Chapter 2
“Thinking Geometrically: Using Proofs”
2-1 If … Then Statements
2-2 Euclid’s Five Postulates
2-3 Using Euclid’s Postulates
2-4 Axioms and Common Notions
Joe Marley, Geoff Johnson
AGS Geometry
M4.3.4
M5.4.5
M8.3.1
M4.4.2
M5.4.5
Chapter 5
“Triangles and Quadrilaterals”
M9.3.1
M9.3.2
M9.3.2
M9.4.1
M10.3.1
M5.3.1
M5.4.1
M4.4.5
M8.3.3
M8.4.2
5-1 Naming Triangles Using Their Sides
5-2 Naming Triangles Using Their Angles
5-3 Special Quadrilaterals
5-4 Quadrilaterals and Their Diagonals
M5.3.1
M5.3.7
M5.3.1
M5.3.7
M5.4.1
M9.3.2
M5.4.1
M9.4.3
Page 3
2-4 Calculator Practice
M1.3.3
M3.4.4
M4.4.3
M8.4.2
M9.4.3
5-5 Angle Sum of Any Triangle
M5.4.1
M9.4.1
5-6 Concave and Convex Polygons
2-6 Algebra Connection: The Distributive Property
M1.3.6
M4.4.5
5-7 Constructing Perpendiculars
M4.3.1
M5.3.1
M10.3.1
M5.3.7
Application: Logical Deductions
M9.3.1
M10.4.2
5-8 Altitudes, Angle Bisectors, and Medians
2-5 A Simple Proof
5-9 Proof of the Angle Sum Theorem
5-10 Algebra Connection: Special
Polynomial Products
Application: Tangram Pictures
Chapter 3
“Parallel Lines and Transversals”
M5.3.7
M5.4.6
M7.3.2
M4.4.3
M5.4.6
M9.4.3
M1.3.1
M4.4.5
M5.4.4
M5.3.5
M9.3.1
M10.3.1
Chapter 6
“Congruent Triangles and
Transformations”
3-1 Parallel Lines
M5.3.7
6-1 Corresponding Parts: SAS Postulate
3-2 Transversals
M5.3.3
6-2 SSS Construction and Triangle
Inequality
3-3 Theorems About Parallel Lines
M7.4.1
M9.4.3
6-3 SSS and ASA Congruencies
3-4 Constructions and Problem Solving
M5.3.7
M8.3.2
6-4 Special Congruencies: Right Triangles
3-5 Quadrilaterals and Parallels
M5.3.7
M5.4.6
6-4 Calculator Practice
3-6 Trapezoids
M5.3.1
6-5 Reflections in the Coordinate Plane
3-7 Proving Lines Parallel
M5.3.7
M7.3.2
6-6 Special Reflections: Symmetries
3-8 Parallel Lines: More Theorems and Converses
M9.3.2
6-7 Slides and Translations
3-9 Algebra Connection: Solving Linear Equations
M4.4.2
M4.4.5
6-8 Rotations
Application: Geometric Quilt Shapes
M5.4.1
M10.3.1
6-9 Algebra Connection: Quadratic
Equations
M1.3.6
M4.4.3
Application: Tessellations
M5.3.5
M5.4.4
M10.3.2
Joe Marley, Geoff Johnson
AGS Geometry
M5.3.3
M5.4.3
M10.3.2
M2.3.4
M5.3.3
M5.3.7
M5.3.3
M5.4.3
M10.4.2
M1.3.6
M5.3.3
M5.4.3
M4.4.3
M2.3.3
M5.3.5
M5.4.4
M5.3.5
M5.4.4
M5.3.5
M5.4.4
M8.3.2
M5.3.5
M5.4.4
Page 4
Quarter Three:
Performance
Standards
Focus:
Chapter 7
“Proportion and Similarity”
7-1 Similar Figures and Proportions
7-1 Calculator Practice
7-2 Similar Triangles
7-3 Angle Measure in Regular Polygons
Calculator Practice
7-4 Enlarging Geometric Figures
7-5 Shrinking Geometric Figures
7-6 Algebra Connection: The Counting Principal
Application: Gearing Up
Quarter Four:
Chapter 10
“Circles and Spheres”
M1.3.4
M4.3.2
M4.4.5
M5.3.3
M4.3.5
M4.4.3
10-1 Definition of a Circle
M4.4.3
M5.4.1
10-2 The Ratio π
M2.3.4
M3.3.4
M4.4.5
M5.3.3
M10.4.2
M3.3.4
M4.3.1
M5.3.1
M5.4.1
M4.3.3
10-3 Approximating the Area of a Circle
M4.3.5
M5.3.3
M10.3.2
M3.4.1
M5.4.1
M5.4.4
M5.3.5
M5.4.6
M7.4.3
M2.3.2
M5.3.3
M5.3.5
M5.4.6
M7.3.1
M4.4.4
M7.4.1
M1.3.4
M7.4.1
M10.3.2
Calculator Practice
10-4 Area and Probability
M6.3.5
10-5 Formula for the Area of a Circle
M4.4.2
M5.2.4
M4.4.3
10-6 Circles and Their Angles and Sectors
M2.4.3
M5.4.1
10-7 Tangents, Circumcircles, and Incircles
M5.4.1
M5.3.7
M5.4.1
10-8 Sine, Cosine, and Tangent
10-9 Solving Triangles Using Trigonometry
10-10 Spheres
10-11 Algebra Connection: Systems of Linear
Equations
Application: Statistics
Chapter 8
“The Pythagorean Theorem”
8-1 Pythagorean Triples
8-2 Pythagorean Triples and a Proof
Joe Marley, Geoff Johnson
AGS Geometry
Performance
Standards
Focus:
M2.4.4
M4.3.5
M4.3.2
M5.3.4
M4.4.2
M4.4.3
M6.4.1
M9.3.1
M10.3.1
Chapter 11
“Solid Geometric Figures and
Their Measures”
M1.4.5
M2.4.4
M4.4.3
M2.4.4
M4.4.5
11-1 Basic Volume Formulas
M4.4.5
M5.3.4
11-2 Volumes of Pyramids and Cones
M4.4.5
M5.3.4
Page 5
8-3 Pythagorean Demonstration
8-4 Pythagorean Theorem and Similar Triangles
8-5 Special Triangles
8-6 Pythagorean Proof and Trapezoids
8-7 Distance Formula: Pythagorean Theorem
8-7 Calculator Practice
8-8 Converse of the Pythagorean Theorem
8-9 Algebra Connection: Denominators and Zero
Application: Architecture and Geometric Shapes
M2.4.4
M5.4.1
M2.4.4
M7.4.2
M8.4.2
M10.3.2
M10.4.2
M2.4.4
M4.4.3
M4.4.5
M5.4.1
M5.2.4
M2.4.4
M5.4.5
M5.3.6
M4.4.3
9-2 Perimeter Formulas
9-3 Perimeters and Diagonals
9-4 Area: Squares, Rectangles, and Parallelograms
9-5 Areas of Trapezoids
9-6 Areas of Triangles
9-6 Calculator Practice
9-7 Algebra Connection: Graphing Inequalities
Application: Fractals
Joe Marley, Geoff Johnson
AGS Geometry
11-4 Surface Areas of Pyramids and Cones
M5.3.4
M10.3.2
M5.3.4
M10.3.1
11-5 Measurements
M2.3.2
11-6 Algebra Connection: Radicals in
Equations
Application: Origami
M3.4.3
M4.3.5
M5.4.6
M10.3.1
M2.4.4
M5.4.5
M1.4.1
M1.4.5
M9.3.1
M10.4.2
Chapter 9
“Perimeter and Area”
9-1 Perimeters of Polygons
11-3 Surface Areas of Prisms and Cylinders
Chapter 12
“Geometry and Imagination”
M4.3.5
M5.2.4
M4.3.4
M5.2.2
M2.4.4
M5.4.5
M5.2.6
M2.3.2
M4.3.5
M5.2.4
M5.4.4
M10.3.2
M5.2.4
M5.4.1
M4.4.5
M5.2.4
M5.4.1
M4.4.3
M4.4.1
M5.4.5
M4.4.4
M10.3.1
12-1 Lines and Planes in Space
M5.3.2
12-2 Loci in the Coordinate Plane
M5.4.5
12-3 Compound Loci
M9.3.1
12-4 Algebra Connection: The Quadratic
Formula
M4.4.1
M4.4.2
Application: Conic Sections
M7.4.1
M9.3.1
Page 6
Location of performance standards covered within this course.
Performance Standard
Lesson, Tasks & Tools used to meet standard
Numeration
M1.3.1 Read, write, model, and order
real numbers, explaining scientific
notation (read only), exponents
(square and cube only)
and percents.
 5-10 Algebra Connection: Special Polynomial Products
M1.4.1 Read, write, model, order,
and define real numbers and subsets.
 1-2 Ruler Postulates
 4-1 Naming Points
 8-9 Algebra Connection: Denominators and Zero
M1.3.3 Translate between equivalent
representations of the same number.
Select a representation that is
appropriate for the situation.
 2-4 Axioms and Common Notions (CP)

M1.4.3 Compare and contrast the
relationship between various
applications of the same operation.
 none
M1.3.4 Describe and model the
relationship of fractions to decimals,
percents, ratios and proportions.
 7-1 Similar Figures and Proportions
 Ch. 7 Application: Gearing Up
M1.4.4 Translate between equivalent
representations of the same
exponential expression.
 1-7 Algebra Connection: Positive Exponents

M1.3.5 Use, explain, and define the
rules of divisibility, prime and
composite numbers, multiples, and
order of operations.
 none
M1.4.5 Recognize, describe, and use
properties of the real number system.
 1-7 Algebra Connection: Positive Exponents
 8-1 Pythagorean Triples
 8-9 Algebra Connection: Denominators and Zero
M1.3.6 Use commutative, identity,
associative, and distributive
properties with variable.
 2-6 Algebra Connection: The Distributive Property
 6-4 Special Congruencies: Right Triangles
 6-9 Algebra Connection: Quadratic Equations
Joe Marley, Geoff Johnson
AGS Geometry
Page 7

Measurement
M2.3.1 Estimate and measure various
dimensions to a specified degree of
accuracy.
 1-4 Angle Measurement
M2.4.1 Evaluate measurements for
accuracy, precision, and error with
respect to the measuring tools,
methods, and the computational
process
 none
M2.3.2 Estimate and convert
measurements within the same
system.
 7-5 Shrinking Geometric Figures
 9-4 Area: Squares, Rectangles, and Parallelograms
 11-5 Measurements
M2.4.2 Estimate and convert
measurements between different
systems.
 none
M2.3.3 Use a variety of methods and
tools to construct and compare plane
figures
 1-4 Angle Measurement
 6-5 Reflections in the Coordinate Plane
M2.4.3 Apply various measurement
systems to describe situations and
solve problems.
 4-8 Algebra Connection: Rate and Mixture Problems
 10-6 Circles and Their Angles and Sectors
M2.3.4 Describe and apply the
relationships between dimensions of
geometric figures to solve problems
using indirect measurement; describe
and apply the concepts of rate and
scale.
M2.4.4 Use indirect methods,
including the Pythagorean Theorem
and right triangle trigonometry, to
find missing dimensions.
 6-2 SSS Construction and Triangle Inequality
 7-2 Similar Triangles
Joe Marley, Geoff Johnson
AGS Geometry
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8-1 Pythagorean Triples
8-2 Pythagorean Triples and a Proof
8-3 Pythagorean Demonstration
8-4 Pythagorean Theorem and Similar Triangles
8-5 Special Triangles
8-7 Distance Formula: Pythagorean Theorem
8-8 Converse of the Pythagorean Theorem
9-3 Perimeters and Diagonals
10-9 Solving Triangles Using Trigonometry
Page 8
M2.3.5 Apply information about time
zones and elapsed time to solve
problems.
 none

Estimation and Computation
M3.4.1 Use estimation to solve
problems and to check the accuracy
of solutions; state whether the
estimation is greater or less than the
exact answer.
 10-3 Approximating the Area of a Circle
M3.3.2 Apply basic operations
efficiently and accurately, using
estimation to check the
reasonableness of results.
M3.4.2 Add and subtract real
numbers using powers.
 none
M3.4.3 Multiply and divide real
numbers in various forms including
powers.
 11-6 Algebra Connection: Radicals in Equations
M3.3.4 Multiply and divide rational
number in various forms including
fractions, decimals, and percents.
 7-2 Similar Triangles
 7-3 Angle Measure in Regular Polygons
M3.4.4 Select, convert, and apply an
equivalent representation of a number
for a specified situation.
 2-4 Axioms and Common Notions (CP)
M3.3.5 Convert between equivalent
fractions, decimals, percents, and
proportions. Convert from exact to
decimal representations of irrational
numbers.
M3.4.5 Use ratios and proportions to
model and solve fraction and percent
problems with variables.
 none
 none
 none

Joe Marley, Geoff Johnson
AGS Geometry
Page 9
Functions and Relationships
M4.3.1 Identify numeric and
geometric patterns to find the next
term and predict the nth term.
 5-6 Concave and Convex Polygons
 7-3 Angle Measure in Regular Polygons
M4.4.1 Identify, graph, and describe
the graphs of basic families of
functions including linear, absolute
value, quadratic, and exponential
using a graphing calculator
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4-2 Horizontal Lines
4-3 Vertical Lines
4-4 Slope of a Line
4-4 Slope of a Line (CP)
4-6 Writing the Equation of a Line (CP)
9-7 Algebra Connection: Graphing Inequalities
12-4 Algebra Connection: The Quadratic Formula
7-1 Similar Figures and Proportions
10-10 Spheres
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3-9 Algebra Connection: Solving Linear Equations
4-6 Writing the Equation of a Line
10-5 Formula for the Area of a Circle
10-11 Algebra Connection: Systems of Linear Equations
12-4 Algebra Connection: The Quadratic Formula
7-3 Angle Measure in Regular Polygons (CP)
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1-5 Complementary and Supplementary Angles (CP)
4-6 Writing the Equation of a Line (CP)
5-9 Proof of the Angle Sum Theorem
6-4 Special Congruencies: Right Triangles (CP)
6-9 Algebra Connection: Quadratic Equations
7-1 Similar Figures and Proportions (CP)
8-1 Pythagorean Triples
8-5 Special Triangles
8-7 Distance Formula: Pythagorean Theorem (CP)
9-6 Areas of Triangles (CP)
10-1 Definition of a Circle
10-5 Formula for the Area of a Circle (CP)
10-11 Algebra Connection: Systems of Linear Equations
4-1 Naming Points
4-2 Horizontal Lines
4-3 Vertical Lines
4-4 Slope of a Line
4-5 Using Algebra: y = mx + b
9-2 Perimeter Formulas
7-6 Algebra Connection: The Counting Principal
Ch. 9 Application: Fractals
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1-5 Complementary and Supplementary Angles
1-6 Algebra and Angles
7-1 Similar Figures and Proportions (CP)
9-1 Perimeters of Polygons
M4.3.2 Identify and describe how a
change in one variable in a function
affects the remaining variables.
M4.4.2 Create and solve linear
equations and inequalities.
M4.3.3 Use a calculator to find a
missing item in arithmetic and a
geometric sequence; predict the graph
of each function.
M4.4.3 Create and solve simple
systems of equations, algebraically
and graphically, using a graphing
calculator
M4.3.4 Translate among and use
tables of ordered pairs, graphs on
coordinate planes, and linear
equations as tools to represent and
analyze patterns.
M4.4.4 Use discrete structures, such
as networks, matrices, sequences, and
iterations, as tools to analyze
patterns, expressions, and equations.
M4.3.5 Find the value of a variable
by evaluating formulas and algebraic
expressions for given values.
Joe Marley, Geoff Johnson
AGS Geometry
Page 10
 9-4 Area: Squares, Rectangles, and Parallelograms
M4.4.5 Add, subtract, multiply,
divide, and simplify rational
expressions; add, subtract, and
multiply polynomials.
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10-2 The Ratio π
10-9 Solving Triangles Using Trigonometry
11-6 Algebra Connection: Radicals in Equations
2-6 Algebra Connection: The Distributive Property
3-9 Algebra Connection: Solving Linear Equations
4-7 Finding the Midpoint of a Segment
5-10 Algebra Connection: Special Polynomial Products
7-1 Similar Figures and Proportions
7-2 Similar Triangles
8-2 Pythagorean Triples and a Proof
8-5 Special Triangles
9-6 Areas of Triangles
11-1 Basic Volume Formulas
11-2 Volumes of Pyramids and Cones
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2-3 Using Euclid’s Postulates
5-1 Naming Triangles Using Their Sides
5-2 Naming Triangles Using Their Angles
5-6 Concave and Convex Polygons
7-3 Angle Measure in Regular Polygons
2-3 Using Euclid’s Postulates
Ch. 3 Application: Geometric Quilt Shapes
5-3 Special Quadrilaterals
5-4 Quadrilaterals and Their Diagonals
5-5 Angle Sum of Any Triangle
7-3 Angle Measure in Regular Polygons
8-3 Pythagorean Demonstration
8-6 Pythagorean Proof and Trapezoids
9-5 Areas of Trapezoids
9-6 Areas of Triangles
10-1 Definition of a Circle
10-3 Approximating the Area of a Circle
10-6 Circles and Their Angles and Sectors
10-7 Tangents, Circumcircles, and Incircles
10-8 Sine, Cosine, and Tangent
9-2 Perimeter Formulas
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3-2 Transversals
6-1 Corresponding Parts: SAS Postulate
6-2 SSS Construction and Triangle Inequality
6-3 SSS and ASA Congruencies
6-4 Special Congruencies: Right Triangles
7-1 Similar Figures and Proportions
7-2 Similar Triangles
7-5 Shrinking Geometric Figures
Geometry
M5.3.1 Identify, classify, compare,
and sketch regular and irregular
polygons.
M5.4.1 Identify and use the
properties of polygons, including
interior and exterior angles, and
circles (including angles, arcs, chord,
secants, and tangents) to solve
problems.
M5.2.2 Compare and contrast plane
and solid figures (e.g., circle/sphere,
square/cube, triangle/pyramid) using
relevant attributes, including the
number of vertices, edges, and the
number and shape of faces.
M5.3.3 Apply the properties of
equality and proportionality to solve
problems involving congruent or
similar shapes.
 10-2 The Ratio π
Joe Marley, Geoff Johnson
AGS Geometry
Page 11
M5.4.3 Identify congruent and
similar figures using Euclidean and
coordinate geometries; apply this
information to solve problems.
 6-1 Corresponding Parts: SAS Postulate
 6-3 SSS and ASA Congruencies
 6-4 Special Congruencies: Right Triangles
M5.2.4 Distinguish between area and
perimeter; find both using a variety
of methods including rulers, grid
paper, and tiles.
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9-1 Perimeters of Polygons
8-6 Pythagorean Proof and Trapezoids
9-4 Area: Squares, Rectangles, and Parallelograms
9-5 Areas of Trapezoids
9-6 Areas of Triangles
10-5 Formula for the Area of a Circle
10-10 Spheres
11-1 Basic Volume Formulas
11-2 Volumes of Pyramids and Cones
11-3 Surface Areas of Prisms and Cylinders
11-4 Surface Areas of Pyramids and Cones
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Ch. 5 Application: Tangram Pictures
6-5 Reflections in the Coordinate Plane
6-6 Special Reflections: Symmetries
6-7 Slides and Translations
6-8 Rotations
Ch. 6 Application: Tessellations
9-4 Area: Squares, Rectangles, and Parallelograms
10-3 Approximating the Area of a Circle
Ch. 5 Application: Tangram Pictures
6-5 Reflections in the Coordinate Plane
6-6 Special Reflections: Symmetries
6-7 Slides and Translations
6-8 Rotations
Ch. 6 Application: Tessellations
7-4 Enlarging Geometric Figures
7-5 Shrinking Geometric Figures
4-1 Naming Points
4-2 Horizontal Lines
4-3 Vertical Lines
4-4 Slope of a Line
4-5 Using Algebra: y = mx + b
4-6 Writing the Equation of a Line
8-7 Distance Formula: Pythagorean Theorem
8-8 Converse of the Pythagorean Theorem
9-3 Perimeters and Diagonals
9-7 Algebra Connection: Graphing Inequalities
9-3 Perimeters and Diagonals
M5.3.4 Estimate and determine
volume and surface areas of solid
figures using manipulatives and
formulas; estimate and find
circumferences and areas of circles.
M5.4.4 Use transformations to
demonstrate geometric properties.
M5.3.5 Draw and describe the results
of transformations including
translations(slides), rotations(turns),
reflections(flips), and
dilations(shrinking or enlarging).
M5.4.5 Use coordinate geometry to
graph linear equations, determine
slopes of lines, identify parallel and
perpendicular lines, and to find
possible solutions to sets of
equations.
M5.2.6 Locate and describe objects
in terms of their position with and
without compass directions; identify
coordinates for a given point or
locate points of given coordinates on
a grid.
M5.3.6 Use coordinate geometry to
represent and interpret relationships
defined by equations and formulas
Joe Marley, Geoff Johnson
AGS Geometry
 8-7 Distance Formula: Pythagorean Theorem
Page 12
including distance and midpoint.
M5.4.6 Construct geometric models,
transformations, and scale drawings
using a variety of methods including
paper folding, compass, straight edge,
protractor, and technology.
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M5.2.7 Sketch and identify line
segments, midpoints, intersections,
parallel, and perpendicular lines.
 1-1 Points and Lines in a Plane
M5.3.7 Draw, measure, and construct
geometric figures including
perpendicular bisectors, polygons
with given dimensions and angles,
circles with given dimensions,
perpendicular and parallel lines.
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1-5 Complementary and Supplementary Angles
Ch. 1 Application: Drawing Networks
5-8 Altitudes, Angle Bisectors, and Medians
7-4 Enlarging Geometric Figures
7-5 Shrinking Geometric Figures
Ch. 12 Application: Origami
1-3 Copying and Bisecting Angles
1-4 Angle Measurement
3-1 Parallel Lines
3-4 Constructions and Problem Solving
4-7 Finding the Midpoint of a Segment
5-1 Naming Triangles Using Their Sides
5-2 Naming Triangles Using Their Angles
5-7 Constructing Perpendiculars
5-8 Altitudes, Angle Bisectors, and Medians
6-2 SSS Construction and Triangle Inequality
10-7 Tangents, Circumcircles, and Incircles
Statistics/Probability
M6.3.1 Collect, analyze, and display
data in a variety of visual displays
including frequency distributions,
circle graphs,
histograms, and scatter plots.
M6.4.1 Analyze and draw inferences
from a wide variety of data sources
that summarize data; construct
graphical displays with and without
technology.
 none
M6.3.2 Interpret and analyze
information found in newspapers,
magazines, and graphical displays.
 none
M6.3.3 Determine and justify a
choice of mean, median, or mode as
the best representation of data for a
practical situation.
M6.3.4 Make projections based on
available data and evaluate whether
or not inferences can be made given
the parameters of the data.
 none
Joe Marley, Geoff Johnson
AGS Geometry
 Ch. 4 Application: Screaming Slopes
 Ch. 10 Application: Statistics
 none
Page 13
M6.3.5 Use tree diagrams and sample
spaces to make predictions about
independent events.
 10-4 Area and Probability
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 Process Skills
 (Problem Solving, Communication, Reasoning, Connections)
Process Skills are assessed but not separately reported on individual student reports.
M7.3.1 Analyze and summarize a
problem using the relationships
between the known facts and
unknown information.
M7.4.1 Recognize and formulate
mathematical problems from within
and outside the field of mathematics.
 7-5 Shrinking Geometric Figures
M7.3.2 Select, modify, and apply a
variety of problem-solving strategies
including graphing, inductive and
deductive reasoning, Venn diagrams,
and spreadsheets.
 3-7 Proving Lines Parallel
 5-8 Altitudes, Angle Bisectors, and Medians
M7.4.2 Apply multi-step, integrated,
mathematical problem-solving
strategies, persisting until a solution
is found or it is clear no solutions
exist.
M7.4.3 Verify the answer by using
an alternative strategy.
 8-4 Pythagorean Theorem and Similar Triangles
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Ch. 1 Application: Drawing Networks
7-6 Algebra Connection: The Counting Principal
Ch. 7 Application: Gearing Up
Ch. 12 Application: Conic Sections
 7-4 Enlarging Geometric Figures
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M8.3.1 Use math vocabulary,
symbols, and notation to represent
information in the problem.
 4-5 Using Algebra: y = mx + b
 4-8 Algebra Connection: Rate and Mixture Problems
M8.3.2 Represent a problem
numerically, graphically, and
symbolically; translate among these
alternative representations.
M8.4.2 Use numerical, graphic, and
symbolic representations to support
oral and written communication
about math ideas.
 3-4 Constructions and Problem Solving
 4-8 Algebra Connection: Rate and Mixture Problems
 6-7 Slides and Translations
M8.3.3 Use appropriate vocabulary,
symbols, and technology to explain,
justify, and defend mathematical
 2-4 Axioms and Common Notions
Joe Marley, Geoff Johnson
AGS Geometry
 2-4 Axioms and Common Notions
 2-5 A Simple Proof
 8-4 Pythagorean Theorem and Similar Triangles
Page 14
solutions.
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M9.3.1 Use informal deductive and
inductive reasoning in both concrete
and abstract contexts.
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M9.4.1 Follow and evaluate an
argument, judging its validity using
inductive or deductive reasoning and
logic.
 2-2 Euclid’s Five Postulates
 5-5 Angle Sum of Any Triangle
M9.3.2 State counterexamples to
disprove statements.
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M9.4.3 Use methods of proofs
including direct, indirect, and
counterexamples, to validate
conjectures.
 3-3 Theorems About Parallel Lines
 5-4 Quadrilaterals and Their Diagonals
 5-9 Proof of the Angle Sum Theorem
2-1 If … Then Statements
Ch. 2 Application: Logical Deductions
Ch. 4 Application: Screaming Slopes
Ch. 5 Application: Tangram Pictures
Ch. 8 Application: Architecture and Geometric Shapes
Ch. 10 Application: Statistics
12-3 Compound Loci
Ch. 12 Application: Conic Sections
2-1 If … Then Statements
2-2 Euclid’s Five Postulates
3-8 Parallel Lines: More Theorems and Converses
5-3 Special Quadrilaterals
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M10.3.1 Apply mathematical skills
and processes to science and
humanities.
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2-2 Euclid’s Five Postulates
Ch. 3 Application: Geometric Quilt Shapes
5-6 Concave and Convex Polygons
Ch. 5 Application: Tangram Pictures
Ch. 9 Application: Fractals
Ch. 10 Application: Statistics
11-4 Surface Areas of Pyramids and Cones
Ch. 11 Application: Origami
M10.3.2 Apply mathematical skills
and processes to situations with peers
and community
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Ch. 1 Application: Drawing Networks
4-2 Horizontal Lines
Ch. 4 Application: Screaming Slopes
6-1 Corresponding Parts: SAS Postulate
Ch. 6 Application: Tessellations
Ch. 7 Application: Gearing Up
8-4 Pythagorean Theorem and Similar Triangles
9-4 Area: Squares, Rectangles, and Parallelograms
 10-2 The Ratio π
 11-3 Surface Areas of Prisms and Cylinders
Joe Marley, Geoff Johnson
AGS Geometry
Page 15
M10.4.2 Describe how mathematics
can be used in knowing how to
prepare for careers.
Joe Marley, Geoff Johnson
AGS Geometry
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Ch. 1 Application: Drawing Networks
Ch. 2 Application: Logical Deductions
4-4 Slope of a Line
6-3 SSS and ASA Congruencies
7-2 Similar Triangles
8-4 Pythagorean Theorem and Similar Triangles
Ch. 8 Application: Architecture and Geometric Shapes