Geometry Curriculum Map
Modified: May 27, 2014
Timeline:
Unit 1: Points, Lines, and Planes
3 weeks/15 days
New Common Core State Standards:
Vocabulary:
G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the
undefined notions of point, line, distance along a line, and distance around a circular arc.
G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge,
string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle;
bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a
line segment; and constructing a line parallel to a given line through a point not on the line.
G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the
distance formula.★
Undefined terms,
Collinear,
Perimeter,
Coplanar,
Line Segment,
Between,
End Points,
Ray,
Opposite Rays,
Intersection,
Postulate,
Axiom,
Coordinate,
Congruent,
Midpoint,
Bisector,
Angle,
Acute,
Right,
Obtuse,
Straight,
Construction,
Perpendicular,
Complementary,
Supplementary,
Adjacent,
Linear Pair,
Vertical Angles,
Polygon,
Convex,
Concave,
Equilateral,
Equiangular,
Regular
Activities:
Resources:
Concepts and Skills:
Strategies:



College Readiness:
(Range 13-15) Basic Operations and Applications: Perform one-operation computation with whole numbers
(Range 13-15) Measurement: Estimate or calculate the length of a line segment based on other lengths given on a geometric
figure
(Range 13-15) Graphical Representations: Identify the location of a point with a positive coordinate on the number line
(Range 16-19) Measurement: Compute the perimeter of polygons when all side lengths are given
(Range 16-19) Measurement: Compute the area of rectangles when whole number dimensions are given
(Range 16-19) Graphical Representations: Locate points on the number line and in the first quadrant
(Range 20-23) Graphical Representations: Comprehend the concept of length on the number line*
(Range 20-23) Graphical Representations: Locate points in the coordinate plane
(Range 20-23) Properties of Plane Figures: Exhibit knowledge of basic angle properties and special sums of
angle measures (e.g., 90°, 180°, and 360°)
(Range 20-23) Expressions, Equations, &Inequalities: Evaluate algebraic expressions by substituting integers for unknown
quantities, Add and subtract simple algebraic expressions, Solve routine first-degree equations, Perform straightforward wordto-symbol translations
(Range 24-27) Expressions, Equations, &Inequalities :Solve real-world problems using first degree equations
(Range 24-27) Graphical Representations: Find the midpoint of a line segment *
(Range 28-32) Graphical Representations: Use the distance formula
(Range 28-32) Graphical Representations: Match number line graphs with solution sets of linear inequalities
NCTM:
Algebra:

understand the meaning of equivalent forms of expressions, equations, inequalities, and relations;

write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency—mentally or
with paper and pencil in simple cases and using technology in all cases;

use symbolic algebra to represent and explain mathematical relationships;
Geometry:

use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze
geometric situations;

investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian
coordinates.

draw and construct representations of two- and three-dimensional geometric objects using a variety of tools;

use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as
art and architecture.

use geometric models to gain insights into, and answer questions in, other areas of mathematics;
Measurement:

make decisions about units and scales that are appropriate for problem situations involving measurement.

analyze precision, accuracy, and approximate error in measurement situations;

use unit analysis to check measurement computations.






Know and describe the
undefined terms
Describe, label, measure
and sketch geometric
figures (including
perimeter, perpendicular
and parallel lines).
Understand and use
equality and congruence of
segments and angles.
Use properties of angles to
solve basic problems using
segments and angles
including the use of
Algebraic equations
Understand and use
bisectors to solve problems
Set up and solve equations
comparing angle to
complement/ supplement.
Use coordinate geometry
to find distance, midpoints,
and endpoints
Classify polygons with
sides and angles
Solve simple area and
perimeter problems
(including circles,
triangles, and rectangles)
Postulates and
Theorems:
Ruler Postulate,
Protractor Postulate,
Segment Addition
Postulate,
Angle Addition
Postulate,
Linear Pair Postulate,
Vertical Angles
Congruence Theorem,
Congruent
Complements
Theorem,
Congruent
Supplements Theorem,
Right Angle
Congruence Theorem
Geometry Curriculum Map
Modified: May 27, 2014
Problem Solving:

build new mathematical knowledge through problem solving;

solve problems that arise in mathematics and in other contexts;

apply and adapt a variety of appropriate strategies to solve problems;

monitor and reflect on the process of mathematical problem solving.
Reasoning and Proof:

recognize reasoning and proof as fundamental aspects of mathematics;

make and investigate mathematical conjectures;

develop and evaluate mathematical arguments and proofs;

select and use various types of reasoning and methods of proof.
Quality Core:
A-1-a. Apply problem-solving skills (e.g., identifying irrelevant or missing information, making
conjectures, extracting mathematical meaning, recognizing and performing multiple steps when
needed, verifying results in the context of the problem) to the solution of real-world problems
A-1- b. Solve single-step and multistep equations and inequalities in one variable
B-1- all
D-1-a. Identify and model plane figures, including collinear and non-collinear points, lines, segments,
rays, and angles using appropriate mathematical symbols
D-1-b. Identify vertical, adjacent, complementary, and supplementary angle pairs and use them to solve
problems (e.g., solve equations, use in proofs)
D-1-d. Use construction techniques, including straightedge and compass, to bisect and trisect
segments and to create parallel and perpendicular lines, perpendicular bisectors, and angle bisectors
D-2-a. Identify and classify triangles by their sides and angles
G-1-b. Apply the midpoint and distance formulas to points and segments to find midpoints, distances,
and missing information
G-1-c. Use coordinate geometry to solve problems about geometric figures (e.g., segments, triangles,
quadrilaterals)
Timeline:
Unit 2: Transformations
2 weeks/10 days
New State Standards:
Vocabulary:
Image,
Preimage,
Isometry,
Vector,
Reflection,
Rotation,
Translation,
Symmetry,
Symmetry of a
Transformation
Composition,
Scalar/Scale Factor,
Dilation
Magnitude
G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe
transformations as functions that take points in the plane as inputs and give other points as outputs. Compare
transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that
carry it onto itself.
G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines,
parallel lines, and line segments.
G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g.,
graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given
figure onto another.
G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid
motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if
they are congruent.
G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor.
a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line
passing through the center unchanged.
b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Activities:
Gates-Transformations
Concepts and Skills:
(Transformations should occur
in both a general plane and the
coordinate plane)
 Perform congruence and
similarity transformations
 Apply basic concepts of
vectors for translations
 Reflect a figure in one/two
lines
 Rotate figures about a
point
 Perform compositions of
two or more
Resources:
Sketchpad LabTransformations
Strategies:
Postulates and
Theorems:
Translation Theorem,
Reflection Theorem,
Rotation Theorem,
Composition Theorem,
Reflections in Parallel
Lines Theorems,
Reflections in
Intersecting Lines
Theorem
Geometry Curriculum Map
Modified: May 27, 2014
G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given
ratio.
College Readiness:
Range(13-15) Number Concepts and Properties: Recognize equivalent fractions and fractions in lowest terms
Range (20-23) Basic Operations and Applications: Solve routine two-step or three-step arithmetic problems involving
concepts such as rate and proportion, tax added, percentage off, and computing with a given average
NCTM:
Algebra:

use symbolic algebra to represent and explain mathematical relationships;

understand and perform transformations such as arithmetically combining, composing, and inverting commonly used
functions, using technology to perform such operations on more-complicated symbolic expressions;

interpret representations of functions of two variables

judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by
technology.

draw reasonable conclusions about a situation being modeled.
Geometry:

analyze properties and determine attributes of two- and three-dimensional objects;

explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric
objects, make and test conjectures about them, and solve problems involving them;

establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by
others;

use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze
geometric situations;

investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian
coordinates.

understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches,
coordinates, vectors, function notation, and matrices;

use various representations to help understand the effects of simple transformations and their compositions.

use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as
art and architecture.

use geometric models to gain insights into, and answer questions in, other areas of mathematics;
Measurement:

make decisions about units and scales that are appropriate for problem situations involving measurement.

analyze precision, accuracy, and approximate error in measurement situations;

use unit analysis to check measurement computations.
Problem Solving:

build new mathematical knowledge through problem solving;

solve problems that arise in mathematics and in other contexts;

apply and adapt a variety of appropriate strategies to solve problems;

monitor and reflect on the process of mathematical problem solving.
Reasoning and Proof:

recognize reasoning and proof as fundamental aspects of mathematics;

make and investigate mathematical conjectures;

select and use various types of reasoning and methods of proof.
Quality Core:
B-1- all
E-1-a. Determine points or lines of symmetry and apply the properties of symmetry to figures
E-1-e. Identify and draw images of transformations and use their properties to solve problems
G-1-e. Determine the effect of reflections, rotations, translations, and dilations and their compositions








transformations and
determine if order matters
Create a coordinate rule for
a transformation
Perform transformations
on basic functions
Figure out transformations
given graphs
Identify symmetries of a
figure
Identify symmetries of a
transformation
Perform dilations
Find and use scale factors
(include effect on area)
Transformations using
matrices (If time allows)
Geometry Curriculum Map
Modified: May 27, 2014
on the coordinate plane
Timeline:
Unit 3: Logic and Proof
2 weeks/15 days
New State Standards:
Starts 12 days from
beginning
G.CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a
transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent;
points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
College Readiness:
Vocabulary:
Conjecture,
Inductive Reasoning,
Counterexample,
Conditional,
Negation,
Equivalent Statements,
Biconditional,
Deductive Reasoning,
Proof,
Hypothesis
Concusion
Theorem
Reflexive
Symmetric
Transitive
Substitution
Detachment
Syllogism
Jusification
Truth Values
Truth Table
Contrapositive
Converse
Activities:
Strategies:
Concepts and Skills:


(Range 13-15) Basic Operations and Applications: Solve problems in one or two steps using whole numbers
(Range 13-15) Expressions, Equations, and Inequalities: Exhibit knowledge of basic expressions
(Range 13-15) Expressions, Equations, and Inequalities: Solve equations in the form x + a = b, where a and b are whole
numbers or decimals
(Range 16-19) Expressions, Equations, and Inequalities: Solve one step equations having integer or decimal answers.
(Range 16-19) Expressions, Equations, and Inequalities: Substitute whole numbers for unknown quantities to evaluate
expressions
(Range 20-23) Expressions, Equations, and Inequalities: Solve routine first-degree equations

NCTM:

Algebra:

understand the meaning of equivalent forms of expressions, equations, inequalities, and relations;

write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency—mentally or
with paper and pencil in simple cases and using technology in all cases;

use symbolic algebra to represent and explain mathematical relationships;

draw reasonable conclusions about a situation being modeled.
Geometry:

analyze properties and determine attributes of two- and three-dimensional objects;

explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric
objects, make and test conjectures about them, and solve problems involving them;

establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by
others;

use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze
geometric situations;

investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian
coordinates.

draw and construct representations of two- and three-dimensional geometric objects using a variety of tools;

use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as
art and architecture.

use geometric models to gain insights into, and answer questions in, other areas of mathematics;
Measurement:

make decisions about units and scales that are appropriate for problem situations involving measurement.

analyze precision, accuracy, and approximate error in measurement situations;

use unit analysis to check measurement computations.
Problem Solving:

build new mathematical knowledge through problem solving;

solve problems that arise in mathematics and in other contexts;

apply and adapt a variety of appropriate strategies to solve problems;

monitor and reflect on the process of mathematical problem solving.
Reasoning and Proof:

recognize reasoning and proof as fundamental aspects of mathematics;
Resources:







Use inductive and
deductive reasoning
Understand geometric
relationships in diagrams
Proof of geometric
relationships
Create conditional
statements
Determine the truth value
of conditional and
biconditional statements
Determine if statements are
equivalent
Determine if a definition
contains all necessary
properties
Use postulates to prove
theorems
Use algebraic properties to
prove logical arguments
Create and use truth tables
Identify converse and
contrapositive and discuss
truth values
Postulates and
Theorems:
Geometry Curriculum Map
Modified: May 27, 2014



make and investigate mathematical conjectures;
develop and evaluate mathematical arguments and proofs;
select and use various types of reasoning and methods of proof.
Quality Core:
A-1- b. Solve single-step and multistep equations and inequalities in one variable
B-1- all
C-1- a. Use definitions, basic postulates, and theorems about points, segments, lines, angles, and
planes to write proofs and to solve problems
C-1- b. Use inductive reasoning to make conjectures and deductive reasoning to arrive at valid
conclusions
C-1- c. Identify and write conditional and biconditional statements along with the converse, inverse, and
contrapositive of a conditional statement; use these statements to form conclusions
C-1- e. Read and write different types and formats of proofs including two-column, flowchart,
paragraph, and indirect proofs
D-1- a. Identify and model plane figures, including collinear and non-collinear points, lines, segments,
rays, and angles using appropriate mathematical symbols
D-1- b. Identify vertical, adjacent, complementary, and supplementary angle pairs and use them to
solve problems (e.g., solve equations, use in proofs)
Unit 4: Parallel and Perpendicular Lines
Timeline:
New State Standards:
2.5 weeks/13 days
Vocabulary:
Parallel lines,
Skew Lines,
Transversal,
Corresponding Angles,
Alternate Interior Angles,
Alternate Exterior Angles,
Consecutive Interior
Angles,
Slope
Standard Form of a Line
Point Slope Form
Slope Intercept Form
Proportionality
G.CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a
transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are
congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s
endpoints.
G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and uses them to solve geometric problems
(e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
College Readiness:
Range(13-15) Number Concepts and Properties: Recognize equivalent fractions and fractions in lowest terms
Range(20-23) Number Concepts and Properties: Exhibit knowledge of elementary number concepts including
rounding, the ordering of decimals, pattern identification, absolute value, primes, and greatest common factor
Range(20-23) Graphical Representations: Exhibit knowledge of slope*
Range(20-23) Properties of Plane Figures: Find the measure of an angle using properties of parallel lines
Range(28-32) Expressions, Equations, and Inequalities: Write expressions, equations, or inequalities with a single
variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using
proportions)
Range(24-27) Expressions, Equations, and Inequalities: Solve first-degree inequalities that do not require reversing the
inequality sign
Range(28-32) Expressions, Equations, and Inequalities: Solve linear inequalities that require reversing the inequality sign
Range(28-32) Graphical Representations: Use properties of parallel and perpendicular lines to determine an equation
of a line or coordinates of a point
NCTM:
Algebra:
Activities:
Gates- Parallel and
Perpendicular Lines
Concepts and Skills:
 Use properties of parallel






and perpendicular lines
Prove relationships using
angle measures
Identify and use angle pair
relationships to solve
problems
Find, compare, and use
slopes of lines in a
coordinate plane.
Find equations of lines to
determine parallel,
perpendicular or neither.
Find intersection of two
lines in the coordinate
plane
Use construction tools to
create parallel and
perpendicular lines
Resources:
Strategies:
Postulates and
Theorems:
Parallel Postulate,
Perpendicular Postulate,
Corresponding Angles
Postulate, Alternate
Interior Angles Theorem,
Alternate Exterior Angle
Theorem, Consecutive
Interior Angles Theorem,
Geometry Curriculum Map
Modified: May 27, 2014


understand the meaning of equivalent forms of expressions, equations, inequalities, and relations;
write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency—mentally or
with paper and pencil in simple cases and using technology in all cases;
use symbolic algebra to represent and explain mathematical relationships;
draw reasonable conclusions about a situation being modeled.


Geometry:

analyze properties and determine attributes of two- and three-dimensional objects;

explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric
objects, make and test conjectures about them, and solve problems involving them;

establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by
others;

use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze
geometric situations;

investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian
coordinates.

draw and construct representations of two- and three-dimensional geometric objects using a variety of tools;

use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as
art and architecture.

use geometric models to gain insights into, and answer questions in, other areas of mathematics;
Measurement:

make decisions about units and scales that are appropriate for problem situations involving measurement.

analyze precision, accuracy, and approximate error in measurement situations;

use unit analysis to check measurement computations.
Problem Solving:

build new mathematical knowledge through problem solving;

solve problems that arise in mathematics and in other contexts;

apply and adapt a variety of appropriate strategies to solve problems;

monitor and reflect on the process of mathematical problem solving.
Reasoning and Proof:

recognize reasoning and proof as fundamental aspects of mathematics;

make and investigate mathematical conjectures;

develop and evaluate mathematical arguments and proofs;

select and use various types of reasoning and methods of proof.
Quality Core:
A-1-b. Identify vertical, adjacent, complementary, and supplementary angle pairs and use them to solve
problems (e.g., solve equations, use in proofs)
A-1-c. Write linear equations in standard form and slope-intercept form when given two points, a point
and the slope, or the graph of the equation
A-1-d. Recognize the concept of slope as a rate of change and determine the slope when given the
equation of a line in standard form or slope-intercept form, the graph of a line, two points, or a verbal
description
A-1-e. Graph a linear equation using a table of values, x- and y-intercepts, or slope-intercept form
B-1- all
C-1- a. Use definitions, basic postulates, and theorems about points, segments, lines, angles, and
planes to write proofs and to solve problems
C-1- d. Use various methods to prove that two lines are parallel or perpendicular (e.g., using
coordinates, angle measures)
D-1- a. Identify and model plane figures, including collinear and noncollinear points, lines, segments,
rays, and angles using appropriate mathematical symbols
D-1-b. Identify vertical, adjacent, complementary, and supplementary angle pairs and use them to solve




Use proportionality to
solve real-world problems
Find distance between two
parallel lines
Find distance from a point
to a line
Draw secant and tangent
line and find equation
(Calculus tie-in)
Geometry Curriculum Map
Modified: May 27, 2014
problems (e.g., solve equations, use in proofs)
D-1-c. Identify corresponding, same-side interior, same-side exterior, alternate interior, and alternate
exterior angle pairs formed by a pair of parallel lines and a transversal and use these special angle
pairs to solve problems (e.g., solve equations, use in proofs)
D-1-f. Apply properties and theorems of parallel and perpendicular lines to solve problems
G-1-a. Use slope to distinguish between and write equations for parallel and perpendicular lines
Timeline:
Unit 5: Congruent Triangles
2.5 weeks/12 days
New State Standards:
Vocabulary:
Scalene,
Isosceles,
Interior Angles,
Exterior Angles,
Corollary,
Congruent Figures,
Corresponding Parts,
CPCTC,
SSS,
ASA,
SAS,
AAS,
HL
Bases Angles,
Legs
Vertex Angle
G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid
motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if
they are congruent.
G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and
only if corresponding pairs of sides and corresponding pairs of angles are congruent.
G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of
congruence in terms of rigid motions.
G.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°;
base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel
to the third side and half the length; the medians of a triangle meet at a point.
College Readiness:
Range(33-36) Properties of Plane Figures: Draw conclusions based on a set of conditions
NCTM:
Algebra:

use symbolic algebra to represent and explain mathematical relationships;

understand and perform transformations such as arithmetically combining, composing, and inverting commonly used
functions, using technology to perform such operations on more-complicated symbolic expressions;

interpret representations of functions of two variables

judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by
technology.

draw reasonable conclusions about a situation being modeled.
Geometry:

analyze properties and determine attributes of two- and three-dimensional objects;

explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric
objects, make and test conjectures about them, and solve problems involving them;

establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by
others;

use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze
geometric situations;

investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian
coordinates.

understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches,
coordinates, vectors, function notation, and matrices;

use various representations to help understand the effects of simple transformations and their compositions.

use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as
art and architecture.

use geometric models to gain insights into, and answer questions in, other areas of mathematics;
Measurement:

make decisions about units and scales that are appropriate for problem situations involving measurement.
Activities:
Gates- Mystery Triangle
Resources:
Strategies:
Concepts and Skills:







Classify a triangle by its
angles and sides
Use triangle sum and
exterior angle sum
theorems to solve
problems
Use isosceles triangle
theorems to solve for
angles and sides
Identify congruent figures
Use theorems to prove
triangle congruence
Use congruence to prove
corresponding parts of the
figures are congruent
Use construction tools to
create congruent triangles
Postulates and
Theorems:
Triangle Interior Angle
Sum Theorem, Triangle
Exterior Angle Theorem,
Corollary to the Triangle
Interior Angle Sum
Theorem, Third Angle
Theorem, SSS
Congruence Postulate,
SAS Congruence
Postulate, HL
Congruence Theorem,
ASA Congruence
Postulate, AAS
Congruence Theorem,
Base Angles Theorem,
Converse of Base Angles
Theorem,
Geometry Curriculum Map
Modified: May 27, 2014

analyze precision, accuracy, and approximate error in measurement situations;

use unit analysis to check measurement computations.
Problem Solving:

build new mathematical knowledge through problem solving;

solve problems that arise in mathematics and in other contexts;

apply and adapt a variety of appropriate strategies to solve problems;

monitor and reflect on the process of mathematical problem solving.
Reasoning and Proof:

recognize reasoning and proof as fundamental aspects of mathematics;

make and investigate mathematical conjectures;

select and use various types of reasoning and methods of proof.
Quality Core:
B-1- all
C-1- a. Use definitions, basic postulates, and theorems about points, segments, lines, angles, and
planes to write proofs and to solve problems
C-1- b. Use inductive reasoning to make conjectures and deductive reasoning to arrive at valid
conclusions
C-1- e. Read and write different types and formats of proofs including two-column, flowchart,
paragraph, and indirect proofs
C-1- f. Prove that two triangles are congruent by applying the SSS, SAS, ASA, AAS, and HL
congruence statements
C-1- g. Use the principle that corresponding parts of congruent triangles are congruent to solve
problems
D-2-a. Identify and classify triangles by their sides and angles
D-2-i. Apply the Angle Sum Theorem for triangles and polygons to find interior and exterior angle
measures given the number of sides, to find the number of sides given angle measures, and to solve
real-world problems
D-2-j. Apply the Isosceles Triangle Theorem and its converse to triangles to solve mathematical and
real-world problems
G-1-c. Use coordinate geometry to solve problems about geometric figures (e.g., segments, triangles,
quadrilaterals)
END 1st Trimester
Unit 6: Similarity
Activities:
Timeline:
New State Standards:
2 weeks/10 days
G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor.
a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line
passing through the center unchanged.
b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are
similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all
corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
G.SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other
Resources:
Strategies:
Concepts and Skills:



Understand similarity in
terms of similarity
transformations.
Use ratios and proportions
to solve geometry
problems.
Use geometric means
(include geometric
Postulates and
Theorems:
AA Similarity Postulate,
SSS Similarity Theorem,
SAS Similarity Theorem,
Triangle Proportionality
Theorem, Parallel
Transversal
Geometry Curriculum Map
Modified: May 27, 2014
Vocabulary:
Ratio,
Proportion,
Geometric Mean,
Scale Factor,
Similar,
Dilation,
Reduction,
Enlargement,
AA,
SSS,
SAS
two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in
geometric figures.
G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given
ratio.
College Readiness:
Range(20-23) Number Concepts and Properties: Exhibit knowledge of elementary number concepts including
rounding, the ordering of decimals, pattern identification, absolute value, primes, and greatest common factor .
Range (20-23) Basic Operations and Applications: Solve routine two-step or three-step arithmetic problems involving
concepts such as rate and proportion, tax added, percentage off, and computing with a given average
Range(24-27) Basic Operations & Applications: Solve multistep arithmetic problems that involve planning or
converting units of measure (e.g., feet per second to miles per hour)
Range(33-36) Measurement: Use scale factors to determine the magnitude of a size change
NCTM:
Algebra:

use symbolic algebra to represent and explain mathematical relationships;

understand and perform transformations such as arithmetically combining, composing, and inverting commonly used
functions, using technology to perform such operations on more-complicated symbolic expressions;

interpret representations of functions of two variables

judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by
technology.

draw reasonable conclusions about a situation being modeled.
Geometry:

analyze properties and determine attributes of two- and three-dimensional objects;

explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric
objects, make and test conjectures about them, and solve problems involving them;

establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by
others;

use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze
geometric situations;

investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian
coordinates.

understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches,
coordinates, vectors, function notation, and matrices;

use various representations to help understand the effects of simple transformations and their compositions.

use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as
art and architecture.

use geometric models to gain insights into, and answer questions in, other areas of mathematics;
Measurement:

make decisions about units and scales that are appropriate for problem situations involving measurement.

analyze precision, accuracy, and approximate error in measurement situations;

use unit analysis to check measurement computations.
Problem Solving:

build new mathematical knowledge through problem solving;

solve problems that arise in mathematics and in other contexts;

apply and adapt a variety of appropriate strategies to solve problems;

monitor and reflect on the process of mathematical problem solving.
Reasoning and Proof:

recognize reasoning and proof as fundamental aspects of mathematics;

make and investigate mathematical conjectures;
construction)
Use guess and check
method to find arithmetic
and geometric means

Use indirect measurement
and similarity to solve
problems

Prove triangles similar
using postulates and
theorems

Identify relationships
within similar right
triangles when an altitude
to a hypotenuse is made.

Use proportions with
triangles and parallel lines
to solve problems.
Perform dilations graphically
and algebraically

Proportionality Theorem,
Angle Bisector of a
Triangle Proportionality
Theorem, Altitude to
Hypotenuse Theorem,
Side-Splitter Theorem
Geometry Curriculum Map
Modified: May 27, 2014

select and use various types of reasoning and methods of proof.
Quality Core:
B-1- all
C-1- a. Use definitions, basic postulates, and theorems about points, segments, lines, angles, and
planes to write proofs and to solve problems
C-1- h. Use several methods, including AA, SAS, and SSS, to prove that two triangles are similar,
corresponding sides are proportional, and corresponding angles are congruent.
D-2-d. Solve problems involving the relationships formed when the altitude to the hypotenuse of a right
triangle is drawn.
E-1-c. Identify similar figures and use ratios and proportions to solve mathematical and real-world
problems (e.g., finding the height of a tree using the shadow of the tree and the height and shadow of a
person)
E-1-d. Use the definition of similarity to establish the congruence of angles, proportionality of sides, and
scale factor of two similar polygons
E-1-f. Apply relationships between perimeters of similar figures, areas of similar figures, and volumes of
similar figures, in terms of scale factor, to solve mathematical and real-world problems
E-1-g. Determine the geometric mean between two numbers and use it to solve problems (e.g., find the
lengths of segments in right triangles)
Unit 7: Right Triangles and Trigonometry
Activities:
Timeline:
New State Standards:
3 weeks/15 days
Vocabulary:
Pythagorean Triple,
Pythagorean Theorem,
Converse of Pythagorean
Theorem,
Trigonometric Ratio,
Tangent,
Sine,
Cosine,
Inverse Tangent,
Inverse Sine,
Inverse Cosine,
Angle of Elevation,
Angle of Depression,
Law of Sines,
Law of Cosines
G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor.
a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line
passing through the center unchanged.
b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are
similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all
corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
G.SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other
two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in
geometric figures.
G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle,
leading to definitions of trigonometric ratios for acute angles.
G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. ★
G.SRT.9 (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex
perpendicular to the opposite side.
G.SRT.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems.
G.SRT.11 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right
and non-right triangles (e.g., surveying problems, resultant forces).
College Readiness:
Resources:
Strategies:
Concepts and Skills:





Use the Pythagorean
Theorem and its converse
to solve real world
problems
Classify a triangle as acute,
obtuse, or right based on
its sides
Use special relationships in
right triangles (30-60-90
and 45-45-90) to solve for
missing sides
Use trigonometric ratios to
solve for missing
information in right
triangles
Use trigonometric ratios to
solve real world problems
Postulates and
Theorems:
Pythagorean Theorem,
Converse to the
Pythagorean Theorem,
Altitude to Hypotenuse
Theorem, Geometric
Mean Theorem, 45-45-90
Theorem, 30-60-90
Theorem, Law of Sines,
Law of Cosines
Geometry Curriculum Map
Modified: May 27, 2014
Range (20-23) Basic Operations and Applications: Solve routine two-step or three-step arithmetic problems involving
concepts such as rate and proportion, tax added, percentage off, and computing with a given average
Range(24-27)Properties of Plane Figures: Recognize Pythagorean triples*
Range(24-27) Functions: Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of
given side lengths
Range(28-32) Basic Operations & Applications: Solve word problems containing several rates, proportions, or
percentages
Range(28-32) Properties of Plane Figures: Apply properties of 30°-60°-90°, 45°-45°-90°, similar, and congruent
triangles
Range(28-32) Properties of Plane Figures: Use the Pythagorean theorem
Range(28-32) Functions: Apply basic trigonometric ratios to solve right-triangle problems
Range (33-36) Functions: Exhibit knowledge of unit circle trigonometry
NCTM:
Algebra:

use symbolic algebra to represent and explain mathematical relationships;

judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by
technology.

draw reasonable conclusions about a situation being modeled.
Geometry:

analyze properties and determine attributes of two- and three-dimensional objects;

explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric
objects, make and test conjectures about them, and solve problems involving them;

establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by
others;

use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze
geometric situations;

investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian
coordinates.

use trigonometric relationships to determine lengths and angle measures..

use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as
art and architecture.

use geometric models to gain insights into, and answer questions in, other areas of mathematics;
Measurement:

make decisions about units and scales that are appropriate for problem situations involving measurement.

analyze precision, accuracy, and approximate error in measurement situations;

use unit analysis to check measurement computations.
Problem Solving:

build new mathematical knowledge through problem solving;

solve problems that arise in mathematics and in other contexts;

apply and adapt a variety of appropriate strategies to solve problems;

monitor and reflect on the process of mathematical problem solving.
Reasoning and Proof:

recognize reasoning and proof as fundamental aspects of mathematics;

make and investigate mathematical conjectures;

select and use various types of reasoning and methods of proof.
Connections:

recognize and use connections among mathematical ideas; make and investigate mathematical conjectures;

understand how mathematical ideas interconnect and build on one another to produce a coherent whole;

recognize and apply mathematics in contexts outside of mathematics.
Quality Core:
B-1- all
Geometry Curriculum Map
Modified: May 27, 2014
D-2-d. Solve problems involving the relationships formed when the altitude to the hypotenuse of a right
triangle is drawn.
D-2-e. Apply the Pythagorean Theorem and its converse to triangles to solve mathematical and realworld problems (e.g., shadows and poles, ladders)
D-2-f. Identify and use Pythagorean triples in right triangles to find lengths of the unknown side
E-1-g. Determine the geometric mean between two numbers and use it to solve problems (e.g., find the
lengths of segments in right triangles)
H-1-a. Apply properties of 45°-45°-90° and 30°-60°-90° triangles to determine lengths of sides of
triangles
H-1-b. Find the sine, cosine, and tangent ratios of acute angles given the side lengths of right triangles
H-1-c. Use trigonometric ratios to find the sides or angles of right triangles and to solve real-world
problems (e.g., use angles of elevation and depression to find missing measures)
Unit 8: Circles
Activities:
Resources:
Concepts and Skills:
Strategies:
Timeline:
New State Standards:
2weeks/10 days
Vocabulary:
Circle,
Radius,
Diameter,
Chord,
Secant,
Tangent,
Central Angle,
Minor Arc,
Major Arc,
Semicircle,
Inscribed Angle,
Intercepted Arc,
Standard Equation of a
Circle
Locus
Arc Length
Focus
Directrix
G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the
undefined notions of point, line, distance along a line, and distance around a circular arc.
G.CO.9 Prove theorems about lines and angles.
G.CO.10 Prove theorems about triangles
G.CO.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles
are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms
with congruent diagonals.
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in
geometric figures.
G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★
G.GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the
square to find the center and radius of a circle given by an equation.
G.GPE.2 Derive the equation of a parabola given a focus and directrix.
G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a
figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, 3) lies
on the circle centered at the origin and containing the point (0, 2).
G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and uses them to solve geometric problems
(e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a
quadrilateral inscribed in a circle.
G.C.4 (+) Construct a tangent line from a point outside a given circle to the circle.
G.C.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius,
and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a
sector..
College Readiness:
Range(24-27)Properties of Plane Figures: Recognize Pythagorean triples*
Range(24-27) Functions: Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of
given side lengths
Range(28-32) Graphical Representations: Use the distance formula
Range(28-32) Graphical Representations: Use properties of parallel and perpendicular lines to determine an equation



Use properties of segments
and lines that intersect
circles (intersecting
inside/outside/on the
circle)
Apply angle relationships
with circles (angle is
inside/outside/on the circle
Graph and find equations
of circles in the coordinate
plane.
Postulates and
Theorems:
Point of Tangency
Theorem, Two Tangents
Theorem, Arc Addition
Postulate, Two Chords
Theorem, Perpendicular
Chords Theorem,
Congruent Chords
Theorem, Inscribed
Angle Theorem,
Inscribed Right Triangle
Theorem, Inscribed
Quadrilateral Theorem,
Angles on a Circle
Theorem, Angles Inside a
Circle Theorem, Angles
Outside a Circle
Theorem, Parts of Chords
Theorem, Two Secants
Theorem, Secant and
Tangent Theorem,
Geometry Curriculum Map
Modified: May 27, 2014
of a line or coordinates of a point
Range(28-32) Basic Operations & Applications: Solve word problems containing several rates, proportions, or
percentages
Range(28-32) Properties of Plane Figures: Apply properties of 30°-60°-90°, 45°-45°-90°, similar, and congruent
triangles
Range(28-32) Properties of Plane Figures: Use the Pythagorean theorem
Range(28-32) Functions: Apply basic trigonometric ratios to solve right-triangle problems
NCTM:
Algebra:

use symbolic algebra to represent and explain mathematical relationships;

judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by
technology.

draw reasonable conclusions about a situation being modeled.
Geometry:

analyze properties and determine attributes of two- and three-dimensional objects;

explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric
objects, make and test conjectures about them, and solve problems involving them;

establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by
others;

use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze
geometric situations;

investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian
coordinates.

use trigonometric relationships to determine lengths and angle measures..

use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as
art and architecture.

use geometric models to gain insights into, and answer questions in, other areas of mathematics;
Measurement:

make decisions about units and scales that are appropriate for problem situations involving measurement.

analyze precision, accuracy, and approximate error in measurement situations;

use unit analysis to check measurement computations.
Problem Solving:

build new mathematical knowledge through problem solving;

solve problems that arise in mathematics and in other contexts;

apply and adapt a variety of appropriate strategies to solve problems;

monitor and reflect on the process of mathematical problem solving.
Reasoning and Proof:

recognize reasoning and proof as fundamental aspects of mathematics;

make and investigate mathematical conjectures;

select and use various types of reasoning and methods of proof.
Connections:

recognize and use connections among mathematical ideas; make and investigate mathematical conjectures;

understand how mathematical ideas interconnect and build on one another to produce a coherent whole;

recognize and apply mathematics in contexts outside of mathematics.
Quality Core:
A-1-c. Write linear equations in standard form and slope-intercept form when given two points, a point
and the slope, or the graph of the equation
A-1-d. Recognize the concept of slope as a rate of change and determine the slope when given the
equation of a line in standard form or slope-intercept form, the graph of a line, two points, or a verbal
description
Geometry Curriculum Map
Modified: May 27, 2014
A-1-e. Graph a linear equation using a table of values, x- and y-intercepts, or slope-intercept form
B-1- all
C-1- a. Use definitions, basic postulates, and theorems about points, segments, lines, angles, and
planes to write proofs and to solve problems
C-1- d. Use various methods to prove that two lines are parallel or perpendicular (e.g., using
coordinates, angle measures)
C-1- g. Use the principle that corresponding parts of congruent triangles are congruent to solve
problems
D-1- a. Identify and model plane figures, including collinear and noncollinear points, lines, segments,
rays, and angles using appropriate mathematical symbols
D-1- b. Identify vertical, adjacent, complementary, and supplementary angle pairs and use them to
solve problems (e.g., solve equations, use in proofs)
D-1-c. Identify corresponding, same-side interior, same-side exterior, alternate interior, and alternate
exterior angle pairs formed by a pair of parallel lines and a transversal and use these special angle
pairs to solve problems (e.g., solve equations, use in proofs)
D-1-e. Locate, describe, and draw a locus in a plane or space
D-1-f. Apply properties and theorems of parallel and perpendicular lines to solve problems
D-2-e. Apply the Pythagorean Theorem and its converse to triangles to solve mathematical and realworld problems (e.g., shadows and poles, ladders)
D-2-f. Identify and use Pythagorean triples in right triangles to find lengths of the unknown side
D-2-g. Identify and classify quadrilaterals, including parallelograms, rectangles, rhombi, squares, kites,
trapezoids, and isosceles trapezoids, using their properties
D-2-i. Apply the Angle Sum Theorem for triangles and polygons to find interior and exterior angle
measures given the number of sides, to find the number of sides given angle measures, and to solve
real-world problems
D-2-j. Apply the Isosceles Triangle Theorem and its converse to triangles to solve mathematical and
real-world problems
D-3-a. Identify and define line segments associated with circles (e.g., radii, diameters, chords, secants,
tangents)
D-3-b. Determine the measure of central and inscribed angles and their intercepted arcs
D-3-c. Find segment lengths, angle measures, and intercepted arc measures formed by chords,
secants, and tangents intersecting inside and outside circles
E-1-b. Identify congruent figures and their corresponding parts
F-1-d. Find arc lengths and circumferences of circles from given information (e.g., radius, diameter,
coordinates)
F-1.e. Find the area of a circle and the area of a sector of a circle from given information (e.g., radius,
diameter, coordinates)
G-1-a. Use slope to distinguish between and write equations for parallel and perpendicular lines
G-1-b. Apply the midpoint and distance formulas to points and segments to find midpoints, distances,
and missing information
G-1-c. Use coordinate geometry to solve problems about geometric figures (e.g., segments, triangles,
quadrilaterals)
G-1-d. Write equations for circles in standard form and solve problems using equations and graphs
H-1-a. Apply properties of 45°-45°-90° and 30°-60°-90° triangles to determine lengths of sides of
triangles
H-1-b. Find the sine, cosine, and tangent ratios of acute angles given the side lengths of right triangles
H-1-c. Use trigonometric ratios to find the sides or angles of right triangles and to solve real-world
problems (e.g., use angles of elevation and depression to find missing measures)
Geometry Curriculum Map
Modified: May 27, 2014
Unit 9: Special Quadrilaterals
Activities:
Sketchpad Lab Quadrilaterals
Timeline:
New State Standards:
2 weeks/10 days
Vocabulary:
Parallelogram,
Rhombus,
Rectangle,
Square,
Trapezoid,
Isosceles Trapezoid,
Kite
Lines of Symmetry
Rotational Symmetry
G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that
carry it onto itself.
G.CO.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles
are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms
with congruent diagonals.
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in
geometric figures.
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. ★
G.GPE.4 Use coordinates to prove simple geometric theorems algebraically
G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and uses them to solve geometric problems
(e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
College Readiness:
Range(24-27)Properties of Plane Figures: Recognize Pythagorean triples*
Range(28-32) Graphical Representations: Use the distance formula
Range(28-32) Graphical Representations: Use properties of parallel and perpendicular lines to determine an equation
of a line or coordinates of a point
Range(28-32) Basic Operations & Applications: Solve word problems containing several rates, proportions, or
percentages
Range(28-32) Properties of Plane Figures: Apply properties of 30°-60°-90°, 45°-45°-90°, similar, and congruent
triangles
Range(28-32) Properties of Plane Figures: Use the Pythagorean theorem
NCTM:
Algebra:

use symbolic algebra to represent and explain mathematical relationships;

judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by
technology.

draw reasonable conclusions about a situation being modeled.
Geometry:

analyze properties and determine attributes of two- and three-dimensional objects;

explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric
objects, make and test conjectures about them, and solve problems involving them;

establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by
others;

use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze
geometric situations;

investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian
coordinates.

use trigonometric relationships to determine lengths and angle measures..

use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as
art and architecture.

use geometric models to gain insights into, and answer questions in, other areas of mathematics;
Measurement:

make decisions about units and scales that are appropriate for problem situations involving measurement.
Resources:
Concepts and Skills:




Use angle relationships
within quadrilaterals
Use theorems to prove
special quadrilaterals
Use properties and
theorems of special
quadrilaterals to
algebraically solve for
missing lengths or angles
Prove special
quadrilaterals in the
coordinate plane
Strategies:
Postulates and
Theorems:
Parallelogram Theorems,
Rhombus Corollary and
Theorems, Rectangle
Corollary and Theorems,
Square Corollary and
Theorems, Trapezoid
Theorems, Kite
Theorems,
Geometry Curriculum Map
Modified: May 27, 2014

analyze precision, accuracy, and approximate error in measurement situations;

use unit analysis to check measurement computations.
Problem Solving:

build new mathematical knowledge through problem solving;

solve problems that arise in mathematics and in other contexts;

apply and adapt a variety of appropriate strategies to solve problems;

monitor and reflect on the process of mathematical problem solving.
Reasoning and Proof:

recognize reasoning and proof as fundamental aspects of mathematics;

make and investigate mathematical conjectures;

select and use various types of reasoning and methods of proof.
Connections:

recognize and use connections among mathematical ideas; make and investigate mathematical conjectures;

understand how mathematical ideas interconnect and build on one another to produce a coherent whole;

recognize and apply mathematics in contexts outside of mathematics.
Quality Core:
A-1-c. Write linear equations in standard form and slope-intercept form when given two points, a point
and the slope, or the graph of the equation
A-1-d. Recognize the concept of slope as a rate of change and determine the slope when given the
equation of a line in standard form or slope-intercept form, the graph of a line, two points, or a verbal
description
A-1-e. Graph a linear equation using a table of values, x- and y-intercepts, or slope-intercept form
B-1- all
C-1- a. Use definitions, basic postulates, and theorems about points, segments, lines, angles, and
planes to write proofs and to solve problems
C-1- d. Use various methods to prove that two lines are parallel or perpendicular (e.g., using
coordinates, angle measures)
C-1- g. Use the principle that corresponding parts of congruent triangles are congruent to solve
problems
C-1-i. Use properties of special quadrilaterals in a proof
D-1- a. Identify and model plane figures, including collinear and noncollinear points, lines, segments,
rays, and angles using appropriate mathematical symbols
D-1- b. Identify vertical, adjacent, complementary, and supplementary angle pairs and use them to
solve problems (e.g., solve equations, use in proofs)
D-1-c. Identify corresponding, same-side interior, same-side exterior, alternate interior, and alternate
exterior angle pairs formed by a pair of parallel lines and a transversal and use these special angle
pairs to solve problems (e.g., solve equations, use in proofs)
D-1-f. Apply properties and theorems of parallel and perpendicular lines to solve problems
D-2-e. Apply the Pythagorean Theorem and its converse to triangles to solve mathematical and realworld problems (e.g., shadows and poles, ladders)
D-2-f. Identify and use Pythagorean triples in right triangles to find lengths of the unknown side
D-2-g. Identify and classify quadrilaterals, including parallelograms, rectangles, rhombi, squares, kites,
trapezoids, and isosceles trapezoids, using their properties
E-1-b. Identify congruent figures and their corresponding parts
E-1-g. Determine the geometric mean between two numbers and use it to solve problems (e.g., find the
lengths of segments in right triangles)
G-1-a. Use slope to distinguish between and write equations for parallel and perpendicular lines
G-1-b. Apply the midpoint and distance formulas to points and segments to find midpoints, distances,
and missing information
Geometry Curriculum Map
Modified: May 27, 2014
G-1-c. Use coordinate geometry to solve problems about geometric figures (e.g., segments, triangles,
quadrilaterals)
H-1-a. Apply properties of 45°-45°-90° and 30°-60°-90° triangles to determine lengths of sides of
triangles
H-1-b. Find the sine, cosine, and tangent ratios of acute angles given the side lengths of right triangles
H-1-c. Use trigonometric ratios to find the sides or angles of right triangles and to solve real-world
problems (e.g., use angles of elevation and depression to find missing measures)
Unit 10: Solids
Activities:
Resources:
Concepts and Skills:
Strategies:
Timeline:
New State Standards:
2 weeks/10 days
Vocabulary:
Net,
Polyhedron,
Face,
Edge,
Solid,
Platonic Solid,
Tetrahedron, Cube
(Hexahedron), Octahedron,
Dodecahedron,
Icosahedron,
Cross Section,
Prism,
Cylinder,
Pyramid,
Cone,
Sphere,
Lateral Area
Surface Area,
Volume ,
Oblique,
Great Circle,
Hemisphere
G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the
undefined notions of point, line, distance along a line, and distance around a circular arc.
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in
geometric figures.
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. ★
G.MG.1 Use geometric shapes, their measures, and their properties to describe objects
G.MG.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile,
BTUs per cubic foot).*
G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical
constraints or minimize cost; working with typographic grid systems based on ratios).*
G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a
cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. ★
G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify threedimensional objects generated by rotations of two-dimensional objects.

College Readiness:
Range(24-27)Properties of Plane Figures: Recognize Pythagorean triples*
Range(24-27) Measurement: Compute the area and circumference of circles after identifying necessary information
Range(24-27) Measurement: Compute the area of triangles and rectangles when one or more additional simple steps

are required
Range(24-27) Measurement: Compute the perimeter of simple composite geometric figures with unknown side
lengths *
Range(24-27) Functions: Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of
given side lengths
Range(28-32) Basic Operations & Applications: Solve word problems containing several rates, proportions, or
percentages
Range(28-32) Properties of Plane Figures: Apply properties of 30°-60°-90°, 45°-45°-90°, similar, and congruent
triangles
Range(28-32) Properties of Plane Figures: Use the Pythagorean theorem
Range(28-32) Functions: Apply basic trigonometric ratios to solve right-triangle problems
Range(28-32) Measurement: Use relationships involving area, perimeter, and volume of geometric figures to
compute another measure
Range(33-36) Measurement: Compute the area of composite geometric figures when planning or visualization is
required






Create or identify a net of a
solid.
Use Euler’s Theorem for
determining the number of
faces, edges, and verities
of a polyhedron.
Identify regular polyhedra.
Solve surface area and
volumes of prisms,
cylinders, pyramids, cones,
and spheres.
Use Cavalieri’s principle
for cross sections and areas
of solids
Use scale factors for
similar solids given length,
area, and volume.
Identify cross sections of
solids.
Find lateral area and base
area of solids
Postulates and
Theorems:
Euler’s Theorems for
Polyhedra, Surface Area
Formulas, Volume
Formulas, Cavalieri’s
Principle, Volume
Addition Postulate,
Similar Solids Theorem
Geometry Curriculum Map
Modified: May 27, 2014
NCTM:
Algebra:

use symbolic algebra to represent and explain mathematical relationships;

judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by
technology.

draw reasonable conclusions about a situation being modeled.
Geometry:

analyze properties and determine attributes of two- and three-dimensional objects;

explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric
objects, make and test conjectures about them, and solve problems involving them;

establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by
others;

use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze
geometric situations;

investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian
coordinates.

use trigonometric relationships to determine lengths and angle measures..

use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as
art and architecture.

use geometric models to gain insights into, and answer questions in, other areas of mathematics;
Measurement:

make decisions about units and scales that are appropriate for problem situations involving measurement.

analyze precision, accuracy, and approximate error in measurement situations;

use unit analysis to check measurement computations.
Problem Solving:

build new mathematical knowledge through problem solving;

solve problems that arise in mathematics and in other contexts;

apply and adapt a variety of appropriate strategies to solve problems;

monitor and reflect on the process of mathematical problem solving.
Reasoning and Proof:

recognize reasoning and proof as fundamental aspects of mathematics;

make and investigate mathematical conjectures;

select and use various types of reasoning and methods of proof.
Connections:

recognize and use connections among mathematical ideas;make and investigate mathematical conjectures;

understand how mathematical ideas interconnect and build on one another to produce a coherent whole;

recognize and apply mathematics in contexts outside of mathematics.
Quality Core:
B-1- all
C-1- a. Use definitions, basic postulates, and theorems about points, segments, lines, angles, and
planes to write proofs and to solve problems
D-1- a. Identify and model plane figures, including collinear and non-collinear points, lines, segments,
rays, and angles using appropriate mathematical symbols
D-2-e. Apply the Pythagorean Theorem and its converse to triangles to solve mathematical and realworld problems (e.g., shadows and poles, ladders)
D-2-f. Identify and use Pythagorean triples in right triangles to find lengths of the unknown side
D-2-h. Identify and classify regular and non-regular polygons (e.g., pentagons, hexagons, heptagons,
octagons, nonagons, decagons, dodecagons) based on the number of sides, the angle measures, and
the side lengths
Geometry Curriculum Map
Modified: May 27, 2014
D-2-j. Apply the Isosceles Triangle Theorem and its converse to triangles to solve mathematical and
real-world problems
D-3-b. Determine the measure of central and inscribed angles and their intercepted arcs
D-3-c. Find segment lengths, angle measures, and intercepted arc measures formed by chords,
secants, and tangents intersecting inside and outside circles
D-3-d. Solve problems using inscribed and circumscribed polygons
D-4-a. Identify and classify prisms, pyramids, cylinders, cones, and spheres and use their properties to
solve problems
D-4-b. Describe and draw cross sections of prisms, cylinders, pyramids, and cones
E-1-b. Identify congruent figures and their corresponding parts
E-1-h. Identify and give properties of congruent or similar solids
F-1-a. Find the perimeter and area of common plane figures, including triangles, quadrilaterals, regular
polygons, and irregular figures, from given information using appropriate units of measurement
F-1-b. Manipulate perimeter and area formulas to solve problems (e.g., finding missing lengths)
F-1-c. Use area to solve problems involving geometric probability
F-1-d. Find arc lengths and circumferences of circles from given information (e.g., radius, diameter,
coordinates)
F-1-e. Find the area of a circle and the area of a sector of a circle from given information (e.g., radius,
diameter, coordinates)
F-2-a. Find the lateral area, surface area, and volume of prisms, cylinders, cones, and pyramids in
mathematical and real-world settings
F-2-b. Use cross sections of prisms, cylinders, pyramids, and cones to solve volume problems
F-2-c. Find the surface area and volume of a sphere in mathematical and real-world settings
H-1-a. Apply properties of 45°-45°-90° and 30°-60°-90° triangles to determine lengths of sides of
triangles
H-1-b. Find the sine, cosine, and tangent ratios of acute angles given the side lengths of right triangles
H-1-c. Use trigonometric ratios to find the sides or angles of right triangles and to solve real-world
problems (e.g., use angles of elevation and depression to find missing measures)
Timeline:
Unit 11: Probability
2 weeks/10 days
New State Standards:
Vocabulary:
Event,
Outcome,
Sample Space,
Experimental Probability,
Theoretical Probability,
Complement of an Event,
Probability Distribution,
Frequency,
Factorial,
S.CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of
the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).
S.CP.2 Understand that two events A and B are independent if the probability of A and B occurring together is the
product of their probabilities, and use this characterization to determine if they are independent.
S.CP.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and
B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional
probability of B given A is the same as the probability of B.
S.CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each
object being classified. Use the two-way table as a sample space to decide if events are independent and to
approximate conditional probabilities. For example, collect data from a random sample of students in your school on
their favorite subject among math, science, and English. Estimate the probability that a randomly selected student
from your school will favor science given that the student is in tenth grade. Do the same for other subjects and
compare the results.
S.CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and
Activities:
Resources:
Strategies:
Concepts and Skills:






To calculate experimental
and theoretical probability
Construct and use event
trees (tree diagrams)
To make and use
frequency tables and
probability distributions
Compute factorials
To use counting principle,
permutations and
combinations to find
probabilities
To identify independent
Postulates and
Theorems:
Probability Formulas,
Counting Principles,
Permutation Formula,
Combination Formulas
Geometry Curriculum Map
Modified: May 27, 2014
Permutation,
Combination,
Counting Principle,
Compound Probability,
Mutually Exclusive,
Independent Events,
Dependent Events,
Conditional Probability,
Event Tree,
Expected Value,
Randomness
Venn Diagrams
everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of
being a smoker if you have lung cancer.
S.CP.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and
interpret the answer in terms of the model.
S.CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the
model.
S.CP.8 (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) =
P(B)P(A|B), and interpret the answer in terms of the model.
S.CP.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems.
S.MD.6 (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
S.MD.7 (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling
a hockey goalie at the end of a game).
College Readiness:
(Range 13-15) Probability, Statistics, & Data Analysis: Perform a single computation using information from a table or
chart
(Range 16-19) Probability, Statistics, & Data Analysis: Perform computations on data from tables and graphs
(Range 16-19) Probability, Statistics, & Data Analysis: Use the relationship between the probability of an event and the
probability of its complement
(Range 16-19) Probability, Statistics, & Data Analysis: Read tables and graphs
(Range 20-23) Probability, Statistics, & Data Analysis: Determine the probability of a simple event
(Range 20-23) Probability, Statistics, & Data Analysis: Determine the probability of a simple event
(Range 24-27) Probability, Statistics, & Data Analysis: Compute straightforward probabilities for common situations
(Range 28-32) Probability, Statistics, & Data Analysis: Interpret and use information from figures, tables, and graphs
(Range 28-32) Probability, Statistics, & Data Analysis: Apply counting techniques
(Range 23-36) Probability, Statistics, & Data Analysis: Exhibit knowledge of conditional and joint probability
NCTM:
Data Analysis, and Probability

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

Select and use appropriate statistical methods to analyze data

Develop and evaluate inferences and predictions that are based on data

Understand and apply basic concepts of probability
Number and Operations

Develop an understanding of permutations and combinations as counting techniques.

Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by
technology
Quality Core:
A-1- f. Find the probability of a simple event
B-1- all
F-1-c. Use area to solve problems involving geometric probability






and dependent events
To find compound
probabilities
To construct and use
probability models
To construct and use
probability models
To understand random
numbers
To use probabilities in
decision-making
Construct and interpret
Venn Diagrams