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Geometry Curriculum Map 7.1
Interior Angle Sum
Theorem
Define the Angle Sum
Theorem.
Illustrate interior angles with
the Angle Sum Theorem with
examples.
7.2
Exterior Angle Sum
Theorem
Apply the Angle Sum Theorem
to convex polygons.
Define the Angle Sum
Theorem.
Quadrilaterals
Illustrate exterior angles with
the Angle Sum Theorem with
examples.
7.3
Using Interior and
Exterior Angles to
Solve Problems
Apply the Angle Sum Theorem
to convex polygons.
Apply the Angle Sum Theorem
to convex polygons.
Combine interior and exterior
angles to solve problems.
Solve problems using the
Angle Sum Theorem.
7.4
Quadrilaterals
Define and identify
quadrilaterals.
Distinguish between types of
quadrilaterals.
8.G.A.5 Use informal arguments to establish facts
about the angle sum and exterior angle of
triangles, about the angles created when parallel
lines are cut by a transversal, and the angle-angle
criterion for similarity of triangles. For example,
arrange three copies of the same triangle so that
the sum of the three angles appears to form a line,
and give an argument in terms of transversals why
this is so.
8.G.A.5 Use informal arguments to establish facts
about the angle sum and exterior angle of
triangles, about the angles created when parallel
lines are cut by a transversal, and the angle-angle
criterion for similarity of triangles. For example,
arrange three copies of the same triangle so that
the sum of the three angles appears to form a line,
and give an argument in terms of transversals why
this is so.
8.G.A.5 Use informal arguments to establish facts
about the angle sum and exterior angle of
triangles, about the angles created when parallel
lines are cut by a transversal, and the angle-angle
criterion for similarity of triangles. For example,
arrange three copies of the same triangle so that
the sum of the three angles appears to form a line,
and give an argument in terms of transversals why
this is so.
2.G.A.1 Recognize and draw shapes having
specified attributes, such as a given number of
angles or a given number of equal faces.1 Identify
triangles, quadrilaterals, pentagons, hexagons, and
cubes.
8.G.A.5 Use informal arguments to establish facts
about the angle sum and exterior angle of
triangles, about the angles created when parallel
lines are cut by a transversal, and the angle-angle
Geometry Curriculum Map 7.5
The Parallelogram
7.6
Parallelogram Proofs
Identify and label the parts of a
parallelogram.
Use midpoints to construct
parallelograms.
Prove that opposite sides of a
parallelogram are congruent.
Prove that opposite angles of a
parallelogram are congruent.
Prove that rectangles are
parallelograms with congruent
diagonals.
Prove that a parallelogram is a
rectangle if and only if its
diagonals are congruent.
criterion for similarity of triangles. For example,
arrange three copies of the same triangle so that
the sum of the three angles appears to form a line,
and give an argument in terms of transversals why
this is so.
G-CO.11 Prove theorems about parallelograms.
G-SRT.B.5 Use congruence and similarity criteria
for triangles to solve problems and to prove
relationships in geometric figures.
G-CO.11 Prove theorems about parallelograms.
Geometry Curriculum Map 7.7
Rhombus Proofs
Prove that if a parallelogram
has two consecutive sides
congruent, it is a rhombus.
G-SRT.B.5 Use congruence and similarity criteria
for triangles to solve problems and to prove
relationships in geometric figures.
G-CO.11 Prove theorems about parallelograms.
Prove that a parallelogram is a
rhombus if and only if each
diagonal bisects a pair of
opposite angles.
7.8
7.9
7.10
7.11
Prove that a parallelogram is a
rhombus if and only if the
diagonals are perpendicular.
Algebraic Proofs
Prove or disprove that a figure
involving
defined by four given points in
Quadrilaterals
the coordinate plane is a
rectangle.
Prove or disprove that the
point (1, sqrt 3) lies on the
circle centered at the origin
and containing the point (0,2).
Applications Involving Apply algebra to solve
Quadrilaterals
problems involving
quadrilaterals.
Modeling Real-Life
Model real-life situations using
Situations with
quadrilaterals.
Quadrilaterals
Solve design problems using
quadrilaterals.
Module Review
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-MG.A.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).
Geometry Curriculum Map 8.1
Rigid Motion in a
Plane
Define and name
transformations.
Examine how to preserving
angles and lengths in
transformations.
Transformations
Identifying transformations in
real life.
8.2
Identifying
Identify types of
Transformations
transformations between
between Two Figures figures.
Examine examples of multiple
transformations of figures.
Determine transformations
between two figures.
G-CO.A.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.B.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.A.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.A.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.B.6 Use geometric descriptions of rigid
Geometry Curriculum Map 8.3
Constructing Multiple
Transformations
Review types of
transformations.
Analyze multiple
transformations on figures.
Construct multiple
transformations on figures
using tracing paper, graphing
paper or software.
8.4
Rotational and
Reflectional
Symmetry
Define rotational and
reflectional symmetry.
Illustrate rotational and
reflectional symmetry through
examples.
Create examples that
distinguish between rotational
and reflectional symmetry.
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.A.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.A.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.B.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.
4.G.A.3 Recognize a line of symmetry for a twodimensional figure as a line across the figure such
that the figure can be folded along the line into
matching parts. Identify line-symmetric figures and
draw lines of symmetry.
Geometry Curriculum Map 8.5
Translations
Solve problems involving
rotational and reflectional
symmetry.
Define translations in the
coordinate plane.
Identify properties of
translations.
Transformations using vectors.
Solving problems involving
translations.
G-CO.A.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.A.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.
Geometry Curriculum Map 8.6
Transformation
Problem Solving
Review rotations, reflections
and translations in the
coordinate plane.
Distinguish between different
transformations.
Solve problems using
transformations.
G-CO.A.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.A.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.B.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.
8.7
Tessellations
Define tessellations and their
use in Geometry.
Generate tessellations using
tools such as paper and
software.
Geometry Curriculum Map 8.8
8.9
Using Tessellations
to Model Real-Life
Problems
Review the definition of
tessellations and how they are
made.
Applications of
Transformations
Analyze tessellations in reallife scenarios.
Review different types of
transformations.
Distinguish between the types
of transformations.
Solve real-life problems
involving transformations.
MP.3 Construct viable arguments and critique the
reasoning of others.
MP.5 Use appropriate tools strategically.
G-CO.A.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.A.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.
8.10
Creating Frieze
Patterns
Define frieze patterns
Create different frieze patterns
using transformations.
Research uses of frieze
patterns in art, architecture,
etc.
8.11
Module Review
Geometry Curriculum Map 9.1
Parts of a Circle
Identify the parts of a circle.
Examine the relationship
between the parts of a circle.
9.2
Circumference and
Area of a Circle
Define the area and
circumference of a circle.
Parts of a Circle
Distinguish between the area
and circumference of circle
problems.
Solve problems involving the
area and circumference of a
circle.
9.3
Arcs and Sectors
9.4
Circumference and
Arc Length
Define arc, minor arc, major
arc, semi-circle, and chord.
Name and identify arcs and
chords and state their
relationship.
Use the arc addition postulate
to solve problems.
Solve problems using the
properties of chords and minor
arcs in congruent circles.
Calculate circumference of a
circle and the length of a
circular arc.
4.G.A.1 Draw points, lines, line segments, rays,
angles (right, acute, obtuse), and perpendicular
and parallel lines. Identify these in two-dimensional
figures.
MP.5 Use appropriate tools strategically.
7.G.B.4 Know the formulas for the area and
circumference of a circle and use them to solve
problems; give an informal derivation of the
relationship between the circumference and area of
a circle.
G-GMD.A.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-C.B.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
Geometry Curriculum Map 9.5
Tangent to a Circle
Use circumference and arc
length to solve real life
problems.
Identify the tangent of a circle.
measure of the angle as the constant of
proportionality; derive the formula for the area of a
sector.
G-C.A.4 (+) Construct a tangent line from a point
outside a given circle to the circle.
Construct a tangent line from a
point outside of a circle using
tools such as compass,
straightedge and software.
Examine the properties of
tangent lines.
9.6
Measuring Angles
with Radians and
Degrees
Solve problems involving the
tangent of a circle.
Define angle measurements
with radians vs degrees.
Convert angles in radian
measure to degree measure.
9.7
Inscribed and
Circumscribed
Angles
9.8
Inscribed Figures in
Circles
Convert angles in degree
measure to radian measure.
Define inscribed and
circumscribed angles in
circles.
Describe the relationships
among inscribed angles, radii
and chords.
Use the inscribed angle
theorem to solve problems
algebraically.
Describe inscribed figures
inside of a circle.
Draw inscribed figures such as
G-C.B.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.
G-C.A.2 Identify and describe relationships among
inscribed angles, radii, and chords. Include the
relationship between central, inscribed, and
circumscribed angles; inscribed angles on a
diameter are right angles; the radius of a circle is
perpendicular to the tangent where the radius
intersects the circle.
G-CO.D.13 Construct an equilateral triangle, a
square, and a regular hexagon inscribed in a circle.
G-C.A.3 Construct the inscribed and circumscribed
Geometry Curriculum Map 9.9
Finding Angles
Involving Tangents
and Circles
triangles, squares and
hexagons in a circle using
tools such as straightedge,
compass or software.
Apply tangents in relation to
circles.
Illustrate angles formed from
tangents on circles.
Solve problems involving
angles formed from tangent
lines on circles.
9.10
9.11
Area
10.1
Equation of a Circle
circles of a triangle, and prove properties of angles
for a quadrilateral inscribed in a circle.
G-C.A.2 Identify and describe relationships among
inscribed angles, radii, and chords. Include the
relationship between central, inscribed, and
circumscribed angles; inscribed angles on a
diameter are right angles; the radius of a circle is
perpendicular to the tangent where the radius
intersects the circle.
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).
Write the equation of a circle in G-GPE.A.1 Derive the equation of a circle of given
the coordinate plane.
center and radius using the Pythagorean Theorem;
Use the equation of a circle to complete the square to find the center and radius
graph the circle and solve
of a circle given by an equation.
related problems.
Module Review
Perimeter of
Polygons
Find the perimeter of various
polygons.
Find the perimeter of polygons
in the coordinate plane.
G.MG.1 Use geometric shapes, their measures,
and their properties to describe objects (e.g.,
modeling a tree trunk or a human torso as a
cylinder).
G-GPE.B.7 Use coordinates to compute perimeters
of polygons and areas of triangles and rectangles,
Geometry Curriculum Map 10.2
Area of Polygons
Find the area of various
polygons.
Find the area of polygons in
the coordinate plane.
10.3
Sector Area
Find the area of a sector.
Find the area of a segment.
10.4
Calculating Area
Find the area of unknown
figures.
10.5
Discovering Solids
10.6
Cubes & Spheres
Use density to calculate other
quantities related to it and
interpret these answers in
terms of their contexts.
Define and classify solids.
10.7
Pyramids & Cones
Find surface area of a cone.
10.8
Cylinders & Prisms
Find surface area of a
pyramid.
e.g., using the distance formula.*
G.MG.1 Use geometric shapes, their measures,
and their properties to describe objects (e.g.,
modeling a tree trunk or a human torso as a
cylinder).
G-GPE.B.7 Use coordinates to compute perimeters
of polygons and areas of triangles and rectangles,
e.g., using the distance formula.*
G-HSG.C.B.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.
G-MG.A.2 Apply concepts of density based on
area and volume in modeling situations (e.g.,
persons per square mile, BTUs per cubic foot).★
CCSS.Math.Content.7.G.B.6 Solve real-world and
mathematical problems involving area, volume and
surface area of two- and three-dimensional objects
composed of triangles, quadrilaterals, polygons,
cubes, and right prisms.
CCSS.Math.Content.7.G.B.6 Solve real-world and
mathematical problems involving area, volume and
surface area of two- and three-dimensional objects
composed of triangles, quadrilaterals, polygons,
cubes, and right prisms.
CCSS.Math.Content.7.G.B.6 Solve real-world and
mathematical problems involving area, volume and
surface area of two- and three-dimensional objects
Geometry Curriculum Map 10.9
Unit Conversions
10.10 Area Applications
10.11
composed of triangles, quadrilaterals, polygons,
cubes, and right prisms.
Find surface area of a prism.
CCSS.Math.Content.7.G.B.6 Solve real-world and
mathematical problems involving area, volume and
surface area of two- and three-dimensional objects
composed of triangles, quadrilaterals, polygons,
cubes, and right prisms.
Find surface area of a cylinder. CCSS.Math.Content.7.G.B.6 Solve real-world and
mathematical problems involving area, volume and
surface area of two- and three-dimensional objects
composed of triangles, quadrilaterals, polygons,
cubes, and right prisms.
Module Review
11.1
Introduction to
Volume
11.2
Volume of Cubes
Define volume.
Analyze volume of objects
problems through examples.
Define the volume of a cube
formula.
Volume
Analyze volume examples with
cube.
Solve problems involving the
volume of cube.
11.3
Volume of Prisms
"Define the volume of a prism
formula.
Analyze volume examples with
prisms.
Solve problems involving the
CCSS.Math.Content.6.G.A.2 Find the volume of a
right rectangular prism with fractional edge lengths
by packing it with unit cubes of the appropriate unit
fraction edge lengths, and show that the volume is
the same as would be found by multiplying the
edge lengths of the prism. Apply the formulas V = l
w h and V = b h to find volumes of right rectangular
prisms with fractional edge lengths in the context of
solving real-world and mathematical problems.
CCSS.Math.Content.7.G.B.6 Solve real-world and
mathematical problems involving area, volume and
surface area of two- and three-dimensional objects
composed of triangles, quadrilaterals, polygons,
cubes, and right prisms.
Geometry Curriculum Map 11.4
Volume of
Rectangular Prisms
volume of prisms.
Define the volume of a
rectangular prism formula.
Distinguish volume examples
with prisms vs rectangular
prisms.
11.5
Volume of Cylinders
Solve problems involving the
volume of rectangular prisms.
Define the volume of cylinders
formula.
Examine problems that involve
the volume of cylinder.
Apply dissection arguments,
Cavalieri’s Principle and
informal limits to solve volume
problems.
11.6
Volume of Spheres
Solve volume problems
involving the volume of
cylinders.
Define the volume of sphere
formula.
Examine problems that involve
the volume of sphere.
CCSS.Math.Content.7.G.B.6 Solve real-world and
mathematical problems involving area, volume and
surface area of two- and three-dimensional objects
composed of triangles, quadrilaterals, polygons,
cubes, and right prisms.
G-HSG.GMD.A.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-HSG.GMD.A.2 (+) Give an informal argument
using Cavalieri's principle for the formulas for the
volume of a sphere and other solid figures.
G-HSG.GMD.A.3 Use volume formulas for
cylinders, pyramids, cones, and spheres to solve
problems.*
G-HSG.GMD.A.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.
Solve volume problems
G-HSG.GMD.A.2 (+) Give an informal argument
involving the volume of sphere. using Cavalieri's principle for the formulas for the
volume of a sphere and other solid figures.
G-HSG.GMD.A.3 Use volume formulas for
cylinders, pyramids, cones, and spheres to solve
Geometry Curriculum Map problems.*
11.7
Volume of Cones
Define the volume of cones
formula.
G-HSG.GMD.A.1 Give an informal argument for
the formulas for the circumference of a circle, area
of a circle, volume of a cylinder, pyramid, and
Analyze problems involving the cone. Use dissection arguments, Cavalieri's
volume of cones.
principle, and informal limit arguments.
Solve problems that involve
finding the volume of cones.
11.8
Volume of Pyramids
G-HSG.GMD.A.3 Use volume formulas for
cylinders, pyramids, cones, and spheres to solve
problems.*
Define the volume of pyramids G-HSG.GMD.A.1 Give an informal argument for
formula.
the formulas for the circumference of a circle, area
of a circle, volume of a cylinder, pyramid, and
Analyze problems involving the cone. Use dissection arguments, Cavalieri's
volume of pyramids.
principle, and informal limit arguments.
Solve volume problems
involving pyramids.
11.9
Changing
Dimensions
G-HSG.GMD.A.2 (+) Give an informal argument
using Cavalieri's principle for the formulas for the
volume of a sphere and other solid figures.
Identify how changing
dimensions effect the resulting
figure.
G-HSG.GMD.A.2 (+) Give an informal argument
using Cavalieri's principle for the formulas for the
volume of a sphere and other solid figures.
G-HSG.GMD.A.3 Use volume formulas for
cylinders, pyramids, cones, and spheres to solve
problems.*
G-GMD.A.3 Use volume formulas for cylinders,
pyramids, cones, and spheres to solve problems.★
Geometry Curriculum Map 11.1O
Solving Real-Life
Volume Problems
11.11
Module Review
Probability
12.1
12.2
Simple Events
Using an Area Model
Solve real-life problems
involving the concept of
volume.
G-GMD.A.3 Use volume formulas for cylinders,
pyramids, cones, and spheres to solve problems.★
Review probability vocabulary.
Calculate the probabilities of
simple events.
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”).
Use an area model to solve
real-life problems and predict
outcomes.
S-CP.A.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.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.A.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.B.6 Find the conditional probability of A given
B as the fraction of B's outcomes that also belong
Geometry Curriculum Map to A, and interpret the answer in terms of the
model.
S- CP.B.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.
12.3
Using a Tree
Diagram
Use a tree diagram to
represent probability situations
and solve problems.
Compare theoretical and
experimental probability.
S-CP.B.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.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.A.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.B.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.B.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.B.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
Geometry Curriculum Map 12.4
Probability Models
Determine which tool (a tree
diagram, a systematic list, or
an area model) is better for
modeling certain situations.
Calculate some expected
values of a "fair" game.
in terms of the model.
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.A.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.B.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.B.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.
12.5
12.6
Unions, Intersections, Use the language for
and Complements
calculating probabilities of
unions, intersections, and
complements of events.
Use precise calculations to
figure out probabilities as well
as communicate findings.
Expected Value
Solve problems involving
chance.
S-CP.B.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.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.1. Describe events as subsets of a sample
space (the set of outcomes) using characteristics
Geometry Curriculum Map 12.7
Counting
12.8
Permutations
12.9
Combinations
12.10 Categorizing
Counting Problems
12.11 Module Review
Analyze and make conjectures
about outcomes.
Look for patterns around
expected value.
Use the Fundamental Principle
of Counting to count
permutations and other
outcomes when there are too
many to list.
Identify permutations.
Develop two formulas for
calculating the number of
permutations.
Identify combinations.
Compare permutations and
combinations.
Develop a method for counting
combinations.
Determine the counting
methods for situations that
involve order and repetition,
order and no repetition, no
order with repetition, and no
order without repetition.
(or categories) of the outcomes, or as unions,
intersections, or complements of other events (“or,”
“and,” “not”).
S-CP.9. (+) Use permutations and combinations to
compute probabilities of compound events and
solve problems.
S-CP.9. (+) Use permutations and combinations to
compute probabilities of compound events and
solve problems.
S-CP.9. (+) Use permutations and combinations to
compute probabilities of compound events and
solve problems.
S-CP.9. (+) Use permutations and combinations to
compute probabilities of compound events and
solve problems.