Download Math High School Geometry Standards Mastery Document 1.0

High School Mathematics/Geometry
Working Document July 22, 2016 PCBOE
Pike County School District
Standards Mastery Document
High School Geometry
Table of Contents
Congruence (G.CO)
4
Similarity, Right Triangles, and
Trigonometry (G.SRT)
17
Modeling with Geometry (G.MG)
28
Geometric Measurement and
Dimension (G.GMD)
31
Expressing Geometric Properties with
Equations (G.GPE)
35
Circles (G.C)
42
Conditional Probability and the Rules
of Probability (S.CP)
47
Using Probability to Make Decisions
(S.MD)
56
2
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Pike County School District
Standards Mastery Document
High School Geometry
The Standards Mastery Document is designed for educators by educators as a resource and tool
to help educators increase their depth of understanding of the Common Core Standards. This
document will enable teachers to plan College & Career Ready curriculum and classroom
instruction that promotes inquiry and higher levels of cognitive demand.
The Standards for Mathematical Practice describe varieties of expertise that mathematics
educators at all levels should seek to develop in their students. These practices rest on
important “processes and proficiencies” with longstanding importance in mathematics
education.
8 Mathematical Practices (MP):
MP 1. Make sense of problems and persevere in solving them.
MP 2. Reason abstractly and quantitatively.
MP 3. Construct viable arguments and critique the reasoning of others.
MP 4. Model with mathematics.
MP 5. Use appropriate tools strategically.
MP 6. Attend to precision.
MP 7. Look for and make use of structure.
MP 8. Look for and express regularity in repeated reasoning.
3
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Pike County School District
Standards Mastery Document
High School Geometry
Congruence (G.CO)
Standard: 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.
Enduring Skills:
MP.6 Attend to precision.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Understand definitions of
angle, circles, perpendicular
lines, parallel lines, and line
segments.
Understand definitions of
point, line, and arc.
Describe the terms, point, line,
and distance along a line in a
plane.
Identify points and lines in a
plane.
Define perpendicular lines,
parallel lines, line segments,
and angles.
Identify and name
perpendicular lines, parallel
lines, line segments, and
angles.
Define circle and the distance
around a circular arc.
Identify and name circular
arcs.
4
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Pike County School District
Standards Mastery Document
High School Geometry
Congruence (G.CO)
Standard: 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).
Enduring Skills:
MP.1 Make sense of problems and persevere in solving them.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.8 Look for and express regularity in repeated reasoning.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Understand the different
types of transformations
including translations,
reflections, rotations, and
dilations.
How are transformations
and functions related?
Represent transformations in
the plane.
Write functions to represent
transformations.
Compare transformations that
preserve distance and angle to
those that do not.
Use technology to represent
and compare rigid and size
transformations and size of
figures in a coordinate plane.
Use technologies such as
transparencies, geometry
software, interactive
whiteboards, and digital
visual presenters to
represent and compare rigid
and size transformations of
figures in a coordinate plane.
Compare transformations
that preserve distance and
angles to those that do not.
Describe and compare
function transformations on
a set of points as inputs to
produce a set of points as
outputs, to include
translations and horizontal
and vertical stretching.
5
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Pike County School District
Standards Mastery Document
High School Geometry
Congruence (G.CO)
Standard: G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the
rotations and reflections that carry it onto itself.
Enduring Skills:
MP.4 Model with mathematics.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Describe rotations and
What types of
reflections that carry a
transformations can be done rectangle, parallelogram,
in a plane?
trapezoid, or regular polygon
that maps each figure onto
itself.
Illustrate how a figure is
mapped onto itself by simply
using a transformation
without changing the shape
or size of the figure.
6
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Pike County School District
Standards Mastery Document
High School Geometry
Congruence (G.CO)
Standard: G.CO.4 Develop definitions of rotations, reflections and translations in terms of
angles, circles, perpendicular lines, parallel lines and line segments.
Enduring Skills:
MP.3 Construct viable arguments and critique the reasoning of others.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Define angles, circles,
perpendicular and parallel
lines, and line segments.
Define rotations, reflections,
and translations.
Develop definitions of
rotations, reflections, and
translations in terms of angles,
circles, perpendicular lines,
parallel lines, and line
segments.
Create accurate definitions
of rotations, reflections, and
translations.
7
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Pike County School District
Standards Mastery Document
High School Geometry
Congruence (G.CO)
Standard: 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.
Enduring Skills:
MP.3 Construct viable arguments and critique the reasoning of others.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.8 Look for and express regularity in repeated reasoning.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Draw a transformed figure.
How to transform a
geometric figure.
Identify the sequence of
transformations that carries
Specify the sequence of
transformations that were used a figure onto another.
to carry the given figure onto
the other.
8
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Pike County School District
Standards Mastery Document
High School Geometry
Congruence (G.CO)
Standard: G.CO.6 Use geometric descriptions of rigid motions to transform figure 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.
Enduring Skills:
MP.3 Construct viable arguments and critique the reasoning of others.
MP.5 Use appropriate tools strategically.
MP.7 Look for and make use of structure.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
How can I use rigid motions
to understand congruence?
Use geometric descriptions of
rigid motions to transform
figures.
Use geometric descriptions of
rigid motions to predict the
effect of a given motion on a
given figure.
Use rigid motions to
transform figures and predict
the effect the motion has on
a specific feature.
Determine when two figures
are congruent.
Determine if two figures are
congruent using the definition
of congruence in terms of rigid
motions.
9
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Pike County School District
Standards Mastery Document
High School Geometry
Congruence (G.CO)
Standard: 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.
Enduring Skills:
MP.3 Construct viable arguments and critique the reasoning of others.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
How can I use rigid motions
to understand congruence?
How to identify
corresponding angles and
sides after transformations.
Identify corresponding angles
and sides of two triangles.
Identify corresponding
angles and sides of triangles.
Justify congruency of two
triangles using transformations. Use corresponding sides and
angles to justify triangle
congruency.
Use the definition of
congruence in terms of rigid
motion to show that two
triangles are congruent if
corresponding pairs of sides
and corresponding pairs of
angles are congruent.
10
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Pike County School District
Standards Mastery Document
High School Geometry
S Congruence (G.CO)
tandard: G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, SSS) follow from
the definition of congruence in terms of rigid motions.
Enduring Skills:
MP.1 Make sense of problems and persevere in solving them.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Define congruence.
Understand triangle
congruence criteria (ASA,
SSS, and SAS).
Informally use rigid motions to
take angles to angles and
segments to segments.
Use dynamic geometric
software, straightedge, and
compass to take angles to
angles and segments to
segments.
Explain how the criteria for
triangle congruence (ASA,
SAS, SSS) follows from the
definition of congruence in
terms of rigid motions.
11
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Pike County School District
Standards Mastery Document
High School Geometry
Congruence (G.CO)
Standard: 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.
Enduring Skills:
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively
MP.3 Construct viable arguments and critique the reasoning of others.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
What strategy can be used
to prove geometric
theorems?
Understand the properties
of vertical angles, parallel
lines with transversals, all
angle relationships,
corresponding angles,
perpendicular lines, and
equidistant from endpoint.
Prove vertical angles are
congruent.
Prove corresponding angles are
congruent when two parallel
lines are cut by a transversal
and converse.
Prove alternate interior angles
are congruent when two
parallel lines are cut by a
transversal and converse.
Prove theorems pertaining
to lines and angles.
Prove vertical angles
congruent.
Prove when a transversal
crosses parallel lines,
alternate interior angles are
congruent and
corresponding angles are
congruent.
Prove points are on a
perpendicular bisector of a line Prove points on a
segment are exactly equidistant perpendicular bisector of a
line segment are exactly
from the segment’s endpoint.
equidistant from the
segment’s endpoints.
12
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Pike County School District
Standards Mastery Document
High School Geometry
Congruence (G.CO)
Standard: 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.
Enduring Skills:
MP.1 Make sense of problems and persevere in solving them.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Understand hypothesis and
conclusion of a theorem.
Understand properties of
triangles that can be used to
prove theorems.
Prove theorems pertaining to
triangles.
Design an argument to prove
theorems about triangles.
Prove the measures of interior
angles of a triangle have a sum
of 180o.
Analyze components of a
theorem.
Prove base angles of isosceles
triangles are congruent.
Prove theorems about
triangles.
Prove the segment joining
midpoints of two sides of a
triangle is parallel to the third
side and half the length.
Prove the medians of a triangle
meet at a point.
Analyze components of a
theorem.
13
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Pike County School District
Standards Mastery Document
High School Geometry
Congruence (G.CO)
Standard: 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.
Enduring Skills:
MP.1 Make sense of problems and persevere in solving them.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.7 Look for and make use of structure.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
What are the types of
quadrilaterals?
Understand properties of
parallelograms.
Prove theorems pertaining to
parallelograms.
Prove opposite sides of
parallelograms are congruent.
Prove opposite sides of
parallelograms are congruent.
Classify types of
quadrilaterals.
Explain theorems for
parallelograms and relate to
figures.
Prove the diagonals of a
parallelogram bisect each
other, and conversely,
rectangles are parallelograms
with congruent diagonals.
Use the principle that
corresponding parts of
congruent triangles are
congruent to solve problems.
Use properties of special
quadrilaterals in a proof.
14
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Pike County School District
Standards Mastery Document
High School Geometry
Congruence (G.CO)
Standard: 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.
Enduring Skills:
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Copy a segment.
What tools can we use to
construct geometric figures?
Copy an angle.
Perform geometric
constructions using a variety
of tools and methods.
Bisect a segment.
Bisect an angle.
Construct perpendicular lies,
including the perpendicular
bisector of a line segment.
Construct a line parallel to a
given line through a point not
on the line.
15
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Pike County School District
Standards Mastery Document
High School Geometry
Congruence (G.CO)
Standard: G.CO.13 Construct an equilateral triangle, a square and a regular hexagon inscribed
in a circle.
Enduring Skills:
MP.4 Model with mathematics.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
What tools can we use to
construct geometric figures?
Construct an equilateral
triangle so that each vertex of
the equilateral triangle is on
the same circle.
Construct an equilateral
triangle, square, and regular
hexagon inscribed in a circle.
Construct a square so that each
vertex of the square is on the
same circle.
Construct a regular hexagon so
that each vertex of the regular
hexagon is on the same circle.
16
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Standards Mastery Document
High School Geometry
Similarity, Right Triangles, and Trigonometry (G.SRT)
Standard: G.SRT.1a 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.
1b - Verify experimentally the properties of dilations given by a center and a scale factor.
b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Enduring Skills:
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively
MP.3 Construct viable arguments and critique the reasoning of others.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
How can transformations
help me to understand
similarity?
Define image, pre-image,
scale factor, center, and
similar figures as they relate
to transformations.
Verify experimentally that a
dilated image is similar to its
pre-image by showing
congruent corresponding
angles and proportional sides.
Verify experimentally that a
dilation takes a line not passing
through the center of the
dilation to a parallel line by
showing the lines are parallel.
Verify experimentally that
dilation leaves a line passing
through the center of the
dilation unchanged, by showing
that it is the same line.
Given a center and a scale
factor, verify experimentally,
that when dilating a figure in
a coordinate plane, a
segment of the pre-image
that does not pass through
the center of the dilation, is
parallel to it’s image when
the dilation is performed.
Given a center and a scale
factor, verify experimentally,
that when performing
dilations of a line segment,
the pre-image, the segment
which becomes the image is
no longer or shorter based
on the ratio given by the
scale factor.
17
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Pike County School District
Standards Mastery Document
High School Geometry
Similarity, Right Triangles, and Trigonometry (G.SRT)
Standard: 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.
Enduring Skills:
MP.1 Make sense of problems and persevere in solving them.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.6 Attend to precision.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Definition of similarity.
How are dilation
transformations and
similarity related?
Given two figures, decide if
they are similar by using the
definition of similarity in terms
of similarity transformations.
Explain that triangles are
similar if all pairs of
corresponding angles are
congruent and all
corresponding pairs of sides
are proportional.
18
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Pike County School District
Standards Mastery Document
High School Geometry
Similarity, Right Triangles, and Trigonometry (G.SRT)
Standard: G.SRT.3 Use the properties of similarity transformations to establish the AA criterion
for two triangles to be similar.
Enduring Skills:
MP.1 Make sense of problems and persevere in solving them.
MP.3 Construct viable arguments and critique the reasoning of others.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Extend the properties of
Understand the properties
similarity transformations to
of similarity transformations. the general case of any two
similar triangles to establish the
AA criterion for similarity of
triangles.
Recall the properties of
similarity and
transformations.
Establish the AA criterion for
similarity of triangles by
extending the properties of
similarity transformations to
the general case of any two
similar triangles.
19
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Pike County School District
Standards Mastery Document
High School Geometry
Similarity, Right Triangles, and Trigonometry (G.SRT)
Standard: 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.
Enduring Skills:
MP.3 Construct viable arguments and critique the reasoning of others.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Understand postulates and
theorems about triangles.
Prove theorems involving
similarity about triangles.
Use AA, SAS, SSS similarity
theorems to prove triangles are
similar.
Prove theorems involving
similarity about triangles.
Use triangle similarity to
prove other theorems about
triangles.
Prove a parallel line to one
side of a triangle divides the
other two proportionally,
and it’s converse.
Prove the Pythagorean
Theorem using triangle
similarity.
20
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Pike County School District
Standards Mastery Document
High School Geometry
Similarity, Right Triangles, and Trigonometry (G.SRT)
Standard: G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to
prove relationships in geometric figures.
Enduring Skills:
MP.1 Make sense of problems and persevere in solving them.
MP.3 Construct viable arguments and critique the reasoning of others.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Recall congruence and
similarity criteria for
triangles.
Use congruency and similarity
theorems for triangles to solve
problems.
Use congruency and similarity
theorems for triangles to prove
relationships in geometric
theorems.
Using similarity theorems,
students prove that two
triangles are congruent.
Prove geometric figures,
other than triangles, are
similar and/or congruent.
Prove geometric figures, other
than triangles, are similar
and/or congruent.
21
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Standards Mastery Document
High School Geometry
Similarity, Right Triangles, and Trigonometry (G.SRT)
Standards: 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.
Enduring Skills:
MP.3 Construct viable arguments and critique the reasoning of others.
MP.8 Look for and express regularity in repeated reasoning.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
How to name the sides of
right triangles.
Recognize that triangles are
similar.
Name the sides of right
triangles as related to an acute
angle.
Recognize that if two right
triangles have a pair of acute,
congruent angles, and the
triangles are similar.
Using a corresponding angle
of similar right triangles,
show that the relationships
of the side ratios are the
same, which leads to the
definition of trigonometric
ratios for acute angles.
22
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Standards Mastery Document
High School Geometry
Similarity, Right Triangles, and Trigonometry (G.SRT)
Standards: G.SRT.7 Explain and use the relationship between the sine and cosine of
complementary angles.
Enduring Skills:
MP.3 Construct viable arguments and critique the reasoning of others.
MP.8 Look for and express regularity in repeated reasoning.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
How do trigonometric ratios
help in solving problems
involving right triangles?
Explore the sine of an acute
angle and the cosine of its
complement and determine
their relationship.
Explain how the sine and
cosine of complementary
angles are related to each
other.
23
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Pike County School District
Standards Mastery Document
High School Geometry
Similarity, Right Triangles, and Trigonometry (G.SRT)
Standard: G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right
triangles in applied problems.
Enduring Skills:
MP.4 Model with mathematics.
MP.7 Look for and make use of structure.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Which methods could be
used to solve right triangles
in applied problems?
Solve for an unknown angle or
side of a right triangle using
sine, cosine, and tangent.
Apply both trigonometric ratios
and Pythagorean Theorem to
solve application problems
involving right triangles.
Apply both trigonometric
ratios and Pythagorean
Theorem to solve application
problems involving right
triangles.
24
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Pike County School District
Standards Mastery Document
High School Geometry
Similarity, Right Triangles, and Trigonometry (G.SRT)
Standard: 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.
Enduring Skills:
MP.4 Model with mathematics.
MP.7 Look for and make use of structure.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Draw an auxiliary line from a
How does trigonometry help vertex, perpendicular to the
in solving problems involving opposite side.
general triangles?
Derive the formula A= ½ ab
sinC for the area of a triangle.
Draw an auxiliary line from a
vertex, perpendicular to the
opposite side.
Derive the formula A= ½ ab
sinC for the area of a
triangle.
25
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Pike County School District
Standards Mastery Document
High School Geometry
Similarity, Right Triangles, and Trigonometry (G.SRT)
Standard: G.SRT.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems.
Enduring Skills:
MP.1 Make sense of problems and persevere in solving them.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.6 Attend to precision.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Prove the Law of Sines.
The Law of Sines and
Cosines.
How to apply the Law of
Sines and Cosines to find
missing angles and sides.
Prove the Law of Cosines.
Use the Law of Sines to solve
problems.
Find missing angles and sides of Use the Law of Cosines to
solve problems.
triangles.
26
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Pike County School District
Standards Mastery Document
High School Geometry
Similarity, Right Triangles, and Trigonometry (G.SRT)
Standard: 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).
Enduring Skills:
MP.1 Make sense of problems and persevere in solving them.
MP.4 Model with mathematics.
MP.6 Attend to precision.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Apply the Law of Sines and
Cosines to find unknown
measurements in right and
non-right triangles.
Find unknown
measurements in right and
non-right triangles using the
Law of Sines and/or Law of
Cosines.
The Law of Sines and
Cosines.
How to apply the Law of
Sines and Cosines to find
missing angles and sides..
27
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Pike County School District
Standards Mastery Document
High School Geometry
Modeling with Geometry (G.MG)
Standard: 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).*(*Modeling Standard)
Enduring Skills:
MP.4 Model with mathematics.
MP.7 Look for and make use of structure
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Classify a real-world object as a
How to relate geometric
known geometric shape.
shapes to real-world objects.
Solve real-world problems
involving geometric shapes.
Given a real-world object,
classify the object as a
known geometric shape –
use this to solve problems in
context.
Use geometric shapes, their
measures, and their
properties to describe
objects.
28
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Pike County School District
Standards Mastery Document
High School Geometry
Modeling with Geometry (G.MG)
Standard: 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).* (*Modeling Standard)
Enduring Skills:
MP.4 Model with mathematics.
MP.7 Look for and make use of structure.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Apply concepts of density
based on area and volume to
model real-world situations..
Use the concept of density
when referring to situations
involving area and volume
models, such as persons per
square mile.
*Definition of density.
29
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Pike County School District
Standards Mastery Document
High School Geometry
Modeling with Geometry (G.MG)
Standard: 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).*(*Modeling Standard)
Enduring Skills:
MP.1 Make sense of problems and persevere in solving them.
MP.4 Model with mathematics.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Apply geometric methods to
solve design problems.
Solve design problems by
designing an object or
structure that satisfies
certain constraints, such as
minimizing cost or working
with a grid system based on
ratios.
Describe a topographical
design system.
Use simulation software and
How can geometric concepts modeling software to explore
be used to describe objects
which model best describes a
found in nature?
set of data or situation.
30
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Pike County School District
Standards Mastery Document
High School Geometry
Geometric Measurement and Dimension (G.GMD)
Standard: 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
Enduring Skills:
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics
MP.5 Use appropriate tools strategically.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Explain the formulas for the
circumference of a circle and
the area of a circle by
determining the meaning of
each term or factor.
Give an informal argument
for the formulas for
circumference and area of a
circle.
How do the properties of
circles provide a basis for
explaining volume formulas
and solving problems?
Give an informal argument
Explain the formulas for the
for the formulas for the
volume of a cylinder, pyramid,
volume of a cylinder,
and cone by determining the
pyramid, and cone.
meaning of each term or factor.
31
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Pike County School District
Standards Mastery Document
High School Geometry
Geometric Measurement and Dimension (G.GMD)
Standard: G.GMD.2 (+) Give an informal argument using Calvalieri’s principle for the formulas
for the volume of a sphere and other solid figures.
Enduring Skills:
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics
MP.5 Use appropriate tools strategically.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Using Cavalieri’s Principle,
provide informal arguments to
develop the formulas for the
volume of spheres and other
solid figures.
Give an informal argument
using Cavalieri’s principle for
the formula for the volume
of a sphere and other solid
figures.
How do the properties of
circles provide a basis for
explaining volume formulas
and solving problems?
32
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Pike County School District
Standards Mastery Document
High School Geometry
Geometric Measurement and Dimension (G.GMD)
Standard: G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve
problems.*(*Modeling Standard)
Enduring Skills:
MP.4 Model with mathematics
MP.6 Attend to precision.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Solve problems using volume
formulas for cylinders,
pyramids, cones, and spheres.
Use volume formulas for
cylinders, pyramids, cones,
and spheres to solve
contextual problems.
Formulas for volume for
various figures
33
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Pike County School District
Standards Mastery Document
High School Geometry
Geometric Measurement and Dimension (G.GMD)
Standard: G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional
objects, and identify three-dimensional objects generated by rotations of two-dimensional
objects
Enduring Skills:
MP.2 Reason abstractly and quantitatively.
MP.4 Model with mathematics
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Given a three-dimensional
object, identify the shape made
when the object is cut into
cross-sections.
Relate the shapes of twodimensional cross-sections
to their three-dimensional
objects.
When rotating a twodimensional figure, such as a
square, know the threedimensional figure that is
generated, such as a cylinder.
Discover three-dimensional
objects generated by
rotations of two-dimensional
objects.
Strategies to help visualize
relationships between twodimensional and threedimensional objects.
Understand that the crosssection of a solid is an
intersection of a plane (twodimensional) and a solid (threedimensional).
34
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Pike County School District
Standards Mastery Document
High School Geometry
Expressing Geometric Properties with Equations (G.GPE)
Standard: 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.
Enduring Skills:
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Use the Pythagorean Theorem
to derive the equation of a
circle, given the center and the
radius.
Derive equation of a circle
using the Pythagorean
Theorem, given coordinates
of the center and length of
the radius,
Definition of a circle.
Know the Pythagorean
Theorem.
How to complete the square
of a quadratic equation.
Given an equation of a circle,
complete the square to find the Determine the center and
center and radius of a circle.
radius of a circle by
completing the square.
35
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Pike County School District
Standards Mastery Document
High School Geometry
Expressing Geometric Properties with Equations (G.GPE)
Standard: G.GPE.2 Derive the equation of a parabola given a focus and a directix.
Enduring Skills:
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Given a focus and directrix,
derive the equation of a
parabola.
Derive the equation of a
parabola given the focus and
directix.
Given a parabola, identify the
vertex, focus, directrix, and axis
of symmetry, noting that every
point on the parabola is the
same distance from the focus
and the directrix.
Given a parabola, identify
the vertex, focus, directrix,
and axis of symmetry, noting
that every point on the
parabola is the same
distance from the focus and
the directrix.
How can a focus and
directrix help in the
derivation of the equation of
a parabola?
Define a parabola including
the relationship of the focus
and the equation of the
directrix to the parabolic
shape.
36
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Pike County School District
Standards Mastery Document
High School Geometry
Expressing Geometric Properties with Equations (G.GPE)
Standard: G.GPE.3 (+) Derive the equations of ellipses and hyperbolas given the foci, using the
fact that the sum or difference of distances from the foci is constant.
Enduring Skills:
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Derive the equations of ellipses
given the foci, using the fact
that the sum of distances from
the foci is constant.
Given the foci, derive the
equation of an ellipse, noting
that the sum of the distances
from the foci to any fixed
point on the ellipse is
constant, identifying that
major and minor axis.
Use definitions of conic
sections and the
Pythagorean Theorem to
derive equations.
Derive the equations of
hyperbolas given the foci, using
the fact that the difference of
distances from the foci is
constant.
Given the foci, derive the
equation on a hyperbola,
noting that the absolute
value of the differences of
the distances form the foci
to a point on the hyperbola
is constant, and identifying
the vertices, center,
transverse axis, conjugate
axis, and asymptotes.
37
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Pike County School District
Standards Mastery Document
High School Geometry
Expressing Geometric Properties with Equations (G.GPE)
Standard: 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).
Enduring Skills:
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Recall previous
understandings of
coordinate geometry
including distance, midpoint,
and slope formulas,
equation of a line,
definitions of parallel and
perpendicular lines.
Derive the equation of a line
through 2 points using similar
right triangles.
Use coordinates to prove
simple geometric theorems
algebraically.
Derive simple proofs involving
circles.
Derive the equation of a line
through 2 points using
similar right triangles.
Derive simple proofs
involving circles.
38
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Pike County School District
Standards Mastery Document
High School Geometry
Expressing Geometric Properties with Equations (G.GPE)
Standard: G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use 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).
Enduring Skills
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Recognize that slopes of
parallel lines are equal.
Find the equation of a line
parallel to a given line that
passes through a given point.
Using slope, prove lines are
parallel or perpendicular.
Recognize that slopes of
perpendicular lines are
opposite reciprocals.
Find the equation of a line
perpendicular to a given line
that passes through a given
point.
Find equations of lines based
on certain slope criteria such
as; finding the equation of a
line parallel or perpendicular
to a given line that passes
through a given point.
Prove the slope criteria for
parallel and perpendicular lines
and use them to solve
geometric problems.
39
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Pike County School District
Standards Mastery Document
High School Geometry
Expressing Geometric Properties with Equations (G.GPE)
Standard: G.GPE.6 Find the point on a directed line segment between two given points that
partitions the segment in a given ratio.
Enduring Skills:
MP.2 Reason abstractly and quantitatively.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Recall the definition of ratio.
Given a line segment (including
those with positive and
negative slopes) and a ratio,
find the point on the segment
that partitions the segment
into the given ratio.
Given two points (line
segment), find the point on
the line segment between
the two points that divides
the segment into a given
ratio.
Recall previous
understandings of
coordinate geometry.
40
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Pike County School District
Standards Mastery Document
High School Geometry
Expressing Geometric Properties with Equations (G.GPE)
Standard: G.GPE.7 Use coordinates to compute perimeters of polygons and area of triangles
and rectangles, e.g., using the distance formula.*(*Modeling Standard)
Enduring Skills:
MP.2 Reason abstractly and quantitatively.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Understand how the
coordinates of the vertices
of a polygon, triangle, and
rectangle relate to find
perimeter and area.
Formulate a model of figures in
contextual problems to
compute area and/or
perimeter.
Use the coordinates of the
vertices of a polygon to find
the necessary dimensions for
finding the perimeter.
Use the coordinates of the
vertices of a triangle to find
the necessary dimensions for
finding the area.
Use the coordinates of the
vertices of a rectangle to find
the necessary dimensions for
finding the area
41
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Pike County School District
Standards Mastery Document
High School Geometry
Circles (G.C)
Standard: G.C.1 Prove that all circles are similar.
Enduring Skills:
MP.5 Use appropriate tools strategically.
MP.8 Look for and express regularity in repeated reasoning.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Recognize when figures are
similar.
Compare the ratio of the
circumference of a circle to the
diameter of the circle.
Use the fact that the ratio of
diameter to circumference is
the same for circles, prove
that all circles are similar.
Discuss, develop, and justify
the ratio of the circumference
of a circle to the diameter of
the circle for several circles.
Determine that the ratio of
diameter to circumference is
constant for all circles.
42
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Pike County School District
Standards Mastery Document
High School Geometry
Circles (G.C)
Standard: G.C.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.
Enduring Skills:
MP.2 Reason abstractly and quantitatively.
MP.7 Look for and make use of structure.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Identify inscribed angles,
radii, central angles,
circumscribed angles,
diameter, and tangent.
Examine the relationship
between central, inscribed, and
circumscribed angles by
applying theorems and their
measures.
Using definitions, properties,
and theorems, identify and
describe relationships
among inscribed angles,
radii, and chords. Include
central, inscribed, and
circumscribed angles.
Recognize that inscribed
angles on a diameter are
right angles.
Recognize that radius of a
circle is perpendicular to the
radius at the point of
tangency.
Understand that inscribed
angles on a diameter are
right angles.
Understand that the radius
of a circle is perpendicular to
the tangent where the radius
intersects the circle.
43
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Pike County School District
Standards Mastery Document
High School Geometry
Circles (G.C)
Standard: G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove
properties of angles for a quadrilateral inscribed in a circle.
Enduring Skills:
MP.4 Model with mathematics
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Define inscribed and
circumscribed circles of a
triangle.
Prove properties of angles for a
quadrilateral inscribed in a
circle.
Construct inscribed circles of
a triangle.
Recall midpoint and bisector
definitions.
Define a point of
concurrency.
Use geometric simulation
software to make geometric
constructions.
Construct circumscribed
circles of a triangle.
Using definitions, properties,
and theorems, prove
properties of angles for a
quadrilateral inscribed in a
circle.
44
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Pike County School District
Standards Mastery Document
High School Geometry
Circles (G.C)
Standard: G.C.4 (+) Construct a tangent line from a point outside a given circle to the circle.
Enduring Skills:
MP.5 Use appropriate tools strategically.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Define tangent, radius,
perpendicular bisector, and
midpoint.
Construct the perpendicular
bisector of the line segment
between the center, C, to the
outside point, P.
Synthesize the theory that
applies to circles that
tangents drawn from
common external points are
congruent.
Identify the center of the
circle.
Construct arcs on circle C from
the midpoint Q, having length
of CQ.
Construct a tangent line.
Synthesize the theory that
applies to circles that a
radius is perpendicular to a
tangent at the point of
tangency.
45
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Pike County School District
Standards Mastery Document
High School Geometry
Circles (G.C)
Standard: 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.
Enduring Skills:
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.5 Use appropriate tools strategically.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Recall how to find the area
and circumference of a
circle.
Justify the radii of any two
circles (r1 and r2) and the arc
lengths (s1 and s2) determined
by congruent central angles are
proportional.
Find the arc length of a
circle.
Recall that all circles are
similar.
Explain that
radians
1o=
pi/18-
Verify that the constant of a
proportion is the same as the
radian measure of the given
angle.
Using similarity, derive the
formula for the area of a
sector.
Find the area od a sector in a
circle.
Determine the constant of
proportionality (scale
factor).
46
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Pike County School District
Standards Mastery Document
High School Geometry
Conditional Probability and the Rules of Probability (S.CP)
Standard: 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”). Statistics and Probability is a Modeling Conceptual Category.
Enduring Skills:
MP.2 Reason abstractly and quantitatively.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Define unions, intersections,
and complements of events.
Describe events as subsets of
sample space (the set of
outcomes) using characteristics
(or categories) of the
outcomes, or as unions,
intersections, or complements
of other events.
Define a sample space and
events within the sample
space. Identify subsets from
sample space given defined
events, including unions,
intersections, and
complements of events.
47
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Pike County School District
Standards Mastery Document
High School Geometry
Conditional Probability and the Rules of Probability (S.CP)
Standard: 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.
Enduring Skills:
MP.2 Reason abstractly and quantitatively.
MP.4 Model with mathematics.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Definition of independent
events.
Understand the properties
of Independence and
Conditional Probabilities.
Categorize events as
independent or not.
Label events as independent
or not.
Explain properties of
Independence and Conditional
Probabilities in context and
simple English.
48
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Pike County School District
Standards Mastery Document
High School Geometry
Conditional Probability and the Rules of Probability (S.CP)
Standard: 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.
Enduring Skills:
MP.2 Reason abstractly and quantitatively.
MP.4 Model with mathematics.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Know the conditional
probability of A given B as
P(A and B)/P(B).
How to define and calculate
conditional probabilities.
Define and calculate
conditional probabilities.
Use the Multiplication Principle
to decide if two events are
independent.
Determine if two events are
independent or dependent.
Calculate conditional
probabilities using the
Multiplication Principle
Calculate conditional
probabilities.
49
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Pike County School District
Standards Mastery Document
High School Geometry
Conditional Probability and the Rules of Probability (S.CP)
Standard: 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.
Enduring Skills:
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
How to use a two way
sample space to decide if
events are independent and
approximate conditional
probabilities.
Interpret two-way frequency
tables of data when two
categories are associated with
each object being classified.
Use two-way frequency
tables of data to determine if
events are independent and
approximate conditional
probabilities
Develop understanding of
independence and
conditional probability.
50
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Pike County School District
Standards Mastery Document
High School Geometry
Conditional Probability and the Rules of Probability (S.CP)
Standard: S.CP.5 Construct and interpret two-way frequency tables of data when two
categories are associated with each object being classified. Use the twoway 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.
Enduring Skills:
MP.1 Make sense of problems and persevere in solving them.
MP.4 Model with mathematics.
MP.6 Attend to precision.
MP.8 Look for and express regularity in repeated reasoning.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Recognize and explain the
How are independence and
concepts of independence and
conditional probability
conditional probability in
related and used to interpret everyday situations
data?
Relate independence and
conditional probability in
everyday language and
everyday situations.
51
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Standards Mastery Document
High School Geometry
Conditional Probability and the Rules of Probability (S.CP)
Standard: 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.
Enduring Skills:
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Definition of conditional
probability.
How to calculate conditional
probabilities.
Find the conditional probability
of event A and event B.
*Interpret answers in terms of
the model.
Calculate conditional
probability of two events.
52
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Pike County School District
Standards Mastery Document
High School Geometry
Conditional Probability and the Rules of Probability (S.CP)
Standard: 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.
Enduring Skills:
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
The definition of mutually
exclusive events.
How to apply the Addition
Rule of probabilities
Calculate probabilities using
the Addition Rule.
Find probabilities using the
Addition rule.
Interpret answers in terms of
the model.
53
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Pike County School District
Standards Mastery Document
High School Geometry
Conditional Probability and the Rules of Probability (S.CP)
Standard: 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.
Enduring Skills:
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.7 Look for and make use of structure.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
How to use the
multiplication rule with
correct notation.
Calculate probabilities using
the General Multiplication Rule. Apply the General
Multiplication Rules to
calculate probabilities.
Apply the General
Multiplication Rule in a uniform
probability model.
Interpret answers in terms of
the model.
54
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Pike County School District
Standards Mastery Document
High School Geometry
Conditional Probability and the Rules of Probability (S.CP)
Standard: S.CP.9 (+) Use permutations and combinations to compute probabilities of
compound events and solve problems.
Enduring Skills:
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.7 Look for and make use of structure.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
How to correctly identify
situations that are
permutations and those that
are combinations.
Use permutations and
combinations to compute
probabilities of compound
events and solve problems.
Identify permutations and
combinations for given
situations.
Solve problems and find
compound probabilities
using permutations and
combinations
55
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Pike County School District
Standards Mastery Document
High School Geometry
Using Probability to Make Decisions (S.MD)
Standard: S.MD.6 (+) Use probabilities to make fair decisions (e.g. drawing by lots, using a
random number generator.) This unit sets the stage for work in Algebra II, where the ideas of
statistical inference are introduced. Evaluating the risks associated with conclusions drawn from
sample data (i.e. incomplete information) requires an understanding of probability concepts.
Statistics and Probability is a Modeling Conceptual Category
Enduring Skills:
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics
MP.5 Use appropriate tools strategically.
MP.8 Look for and express regularity in repeated reasoning.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
How to compute theoretical
and experimental
probabilities.
Recall previous
understandings of
probability.
Use probabilities to make fair
decisions.
Use random number
generators or other probability
software.
Make decisions based on
expected values. Use
expected values to compare
long term benefits of several
situations.
Use expected values to
compare long term benefits of
several situations.
56
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Pike County School District
Standards Mastery Document
High School Geometry
Using Probability to Make Decisions (S.MD)
Standard: 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.) Statistics and Probability
is a Modeling Conceptual Category.
Enduring Skills:
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.5 Use appropriate tools strategically.
Know: What content does the
Do: What skill must the student
Mastery: How does the student
student need to know to demonstrate
this standard?
demonstrate?
demonstrate the earning of the
standard?
Recall previous
understanding of
probability.
How can I evaluate
outcomes of decisions using
probability?
Analyze decisions and
strategies using probability
concepts.
Analyze decisions and
strategies using probability
concepts.
Explain in context decisions
made based on expected
values.
57
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