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2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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TABLE OF CONTENTS
SECTIONS PAGES IN THIS DOC
Section 1: Introduction to Geometry – Points, Lines and Planes 2-3
Section 2: Introduction to Geometry – Transformations and Constructions 4-7
Section 3: Angles 8-10
Section 4: Introduction to Polygons – Part 1 11-13
Section 5: Introduction to Polygons – Part 2 14-15
Section 6: Triangles – Part 1 16-17
Section 7: Triangles – Part 2 18-19
Section 8: Right Triangles 20-22
Section 9: Quadrilaterals – Part 1 23-25
Section 10: Quadrilaterals – Part 2 26-27
Section 11: Properties of 𝑁-gons 28-30
Section 12: Circles – Part 1 31-33
Section 13: Circles – Part 2 34-35
Section 14: Three Dimensional Geometry 36-38
Section 15: Additional Modeling with Geometry 39-40
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SECTION 1: INTRODUCTION TO GEOMETRY – POINTS, LINES AND PLANES
Section 1, Topic 1:
Basics of Geometry – Part 1
MAFS.912.G-CO.1.1 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.
This topic focuses on defining and
representing points, lines, line segments,
planes, rays, and angles, as the building
blocks of Geometry.
Section 1, Topic 2:
Basics of Geometry – Part 2
MAFS.912.G-CO.1.1 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.
This topic is the second part of defining
and representing points, lines, line
segments, planes, rays, and angles, as the
building blocks of Geometry.
Section 1, Topic 3:
Midpoint and Distance in the Coordinate Plane
– Part 1
MAFS.912.G-CO.1.1 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.
MAFS.912.G-GPE.2.6 Find the point on a given
line segment between two given points that
partitions a segment in a given ratio.
MAFS.912.G-GPE.2.7 Use coordinates to
compute the perimeter of polygons and areas
of triangles and rectangles.
This topic focuses on midpoint and
distance, and applications on a
coordinate plane by either finding
midpoint coordinates, endpoint
coordinates or length of segments.
Section 1, Topic 4:
Midpoint and Distance in the Coordinate Plane
– Part 2
MAFS.912.G-CO.1.1 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.
MAFS.912.G-GPE.2.6 Find the point on a given
line segment between two given points that
partitions a segment in a given ratio.
MAFS.912.G-GPE.2.7 Use coordinates to
compute the perimeter of polygons and areas
of triangles and rectangles.
This topic teaches students how to use the
commutative and associative properties to
identify equivalent expressions. Students
will determine which properties (distribute,
associative, and commutative) have been
used when writing equivalent expressions.
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Section 1, Topic 5:
Partitioning a Line Segment – Part 1
MAFS.912.G-GPE.2.6 Find the point on a
directed line segment between two given
points that partitions the segment in a given
ratio.
This topic focuses on finding the point on a
directed line segment between two given
points that partitions the segment in a
given ratio.
Section 1, Topic 6:
Partitioning a Line Segment – Part 2
MAFS.912.G-GPE.2.6 Find the point on a
directed line segment between two given
points that partitions the segment in a given
ratio.
This topic is the second part on finding the
point on a directed line segment between
two given points that partitions the
segment in a given ratio.
Section 1, Topic 7:
Parallel and Perpendicular Lines – Part 1
MAFS.912.G-CO.1.1 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.
MAFS.912.G-GPE.2.5 Prove the slope criteria for
parallel and perpendicular lines and use them
to solve geometric problems.
This topic focuses on identifying parallel
and perpendicular lines, and writing
equations of lines parallel or perpendicular
to another line.
Section 1, Topic 8:
Parallel and Perpendicular Lines – Part 2
MAFS.912.G-CO.1.1 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.
MAFS.912.G-GPE.2.5 Prove the slope criteria for
parallel and perpendicular lines and use them
to solve geometric problems.
This topic is the second part on identifying
parallel and perpendicular lines, and
writing equations of lines parallel or
perpendicular to another line.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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SECTION 2: INTRODUCTION TO GEOMETRY – TRANSFORMATIONS AND CONSTRUCTIONS
Section 2, Topic 1:
Introduction to Transformations
MAFS.912.G-CO.1.2 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.
MAFS.912.G-CO.1.4 Develop definitions of rotations, reflections,
and translations in terms of angles, circles, perpendicular lines,
parallel lines, and line segments.
MAFS.912.G-CO.1.5 Given a geometric figure and a rotation,
reflection, or translation, draw the transfoemed figure. Specify a
sequence of transformations that will carry a given figure onto
itself.
This topic focuses on introducing
rigid and non-rigid transformations,
translation, reflection, rotation, and
dilation.
Section 2, Topic 2:
Examining and Using Translations
MAFS.912.G-CO.1.2 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.
MAFS.912.G-CO.1.4 Develop definitions of rotations, reflections,
and translations in terms of angles, circles, perpendicular lines,
parallel lines, and line segments.
MAFS.912.G-CO.1.5 Given a geometric figure and a rotation,
reflection, or translation, draw the transfoemed figure. Specify a
sequence of transformations that will carry a given figure onto
itself.
This topic focuses on performing
translations of points and line
segments on a coordinate plane.
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Section 2, Topic 3:
Examining and Using Dilations – Part 1
MAFS.912.G-CO.1.2 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.
MAFS.912.G-CO.1.4 Develop definitions of rotations, reflections,
and translations in terms of angles, circles, perpendicular lines,
parallel lines, and line segments.
MAFS.912.G-CO.1.5 Given a geometric figure and a rotation,
reflection, or translation, draw the transfoemed figure. Specify a
sequence of transformations that will carry a given figure onto
itself.
This topic focuses on performing
dilations of points and line
segments on a coordinate plane.
Section 2, Topic 4:
Examining and Using Dilations – Part 2
MAFS.912.G-CO.1.2 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.
MAFS.912.G-CO.1.4 Develop definitions of rotations, reflections,
and translations in terms of angles, circles, perpendicular lines,
parallel lines, and line segments.
MAFS.912.G-CO.1.5 Given a geometric figure and a rotation,
reflection, or translation, draw the transfoemed figure. Specify a
sequence of transformations that will carry a given figure onto
itself.
This topic focuses on performing
dilations of points and line
segments on a coordinate plane.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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Section 2, Topic 5:
Examining and Using Rotations
MAFS.912.G-CO.1.2 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.
MAFS.912.G-CO.1.4 Develop definitions of rotations, reflections,
and translations in terms of angles, circles, perpendicular lines,
parallel lines, and line segments.
MAFS.912.G-CO.1.5 Given a geometric figure and a rotation,
reflection, or translation, draw the transformed figure. Specify a
sequence of transformations that will carry a given figure onto
itself.
This topic focuses on performing
rotation of points and line segments
on a coordinate plane.
Section 2, Topic 6:
Examining and Using Reflections
MAFS.912.G-CO.1.2 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.
MAFS.912.G-CO.1.4 Develop definitions of rotations, reflections,
and translations in terms of angles, circles, perpendicular lines,
parallel lines, and line segments.
MAFS.912.G-CO.1.5 Given a geometric figure and a rotation,
reflection, or translation, draw the transformed figure. Specify a
sequence of transformations that will carry a given figure onto
itself.
This topic focuses on performing
reflection of points and line
segments on a coordinate plane.
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Section 2, Topic 7:
Basic Constructions – Part 1
MAFS.912.G-CO.4.12 Make formal geometric constructions with
a variety of tools and methods. 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.
This topic focuses on constructions
of line segments.
Section 2, Topic 8:
Basic Constructions – Part 2
MAFS.912.G-CO.4.12 Make formal geometric constructions with
a variety of tools and methods. 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 l ine parallel to a
given line through a point not on the line.
This topic follows up the previous
one on constructions, but it focuses
on perpendicular bisectors.
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SECTION 3: ANGLES
Section 3, Topic 1:
Introduction to Angles – Part 1
MAFS.912.G-CO.1.1 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.
This topic focuses on how to measure and
classify an angle.
Section 3, Topic 2:
Introduction to Angles – Part 2
MAFS.912.G-CO.1.1 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.
This topic follows up on how to measure and
classify an angle.
Section 3, Topic 3:
Angle Pairs – Part 1
MAFS.912.G-CO.3.9 Prove theorems about
lines and angles; use theorems about lines and
angles to solve problems.
This topic focuses on angle pairs, linear pairs,
adjacent angles, and vertical angles. It also
introduces the concept of an, angle
bisector. The Linear Pair Postulate, the
Congruent Complements Theorem, the
Congruent Supplement Theorem, and the
Right Angles Theorem are also introduced.
Section 3, Topic 4:
Angle Pairs – Part 2
MAFS.912.G-CO.3.9 Prove theorems about
lines and angles; use theorems about lines and
angles to solve problems.
This topic follows up on angle pairs, linear
pairs, adjacent angles, and vertical angles. It
also provides practice exercises on tangle
bisectors, the Linear Pair Postulate, the
Congruent Complements Theorem, the
Congruent Supplement Theorem, and the
Right Angles Theorem.
Section 3, Topic 5:
Special Types of Angle Pairs Formed by
Transversals and Non-Parallel Lines
MAFS.912.G-CO.1.1 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.
MAFS.912.G-CO.3.9 Prove theorems about
lines and angles; use theorems about lines and
angles to solve problems.
This topic focuses on discussing the special
Types of angle pairs formed by transversals
and non-parallel lines.
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Section 3, Topic 6:
Special Types of Angle Pairs Formed by
Transversals and Parallel Lines – Part 1
MAFS.912.G-CO.1.1 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.
MAFS.912.G-CO.3.9 Prove theorems about
lines and angles; use theorems about lines and
angles to solve problems.
This topic focuses on the relationship
between angle pairs when the transversal
cut two parallel lines.
Section 3, Topic 7:
Special Types of Angle Pairs Formed by
Transversals and Parallel Lines – Part 2
MAFS.912.G-CO.1.1 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.
MAFS.912.G-CO.3.9 Prove theorems about
lines and angles; use theorems about lines and
angles to solve problems.
This topic is the second part on the
relationship between angle pairs when the
transversal cut two parallel lines.
Section 3, Topic 8:
Perpendicular Transversals
MAFS.912.G-CO.1.1 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.
MAFS.912.G-CO.3.9 Prove theorems about
lines and angles; use theorems about lines and
angles to solve problems.
This topic focuses on transversals that
perpendicular to 2 or more lines.
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Section 3, Topic 9:
Angle-Preserving Transformations
MAFS.912.G-CO.1.2 Compare transformations
that preserve distance and angle to those that
do not.
MAFS.912.G-CO.1.4 Develop definitions of
rotations, reflections, and translations in terms
of angles, circles, perpendicular lines, parallel
lines and line segments.
MAFS.912.G-CO.1.5 Given a geometric figure
and a rotation, reflection, or translation, draw
the transformed figure.
MAFS.912.G-CO.3.9 Prove theorems about
angles and use theorems about angles and
lines to solve problems.
This topic focuses on applying
transformations to figures formed by parallel
lines crossed by a transversal. Most
importantly, it focuses on angle-preserving
transformations.
Section 3, Topic 10:
Constructions of Angles, Perpendicular Lines,
and Parallel Lines
MAFS.912.G-CO.4.12 Make formal geometric
constructions with a variety of tools and
methods. Copying a segment; copying an
angle; bisecting a segment; bisecting an
angle; constructing perpendicular lines,
This topic focuses on constructions of parallel
and perpendicular lines.
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SECTION 4: INTRODUCTION TO POLYGONS – PART 1
Section 4, Topic 1:
Introduction to Polygons – Part 1
MAFS.912.G-MG.1.1 Use geometric shapes, their
measures, and their properties to describe objects.
MAFS.912.G-CO.3.10 Prove theorems about triangles.
Use theorems about triangles to solve problems:
measures of interior angles of a triangle sum to 180.
This topic introduces polygons and it
compares and contrasts regular and
irregular polygons, convex and concave
polygons, and simple and complex
polygons.
Section 4, Topic 2:
Introduction to Polygons – Part 2
MAFS.912.G-MG.1.1 Use geometric shapes, their
measures, and their properties to describe objects.
MAFS.912.G-CO.3.10 Prove theorems about triangles.
Use theorems about triangles to sovle problems:
measures of interior angles of a triangle sum to 180.
This topic is the second part on
introducing polygons, comparing and
contrasting regular and irregular
polygons, convex and concave
polygons, and simple and complex
polygons.
Section 4, Topic 3:
Angles of Polygons
MAFS.912.G-CO.1.1 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.
MAFS.912.G-MG.1.1 Use geometric shapes, their
measures, and their properties to describe objects.
This topic focuses on measuring the
interior and exterior angles of regular
and irregular polygons.
Section 4, Topic 4:
Translation of Polygons
MAFS.912.G-CO.1.2 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.
MAFS.912.G-CO.1.4 Develop definitions of rotations,
reflections, and translations in terms of angles, circles,
perpendicular lines, parallel lines and line segments.
MAFS.912.G-CO.1.5 Given a geometric figure and a
rotation, reflection, or translation, draw the
transformed figure. Specify a sequence of
transformations that will carry a given figure onto
itself.
This topic focuses on performing
translations of polygons on a coordinate
plane and finding the coordinates or
location of the image and the pre-
image.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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Section 4, Topic 5:
Reflection of Polygons
MAFS.912.G-CO.1.2 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.
MAFS.912.G-CO.1.4 Develop definitions of rotations,
reflections, and translations in terms of angles, circles,
perpendicular lines, parallel lines and line segments.
MAFS.912.G-CO.1.5 Given a geometric figure and a
rotation, reflection, or translation, draw the
transformed figure. Specify a sequence of
transformations that will carry a given figure onto
itself.
This topic focuses on performing
reflections of polygons on a coordinate
plane and finding the coordinates or
location of the image and the pre-
image.
Section 4, Topic 6:
Rotation of Polygons – Part 1
MAFS.912.G-CO.1.2 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.
MAFS.912.G-CO.1.4 Develop definitions of rotations,
reflections, and translations in terms of angles, circles,
perpendicular lines, parallel lines and line segments.
MAFS.912.G-CO.1.5 Given a geometric figure and a
rotation, reflection, or translation, draw the
transformed figure. Specify a sequence of
transformations that will carry a given figure onto
itself.
This topic focuses on performing rotations
of polygons on a coordinate plane and
finding the coordinates or location of the
image and the pre-image.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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Section 4, Topic 7:
Rotation of Polygons – Part 2
MAFS.912.G-CO.1.2 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.
MAFS.912.G-CO.1.4 Develop definitions of rotations,
reflections, and translations in terms of angles, circles,
perpendicular lines, parallel l ines and line segments.
MAFS.912.G-CO.1.5 Given a geometric figure and a
rotation, reflection, or translation, draw the
transformed figure. Specify a sequence of
transformations that will carry a given figure onto
itself.
This is the second part of the set of topics
focusing on performing rotations of
polygons on a coordinate plane and
finding the coordinates or location of the
image and the pre-image.
Section 4, Topic 8:
Dilation of Polygons
MAFS.912.G-CO.1.2 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.
MAFS.912.G-SRT.1.1 Verify experimentally the
properties of dilations given by a center and a scale
factor: a. A dilation takes a line not passing through
the center of the dilation to a parallel line and leaves
a line passing through the center unchanged. b. The
dilation of a line segment is longer or shorter in the
raitio given by the scale factor.
This topic focuses on performing dilations
of polygons on a coordinate plane and
finding the coordinates or location of the
image and the pre-image.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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SECTION 5: INTRODUCTION TO POLYGONS – PART 2
Section 5, Topic 1:
Compositions of Transformations of
Polygons – Part 1
MAFS.912.G-CO.1.5 Given a geometric figure and a
rotation, reflection, or translation, draw the transformed
figure. Specify a sequence of transformations that will
carry a given figure onto itself.
This topic focuses on discussing the
different compositions of transformations
such as glide reflection, double
reflection, and composition of isometries.
Section 5, Topic 2:
Compositions of Transformations of
Polygons – Part 2
MAFS.912.G-CO.1.5 Given a geometric figure and a
rotation, reflection, or translation, draw the transformed
figure. Specify a sequence of transformations that will
carry a given figure onto itself.
This topic is the second part on discussing
the different compositions of
transformations such as glide reflection,
double reflection, and composition of
isometries.
Section 5, Topic 3:
Symmetries of Regular Polygons
MAFS.912.G-CO.1.3 Given a rectangle, parallelogram,
trapezoid, or regular polygon, describe the rotations and
reflections that carry it onto itself.
MAFS.912.G-CO.1.5 Given a geometric figure and a
rotation, reflection, or translation, draw the transformed
figure. Specify a sequence of transformations that will
carry a given figure onto itself.
This topic focuses on discussing
reflections and rotations that carry a
geometric figure onto itself.
Section 5, Topic 4:
Congruence and Similarity of Polygons –
Part 1
MAFS.912.G-CO.2.6 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.
MAFS.912.G-CO.2.7 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.
MAFS.912.G-SRT.1.2 Given two figures, use the definition 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.
This topic focuses on distinguishing
between transformations that produce
congruent images and transformations
that produce similar images.
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Section 5, Topic 5:
Congruence and Similarity of Polygons –
Part 2
MAFS.912.G-CO.2.6 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.
MAFS.912.G-CO.2.7 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.
MAFS.912.G-SRT.1.2 Given two figures, use the definition 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.
This topic focuses on distinguishing
between transformations that produce
congruent images and transformations
that produce similar images.
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SECTION 6: TRIANGLES – PART 1
Section 6, Topic 1:
Introduction to Triangles – Part 1
MAFS.912.G-CO.3.10 Prove theorems about
triangles; use theorems about triangles to solve
problems.
MAFS.912.G-GPE.2.5 Prove the slope criteria for
parallel and perpendicular lines and use them
to solve geometric problems.
This topic focuses on classifying triangles by
sides and angles, and using triangles’
characteristics to find missing sides, angles or to
apply algebraic skills. It also proves the Triangle
Sum theorem.
Section 6, Topic 2:
Introduction to Triangles – Part 2
MAFS.912.G-CO.3.10 Prove theorems about
triangles; use theorems about triangles to solve
problems.
MAFS.912.G-GPE.2.5 Prove the slope criteria for
parallel and perpendicular lines and use them
to solve geometric problems.
This topic offers more opportunities for
practicing on classifying triangles by sides and
angles, and using triangles’ characteristics to
find missing sides, angles or to apply algebraic
skills. It also proves the Triangle Sum theorem.
Section 6, Topic 3:
Area and Perimeter on the Coordinate Plane –
Part 1
MAFS.912.G-GPE.2.7 Use coordinates to
computer perimeters of polygons and areas of
triangles and rectangles.
This topic focuses on calculating area and
perimeter of a triangle, and using perimeter
and area to find missing sides.
Section 6, Topic 4:
Area and Perimeter on the Coordinate Plane –
Part 2
MAFS.912.G-GPE.2.7 Use coordinates to
computer perimeters of polygons and areas of
triangles and rectangles.
This topic offers more opportunities for
practicing on calculating area and perimeter
of a triangle, and using perimeter and area to
find missing sides.
Section 6, Topic 5:
Triangle Congruence – SSS and SAS – Part 1
MAFS.912.G-CO.2.8 Explain how the criteria for
triangle congruence (ASA, SAS, SSS, and
Hypotenuse Leg) follow from the definition of
congruence in terms of rigid motions.
MAFS.912.G-SRT.2.5 Use congruence and
similarity criteria for triangles to solve problems
and to prove relationships in geometric figure.
This topic guides students through the method
of using Side-Side-Side and Side-Angle-Side
theorems to find missing sides or angles, and to
prove certain characteristics of triangles.
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Section 6, Topic 6:
Triangle Congruence – SSS and SAS – Part 2
MAFS.912.G-CO.2.8 Explain how the criteria for
triangle congruence (ASA, SAS, SSS, and
Hypotenuse Leg) follow from the definition of
congruence in terms of rigid motions.
MAFS.912.G-SRT.2.5 Use congruence and
similarity criteria for triangles to solve problems
and to prove relationships in geometric figure.
This topic keeps on guiding students through
the method of using Side-Side-Side and Side-
Angle-Side theorems to find missing sides or
angles, and to prove certain characteristics of
triangles.
Section 6, Topic 7:
Triangle Congruence – ASA and AAS – Part 1
MAFS.912.G-CO.2.8 Explain how the criteria for
triangle congruence (ASA, SAS, SSS, and
Hypotenuse Leg) follow from the definition of
congruence in terms of rigid motions.
MAFS.912.G-SRT.2.5 Use congruence and
similarity criteria for triangles to solve problems
and to prove relationships in geometric figures.
This topic guides students through the method
of using Angle-Side-Angle and Angle-Angle-
Side theorems to find missing sides or angles,
and to prove certain characteristics of
triangles.
Section 6, Topic 8:
Triangle Congruence – ASA and AAS – Part 2
MAFS.912.G-CO.2.8 Explain how the criteria for
triangle congruence (ASA, SAS, SSS, and
Hypotenuse Leg) follow from the definition of
congruence in terms of rigid motions.
MAFS.912.G-SRT.2.5 Use congruence and
similarity criteria for triangles to solve problems
and to prove relationships in geometric figures.
This topic keeps on guiding students through
the method of using Angle-Side-Angle and
Angle-Angle-Side theorems to find missing sides
or angles, and to prove certain characteristics
of triangles.
Section 6, Topic 9:
Using Triangle Congruency to Find Missing
Variables
MAFS.912.G-CO.2.8 Explain how the criteria for
triangle congruence (ASA, SAS, SSS, and
Hypotenuse Leg) follow from the definition of
congruence in terms of rigid motions.
MAFS.912.G-SRT.2.5 Use congruence and
similarity criteria for triangles to solve problems
and to prove relationships in geometric figures.
This topic focuses on using triangle congruency
theorems to find missing sides by using
algebraic skills.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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SECTION 7: TRIANGLES – PART 2
Section 7, Topic 1:
Triangle Similarity – Part 1
MAFS.912.G-SRT.1.2: 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.
MAFS.912.G-SRT.1.3 Use the properties of similarity
transformations to establish the AA criterion for two
triangles to be similar.
MAFS.912.G-SRT.2.5 Use congruence and similarity
criteria for triangles to solve problems and to prove
relationships in geometric figures.
This topic guides students through
different triangle similarity criteria to
prove that two triangles are similar or
certain lengths of two triangles are
similar.
Section 7, Topic 2:
Triangle Similarity – Part 2
MAFS.912.G-SRT.1.2: 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.
MAFS.912.G-SRT.1.3 Use the properties of similarity
transformations to establish the AA criterion for two
triangles to be similar.
MAFS.912.G-SRT.2.4 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.
MAFS.912.G-SRT.2.5 Use congruence and similarity
criteria for triangles to solve problems and to prove
relationships in geometric figures.
This topic keeps on guiding students
through different triangle similarity
criteria to prove that two triangles are
similar or certain lengths of two
triangles are similar.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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Section 7, Topic 3:
Triangle Midsegment Theorem – Part 1
MAFS.912.G-CO.3.10 Prove theorems about triangles;
use theorems about triangles to solve problems.
This topic focuses on understanding
and applying the Triangle Midsegment
Theorem.
Section 7, Topic 4:
Triangle Midsegment Theorem – Part 2
MAFS.912.G-CO.3.10 Prove theorems about triangles;
use theorems about triangles to solve problems.
This topic keeps focusing on
understanding and applying the
Triangle Midsegment Theorem.
Section 7, Topic 5:
Triangle Inequalities
MAFS.912.G-CO.3.10 Prove theorems about triangles;
use theorems about triangles to solve problems.
This topic introduces the Triangle
Inequality Theorem, the Hinge Theorem
and the Converse of the Hinge
Theorem,
Section 7, Topic 6:
More Triangle Proofs
MAFS.912.G-CO.3.10 Prove theorems about triangles;
use theorems about triangles to solve problems.
This topic wraps up all the theorems
introduced this section and use them
to prove different features of triangles.
Section 7, Topic 7:
Inscribed and Circumscribed Circles of
Triangles
MAFS.912.G-C.1.3 Construct the inscribed and
circumscribed circles of a triangle, and prove
properties of angles for a quadrilateral inscribed in a
circle.
This topic focuses on constructing
triangles and it reviews incircle,
circumcircle and circumcenter based
on a triangle.
Section 7, Topic 8:
Medians of a Triangle
MAFS.912.G-CO.3.10 Prove theorems about triangles;
use theorems about triangles to solve problems.
MAFS.912.G-GPE.2.4 Use coordinates to prove simple
geometric theorems algebraically.
This topic focuses on medians in a
triangle, the lengths of medians and
the ratio of the length from the vertex
to the centroid to the length from the
centroid to the midpoint of the side.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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SECTION 8: RIGHT TRIANGLES AND INTRODUCTION TO TRIGONOMETRY
Section 8, Topic 1:
The Pythagorean Theorem
MAFS.912.G-SRT.3.8 Use trigonometric ratios and
Pythagorean Theorem to solve right triangles in
applied problems.
MAFS.912.G-SRT.2.4 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.
This topic introduces the Pythagorean
Theorem and Pythagorean triples and
focuses on its applications
Section 8, Topic 2:
The Converse of the Pythagorean Theorem MAFS.912.G-SRT.3.8 Use trigonometric ratios and
Pythagorean Theorem to solve right triangles in
applied problems.
This topic introduces Converse of the
Pythagorean Theorem and focuses on
its applications.
Section 8, Topic 3:
Proving Right Triangles Congruent
MAFS.912.G-CO.2.8 Explain how the criteria for
triangle congruence (ASA, SAS, SSS, and Hypotenuse-
Leg) follow from the definition of congruence in terms
of rigid motions.
MAFS.912.G-CO.3.10 Prove theorems about triangles;
use theorems about triangles to solve problems.
This topic teaches us the Hypotenuse-
Leg Theorem to prove right triangles
congruent.
Section 8, Topic 4:
Special Right Triangles: 45-45-90
MAFS.912.G-CO.3.10 Prove theorems about triangles;
use theorems about triangles to solve problems.
MAFS.912.G-SRT.3.8 Use trigonometric ratios and
Pythagorean Theorem to solve right triangles in
applied problems.
This topic focuses on using the features
of 45-45-90 right triangles to solve
problems.
Section 8, Topic 5:
Special Right Triangles: 30-60-90
MAFS.912.G-SRT.3.8 Use trigonometric ratios and
Pythagorean Theorem to solve right triangles in
applied problems.
This topic focuses on using the features
of 30-60-90 right triangles to solve
problems.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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Section 8, Topic 6:
Right Triangles Similarity – Part 1
MAFS.912.G-SRT.1.2 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.
MAFS.912.G-SRT.2.4 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.
MAFS.912.G-SRT.2.5 Use congruence and similarity
criteria for triangles to solve problems and to prove
relationships in geometric figures.
MAFS.912.G-SRT.3.6 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.
This topic introduces the Right Triangle
Altitude Theorem and Geometric Mean
theorems to work with similar right
triangles.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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Section 8, Topic 7:
Right Triangles Similarity – Part 2
MAFS.912.G-SRT.1.2 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.
MAFS.912.G-SRT.2.4 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.
MAFS.912.G-SRT.2.5 Use congruence and similarity
criteria for triangles to solve problems and to prove
relationships in geometric figures.
MAFS.912.G-SRT.3.6 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.
This topic is the second part on working
with similar right triangles, but with more
applications problems.
Section 8, Topic 8:
Introduction to Trigonometry – Part 1
MAFS.912.G-SRT.3.7 Explain and use the relationship
between the sine and cosine of complementary
angles.
MAFS.912.G-SRT.3.8 Use trigonometric ratios and
Pythagorean Theorem to solve right triangles in
applied problems.
This topic introduces trigonometric ratios
and functions to use when finding a
missing side or a missing angle in a right
triangle.
Section 8, Topic 9:
Introduction to Trigonometry – Part 2
MAFS.912.G-SRT.3.7 Explain and use the relationship
between the sine and cosine of complementary
angles.
MAFS.912.G-SRT.3.8 Use trigonometric ratios and
Pythagorean Theorem to solve right triangles in
applied problems.
This topic is the second part of the
introduction of trigonometric ratios and
functions to use when finding a missing
side or a missing angle in a right triangle.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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SECTION 9: QUADRILATERALS – PART 1
Section 9, Topic 1:
Introduction to Quadrilaterals – Part 1
MAFS.912.G-CO.1.1 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.
MAFS.912.G-CO.3.11 Prove theorems about
parallelograms; use theorems about parallelograms
to solve problems.
MAFS.912.G-MG.1.1 Use geometric shapes, their
measures and their properties to describe objects.
This topic introduces the properties and
characteristics of quadrilateral, and
distinguishing between different types of
quadrilaterals.
Section 9, Topic 2:
Introduction to Quadrilaterals – Part 2
MAFS.912.G-CO.1.1 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.
MAFS.912.G-CO.3.11 Prove theorems about
parallelograms; use theorems about parallelograms
to solve problems.
MAFS.912.G-MG.1.1 Use geometric shapes, their
measures and their properties to describe objects.
MAFS.912.G-GPE.2.4 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.
This topic is the second part on exploring
the properties and characteristics of
quadrilateral, using coordinates to
distinguish between different types of
quadrilaterals, and finding area and
perimeter.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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Section 9, Topic 3:
Introduction to Quadrilaterals – Part 3
MAFS.912.G-CO.1.1 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.
MAFS.912.G-CO.3.11 Prove theorems about
parallelograms; use theorems about parallelograms
to solve problems.
MAFS.912.G-MG.1.1 Use geometric shapes, their
measures and their properties to describe objects.
MAFS.912.G-GPE.2.4 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.
This topic is the third part on exploring
and mostly applying the properties and
characteristics of quadrilateral.
Section 9, Topic 4:
Parallelograms – Part 1
MAFS.912.G-CO.1.1 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.
MAFS.912.G-CO.3.11 Prove theorems about
parallelograms; use theorems about parallelograms
to solve problems.
This topic focuses on using theorems of
parallelograms to solve problems or
prove certain characteristics or
relationships in quadrilaterals.
Section 9, Topic 5:
Parallelograms – Part 2
MAFS.912.G-CO.1.1 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.
MAFS.912.G-CO.3.11 Prove theorems about
parallelograms; use theorems about parallelograms
to solve problems.
This topic is the second part on on using
theorems of parallelograms to solve
problems or prove certain characteristics
or relationships in quadrilaterals.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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Section 9, Topic 6:
Rectangles and Squares – Part 1
MAFS.912.G-CO.1.1 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.
MAFS.912.G-CO.3.11 Prove theorems about
parallelograms; use theorems about parallelograms
to solve problems.
This topic focuses on using properties and
theorems of rectangles to solve problems
or prove certain characteristics or
relationships in quadrilaterals.
Section 9, Topic 7:
Rectangles and Squares – Part 2
MAFS.912.G-CO.1.1 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.
MAFS.912.G-CO.3.11 Prove theorems about
parallelograms; use theorems about parallelograms
to solve problems.
This topic focuses on using properties and
theorems of squares and rhombi to solve
problems or prove certain characteristics
or relationships in quadrilaterals.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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SECTION 10: QUADRILATERALS – PART 2
Section 10, Topic 1:
Rhombi
MAFS.912.G-CO.1.1 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.
MAFS.912.G-CO.3.11 Prove theorems about
parallelograms; use theorems about
parallelograms to solve problems.
This topic focuses on using properties and
theorems of rhombi, specifically, to solve
problems or prove certain characteristics or
relationships in quadrilaterals.
Section 10, Topic 2:
Kites
MAFS.912.G-CO.1.1 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.
MAFS.912.G-MG.1.1 Use geometric shapes,
their measures and their properties to describe
objects.
This topic focuses on using properties and
theorems of kites to solve problems or prove
certain characteristics or relationships in
quadrilaterals.
Section 10, Topic 3:
Trapezoids
MAFS.912.G-CO.1.1 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.
MAFS.912.G-MG.1.1 Use geometric shapes,
their measures and their properties to describe
objects.
This topic focuses on using properties and
theorems of trapezoids to solve problems or
prove certain characteristics or relationships in
quadrilaterals.
Section 10, Topic 4:
Midsegment of Trapezoids
MAFS.912.G-CO.1.1 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.
MAFS.912.G-MG.1.1 Use geometric shapes,
their measures and their properties to describe
objects.
This topic focuses on using the Midsegment
theorem for trapezoids to solve problems or
prove certain characteristics or relationships in
quadrilaterals.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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Section 10, Topic 5:
Quadrilaterals in Coordinate Geometry – Part 1
MAFS.912.G-CO.1.1 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.
MAFS.912.G-GPE.2.4 Use coordinates to prove
simple geometric theorems algebraically.
MAFS.912.G-GPE.2.7 Use coordinates to
compute perimeters of polygons and areas of
triangles and rectangles, e.g., using the
distance formula.
This topic revisits the distance formula,
midpoint formula and slope formula to use
when developing coordinate geometry proofs
for quadrilaterals and identifying different
types of quadrilaterals based on the
coordinates of their vertices.
Section 10, Topic 6:
Quadrilaterals in Coordinate Geometry – Part 2
MAFS.912.G-CO.1.1 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.
MAFS.912.G-CO.3.11 Students will prove
theorems about parallelograms. Students will
use properties of parallelograms to solve
problems.
MAFS.912.G-GPE.2.4 Use coordinates to prove
simple geometric theorems algebraically.
MAFS.912.G-GPE.2.7 Use coordinates to
compute perimeters of polygons and areas of
triangles and rectangles, e.g., using the
distance formula.
This topic continue to revisit the distance
formula, midpoint formula and slope formula to
use when developing coordinate geometry
proofs for quadrilaterals and identifying
different types of quadrilaterals based on the
coordinates of their vertices.
Section 10, Topic 7:
Constructions of Quadrilaterals
MAFS.912.G-CO.4.12 Make formal geometric
constructions with a variety of tools and
methods.
MAFS.912.G-CO.4.13 Construct an equilateral
triangle, a square, and a regular hexagon
inscribed in a circle.
This topic focuses on constructing
quadrilaterals such as rectangles, kites and
trapezoids. It also emphasizes on how to use
construction techniques to make sure all the
properties of the quadrilaterals are evident in
the constructions.
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SECTION 11: Properties of 𝑵-gons
Section 11, Topic 1:
Introduction of 𝑁-gons – Part 1
MAFS.912.G-GPE.2.7 Use coordinates to
computer perimeter and areas of polygons,
triangles and rectangles. (In items that require
students to find the area, the polygon must be
able to be divided into triangles or rectangles.)
MAFS.912.G-MG.1.1 Use geometric shapes.
their measures, and their properties to describe
objects.
MAFS.912.G-SRT.2.5 Use congruence and
similarity criteria for triangles to solve problems
and to prove relationships in geometric figures.
The topic introduces polygons with more than 4
sides, and explores the different features of
these polygons as well as ways to break them
into polygons with 3 or 4 sides.
Section 11, Topic 2:
Introduction of 𝑁-gons – Part 2
MAFS.912.G-GPE.2.7 Use coordinates to
computer perimeter and areas of polygons,
triangles and rectangles. (In items that require
students to find the area, the polygon must be
able to be divided into triangles or rectangles.)
MAFS.912.G-MG.1.1 Use geometric shapes.
their measures, and their properties to describe
objects.
MAFS.912.G-SRT.2.5 Use congruence and
similarity criteria for triangles to solve problems
and to prove relationships in geometric figures.
The topic continues to explore the different
features of polygons with more than 4 sides, as
well as strategies to find area and perimeter.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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Section 11, Topic 3:
Angles of 𝑁-gons – Part 1
MAFS.912.G-CO.1.1 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.
MAFS.912.G-MG.1.1 Use geometric shapes.
their measures, and their properties to describe
objects.
MAFS.912.G-SRT.2.5 Use congruence and
similarity criteria for triangles to solve problems
and to prove relationships in geometric figures.
This topic focuses on calculating the base
angles and interior angles of regular polygons
with more than 4 sides.
Section 11, Topic 4:
Angles of 𝑁-gons – Part 2
MAFS.912.G-CO.1.1 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.
MAFS.912.G-MG.1.1 Use geometric shapes.
their measures, and their properties to describe
objects.
MAFS.912.G-SRT.2.5 Use congruence and
similarity criteria for triangles to solve problems
and to prove relationships in geometric figures.
This topic focuses on calculating the exterior
angles of regular polygons with more than 4
sides, and angles of irregular polygons.
Section 11, Topic 5:
Segments in regular 𝑁-gons – Part 1
MAFS.912.G-MG.1.1 Use geometric shapes.
their measures, and their properties to describe
objects.
MAFS.912.G-MG.1.3 Apply geometric methods
to solve design problems.
This topic focuses on finding diagonals,
diameters, radius and apothem in polygons
with more than 4 sides.
Section 11, Topic 6:
Segments in regular 𝑁-gons – Part 2
MAFS.912.G-MG.1.1 Use geometric shapes.
their measures, and their properties to describe
objects.
MAFS.912.G-MG.1.3 Apply geometric methods
to solve design problems.
This topic focuses on finding side, radius and
apothem in polygons with more than 4 sides
using trigonometry.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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Section 11, Topic 7:
Area of 𝑁-gons
MAFS.912.G-GPE.2.7 Use coordinates to
compute perimeters of polygons and areas of
triangles and rectangles.
MAFS.912.G-MG.1.3 Apply geometric methods
to solve design problems.
MAFS.912.G-MG.1.1 Use geometric shapes,
their measures, and their properties to describe
objects.
MAFS.912.G-SRT.2.5 Use congruence criteria for
triangles to solve problems and prove
geometric relationships.
This topic focuses on finding the area of regular
and irregular polygons with more than 4 sides.
Section 11, Topic 8:
Coordinate Geometry – Part 1
MAFS.912.G-GPE.2.4 Use coordinates to prove
simple geometric theorems algebraically.
MAFS.912.G-GPE.2.7 Use coordinates to
compute perimeters of polygons and areas of
triangles and rectangles.
MAFS.912.G-MG.1.1 Use geometric shapes,
their measures, and their properties to describe
objects.
This topic focuses on using coordinate
geometry to classify polygons with more than 4
sides.
Section 11, Topic 9:
Coordinate Geometry – Part 2 MAFS.912.G-GPE.2.4 Use coordinates to prove
simple geometric theorems algebraically.
MAFS.912.G-GPE.2.7 Use coordinates to
compute perimeters of polygons and areas of
triangles and rectangles.
MAFS.912.G-MG.1.1 Use geometric shapes,
their measures, and their properties to describe
objects.
This topic focuses on using coordinate
geometry to classify polygons with more than 4
sides.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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SECTION 12: CIRCLES – PART 1
Section 12, Topic 1:
Circumference of a Circle
MAFS.912.G-C.1.2 Identify and describe relationships among
inscribed angles, radii, and chords. Include the relationships
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. {Items may include finding or describing the
length of arcs when given information.}
MAFS.912.G-GMD.1.1 Give an informal argument for the
formulas for the circumference of a circle, area of a circle,
volume of a circle, pyramid and cone.
This topic focuses on calculating
and using the circumference of a
circle to solve problems.
Section 12, Topic 2:
Arcs and Circumference of a Circle
MAFS.912.G-C.1.2 Identify and describe relationships among
inscribed angles, radii, and chords. Include the relationships
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. {Items may include finding or describing the
length of arcs when given information.}
MAFS.912.G-GMD.1.1 Give an informal argument for the
formulas for the circumference of a circle, area of a circle,
volume of a circle, pyramid and cone.
This topic focuses on calculating
and using the circumference of a
circle to solve problems.
Section 12, Topic 3:
Area of a Circle
MAFS.912.G-C.1.2 Identify and describe relationships among
inscribed angles, radii, and chords. Include the relationships
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. {Items may include finding or describing the
length of arcs when given information.}
MAFS.912.G-GMD.1.1 Give an informal argument for the
formulas for the circumference of a circle, area of a circle,
volume of a circle, pyramid and cone.
This topic focuses on calculating
and using the area of a circle to
solve problems.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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Section 12, Topic 4:
Sectors of a Circle
MAFS.912.G-C.1.2 Identify and describe relationships among
inscribed angles, radii, and chords. Include the relationships
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. {Items may include finding or describing the
length of arcs when given information.}
MAFS.912.G-C.2.5 Derive the formula for the area of a sector.
MAFS.912.G-GMD.1.1 Give an informal argument for the
formulas for the circumference of a circle, area of a circle,
volume of a circle, pyramid and cone.
This topic focuses on calculating
and using the area of a circle and
sectors to solve problems.
Section 12, Topic 5:
Circles in the Coordinate Plane: Standard
Form
MAFS.912.G-C.1.2 Identify and describe relationships among
inscribed angles, radii, and chords. Include the relationships
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.
MAFS.912.G-GPE.1.1 Derive the equation of a circle of given
center and radius using the Pythagorean Theorem; complete
the square to find the the center and radius of a circle given by
an equation.
MAFS.912.G-GPE.2.4 Use coordinates to prove simple geometric
theorems algebraically.
In this topic, students learn how
derive and apply the equation of
a circle in standard form on a
coordinate plane.
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Section 12, Topic 6:
Circles in the Coordinate Plane: General
Form
MAFS.912.G-C.1.2 Identify and describe relationships among
inscribed angles, radii, and chords. Include the relationships
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.
MAFS.912.G-GPE.1.1 Derive the equation of a circle of given
center and radius using the Pythagorean Theorem; complete
the square to find the the center and radius of a circle given by
an equation.
MAFS.912.G-GPE.2.4 Use coordinates to prove simple geometric
theorems algebraically.
In this topic, students learn how
derive and apply the equation of
a circle in general form on a
coordinate plane.
Section 12, Topic 7:
Circle Transformations
MAFS.912.G-C.1.1 Prove that all circles are similar.
MAFS.912.G-CO.1.2 Represent transformations in the plane,
describe transformations as functions that take points in the
plane as inputs and give points as outputs. Compare
transformations that preserve distance and angle to those that
do not.
MAFS.912.G-SRT.1.1 Verify experimentally the proportions of
dilations given by a center and a scale factor.
This topic focuses on
understanding how to transform
circles, especially dilating a circle
centered at the origin or centered
on another point.
Section 12, Topic 8:
Radians and Degrees
MAFS.912.G-C.1.2 Identify and describe relationships among
inscribed angles, radii, and chords. Include the relationships
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. {Items may include finding or describing the
length of arcs when given information.}
MAFS.912.G-C.2.5 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.
This topic focuses on converting
from radians to degree, and from
degrees to radians, and
understanding the applications of
radians and degrees.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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SECTION 13: CIRCLES – PART 2
Section 13, Topic 1:
Arcs and Inscribed Angles – Part 1
MAFS.912.G-C.1.2 Identify and describe relationships
among inscribed angles, radii, and chords. Include
the relationships 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.
This topic focuses on discovering and
applying inscribed angles conjectures to
solve problems.
Section 13, Topic 2:
Arcs and Inscribed Angles – Part 2
MAFS.912.G-C.1.2 Identify and describe relationships
among inscribed angles, radii, and chords. Include
the relationships 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.
This topic is the second part on
discovering and applying inscribed angles
conjectures to solve problems.
Section 13, Topic 3:
Inscribed Polygons in a Circle
MAFS.912.G-C.1.3 Construct the inscribed and
circumscribed circles of a triangle, and prove
properties of angles for a quadrilateral inscribed in a
circle.
MAFS.912.G-CO.4.13 Construct an equilateral
triangle, a square, and a regular hexagon inscribed
in a circle.
This topic focuses on exploring and using
properties of a cyclic quadrilateral and
other polygons inscribed in a circle.
Section 13, Topic 4:
Constructing Inscribed Polygons in a Circle
MAFS.912.G-C.1.3 Construct the inscribed and
circumscribed circles of a triangle, and prove
properties of angles for a quadrilateral inscribed in a
circle.
MAFS.912.G-CO.4.13 Construct an equilateral
triangle, a square, and a regular hexagon inscribed
in a circle.
This topic focuses on constructing an
equilateral triangle, a square, and a
regular hexagon inscribed in a circle.
Section 13, Topic 5:
Tangent Lines, Secants and Chords – Part 1
MAFS.912.G-C.1.2 Identify and describe relationships
among inscribed angles, radii, and chords. Include
the relationships 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.
This topic focuses on proving and
applying properties and theorems about
tangent lines, secants and chords.
Theorems include the Tangent theorem
and the Tangent Segment theorem.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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Section 13, Topic 6:
Tangent Lines, Secants and Chords – Part 2
MAFS.912.G-C.1.2 Identify and describe relationships
among inscribed angles, radii, and chords. Include
the relationships 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.
This topic keeps focusing on proving and
applying properties and theorems about
tangent lines, secants and chords.
Theorems include the perpendicular-to-a-
chord theorem. chords distance to center
theorem, and intersecting chords
theorem.
Section 13, Topic 7:
Circumscribed Angles and Beyond – Part 1
MAFS.912.G-C.1.2 Identify and describe relationships
among inscribed angles, radii, and chords. Include
the relationships 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.
This topic focuses on identifying and
calculating tangent-chord angles and
circumscribed angles.
Section 13, Topic 8:
Circumscribed Angles and Beyond – Part 2
MAFS.912.G-C.1.2 Identify and describe relationships
among inscribed angles, radii, and chords. Include
the relationships 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.
This topic keeps identifying and
calculating tangent-chord angles and
circumscribed angles.
Section 13, Topic 9:
Constructing Inscribed and Circumscribed
Circles of Triangles
MAFS.912.G-C.1.3 Construct the inscribed and
circumscribed circles of a triangle, and prove
properties of angles for a quadrilateral inscribed in a
circle.
MAFS.912.G-CO.4.13 Construct an equilateral
triangle, a square, and a regular hexagon inscribed
in a circle.
This topic focuses on constructing
inscribed and circumscribed circles on a
triangle.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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SECTION 14: THREE DIMENSIONAL GEOMETRY
Section 14, Topic 1:
Geometry Nets and Three Dimensional Figures
MAFS.912.G-GMD.1.1 Give an informal
argument for the formulas for the
circumference of a circle, area of a circle,
volume of a cylinder, pyramid, and cone.
This topic focuses on understanding how to
unfold a geometric solid into a geometry nets
and vice versa, including the discussion of the
different components of the nets.
Section 14, Topic 2:
Cavalieri’s Principle for Area
MAFS.912.G-GMD.1.1 Give an informal
argument for the formulas for the
circumference of a circle, area of a circle,
volume of a cylinder, pyramid, and cone.
MAFS.912.G-MG.1.1 Use geometric shapes, their
measures, and their properties to describe
objects.
This topic focuses on the 2-dimensional and 3-
dimensional case for the use of the Cavalieri’s
Principle to estimate area.
Section 14, Topic 3:
Cavalieri’s Principle for Volume
MAFS.912.G-GMD.1.1 Give an informal
argument for the formulas for the
circumference of a circle, area of a circle,
volume of a cylinder, pyramid, and cone.
MAFS.912.G-GMD.2.4 Identify the shapes of
two-dimensional cross-sections of three-
dimensional objects and identify three-
dimensional objects generated by rotations of
two-dimensional objects.
MAFS.912.G-MG.1.1 Use geometric shapes, their
measures, and their properties to describe
objects.
This topic focuses on the 3-dimensional case for
the use of the Cavalieri’s Principle to estimate
volume.
Section 14, Topic 4:
Volume of Prisms and Cylinders
MAFS.912.G-GMD.1.3 Use volume for cylinders,
pyramids, cones, and spheres to sovle
problems.
MAFS.912.G-MG.1.1 Use geometric shapes, their
measures, and their properties to describe
objects.
MAFS.912.G-MG.1.2 Apply concepts of density
based on area and volume in modeling
situations.
This topic focuses on understanding, calculating
and applying the volume of prisms and
cylinders.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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Section 14, Topic 5:
Surface Area of Prisms and Cylinders
MAFS.912.G-MG.1.1 Use geometric shapes, their
measures, and their properties to describe
objects.
MAFS.912.G-MG.1.2 Apply concepts of density
based on area and volume in modeling
situations.
This topic focuses on understanding, calculating
and applying the lateral area and surface area
of prisms and cylinders.
Section 14, Topic 6:
Volume of Pyramids and Cones
MAFS.912.G-GMD.1.3 Use volume for cylinders,
pyramids, cones, and spheres to sovle
problems.
MAFS.912.G-MG.1.1 Use geometric shapes, their
measures, and their properties to describe
objects.
MAFS.912.G-MG.1.2 Apply concepts of density
based on area and volume in modeling
situations.
This topic focuses on understanding, calculating
and applying the volume of pyramids and
cones.
Section 14, Topic 7:
Surface Area of Pyramids and Cones
MAFS.912.G-MG.1.1 Use geometric shapes, their
measures, and their properties to describe
objects.
This topic focuses on understanding, calculating
and applying the lateral area and surface area
of pyramids and cones.
Section 14, Topic 8:
Spheres
MAFS.912.G-GMD.1.3 Use volume for cylinders,
pyramids, cones, and spheres to solve
problems.
MAFS.912.G-MG.1.1 Use geometric shapes, their
measures, and their properties to describe
objects.
MAFS.912.G-MG.1.3 Apply geometric methods
to solve design problems.
This topic focuses on understanding, calculating
and applying the surface area and volume of
spheres and hemispheres.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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Section 14, Topic 9:
Similar Shapes
MAFS.912.G-GMD.1.3 Use volume for cylinders,
pyramids, cones, and spheres to solve
problems.
MAFS.912.G-SRT.1.2 Given two figures, use the
definition 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.
This topic explores the characteristics of similar
solid and how to use those characteristics to find
lateral area, surface area, volume or missing
segments.
Section 14, Topic 10:
Cross Sections and Plane Rotations
MAFS.912.G-GMD.2.4 Identify the shapes of
two-dimensional cross-sections of three-
dimensional objects, and identify three-
dimensional objects generated by rotations of
two-dimensional objects.
MAFS.912.G-MG.1.1 Use geometric shapes, their
measures, and their properties to describe
objects.
This topic focuses on visualizing the 2-
dimensional cross-sections of prisms by removing
part of the solid. It also explores the plane
rotations of 2-dimensional figures to form 3-
dimensional figures.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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SECTION 15: ADDITIONAL MODELING WITH GEOMETRY
Section 15, Topic 1:
Density
MAFS.912.G-MG.1.2 Apply concepts of density
based on area and volume in modeling
situations.
MAFS.912.G-GMD.1.3 Use volume formulas for
cylinders, pyramids, cones, and spheres to solve
problems.
This topic focuses on how to apply concepts of
density based on area and volume in real world
modeling situations.
Section 15, Topic 2:
Minimizing and Maximizing
MAFS.912.G-MG.1.3 Apply geometric methods
to solve design problems.
MAFS.912.G-GMD.1.3 Use volume formulas for
cylidners, pyramids, cones and spheres to solve
problems.
MAFS.912.G-MG.1.1 Use geometric shapes, their
measures, and their properties to describe
objects.
This topic focuses on how to apply geometric
methods to real world modeling situation such as
minimizing cost or maximizing profit or area.
Section 15, Topic 3:
Angles of Elevation and Depression
MAFS.912.G-SRT.3.6 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.
MAFS.912.G-SRT.3.7 Explain and use the
relationship between the sine and cosine of
complementary angles.
MAFS.912.G-SRT.3.8 Use trigonometric ratios and
Pythagorean Theorem to solve right triangles in
applied problems.
This topic discusses how to use trigonometric
ratios and Pythagorean Theorem to solve right
triangles that are modeled or formed by angles
of elevation and depression. Students learn how
to calculate angles, distance and height.
2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
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Section 15, Topic 4:
Typographic Grid Systems Based on Ratios
MAFS.912.G-MG.1.3 Apply geometric methods
to solve design problems.
MAFS.912.G-GMD.1.3 Use volume formulas for
cylinders, pyramids, cones, and spheres to solve
problems.
MAFS.912.G-GPE.2.7 Use coordinates to
computer perimeters of polygons and areas of
triangles and rectangles, e.g., using the
distance formula
This topic focuses on how to apply geometric
methods to solve design problems when working
with typographic grid systems based on ratios.
Section 15, Topic 5:
Areas in Real-World Contexts
MAFS.912.G-MG.1.1 Use geometric shapes, their
measures, and their properties to describe
objects.
MAFS.912.G-MG.1.3 Apply geometric methods
to solve design problems.
This topic applies the concept of 2-dimensional
areas and 3-dimensional lateral and surface
areas to solve real world problems.
Section 15, Topic 6:
Volume in Real-World Contexts
MAFS.912.G-MG.1.1 Use geometric shapes, their
measures, and their properties to describe
objects.
MAFS.912.G-MG.1.3 Apply geometric methods
to solve design problems.
MAFS.912.G-GMD.1.3 Use volume formulas for
cylinders, pyramids, cones, and spheres to solve
problems.
This topic applies the concept of volume to
solve real world problems.