2016%2017math’nation’geometry’scope’&’sequence:’mafs...
TRANSCRIPT
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 1
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 25-‐27
Section 11: Properties of 𝑁-‐gons 28-‐30
Section 12: Circles – Part 1 31-‐34
Section 13: Circles – Part 2 35-‐36
Section 14: Three Dimensional Geometry 37-‐39
Section 15: Additional Modeling with Geometry
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 2
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.
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 3
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
www.MathNation.com 4
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.
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 5
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
www.MathNation.com 6
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.
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 7
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 line 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.
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 8
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.
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 9
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.
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.
This topic focuses on applying transformations to figures formed by parallel
lines crossed by a transversal. Most importantly, it focuses on angle-preserving
transformations.
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 10
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.
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.
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 11
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.
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
www.MathNation.com 12
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.
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
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
www.MathNation.com 13
transformations that will carry a given figure onto itself.
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 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 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
www.MathNation.com 14
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
This topic focuses on distinguishing between transformations that produce congruent
images and transformations that produce similar images.
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 15
triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
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.
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 16
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.
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.
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.
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 17
MAFS.912.G-SRT.2.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figure.
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
www.MathNation.com 18
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.
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
www.MathNation.com 19
MAFS.912.G-SRT.2.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
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
www.MathNation.com 20
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.
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
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
www.MathNation.com 21
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.
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.
This topic is the second part on working with similar right triangles, but with more
applications problems.
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 22
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.
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
www.MathNation.com 23
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.
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
This topic is the third part on exploring and mostly applying the properties and
characteristics of quadrilateral.
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 24
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.
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.
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
This topic focuses on using properties and theorems of rectangles to solve problems or
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 25
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.
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
www.MathNation.com 26
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
www.MathNation.com 27
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.
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 28
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.
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.
This topic focuses on calculating the base angles and interior angles of regular polygons
with more than 4 sides.
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 29
MAFS.912.G-SRT.2.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
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.
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.
This topic focuses on finding the area of regular and irregular polygons with more than 4 sides.
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 30
MAFS.912.G-SRT.2.5 Use congruence criteria for triangles to solve problems and prove geometric relationships.
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
www.MathNation.com 31
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.}
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
www.MathNation.com 32
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.
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.
In this topic, students learn how derive and apply the equation of a circle in standard form
on a coordinate plane.
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 33
MAFS.912.G-GPE.2.4 Use coordinates to prove simple geometric theorems algebraically.
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;
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
www.MathNation.com 34
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.
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 35
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
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
www.MathNation.com 36
angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
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
www.MathNation.com 37
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
www.MathNation.com 38
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.
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
This topic explores the characteristics of similar solid and how to use those characteristics to find
lateral area, surface area, volume or missing segments.
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 39
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.
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
www.MathNation.com 40
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.
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.
This topic focuses on how to apply geometric methods to solve design problems when working
with typographic grid systems based on ratios.
2016-‐‑2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment
www.MathNation.com 41
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
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.