2016-2017 Math Nation Geometry Scope & Sequence: MAFS ... · 2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment 2 SECTION 1: INTRODUCTION TO GEOMETRY

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



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






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-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-GPE.2.6 Find the point on a given

line segment between two given points that

partitions a segment in a given ratio.


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.



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


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


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-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









This topic is the second part on identifying

parallel and perpendicular lines, and

writing equations of lines parallel or

perpendicular to another line.



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






do not.







itself.

This topic focuses on performing

translations of points and line

segments on a coordinate plane.



Section 2, Topic 3:

Examining and Using Dilations – Part 1






do not.







itself.


dilations of points and line


Section 2, Topic 4:

Examining and Using Dilations – Part 2






do not.







itself.


dilations of points and line




Section 2, Topic 5:

Examining and Using Rotations






do not.





reflection, or translation, draw the transformed figure. Specify a


itself.


rotation of points and line segments

on a coordinate plane.

Section 2, Topic 6:

Examining and Using Reflections






do not.





reflection, or translation, draw the transformed figure. Specify a


itself.


reflection of points and line




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.



SECTION 3: ANGLES

Section 3, Topic 1:

Introduction to Angles – Part 1






This topic focuses on how to measure and

classify an angle.

Section 3, Topic 2:

Introduction to Angles – Part 2






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




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









This topic focuses on discussing the special

Types of angle pairs formed by transversals

and non-parallel lines.



Section 3, Topic 6:


Transversals and Parallel Lines – Part 1









This topic focuses on the relationship

between angle pairs when the transversal

cut two parallel lines.

Section 3, Topic 7:


Transversals and Parallel Lines – Part 2









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









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.

MAFS.912.G-CO.1.5 Given a geometric figure

and a rotation, reflection, or translation, draw

the transformed figure.


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.



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-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


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 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.


translations of polygons on a coordinate

plane and finding the coordinates or

location of the image and the pre-

image.



Section 4, Topic 5:

Reflection of Polygons














itself.


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














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.



Section 4, Topic 7:

Rotation of Polygons – Part 2









perpendicular lines, parallel l ines and line segments.





itself.

This is the second part of the set of topics

focusing on performing rotations of

polygons on a coordinate plane and



Section 4, Topic 8:

Dilation of Polygons







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





SECTION 5: INTRODUCTION TO POLYGONS – PART 2

Section 5, Topic 1:

Compositions of Transformations of

Polygons – Part 1


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





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.





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.



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



This topic focuses on distinguishing

between transformations that produce

congruent images and transformations

that produce similar images.



SECTION 6: TRIANGLES – PART 1

Section 6, Topic 1:

Introduction to Triangles – Part 1


triangles; use theorems about triangles to solve

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


triangles; use theorems about triangles to solve

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


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




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







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







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








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








This topic focuses on using triangle congruency

theorems to find missing sides by using

algebraic skills.



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



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.



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



This topic keeps focusing on

understanding and applying the

Triangle Midsegment Theorem.

Section 7, Topic 5:

Triangle Inequalities



This topic introduces the Triangle

Inequality Theorem, the Hinge Theorem

and the Converse of the Hinge

Theorem,

Section 7, Topic 6:

More Triangle Proofs



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-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.



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.






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


applied problems.

This topic introduces Converse of the

Pythagorean Theorem and focuses on

its applications.

Section 8, Topic 3:

Proving Right Triangles Congruent


triangle congruence (ASA, SAS, SSS, and Hypotenuse-

Leg) follow from the definition of congruence in terms

of rigid motions.



This topic teaches us the Hypotenuse-

Leg Theorem to prove right triangles

congruent.

Section 8, Topic 4:

Special Right Triangles: 45-45-90





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



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



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.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.



Section 8, Topic 7:

Right Triangles Similarity – Part 2




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.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.



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.



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.



SECTION 9: QUADRILATERALS – PART 1

Section 9, Topic 1:

Introduction to Quadrilaterals – Part 1







parallelograms; use theorems about parallelograms

to solve problems.


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:









to solve problems.




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:









to solve problems.




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








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








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








to solve problems.

This topic focuses on using properties and

theorems of rectangles to solve problems

or prove certain characteristics or


Section 9, Topic 7:

Rectangles and Squares – Part 2








to solve problems.


theorems of squares and rhombi to solve

problems or prove certain characteristics

or relationships in quadrilaterals.



SECTION 10: QUADRILATERALS – PART 2


Rhombi







parallelograms; use theorems about

parallelograms to solve problems.


theorems of rhombi, specifically, to solve

problems or prove certain characteristics or



Kites






MAFS.912.G-MG.1.1 Use geometric shapes,

their measures and their properties to describe

objects.


theorems of kites to solve problems or prove

certain characteristics or relationships in

quadrilaterals.


Trapezoids








objects.


theorems of trapezoids to solve problems or

prove certain characteristics or relationships in

quadrilaterals.


Midsegment of Trapezoids








objects.

This topic focuses on using the Midsegment

theorem for trapezoids to solve problems or

prove certain characteristics or relationships in

quadrilaterals.




Quadrilaterals in Coordinate Geometry – Part 1






MAFS.912.G-GPE.2.4 Use coordinates to prove

simple geometric theorems algebraically.


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.


Quadrilaterals in Coordinate Geometry – Part 2






MAFS.912.G-CO.3.11 Students will prove

theorems about parallelograms. Students will

use properties of parallelograms to solve

problems.






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.


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.


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.



SECTION 11: Properties of 𝑵-gons


Introduction of 𝑁-gons – Part 1


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.




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.


Introduction of 𝑁-gons – Part 2


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.)



objects.




The topic continues to explore the different

features of polygons with more than 4 sides, as

well as strategies to find area and perimeter.




Angles of 𝑁-gons – Part 1








objects.




This topic focuses on calculating the base

angles and interior angles of regular polygons

with more than 4 sides.


Angles of 𝑁-gons – Part 2








objects.




This topic focuses on calculating the exterior

angles of regular polygons with more than 4

sides, and angles of irregular polygons.


Segments in regular 𝑁-gons – Part 1



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.


Segments in regular 𝑁-gons – Part 2



objects.



This topic focuses on finding side, radius and

apothem in polygons with more than 4 sides

using trigonometry.




Area of 𝑁-gons








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.


Coordinate Geometry – Part 1








objects.

This topic focuses on using coordinate

geometry to classify polygons with more than 4

sides.


Coordinate Geometry – Part 2 MAFS.912.G-GPE.2.4 Use coordinates to prove







objects.

This topic focuses on using coordinate

geometry to classify polygons with more than 4

sides.



SECTION 12: CIRCLES – PART 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.


Arcs and Circumference of a Circle












and using the circumference of a

circle to solve problems.


Area of a Circle












and using the area of a circle to

solve problems.




Sectors of a Circle








MAFS.912.G-C.2.5 Derive the formula for the area of a sector.





and using the area of a circle and

sectors to solve problems.


Circles in the Coordinate Plane: Standard

Form






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.




Circles in the Coordinate Plane: General

Form







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.


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


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.


Radians and Degrees








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.



SECTION 13: CIRCLES – PART 2


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


This topic focuses on discovering and

applying inscribed angles conjectures to

solve problems.


Arcs and Inscribed Angles – Part 2








This topic is the second part on

discovering and applying inscribed angles

conjectures to solve problems.


Inscribed Polygons in a Circle




circle.


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.


Constructing Inscribed Polygons in a Circle




circle.



in a circle.

This topic focuses on constructing an

equilateral triangle, a square, and a

regular hexagon inscribed in a circle.


Tangent Lines, Secants and Chords – Part 1








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.




Tangent Lines, Secants and Chords – Part 2








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.


Circumscribed Angles and Beyond – Part 1








This topic focuses on identifying and

calculating tangent-chord angles and

circumscribed angles.


Circumscribed Angles and Beyond – Part 2








This topic keeps identifying and

calculating tangent-chord angles and

circumscribed angles.


Constructing Inscribed and Circumscribed

Circles of Triangles




circle.



in a circle.


inscribed and circumscribed circles on a

triangle.



SECTION 14: THREE DIMENSIONAL GEOMETRY


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.


Cavalieri’s Principle for Area






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.


Cavalieri’s Principle for Volume





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.



objects.

This topic focuses on the 3-dimensional case for

the use of the Cavalieri’s Principle to estimate

volume.


Volume of Prisms and Cylinders

MAFS.912.G-GMD.1.3 Use volume for cylinders,

pyramids, cones, and spheres to sovle

problems.



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.




Surface Area of Prisms and Cylinders



objects.



situations.


and applying the lateral area and surface area

of prisms and cylinders.


Volume of Pyramids and Cones


pyramids, cones, and spheres to sovle

problems.



objects.



situations.


and applying the volume of pyramids and

cones.


Surface Area of Pyramids and Cones



objects.


and applying the lateral area and surface area

of pyramids and cones.


Spheres


pyramids, cones, and spheres to solve

problems.



objects.




and applying the surface area and volume of

spheres and hemispheres.




Similar Shapes


pyramids, cones, and spheres to solve

problems.


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



This topic explores the characteristics of similar

solid and how to use those characteristics to find

lateral area, surface area, volume or missing

segments.


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.



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.



SECTION 15: ADDITIONAL MODELING WITH GEOMETRY


Density



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.


Minimizing and Maximizing




cylidners, pyramids, cones and spheres to solve

problems.



objects.

This topic focuses on how to apply geometric

methods to real world modeling situation such as

minimizing cost or maximizing profit or area.


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.



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.




Typographic Grid Systems Based on Ratios





problems.




distance formula

This topic focuses on how to apply geometric

methods to solve design problems when working

with typographic grid systems based on ratios.


Areas in Real-World Contexts



objects.



This topic applies the concept of 2-dimensional

areas and 3-dimensional lateral and surface

areas to solve real world problems.


Volume in Real-World Contexts



objects.





problems.

This topic applies the concept of volume to

solve real world problems.

Documents

2016-2017 Math Nation Geometry Scope & Sequence: MAFS ... · 2016-2017 Math Nation Geometry Scope & Sequence: MAFS Topics and Standards Alignment 2 SECTION 1: INTRODUCTION TO GEOMETRY