Complete Geometry Pacing Chart - High School Math Teachers€¦ · COMPLETE GEOMETRY PACING CHART HIGHSCHOOLMATHTEACHERS.COM@2018 . Contents Unit 1 Geometric Transformation..... 2

COMPLETE GEOMETRY PACING CHART

HIGHSCHOOLMATHTEACHERS.COM@2018

Contents

Unit 1 Geometric Transformation ........................................................................................................................................................... 2

Unit 2 Angles and Line ........................................................................................................................................................................... 7

Unit 3 Triangles .................................................................................................................................................................................... 11

Unit 4 Triangle Congruence.................................................................................................................................................................. 15

Unit 5 Similarity Transformation.......................................................................................................................................................... 19

Unit 6 Right Triangle Relationships and Trigonometry ....................................................................................................................... 23

Unit 7 Quadrilaterals ............................................................................................................................................................................. 27

Unit 8 Circles ........................................................................................................................................................................................ 31

Unit 9 Geometric Modeling in Two Dimensions ................................................................................................................................. 36

Unit 10 Understanding and Modeling Three Dimensional Figures ...................................................................................................... 41

Unit 1 Pacing Chart

HighSchoolMathTeachers.com @2018

Page 2

Unit 1 Unit Week Day CCSS Standards Objective I Can Statements

Unit 1 Geometric

Transformations

Week 1 – Definitions

1

CCSS.MATH.CONTENT.HSG.CO.A.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.

Know precise definitions of angle, based on the undefined notions of

point, line, distance along a line, and distance around a circular arc. Give types the basic types of angles

that are not described using any form algebra.

I can define an angle I can identify situations or cases where angles

appear in day to day life

Unit 1 Geometric

Transformations


2




Know precise definitions of circle and line segment based on the

undefined notions of point, line, distance along a line, and distance

around a circular arc. Parts of circles; types of circles when in

groups.

I can define and identify line segment

I can define and identify a circle

I can identify lines and segments found in a

circle I can identify situations or cases where circles are applied in real life

situation

Unit 1 Geometric

Transformations


3




Know precise definitions of perpendicular line based on the undefined notions of point, line,


I can define and identify perpendicular line

I can be able to identify a case where

perpendicular lines have been used in a classroom

Unit 1 Pacing Chart


Page 3

Unit 1 Geometric

Transformations


4




Know precise definitions of parallel lines based on the undefined

notions of point, line, distance along a line, and distance around a

circular arc.

I can define and identify parallel lines

I can be able to identify a case where parallel lines

have been used in a classroom

Unit 1 Geometric

Transformations


5 Assessment Assessment Assessment

Unit 1 Geometric

Transformations

Week 2 – Rotations,

Reflections, and

Translations

6

CCSS.MATH.CONTENT.HSG.CO.A.2 Represent transformations in the

plane using, e.g., transparencies and geometry software; describe

transformations as functions that take points in the plane as inputs and give

other points as outputs. Compare transformations that preserve

distance and angle to those that do not (e.g., translation versus horizontal

stretch).

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.

Give short and precise definitions of transformations (translation, reflection, rotation, dilation).

Compare transformations that preserve distance and angle to

those that do not (e.g., translation versus horizontal stretch).

I can define what a transformation and state

a few common transformations.

I can briefly say what these transformations

are I can describe

transformation as functions having inputs

and outputs I can compare

transformations that preserve distance and

angle with those that do not

Unit 1 Pacing Chart


Page 4

Unit 1 Geometric

Transformations


Reflections, and

Translations

7

CCSS.MATH.CONTENT.HSG.CO.A.3 Given a rectangle, parallelogram,

trapezoid, or regular polygon, describe the rotations and reflections

that carry it onto itself.

Given a rectangle, parallelogram, trapezoid, or regular polygon,

describe the rotations and reflections that carry it onto itself.

I can describe the rotations and reflections

that carry a rectangle, parallelogram, trapezoid, or regular polygon into

itself

Unit 1 Geometric

Transformations


Reflections, and

Translations

8

CCSS.MATH.CONTENT.HSG.CO.A.4 Develop definitions of rotations,

reflections, and translations in terms of angles, circles, perpendicular lines,

parallel lines, and line segments.

Develop definitions of rotations, reflections, and translations in

terms of angles, circles, perpendicular lines, parallel lines,

and line segments.

I can develop definitions of rotations, reflections, and translations in terms

of angles, circles, perpendicular lines,

parallel lines, and line segments.

Unit 1 Geometric

Transformations


Reflections, and

Translations

9

CCSS.MATH.CONTENT.HSG.CO.A.5 Given a geometric figure and a

rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or

geometry software. Specify a sequence of transformations that will

carry a given figure onto another.

Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or

geometry software. Specify a sequence of transformations that

will carry a given figure onto another.

I can draw the transformed figure (using graph paper,

tracing paper, or geometry software)

under rotation, reflection, or translation

given the object (original) figure

I can specify a sequence of transformations that will carry a given figure

onto another.

Unit 1 Pacing Chart


Page 5

Unit 1 Geometric

Transformations


Reflections, and

Translations


Unit 1 Geometric

Transformations

Week 3 – Congruence

11

CCSS.MATH.CONTENT.HSG.CO.B.6 Use geometric descriptions of rigid motions to transform figures and to

predict the effect of a given rigid motion on a given figure; given two

figures, use the definition of congruence in terms of rigid motions

to decide if they are congruent.

Use geometric descriptions of rigid motions to transform figures (2d-

figures)

I can use geometric descriptions of rigid

motions to transform figures (2d- figures)

Unit 1 Geometric

Transformations


12





Given two figures,the image and the object, identify the

transformation(s) involved.

I can identify the transformation(s)

involved from one figure to another (image to an

object)

Unit 1 Geometric

Transformations


13





Use geometric descriptions of rigid motion to predict the effect of a

given rigid motion on a given figure

I can use geometric descriptions of rigid

motion to predict the effect of a given rigid

motion on a given figure

Unit 1 Pacing Chart


Page 6

Unit 1 Geometric

Transformations


14





Given two figures, use the definition of congruence in terms of rigid motions to decide if they are

congruent.

Given two figures, I can use the definition of

congruence in terms of rigid motions to decide if

they are congruent.

Unit 1 Geometric

Transformations



Unit 2 Pacing Chart


Page 7

Unit 2

Unit Week Day CCSS Standards Objective I Can Statements

Unit 2 Angles

and Lines

Week 4 – Algebraic

Definitions 16

CCSS.MATH.CONTENT.HSG.CO.A.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.

Know precise algebraic definitions of angle; complementary, supplementary

angles and angles on a straight line

I can give the precise algebraic definitions

complementary, supplementary angles and

angles on a straight line

Unit 2 Angles

and Lines


Definitions 17




Know precise algebraic definitions of angle; angles at a point

I can give precise algebraic definitions of angle at a

point

Unit 2 Angles

and Lines


Definitions 18




Know precise algebraic definitions of angle; Corresponding and alternate

angles

I can give algebraic definitions of

corresponding and alternate angles

Unit 2 Angles

and Lines


Definitions 19




Know precise algebraic definitions of angle; vertical and interior angles

I can give the precise algebraic definitions of

vertical and interior angles

Unit 2 Pacing Chart


Page 8

Unit 2 Angles

and Lines


Definitions 20 Assessment Assessment Assessment

Unit 2 Angles

and Lines

Week 5 – Prove Geometric Theorems

21

CCSS.MATH.CONTENT.HSG.CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses

parallel lines, alternate interior angles are congruent, and corresponding angles are

congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

Prove that vertical angles are congruent

I can prove that vertical angles are congruent

Unit 2 Angles

and Lines


22




Prove that alternate interior angles are congruent

I can prove that alternate interior angles are

congruent

Unit 2 Angles

and Lines


23




Prove that corresponding angles are congruent

I can prove that corresponding angles are

congruent

Unit 2 Pacing Chart


Page 9

Unit 2 Angles

and Lines


24




Prove that points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's

endpoints.

I can prove that points on a perpendicular bisector of a

line segment are exactly those equidistant from the

segment's endpoints.

Unit 2 Angles

and Lines



Unit 2 Angles

and Lines

Week 6 – Prove Algebraically

26




Given an angle, use the algebraic properties to show that alternate, vertical and corresponding angles

among others are equal

Given an angle, I can use the algebraic properties to

show that alternate, vertical and corresponding angles among others are

equal

Unit 2 Angles

and Lines


27

CCSS.MATH.CONTENT.HSG.GPE.B.5 Prove the slope criteria for parallel and

perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given

line that passes through a given point).

Prove the slope criteria for parallel and perpendicular lines

I can prove the slope criteria for parallel and

perpendicular lines

Unit 2 Pacing Chart


Page 10

Unit 2 Angles

and Lines


28

CCSS.MATH.CONTENT.HSG.GPE.B.5 Prove the slope criteria for parallel and

perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given


Use slope criteria to solve geometric problems (e.g., find the equation of a

line parallel or perpendicular to a given line that passes through a given point).

I can use slope criteria to solve geometric problems (e.g., finding the equation

of a line parallel or perpendicular to a given


Unit 2 Angles

and Lines


29

CCSS.MATH.CONTENT.HSG.GPE.B.6 Find the point on a directed line segment

between two given points that partitions the segment in a given ratio.

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

I can find the point on a directed line segment

between two given points that partitions the segment

in a given ratio.

Unit 2 Angles

and Lines



Unit 3 Pacing Chart


Page 11

Unit 3


Unit 3 Triangles

Week 7 – Prove Theorems

about Triangles 31

CCSS.MATH.CONTENT.HSG.CO.C.10 Prove theorems about triangles. Theorems include:

measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the

segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the

medians of a triangle meet at a point.

Prove that measures of interior angles of a triangle

sum to 180°

I can prove that measures of interior angles of a triangle sum

to 180°

Unit 3 Triangles


about Triangles 32





Prove that base angles of isosceles triangles are

congruent

I can prove that base angles of isosceles triangles are congruent

Unit 3 Triangles


about Triangles 33





Prove that the medians of a triangle meet at a point.

I can prove that the medians of a triangle meet at a point.

Unit 3 Triangles


about Triangles 34





Summarize the week's topics

I can prove that measures of interior angles of a triangle sum

to 180° I can prove that base angles of

isosceles triangles are congruent I can prove that the medians of a

triangle meet at a point.

Unit 3 Pacing Chart


Page 12

Unit 3 Triangles


about Triangles 35 Assessment Assessment Assessment

Unit 3 Triangles

Week 8 – Geometric

Constructions 36

CCSS.MATH.CONTENT.HSG.CO.D.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric

software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing

perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line

parallel to a given line through a point not on the line.

Make formal geometric constructions with a variety

of tools and methods (compass and straightedge,

string, reflective devices, paper folding, dynamic

geometric software, etc.). Copying a segment;

copying an angle; bisecting a segment; bisecting an

angle;

I can copy a segment; an angle; bisecting a segment and bisecting

an angle using variety of tools and methods (compass and

straightedge, string, reflective devices, paper folding, dynamic

geometric software, etc.)

Unit 3 Triangles


Constructions 37




parallel to a given line through a point not on the line.

Make formal geometric constructions with a variety

of tools and methods (compass and straightedge,

string, reflective devices, paper folding, dynamic

geometric software, etc.).constructing

perpendicular lines, including the perpendicular bisector of a line segment

I can construct perpendicular

lines, including the perpendicular bisector of a line segment using

variety of tools and methods (compass and straightedge,

string, reflective devices, paper folding, dynamic geometric

software, etc.)

Unit 3 Pacing Chart


Page 13

Unit 3 Triangles


Constructions 38




parallel to a given line through a point, not on the line.

Make formal geometric

constructions with a variety of tools and methods

(compass and straightedge, string, reflective devices, paper folding, dynamic

geometric software, etc.). Constructing a line parallel

to a given line through a point, not on the line.

I can construct a line parallel to a given line through a point, not on

the line using a variety of tools and methods (compass and

straightedge, string, reflective devices, paper folding, dynamic

geometric software, etc.)

Unit 3 Triangles


Constructions 39




parallel to a given line through a point, not on the line.

Summarize- 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.

I can copy a line segment; an angle; bisecting a segment and

an angle I can construct perpendicular

lines, including the perpendicular bisector of a line segment

I can construct a line parallel to a given line through a point, not on

the line.

Unit 3 Triangles


Constructions 40 Assessment Assessment Assessment

Unit 3 Pacing Chart


Page 14

Unit 3 Triangles

Week 9 – Inscribed and Circumscribed

Circles of a Triangle

41 CCSS.MATH.CONTENT.HSG.CO.D.13

Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.

Construct an equilateral triangle inscribed in a

circle.

I can construct an equilateral triangle inscribed in a circle.

Unit 3 Triangles





Construct a square inscribed in a circle.

I can construct a square inscribed in a circle.

Unit 3 Triangles





Construct a regular hexagon inscribed in a

circle.

I can construct a regular hexagon inscribed in a circle.

Unit 3 Triangles





Sammarize - Construction of a equilateral triangle, a

square, and a regular hexagon inscribed in a

circle

I can construct an equilateral triangle inscribed in a circle.

I can construct an square inscribed in a circle.

I can construct a regular hexagon inscribed in a circle.

Unit 3 Triangles




Unit 4 Pacing Chart


Page 15

Unit 4


Unit 4 Triangle

Congruence

Week 10 – Transformat

ions to Theorems

46

CCSS.MATH.CONTENT.HSG.CO.B.6 Use geometric descriptions of rigid motions

to transform figures and to predict the effect of a given rigid motion on a given

figure; given two figures, use the definition of congruence in terms of rigid motions to

decide if they are congruent.

Come up with a result(conclusion) as a result:

Any rigid motion preserves angle measure.

Any rigid motion of the plane is a reflection, rotation, translation or a

glide reflection. Any rigid motion maps straight

segments to straight segments, lines to lines, and circles to circles.

A rigid motion maps any three non-collinear points into non-collinear

points.

I can explain how and why: Any rigid motion preserves angle

measure. Any rigid motion of the plane is a reflection, rotation, translation or

a glide reflection. Any rigid motion maps straight segments to straight segments,

lines to lines, and circles to circles.

A rigid motion maps any three non-collinear points into non-

collinear points.

Unit 4 Triangle

Congruence


ions to Theorems

47





Come up with a result(conclusion) as a result:

Any rigid plane motion is invertible. Any rigid motion with a fixed point is

either a reflection or a rotation

I can explain how and why: Any rigid plane motion is

invertible. Any rigid motion with a fixed

point is either a reflection or a rotation

Unit 4 Triangle

Congruence


ions to Theorems

48





Come up with a conclusion as a result:

The composition of two rigid motions is also a rigid motion

The composition of a half-turn and a reflection is a glide reflection.

I can explain how and why: The composition of two rigid motions is also a rigid motion The composition of a half-turn

and a reflection is a glide reflection.

Unit 4 Pacing Chart


Page 16

Unit 4 Triangle

Congruence


ions to Theorems

49





Come up with a conclusion as a result:

Successive reflection in two intersecting mirror lines produces a

rotation about the point of intersection through twice the angle

between the mirror lines. Successive reflection in parallel

mirror lines produces a translation in a direction perpendicular to the

mirrors through a distance equal to twice the distance between the

mirrors Any rigid motion of the Euclidean

plane can be written as a composition of no more than 3

reflections.

I can explain how and why; Successive reflection in two

intersecting mirror lines produces a rotation about the point of

intersection through twice the angle between the mirror lines. Successive reflection in parallel

mirror lines produces a translation in a direction

perpendicular to the mirrors through a distance equal to twice the distance between the mirrors

and

Any rigid motion of the Euclidean

plane can be written as a composition of no more than 3

reflections.

Unit 4 Triangle

Congruence


ions to Theorems


Unit 4 Triangle

Congruence

Week 11 – Proofs of

Congruent Triangles

51

CCSS.MATH.CONTENT.HSG.CO.B.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.

Identifying Congruent sides of a triangle

I can Identify congruent sides of a triangle

Unit 4 Pacing Chart


Page 17

Unit 4 Triangle

Congruence


Congruent Triangles

52


are congruent.

Identifying Congruent angles of a triangle

I can Identify congruent angles of a triangle

Unit 4 Triangle

Congruence


Congruent Triangles

53


are congruent.

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.

I can 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.

Unit 4 Triangle

Congruence


Congruent Triangles

54


are congruent.

Show Congrence of image and object distance in dilation if the scale factor

is -1.

I can show congruence of image and object distance in dilation if

the scale factor is -1.

Unit 4 Triangle

Congruence


Congruent Triangles


Unit 4 Triangle

Congruence

Week 12 – Congruent

Parts of Congruent Figures are Congruent

56

CCSS.MATH.CONTENT.HSG.CO.B.8 Explain how the criteria for triangle

congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid

motions.

Use the postulate SSS to show that triangles are congruent. Also, apply it so solve other geometric problems.

I can use the postulate SSS to show that triangles are

congruent. I can apply the postulate so solve

other geometric problems.

Unit 4 Pacing Chart


Page 18

Unit 4 Triangle

Congruence



57



motions.

Use the postulate ASA to show that triangles are congruent. Also, apply it so solve other geometric problems.

Use the postulate ASA to show that triangles are congruent. Also, apply it so solve other

geometric problems.

Unit 4 Triangle

Congruence



58



motions.

Use the postulate SAS to show that triangles are congruent. Also, apply it so solve other geometric problems.

I can use the postulate SAS to show that triangles are

congruent. I can apply the postulate to solve

other geometric problems.

Unit 4 Triangle

Congruence



59



motions.

Use the postulates SSS, SAS, and ASA to show that triangles are congruent.

Also, apply them to solve other geometric problems.

I can use the postulates SSS, SAS, and ASA to show that triangles are congruent and also apply

them to solve other geometric problems.

Unit 4 Triangle

Congruence




Unit 5 Pacing Chart


Page 19

Unit 5 Unit Week Day CCSS Standards Objective I Can Statements

Unit 5 Similarity

Transformations

Week 14 – Midpoint Theorem

66


measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are

congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

Show that when a line is bisected, the portions are

equal. Find the size of a line given a portion of the

bisecting line. Find the size of each portion of the line

is bisected etc

I can show that when a line is bisected, the portions are equal.

I can find the size of a line given a portion of the bisecting line.

I can find the size of each portion of the line is bisected

Unit 5 Similarity

Transformations


67




Proving midpoint theorem I can prove midpoint theorem

Unit 5 Similarity

Transformations


68




Explain how midpoint theorem leads to dilation

I can explain how midpoint theorem gives rise of a dilation

Unit 5 Similarity

Transformations


69




Apply midpoint theorem to find the length of other

lines. Use dilation

I can apply midpoint theorem to find the length of other lines. Use

dilation

Unit 5 Pacing Chart


Page 20

Unit 5 Similarity

Transformations



Unit 5 Similarity

Transformations

Week 15 – Dilations

and Similarity

71

CCSS.MATH.CONTENT.HSG.SRT.A.1 Verify experimentally the properties of dilations

given by a center and a scale factor: CCSS.MATH.CONTENT.HSG.SRT.A.1.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. CCSS.MATH.CONTENT.HSG.SRT.A.1.B

The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

Verify experimentally the properties of dilations given by a center and a

scale factor:

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.

The dilation of a line segment is longer or

shorter in the ratio given by the scale factor.

I can verify experimentally the properties of dilations given by a

center and a scale factor:

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.

The dilation of a line segment is

longer or shorter in the ratio given by the scale factor.

Unit 5 Similarity

Transformations


and Similarity

72

CCSS.MATH.CONTENT.HSG.SRT.A.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.

Given two figures, use the definition of similarity in

terms of similarity transformations to decide

if they are similar

Given two figures, I can use the definition of similarity in terms of

similarity transformations to decide if they are similar

Unit 5 Pacing Chart


Page 21

Unit 5 Similarity

Transformations


and Similarity

73

CCSS.MATH.CONTENT.HSG.SRT.A.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.

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.

I can 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.

Unit 5 Similarity

Transformations


and Similarity

74

CCSS.MATH.CONTENT.HSG.SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be

similar.

Use the properties of similarity transformations

to establish the AA criterion for two triangles

to be similar.

I can use the properties of similarity transformations to

establish the AA criterion for two triangles to be similar.

Unit 5 Similarity

Transformations


and Similarity


Unit 5 Similarity

Transformations

Week 16 – Prove

Theorems using

Similarity

76

CCSS.MATH.CONTENT.HSG.SRT.B.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.

Prove that a line parallel to one side of a triangle divides the other two

proportionally

I can prove that a line parallel to one side of a triangle divides the

other two proportionally

Unit 5 Pacing Chart


Page 22

Unit 5 Similarity

Transformations

Week 16 – Prove

Theorems using

Similarity

77

CCSS.MATH.CONTENT.HSG.SRT.B.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.

Pythagorean Theorem proved using triangle

similarity.

I can prove Pythagorean Theorem using triangle similarity.

Unit 5 Similarity

Transformations

Week 16 – Prove

Theorems using

Similarity

78

CCSS.MATH.CONTENT.HSG.SRT.B.5 Use congruence and similarity criteria for triangles

to solve problems and to prove relationships in geometric figures.

Use congruence and similarity criteria for

triangles to solve problems

I can use congruence and similarity criteria for triangles to

solve problems

Unit 5 Similarity

Transformations

Week 16 – Prove

Theorems using

Similarity

79

CCSS.MATH.CONTENT.HSG.SRT.B.5 Use congruence and similarity criteria for triangles

to solve problems and to prove relationships in geometric figures.

Use congruence and similarity criteria for

triangles prove relationships in geometric

figures.

I can use congruence and similarity criteria for triangles

prove relationships in geometric figures.

Unit 5 Similarity

Transformations

Week 16 – Prove

Theorems using

Similarity


Unit 6 Pacing Chart


Page 23

Unit 6


Unit 6 Right

Triangle Relationships

and Trigonometry

Week 18 – Indirect

Measurements 86

CCSS.MATH.CONTENT.HSG.SRT.C.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.

Identify opposite, adjacent and hypotenuse of right

triangles. Define trigonometric ratios.

I can Identify opposite, adjacent and hypotenuse of

right triangles I can define trigonometric

ratios.

Unit 6 Right


and Trigonometry


Measurements 87



acute angles.

Find trigonometric ratios of angles

I can find trigonometric ratios of angles

Unit 6 Right


and Trigonometry


Measurements 88



acute angles.

Define trigonometric ratios of compliments.

I can define trigonometric ratios of compliments.

Unit 6 Right


and Trigonometry


Measurements 89



acute angles.

Use similarity to find the trigonometric ratios of triangles with common

angles.

I can use similarity to find the trigonometric ratios of

triangles with common angles.

Unit 6 Pacing Chart


Page 24

Unit 6 Right


and Trigonometry


Measurements 90 Assessment Assessment Assessment

Unit 6 Right


and Trigonometry

Week 19 – Trigonometric

Ratios 91

CCSS.MATH.CONTENT.HSG.SRT.C.7 Explain and use the relationship between the sine

and cosine of complementary angles.

Explain the relationship between sine and cosine of

complementary angles

I can explain the relationship between sine

and cosine of complementary angles

Unit 6 Right


and Trigonometry


Ratios 92

CCSS.MATH.CONTENT.HSG.SRT.C.7 Explain and use the relationship between the sine

and cosine of complementary angles.

Use the relationship between the sine and cosine of complementary angles to solve geometric problems

I can use the relationship between the sine and cosine of complementary angles to solve geometric problems

Unit 6 Right


and Trigonometry


Ratios 93

CCSS.MATH.CONTENT.HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean

Theorem to solve right triangles in applied problems.*

Use trigonometric ratios to solve a triangle

I can use trigonometric ratios to solve a triangle

Unit 6 Right


and Trigonometry


Ratios 94

CCSS.MATH.CONTENT.HSG.SRT.C.8 Use trigonometric ratios and the Pythagorean

Theorem to solve right triangles in applied problems.*

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in

word problems

I can use trigonometric ratios and the Pythagorean

Theorem to solve right triangles in word problems

Unit 6 Pacing Chart


Page 25

Unit 6 Right


and Trigonometry


Ratios 95 Assessment Assessment Assessment

Unit 6 Right


and Trigonometry

Week 20 – Special Right

Triangles 96



acute angles.

Find the trigonometric ratios of 30-60-90 right triangle

I can find the trigonometric ratios of 30-60-90 right

triangle

Unit 6 Right


and Trigonometry


Triangles 97



acute angles.

Solve 30-60-90 right triangle I can solve 30-60-90 right

triangle

Unit 6 Right


and Trigonometry


Triangles 98



acute angles.

Find the trigonometric ratios of 45-45-90 right triangle

I can find the trigonometric ratios of 45-45-90 right

triangle

Unit 6 Right


and Trigonometry


Triangles 99



acute angles.

Solve 45-45-90 right triangle I can solve 45-45-90 right

triangle

Unit 6 Pacing Chart


Page 26

Unit 6 Right


and Trigonometry


Triangles 100 Assessment Assessment Assessment

Unit 7 Pacing Chart


Page 27

Unit 7


Unit 7 Quadrilaterals

Week 22 – Defining

Quadrilaterals with

Coordinates

106

CCSS.MATH.CONTENT.HSG.GPE.B.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point

(1, √3) lies on the circle centered at the origin and containing the point (0, 2).

Define and identify quadrilaterals

I can define and identify quadrilaterals



Quadrilaterals with

Coordinates

107



Determine the properties that can be

used to identify a square and a rectangle on an xy

plane. Determine the coordinate of the

missing vertex that makes up a rectangle or

a square.

I can determine the properties that can be used to identify a square and a rectangle on an

xy plane. I can determine the

coordinate of the missing vertex that makes up a rectangle or a square.



Quadrilaterals with

Coordinates

108




used to identify a rhombus and a

parallelogram on an xy plane. Determine the

coordinate of the missing vertex that

makes up a rectangle or a square.

I can determine the properties that can be used to identify a rhombus and a parallelogram

on an xy plane. I can determine the


Unit 7 Pacing Chart


Page 28



Quadrilaterals with

Coordinates

109




used to identify a trapezoid on an xy

plane. Determine the coordinate of the

missing vertex that makes up a rectangle or

a square.

I can determine the properties that can be used to identify a

trapezoid on an xy plane I can Determine the




Quadrilaterals with

Coordinates



Week 23 – Parallelogram

Proofs 111

CCSS.MATH.CONTENT.HSG.CO.C.11 Prove theorems about parallelograms. Theorems

include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect

each other, and conversely, rectangles are parallelograms with congruent diagonals.

Prove that Opposite sides of a parallelogram

are equal

I can prove that Opposite sides of a parallelogram are

equal



Proofs 112




Prove that Opposite angles of a

parallelogram are equal

I can prove that Opposite angles of a parallelogram are

equal

Unit 7 Pacing Chart


Page 29



Proofs 113




Prove that diagonals of a parallelogram are not

equal. Show that at their intersection,

opposite angles are equal and adjacent

angles are supplementary angles.

I can prove that diagonals of a parallelogram are not equal.

I can show that at their intersection, opposite angles are equal and adjacent angles

are supplementary angles.



Proofs 114




Prove that diagonals of a rectangle are equal.

Show that at their intersection, opposite angles are equal and adjacent angles are

supplementary angles.

Prove that diagonals of a rectangle are equal. Show that at their intersection, opposite angles are equal and adjacent

angles are supplementary angles.



Proofs 115 Assessment Assessment Assessment


Week 24 – Coordinate

Proofs 116

CCSS.MATH.CONTENT.HSG.GPE.B.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the

distance formula.*

Find perimeter and area of the triangle on xy

plane

I can find perimeter and area of the triangle on xy plane

Unit 7 Pacing Chart


Page 30



Proofs 117


distance formula.*

Find perimeter and area of square and rectangle

on xy plane

I can find perimeter and area of square and rectangle on xy

plane



Proofs 118


distance formula.*

Find perimeter and area of rhombus and

parallelogram on xy plane

I can find perimeter and area of rhombus and parallelogram

on xy plane



Proofs 119


distance formula.*

Find perimeter and area of the trapezoid on xy

plane

I can find perimeter and area of the trapezoid on xy plane



Proofs 120 Assessment Assessment Assessment

Unit 8 Pacing Chart


Page 31

Unit 8


Unit 8 Circles

Week 25 – Inscribed in a

Circle 121

CCSS.MATH.CONTENT.HSG.C.A.1 Prove that all circles are similar.

Prove that all circles are similar.

I can prove that all circles are similar.

Unit 8 Circles


Circle 122

CCSS.MATH.CONTENT.HSG.C.A.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a

diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the

circle.

Identify and describe relationships among

inscribed angles, radii, and chords.

I can Identify and describe relationships among inscribed

angles, radii, and chords.

Unit 8 Circles


Circle 123



circle.

Include the relationship between central,

inscribed, and circumscribed angles

I can Include the relationship between central, inscribed, and circumscribed angles

Unit 8 Circles


Circle 124



circle.

Inscribed angles on a diameter are right

angles; The radius of a circle is perpendicular to the

tangent where the radius intersects the circle.

I know that Inscribed angles on a diameter are right angles;

I know that the radius of a circle is perpendicular to the

tangent where the radius intersects the circle.

Unit 8 Pacing Chart


Page 32

Unit 8 Circles


Circle 125 Assessment Assessment Assessment

Unit 8 Circles

Week 26 – Circle

Relationships 126

CCSS.MATH.CONTENT.HSG.C.A.3 Construct the inscribed and circumscribed circles of a

triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

Construct the inscribed and circumscribed circles

of a triangle

I can construct the inscribed and circumscribed circles of a

triangle

Unit 8 Circles

Week 26 – Circle

Relationships 127

CCSS.MATH.CONTENT.HSG.C.A.4 (+) Construct a tangent line from a point outside a given circle

to the circle.

Construct a tangent line from a point outside a

given circle to the circle.

I can construct a tangent line from a point outside a given

circle to the circle.

Unit 8 Circles

Week 26 – Circle

Relationships 128

CCSS.MATH.CONTENT.HSG.GPE.A.1 Derive the equation of a circle of given center and radius

using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Derive the equation of a circle of given center and

radius using the Pythagorean Theorem

I can derive the equation of a circle of given center and

radius using the Pythagorean Theorem

Unit 8 Circles

Week 26 – Circle

Relationships 129

CCSS.MATH.CONTENT.HSG.GPE.A.1 Derive the equation of a circle of given center and radius

using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Complete the square to find the center and

radius of a circle given by an equation.

I can complete the square to find the center and radius of a

circle given by an equation.

Unit 8 Pacing Chart


Page 33

Unit 8 Circles

Week 26 – Circle

Relationships 130 Assessment Assessment Assessment

Unit 8 Circles

Week 27 – Proofs with

Circles 131

CCSS.MATH.CONTENT.HSG.C.A.3 Construct the inscribed and circumscribed circles of a

triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

Prove properties of angles for a quadrilateral

inscribed in a circle.

I can prove properties of angles for a quadrilateral

inscribed in a circle.

Unit 8 Circles


Circles 132

CCSS.MATH.CONTENT.HSG.C.B.5 Derive using similarity the fact that the length of the arc

intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of

proportionality; derive the formula for the area of a sector.

Derive using similarity the fact that the length

of the arc intercepted by an angle is proportional

to the radius, and

I can derive using similarity the fact that the length of the arc intercepted by an angle is

proportional to the radius, and

Unit 8 Circles


Circles 133




Define the radian measure of the angle as

the constant of proportionality

I can define the radian measure of the angle as the constant of proportionality

Unit 8 Circles


Circles 134




Derive the formula for the area of a sector.

I can derive the formula for the area of a sector.

Unit 8 Pacing Chart


Page 34

Unit 8 Circles


Circles 135 Assessment Assessment Assessment

Unit 8 Circles

Week 28 – Conics

136 CCSS.MATH.CONTENT.HSG.GPE.A.2

Derive the equation of a parabola given a focus and directrix. Find the directrix and the

focus of a parabola I can find the directrix and the

focus of a parabola

Unit 8 Circles

Week 28 – Conics

137 CCSS.MATH.CONTENT.HSG.GPE.A.2

Derive the equation of a parabola given a focus and directrix.

Find the equation of the parabola given the

directrix and the focus

I can find the equation of the parabola given the directrix

and the focus

Unit 8 Circles

Week 28 – Conics

138

CCSS.MATH.CONTENT.HSG.GPE.A.3 (+) Derive the equations of ellipses and hyperbolas given the

foci, using the fact that the sum or difference of distances from the foci is constant.

Derive the equations of ellipses given the foci, using the fact that the sum or difference of

distances from the foci is constant.

I can derive the equations of ellipses given the foci, using

the fact that the sum or difference of distances from

the foci is constant.

Unit 8 Circles

Week 28 – Conics

139

CCSS.MATH.CONTENT.HSG.GPE.A.3 (+) Derive the equations of ellipses and hyperbolas given the

foci, using the fact that the sum or difference of distances from the foci is constant.

Derive the equations of hyperbolas given the foci,

using the fact that the sum or difference of

distances from the foci is constant.

I can derive the equations of hyperbolas given the foci,

using the fact that the sum or difference of distances from

the foci is constant.

Unit 8 Pacing Chart


Page 35

Unit 8 Circles

Week 28 – Conics


Unit 9 Pacing Chart


Page 36

Unit 9


Unit 9 Geometric

Modeling in Two

Dimensions

Week 28 – 2D

Applications 141

CCSS.MATH.CONTENT.HSG.GMD.A.1 Give an informal argument for the formulas for the

circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection

arguments, Cavalieri's principle, and informal limit arguments.

Give an informal argument for the formulas for the circumference

I can give an informal argument for the formulas for

the circumference

Unit 9 Geometric

Modeling in Two

Dimensions

Week 28 – 2D

Applications 142




Applications of circumference

I can discuss the applications of circumference

Unit 9 Geometric

Modeling in Two

Dimensions

Week 28 – 2D

Applications 143




Give an informal argument for the

formulas for area of a circle


area of a circle

Unit 9 Geometric

Modeling in Two

Dimensions

Week 28 – 2D

Applications 144




Applications of area of a circle

I can discuss the applications of area of a circle

Unit 9 Pacing Chart


Page 37

Unit 9 Geometric

Modeling in Two

Dimensions

Week 28 – 2D

Applications 145 Assessment Assessment Assessment

Unit 9 Geometric

Modeling in Two

Dimensions

Week 29 – Solve Design

Problem 146

CCSS.MATH.CONTENT.HSG.MG.A.3 Apply geometric methods to solve design problems

(e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with

typographic grid systems based on ratios).*

Use triangular, square and rectangular designs

in modeling without interchanging between

any two or more designs

I can use triangular, square and rectangular designs in

modeling without interchanging between any

two or more designs

Unit 9 Geometric

Modeling in Two

Dimensions


Problem 147





in modeling by interchanging between


I can use triangular, square and rectangular designs in modeling by interchanging between any two or more

designs

Unit 9 Geometric

Modeling in Two

Dimensions


Problem 148




Use circular and quadrilateral designs in

modeling

I can use circular and quadrilateral designs in

modeling

Unit 9 Geometric

Modeling in Two

Dimensions


Problem 149




Use 2D designs in modeling

I can use 2D designs in modeling

Unit 9 Pacing Chart


Page 38

Unit 9 Geometric

Modeling in Two

Dimensions


Problem 150 Assessment Assessment Assessment

Unit 9 Geometric

Modeling in Two

Dimensions

Week 28 – 2D

Applications 141




Give an informal argument for the formulas for the circumference


the circumference

Unit 9 Geometric

Modeling in Two

Dimensions

Week 28 – 2D

Applications 142




Applications of circumference

I can discuss the applications of circumference

Unit 9 Geometric

Modeling in Two

Dimensions

Week 28 – 2D

Applications 143




Give an informal argument for the

formulas for area of a circle


area of a circle

Unit 9 Geometric

Modeling in Two

Dimensions

Week 28 – 2D

Applications 144




Applications of area of a circle

I can discuss the applications of area of a circle

Unit 9 Pacing Chart


Page 39

Unit 9 Geometric

Modeling in Two

Dimensions

Week 28 – 2D

Applications 145 Assessment Assessment Assessment

Unit 9 Geometric

Modeling in Two

Dimensions


Problem 146





in modeling without interchanging between


I can use triangular, square and rectangular designs in

modeling without interchanging between any

two or more designs

Unit 9 Geometric

Modeling in Two

Dimensions


Problem 147





in modeling by interchanging between


I can use triangular, square and rectangular designs in modeling by interchanging between any two or more

designs

Unit 9 Geometric

Modeling in Two

Dimensions


Problem 148




Use circular and quadrilateral designs in

modeling

I can use circular and quadrilateral designs in

modeling

Unit 9 Geometric

Modeling in Two

Dimensions


Problem 149




Use 2D designs in modeling

I can use 2D designs in modeling

Unit 9 Pacing Chart


Page 40

Unit 9 Geometric

Modeling in Two

Dimensions


Problem 150 Assessment Assessment Assessment

Unit 10 Pacing Chart


Page 41

Unit 10


Unit 10 Understanding and Modeling

Three-Dimensional

Figures

Week 30 – Volume

151


circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments,

Cavalieri's principle, and informal limit arguments.

CCSS.MATH.CONTENT.HSG.GMD.A.2 (+) Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other

solid figures.

Give an informal argument using

Cavalieri's principle for the formulas for the

volume of a sphere and other solid figures.

I can give an informal argument using Cavalieri's

principle for the formulas for the volume of a sphere and

other solid figures.


Three-Dimensional

Figures

Week 30 – Volume

152




CCSS.MATH.CONTENT.HSG.GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and

spheres to solve problems.*

Discuss the application of volume of a sphere

I can discuss the application of volume of a sphere


Three-Dimensional

Figures

Week 30 – Volume

153






Discuss the application of volume of a cylinder

I can discuss the application of volume of a cylinder



Page 42


Three-Dimensional

Figures

Week 30 – Volume

154






Discuss the application of volume of pyramids

and cones

I can discuss the application of volume of pyramids and

cones


Three-Dimensional

Figures

Week 30 – Volume



Three-Dimensional

Figures

Week 31 – Cross

Sections 156

CCSS.MATH.CONTENT.HSG.GMD.B.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.

Identify the shapes of two-dimensional cross-

sections(polygon sections) of three-

dimensional objects

I can Identify the shapes of two-dimensional cross-

sections(polygon sections) of three-dimensional objects


Three-Dimensional

Figures

Week 31 – Cross

Sections 157




Identify the shapes of two-dimensional cross-

sections(circular sections) of three-dimensional

objects

I can Identify the shapes of two-dimensional cross-

sections(circular sections) of three-dimensional objects



Page 43


Three-Dimensional

Figures

Week 31 – Cross

Sections 158




identify three-dimensional objects

generated by rotations of polygon and circular

faces

I can identify three-dimensional objects generated

by rotations of polygon and circular faces


Three-Dimensional

Figures

Week 31 – Cross

Sections 159




identify three-dimensional objects

generated by rotations of 2D fused faces

I can identify three-dimensional objects generated by rotations of 2D fused faces


Three-Dimensional

Figures

Week 31 – Cross

Sections 160 Assessment Assessment Assessment


Three-Dimensional

Figures

Week 32 – 3D

Applications

161

CCSS.MATH.CONTENT.HSG.MG.A.1 Use geometric shapes, their measures, and their

properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).*

Model a tree trunk. Identify all the objects

used in modeling. Suggest any other objects that may be used instead

of the one(s) used.

I can model a tree trunk. I can Identify all the objects

used in modeling. I can suggest any other objects that

may be used instead of the one(s) used.


Three-Dimensional

Figures

Week 32 – 3D

Applications

162



Model a human torso. Identify all the objects

used in modeling. Suggest any other objects that may be used instead

of the one(s) used.

I can Model a human torso. I can Identify all the objects

used in modeling. I can suggest any other objects

that may be used instead of the one(s) used.



Page 44


Three-Dimensional

Figures

Week 32 – 3D

Applications

163



Come up with different models of a house.

Identify all the objects used in modeling.

Suggest any other objects that may be used instead

of the one(s) used.

I can come up with different models of a house.

I can Identify all the objects used in modeling.

I can suggest any other objects that may be used instead of

the one(s) used.


Three-Dimensional

Figures

Week 32 – 3D

Applications

164

CCSS.MATH.CONTENT.HSG.MG.A.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs

per cubic foot).

Apply concepts of density based on area and

volume in modeling situations (e.g., persons

per square mile, BTUs per cubic foot).

I can apply concepts of density based on area and volume in

modeling situations (e.g., persons per square mile, BTUs

per cubic foot).


Three-Dimensional

Figures

Week 32 – 3D

Applications



Three-Dimensional

Figures

Week 33 – 3D Design Problems

166

CCSS.MATH.CONTENT.HSG.MG.A.3 Apply geometric methods to solve design problems (e.g.,

designing an object or structure to satisfy physical constraints or minimize cost; working with typographic

grid systems based on ratios).*

Apply geometric methods to solve design problems of the Conical structures

or object to satisfy physical constraints or minimize cost; working with typographic grid

systems based on ratios

I can apply geometric methods to solve design problems of

the Conical structures or object to satisfy physical

constraints or minimize cost; working with typographic grid




Page 45


Three-Dimensional

Figures


167




Apply geometric methods to solve design problems

of the Cylindrical structures or object to

satisfy physical constraints or minimize

cost; working with typographic grid systems

based on ratios

I can apply geometric methods to solve design problems of the Cylindrical structures or

object to satisfy physical constraints or minimize cost; working with typographic grid



Three-Dimensional

Figures


168




Apply geometric methods to solve design problems

of the cubical and cuboidal structures or

object to satisfy physical constraints or minimize

cost; working with typographic grid systems

based on ratios


the cubical and cuboidal structures or object to satisfy

physical constraints or minimize cost; working with typographic gridd systems

based on ratios


Three-Dimensional

Figures


169




Apply geometric methods to solve design problems of the pyramid structure

or object to satisfy physical constraints or minimize cost; working with typographic grid



the pyramid structure or object to satisfy physical

constraints or minimize cost; working with typographic grid



Three-Dimensional

Figures



Documents

Complete Geometry Pacing Chart - High School Math Teachers€¦ · COMPLETE GEOMETRY PACING CHART HIGHSCHOOLMATHTEACHERS.COM@2018 . Contents Unit 1 Geometric Transformation..... 2