Unit 1 – Essentials of · PDF fileUnit 1 – Essentials of Geometry Lesson Title...

Geometry Scope and Sequence 2012-2013

1

Semester 1

Unit 1 – Essentials of Geometry

Lesson Title Content Larson

Section

Burger

Section

Common

Core

Standards

Constructions Proofs

Points, Lines

and Planes

• Definitions of Points,

Lines, Planes, and

Segments

• Intersections

1.1 1.1 G.CO.1

Using

Segments and

Congruence

• Length of segments

• Congruent Segments

• Segment Addition

Postulate

1.2 1.2 G.CO.1 Congruent

segments (Pg.

14 Burger)

Segment

Bisector

(Pg. 16 Burger)

Distance and

midpoint

Formulas

• Midpoints and

segment bisectors

• Finding the length

and midpoints of

segments on a

number line.

• Solving problems

involving midpoints

1.3 1.6 G.GPE.7

Measure and

Classify

Angles

• Classifying angles

• Problems involving

the Angle Addition

Postulate and Angle

bisectors

1.4 1.3 G.CO.1 Congruent

angles (pg. 22

Burger

Angle Bisectors

(pg. 23 Burger)


2


Section

Burger

Section

Common

Core

Standards


Angle Pair

Relationships

• Adjacent, Vertical,

Linear Pairs,

Complementary and

Supplementary

angles

• Solving Problems

using angle pairs

1.5 1.4 G.MG.1

Quiz 1 – Larson - Sections 1.1-1.3

- Burger - Sections 1.1,1.2,1.6

Quiz 2 – Larson – Sections 1.4-1.5

- Burger - Sections

Test 1 - Larson - Sections 1.1-1.5

- Burger - Sections 1.3 -1.4

Days to complete - 45 minute block - 15 days

- 90 mInute block - 8 days


3

Unit 2 – Proof and Deduction


Section

Burger

Section

Common

Core

Standards

Proofs

Analyzing

Conditional

Statements

• Converse, inverse and

contrapositive

• Analyzing the truth

value of conditionals

• Biconditionals

2.2 2.2,

2.4

Prep for

G.CO.9,10

11

G.SRT.4

Verifying

conjectures

• Law of Syllogism

• Law of Detachment

• Applying the laws

2.3 2.3 Prep for

G.CO.9,10

11

G.SRT.4

Using

postulates

and diagrams

• Additional postulates

using points, lines and

planes

• Making geometric

sketches

• Interpreting diagrams

2.4 Supple

mental

Prep for

G.CO.9,10

11

G.SRT.4

Reasoning

using

properties of

Algebra

• Properties of equality

• Properties of

congruence

• Writing Algebraic

Proofs

2.5 2.5 Prep for

G.CO.9,10

11

G.SRT.4

Algebraic

proofs

Geometric

Proofs about

segments and

angles

• Writing two-column

proofs involving

Segments and Angles

2.6 2.6 G.CO.9 Segment and

angle proofs

Proving angle

pair

relationships

• Writing two column

proofs about vertical

angles, linear pairs,

complements and

supplements.

2.7 2.6 G.CO.9 Prove vertical

angles are

congruent

Test 1 - Larson - Section 2.2 -2.4

- Burger - Sections 2.2 -2.4, supplemental

Test 2 - Larson - Sections 2.5 – 2.7

- Burger - Sections 2.5 - 2.6

Day to complete – 45 minute block - 18 days

90 minute block - 9 days


4

Unit 3 Parallel and Perpendicular Lines


Section

Burger

Section

Common

Core

Standards


Identify Pairs

of Lines and

Angles

• Parallel,

perpendicular and

skew lines

• Angle pairs with lines

and transversals

3.1 3.1 G.CO.1

Use Parallel

Lines and

Transversals

• Solve for unknowns

and angle sizes

• Proof angle pairs are

congruent or

supplementary using

parallel lines

3.2 3.2 G.CO.9 Prove alternate

interior and

corresponding

angles are

congruent

Prove Lines

are Parallel

• Solve problems to

show lines are parallel

• Write two column

proofs showing two

lines are parallel

3.3 3.3 G.CO.9

Perpendicular

lines

• Theorems relating to

parallel lines

• Justifying Statements

involving

perpendicular lines

using conditionals (no

formal proofs

3.6 3.4 G.CO.9 Perpendicular

lines. (pg. 190

Larson, Pg 179

Burger)

Parallel Lines

(pg 190 Larson,

Pg 163 Burger)


5


Section

Burger

Section

Common

Core

Standards


Find and use

slopes of

lines

• Determine from

pictures whether

lines have positive,

negative, zero or no

slope

• Graph lines that are

perpendicular or

parallel to given lines

through given points

• Find the slope give

two points.

• Determine whether

two lines are parallel

or perpendicular by

finding their slopes

3.4 3.5 G.GPE.5

Write and

graph

Equations of

Lines

• Write an equation

from a graph

• Graph an equation

written in standard

form Write equations

of lines through

points that are

parallel or

perpendicular to

given lines

• Writing and graphing

equations in

standard, point-slope,

and slope intercept

form.

3.5 3.6 G.GPE.5

Quiz 1 – Larson - Sections 3.1-3.3, 3.6


Quiz 2 – Larson - Sections 3.4, 3.5

- Burger - Sections 3.5, 3.6



Days to complete – 45 minute block – 15 days

Days to complete – 90 minute block - 8 days


6

Unit 4 Congruent Triangles


Section

Burger

Section

Common

Core

Standards


Apply Angle

Sum

Theorem

• Find sizes of angles

based on the angle

sum theorem and the

Exterior angle

theorem

4.1 4.2 and

4.3

G.CO.10 Proof the

triangle angle

sum theorem

Use Isosceles

and

Equilateral

triangles

• Find angle measures

and side lengths using

properties of isosceles

triangles

4.8 4.9 G.CO.10 Skipped: Proof

base angles of

an isosceles

triangle are

congruent

Angle

congruence

and triangles

• Definition of

congruent figures

• Determining if

triangles are

congruent based on

the definition of

congruence

4.2 4.4 G.CO.7

Transformati

ons and

congruence

• Use rigid motion

transformations to

determine whether

triangles are

congruent

• Perform rigid motion

transformation

algebraically

4.3, 4.9 4.1 G.CO.6,

G.CO.2

CC: Rigid

motion and

congruence

(pg. 254

Larson)


7


Section

Burger

Section

Common

Core

Standards


Prove triangle

congruent by

SSS

• Congruence

statements

• Determining if

triangles are

congruent in the

coordinate

plane given

coordinates of

vertices

• Determine if

triangles are

congruent by

SSS

• Prove triangles

are congruent

using SSS

4.4 4.5 G.CO.8

Prove triangles

congruent by

SAS and HL

• Naming

included angles

and included

sides

• Determining if

triangles are

congruent by

SAS and HL

• Proofing

triangles are

congruent by

SAS and HL

4.5 4.5, 4.6 G.CO.8 SAS and HL

Prove Triangles

by ASA and AAS

• Identify whether

triangles are

congruent by

ASA or AAS

• CC Rigid Motion

and congruence

(Pg 254)

4.6 4.6 G.CO.8 ASA and AAS


8


Section

Burger

Section

Common

Core

Standards


Use congruent

triangles

• Determine

whether angles

or sides are

congruent

using CPCTC

• Write proofs

including

CPCTC

4.7 4.7 G.CO.10,

G.CO.12

CPCTC

Quiz 1 – Larson - Sections 4.1,4.2,4.8

- Burger - Sections 4.2-4.4, 4.9

Test 1 – Larson - Sections 4.1-4.3, 4.8, 4.9

- Burger - Sections 4.1-4.4, 4.9

Quiz 2 - Larson - Sections 4.4 – 4.6

- Burger - Sections 4.5 – 4.6


- Burger - Sections 4.5-4.7

Days to complete – 45 minute class - 22 days

Days to complete – 90 minute class - 11 days


9

Unit 5 Relationships within Triangles


Section

Burger

Section

Common

Core

Standards


Using

perpendicular

Bisectors

• Perpendicular

bisector

theorem

• Concurrency of

Perpendicular

bisectors in a

triangle

• Circumcenter

• Finding missing

segment length

5.2 5.1, 5.2 G.CO.9,

G.CO.13

Construct a

triangle

inscribed in a

circle.

Construct a

circle

inscribed in a

triangle

Prove the

Perpendicular

bisector

theorem

Use Angle

Bisectors

• Angle bisector

theorem

• Concurrency of

angle bisectors

• Incenter

• Finding missing

segment

lengths

5.3 5.1,5.2 G.C.3

Using Medians

and Altitudes

• Concurrency of

medians and

altitude

• Centroids and

Orthocenters

• Finding lengths

of segments

created by

medians and

altitudes in

triangles

5.4 5.3 G.C0.10

The triangle

midsegment

theorem

• Using the

midsegment

theorem,

determine the

lengths of

missing sides of

triangles

• Determine

whether

segments in a

drawing are

parallel

5.1 5.4 G.GPE.4


10


Section

Burger

Section

Common

Core

Standards


Use inequalities

in triangles

• Determine the

relative lengths

and degree

measure of

segments and

angles based

on inequality

theorems

5.5 5.5 G.CO.10

The Hinge

theorem and its

converse

• Use the hinge

theorem and its

converse to

determine the

relative sizes of

segments and

angles in two

different

triangle

5.6 5.6 G.CO.10

Quiz 1 - Larson - Sections 5.2 - 5.4

Burger - Sections 5.1-5.3

Quiz 2 - Larson - Sections 5.1, 5.5, 5.6




Days to complete - 45 minute class - 14 days

- 90 minute class - 7 days


11

Semester 2

Unit 6 – Similarity


Section

Burger

Section

Common

Core

Standards


Use similar

polygons

• Definition of

similar figures

• Write similarity

statements

• Determine the

scale factor of

similar figures

• Determine if two

figures are

similar from the

definition

• Find missing

lengths of sides

of similar figures

• Perimeter of

similar figures

6.1 7.1 G.SRT.5

Relate

transformations

and similarity

• Determining the

scale factor of a

dilation that

maps one figure

to another

• Use

transformation

to determine

whether two

figures are

similar or not

6.2 7.2 G.SRT.2

Perform

Similarity

transformations

• Apply similarity

properties in the

coordinate plane

• Create dilations

on the

coordinate plane

algebraically

using scale

factors

6.6 7.6 G.CO.2


12


Section

Burger

Section

Common

Core

Standards


Prove triangles

similar by AA

• Determine or

show two

triangles are

similar by AA

• Find missing side

lengths using AA

• Solve word

problems using

AA

6.3 7.3, 7.5 G.SRT.3 Prove

triangles are

similar by

AA

Prove triangles

similar by SSS

and SAS

• Determine if

triangles are

similar by SSS or

SAS

• Find the scale

factor of

triangles

• Determine side

lengths and

angle measures

from diagrams of

triangles similar

by SAS and SSS

6.4 7.3, 7.5 G.SRT.4 Prove

triangles are

similar by

SSS and SAS

Use

proportionality

theorems

• Find segment

lengths using

theorems of

similar triangle

proportionality

6.5 7.4 G.SRT.4 Proof the

triangle

proportional

ity theorem

Quiz 1 - Larson - Sections 6.1, 6.2, 6.6

Burger - Sections 7.1, 7.2, 7.6

Quiz 2 - Larson - Sections 6.3 - 6.5

Burger - Sections 7.3 - 7.5






13

Unit 7 – Right Triangles and Trigonometry


Section

Burger

Section

Common

Core

Standards


Apply the

Pythagorean

Theorem

• Find missing side

lengths using the

Pythagorean

theorem

• Use Pythagorean

triples to find the

third side of right

triangles

7.1 5.7 G.SRT.8 Prove the

Pythagorean

theorem

using

triangle

similarity

Use the

converse of the

Pythagorean

theorem

• Determine

whether a

triangle is right

based on the

side lengths

• Classify a triangle

as acute, obtuse

or right based

theorems related

to the

Pythagorean

theorem

7.2 5.7 G.SRT.8

Use similar

right triangles

• Use properties of

similarity to find

the lengths of

segments in a

right triangle

with an altitude

drawn from the

right angle of the

triangle

• The geometric

mean

7.3 8.1 G.SRT.5

Special right

triangles

• Find the lengths

of sides of

special right

triangles

7.4 Supple

ment

G.SRT.6


14


Section

Burger

Section

Common

Core

Standards


Apply the

tangent ratio

• Definitions of the

terms “Opposite

Leg” and

“Adjacent Leg


of sides using the

tangent ratio

• Word problems

involving the

tangent ratio

7.5 8.2 G.SRT.8

Apply the Sine

and Cosine

ratio


of sides using the

sine and cosine

ratio.

• Determine the

sine and cosine

ratio from side

lengths

• Word problems

involving side

ratios, including

the angles of

elevation and

depression

7.6 8.2, 8.4 G.SRT.8


15


Section

Burger

Section

Common

Core

Standards


Solve Right

Triangles

• Use inverse trig

functions to find

angle sizes

• Find all angle

measures and

side lengths of

right triangles

7.7 8.3 G.SRT.8

Law of Sines

and Cosines

(Honors only)

• Using the law of

Sines and

Cosines to solve

triangles

• Solving word

problems using

these laws

Al.5,

Al.10,

Pg. 484

and

485

8.5 G.SRT.10(

+)

G.SRT.11

(+)

Quiz 1 - Larson - Sections 7.1-7.2

- Burger - Sections 5.7


- Burger - Sections 5.7, 8.1, supplemental

Test 2 - Larson - Sections 7.5 - 7.7 (Honors add Pg. 484-485)

- Burger - Sections 8.2 - 8.4 (Honors add Section 8.5)




16

Unit 8 - Quadrilaterals


Section

Burger

Section

Common

Core

Standards


Classify

Polygons

• Naming polygons

• Properties of

polygons

• Finding missing

side lengths of

polygons

1.6 6.1 G.GMD.4

G.MG.1

Find angle

measures in

polygons

• Interior and

exterior angles of

polygons

• Finding the sum

of interior and

exterior angles

and the sizes of

angles of regular

polygons

8.1 6.1 G.MG.1

Properties of

parallelograms

• Use properties of

parallelogram to

find side lengths

and angles sizes

8.2 6.2 G.CO.11

G.SRT.5

Opposite

sides of a

parallelogra

m are

congruent

Opposite

angles are

congruent

Diagonals

bisect each

other

Show that a

Quadrilateral is

a parallelogram

• Find what side

lengths or angle

sizes would show

the quadrilateral

is a

parallelogram

• Use Coordinate

Geometry to

prove a

quadrilateral is a

Parallelogram

8.3 6.3 G.CO.11

G.SRT.5


17


Section

Burger

Section

Common

Core

Standards


Rhombi,

Rectangle, and

Squares

• Classify

parallelograms as

a rectangle,

rhombus or

square

• Proof related to

rectangles

• Determine the

side lengths and

angle sizes based

on their

properties

8.4 6.4,

supple

mental

G.CO.11

G.SRT.5

G.GPE.7

Prove

rectangles are

parallelogram

s with

congruent

diagonals. Use

coordinate

geometry to

prove

properties of

special

quadrilaterals

Trapezoids • Determine

whether a

quadrilateral is a

trapezoid on the

coordinate plane

• Determine the

length of a

midsegment of a

trapezoid

• Find missing

angle measures

8.5 6.6 G.SRT.5

G.GPE.4

Identify special

quadrilaterals

• Based on given

properties,

determine which

quadrilateral

they apply to

• Classify special

quadrilateral

from pictures

and descriptions

8.6 6.4,

supple

mental

G.CO.11

Quiz 1 - Larson - Sections 1.6, 8.1-8.3

Burger - Sections 6.1-6.3


Burger - Sections 6.4-6.5, supplemental

Test 1 - Larson - Sections 1.6, 8.1-8.6

- Burger - Sections 6.1-6.5, supplemental




18

Unit 9 - Circles


Section

Burger

Section

Common

Core

Standards


Use properties

of tangents

• Learn key

vocabulary

related to circles

• Use common

tangents to find

segment lengths

• Use tangents

perpendicular to

radii to find

segment lengths

10.1 12.1 G.CO.1

Find Arc

Measures

• Define the

concepts of arcs,

minor arcs,

major arcs and

semicircles

• Find arc

measures based

on the size of

central angles.

• Utilize the arc

addition

postulate

10.2 12.2 G.CO.1

Apply

properties of

chords

• Determine the

size of arcs,

angles and

segment lengths

based on

relationships

between chords

and arcs

10.3 12.2 G.C.2

Use inscribed

angles and

polygons

• Using

intercepted arcs,

determine the

degree measure

of inscribed

angles, and vice

versa.

10.4 12.4 G.C.3 Prove the

opposite angles

of a

quadrilateral

inscribed in a

circle are

supplementary


19


Section

Burger

Section

Common

Core

Standards


Apply other

angle

relationships in

circles

• Determine the

size of angles and

arcs formed by

intersecting

chords, tangent-

secants, and

secant-secant

angles

10.5 12.5 G.C.2

Find segment

lengths in

circles

• Determine

segment lengths

formed by

intersecting

chords, secants

intersecting

outside of the

circle, and

tangent-secants

intersecting

outside the circle

10.6 12.6 G.C.2

Write and

graph

equations of

circles

• Find the

equation of a

circle given a

picture of a circle

with a given

center and

radius.

• Draw a circle in

the coordinate

plane with a

given center and

radius

Honors - Find the

equation of a

parabola

10.7,

AL.14

(honor

s)

12.7 G.GPE.1

Circumference

and arc length

• Use the formula

for arc length to

solve for central

angles, arc

measure, radii

length, and arc

lengths.

• Measure angles

in Radians

11.1,

Pg 717

Pg.

816,12.

3

G.C.5 Prove all

circles are

similar using

the ratio of

circumferen

ce to

diameter


20


Section

Burger

Section

Common

Core

Standards


Areas of circles

and sectors

• Use the area of a

sector formula to

determine Arc

measure, radii

lengths, area of

sectors and

segments

11.2 12.3 G.C.5


- Burger - Sections 12.1, 12.2, 12.4

Test 1 - Larson - Sections 10.1 - 10.5

- Burger - Sections 12.1,12.2,12.4,12.5


- Burger - Sections 12.6 -12.7


- Burger - 12.3, 12.6, 12.7


- 90 minute block - 10 days


21

Unit 10 - Measurements of Figures and Solids


Section

Burger

Section

Common

Core

Standards


Exploring Solids • Definitions of

solids and

polyhedra as well

as other solid

related terms

• Cross sections of

solids

• Euler’s Theorem

11.5 11.1 G.GMD.4

Volume of

Prisms and

Cylinders

• Finding the

volume of

prisms, cylinders

and irregular

solids formed by

them.

11.6 11.2 G.GMD.3

Volume of

Pyramids and

Cones

• Finding the

volume of

pyramids, cones

and irregular

solids formed by

them.

11.7 11.3 G.GMD.3

Surface Area

and Volume of

Spheres

• Finding the

surface area and

volume of

spheres

• Solving

application word

problems

involving spheres

11.8 11.4 G.GMD.3


22


Section

Burger

Section

Common

Core

Standards


Exploring

Similar solids

• Using the scale

factors of similar

solids, as well as

the ratio of

surface area and

volumes of

similar solids, to

determine the

surface areas or

volume of a solid

• Given the surface

areas or volume

of similar solids,

determine the

ratio of their

surface areas,

volumes, or scale

factor of the

solids

11.9 Pg.

775,

supple

mental

G.GMD.3

Quiz 1 - Larson- Sections 11.5-11.7

- Burger- Sections 11.1 - 11.3

Test 1 - Larson- Sections 11.5-11.9

- Burger- Sections 11.1 -11.4, supplemental




23

Unit 11 - Transformations


Section

Burger

Section

Common

Core

Standards


Translate figures

and use vectors

• To understand

the concept of a

vector and

represent a

vector in

component

form

9.1 9.2 G.CO.5

Perform

reflections

• To reflect an

pre-image over

a line of

reflection

• Use coordinate

rules of

reflection to

reflect pre-

images over

common lines

of reflection

9.3 9.1 G.CO.5

Perform

rotations

• Understand the

concepts of

center of

rotation and

angles of

rotation

• Use coordinate

rules for

creating

rotations based

on 90 degree

intervals.

9.4 9.3 G.CO.5


24


Section

Burger

Section

Common

Core

Standards


Apply

compositions of

transformations

• Perform

compositions of

transformations

, including glide

reflections

• Find the image

of composition

of

transformations

• Determine

single

transformations

that produce

the same image

as the

composition of

translations.

9.5 9.4 G.CO.5

Identify

symmetry

• Determine the

number of lines

of symmetry a

figure has

• Determine

whether a

figure has

rotational

symmetry and

what rotation

maps an image

onto itself.

9.6 9.5 G.CO.3

Identify and

perform

dilations

• Draw dilations

of figures using

scale factors

and scalar

multiplication of

matrices

9.7 9.7 G.SRT.1

Test 1 - Larson - 9.1, 9.3-9.7

- Burger - 9.1-9.5, 9.7

Number of days to complete - 45 minute block - 8 days



25

Unit 12 - Probability


Section

Burger

Section

Common

Core

Standards


Finding

Probability and

odds

• Find theoretical

probability of an

event

• Find

experimental

probability of

events

• Determine the

odds in favor or

against an event

occurring

12.1 13.2 S.CP.9

Find probability

of overlapping

and disjoint

events

• Find probability

of compound

events that are

and are not

mutually

exclusive

• Find probability

of events using

formulas for

compound

events

12.4 13.5 S.CP.7

Find the

probability of

independent

and dependant

events

• Determine the

probability of

independent

and dependent

events.

• Find conditional

probabilities

12.5 13.3 S.CP.5

Test 1 - Larson - Sections 12.1, 12.4, and 12.5

-Burger - Sections 13.2, 13.3 and 13.5

Number of Days to complete - 45 minute block - 10 days


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