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1

UNIT 1

Congruence, Proof, and Construction

Total Number of Days: 26 days Grade/Course: __Geometry 10th grade__

ESSENTIAL QUESTIONS ENDURING UNDERSTANDINGS

1. How do you identify corresponding parts of

congruent triangles?

2. How can you make a conjecture and prove

that triangles are congruent?

3. How can you describe the attributes of a

segment or angle?

4. If two triangles are congruent, then every pair of their corresponding parts is also congruent.

5. Given information, definitions, properties, postulates, and previously proven theorems can be

used as reasons in a proof.

6. Number operations can be used to find and compare the lengths of segments.

7. The Ruler and Segment Addition Postulates can be used in reasoning about lengths.

8. The Protractor and Angle Addition Postulates can be used in reasoning about angle measures.

PACE CONTENT SKILLS STANDARDS

(CCSS/MP)

RESOURCES

LEARNING ACTIVITIES and

ASSESSMENTS Pearson

OTHER

(e.g., tech)

2 days

1.

Getting Ready

for Geometry:

Basic Skills

(Squaring

numbers,

Evaluating

Square numbers when

calculating areas of certain

figures.

Example:

1) The number you get when

you multiply an integer by

itself.

8.EE.2

Students recognize perfect

squares and cubes,

understanding that non-perfect

squares and non-perfect cubes

are

Irrational.

Pearson

Chapter #1

Get Ready

Interactive website for

exponent:

http://www.mathsisfun

.com/exponent.html

Interactive practice

Website related to step to solve

equations:

www.svmimac.org/images/MNM.

052913.stsec.pdf

http://www.mathsisfun.com/exponent.html

http://www.mathsisfun.com/exponent.html

http://www.svmimac.org/images/MNM.052913.stsec.pdf

http://www.svmimac.org/images/MNM.052913.stsec.pdf

2

Expressions,

Finding

Absolute Value,

Solving

Equations)

4 × 4 = 16, so 16 is a square

number.

2) 32 = 9

3) 42 = 16

Evaluate expressions by

substituting given values.

-Example:

Evaluate each using the

values given:

p m; use m , and p

8.EE.7

Students solve one-variable

equations including those with

the variables being on both sides

of the equal sign. Students

recognize that the solution to the

equation is the value(s) of the

variable, which make a true

equality when substituted back

into the equation. Equations shall

include rational numbers,

distributive property and

combining like terms.

MP.1

MP.2

Text book

page #1

games:

classroom.jc-

schools.net/basic/math-

expon.html

Video:

www.mathplayground.c

om/howto_algebraeq1.

Lesson Check:

Text book Get Ready page 1

30mn.

Basic skills

Review:

HSPA

Use Apply Pythagorean Theorem

in real life problems:

Ex Example:

G.SRT.8 Use trigonometric ratios

and the Pythagorean Theorem

to solve right triangles in applied

Pearson

Chapter #1

Get Ready

Web link for

Pythagorean Theorem

and the distance

Pythagorean Theorem Power

point presentation:

www.jamestownpublicschools.o

3

PREP/PARCC/S

AT

Michelle was fishing in her

canoe at point A in the lake

depicted above. After trying

to fish there, she decided to

paddle due east at a steady

speed of 10 miles per hour.

As she paddled, a wind

blowing due south at 5 miles

per hour caused a change in

her direction. What is the

speed of her canoe,

measured to the nearest

tenth of a mile per hour,

which has a velocity

represented by vector AC?

Michelle

problems.

Text book

page #1

formula.

www.mathscore.com/m

ath/practice/Pythagore

an%20Theorem

Kuta software for

worksheets

www.kutasoftware.co

m

rg/highschool/faculty/.../pythag

thm.ppt

1 day

1.

Nets and

Drawing for

Visualizing

Geometry

Construct nets and drawings

of three- dimensional figures.

Example: refer to link under

resources on discovering 3-D

shapes.

Example:

Find the surface area of this

G.CO.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.

Pearson

Chapter 1

Text book

page #4-9

Interactive Animated

polyhedron models:

www.mathsisfun.com/g

eometry/polyhedron-

3-Dimentional shapes

videos and worksheets

1. Basic: problems 1-4 Exs

6-19 all, 20-26 even, 27, 28-36

even,

43-51

2. Average: problems 1-4

Exs. 7-19 odd, 20-38, 43-51

http://www.kutasoftware.com/


4

box below

MP.3

MP.7

www.onlinemathlearnin

g.com/3d-shapes-

nets

Web link for 3D shapes:

http://www.xtec.cat/mo

nografics/cirel/pla_le/nil

e/mrosa_garcia/worksh

eets.pdf

3. Advanced: Problems 1-4

Exs. 7-19 odd, 20-51

30mn

Basic skills

Review:

HSPA

PREP/PARCC/SA

T

Identify congruent figures

and their corresponding

parts.

Example:

A design follows this pattern:

an equilateral triangle is

divided into 4 congruent

triangles as shown below in

Stage 1. Then, the top triangle

is divided into 4 congruent

triangles and the pattern

repeats for each stage. In

Stage 2, what is the ratio of

the area of the larger shaded

triangle to the area of the

G.SRT.5

Use congruence and similarity

criteria for triangles to solve

problems and to prove

relationships in geometric

figures.

Pearson

Chapter 4-1

Text book

page #4-9

Web link for congruent

triangles:

www.mathopenref.com

/congruenttriangles.ht

Standardized Test Prep

(SAT/HSPA)

Text book page 224 Q. 50-53

5

smaller shaded triangle?

1 day

1.

Points, Lines,

Planes

- To understand basic terms

and postulates of Geometry

Example:

Line

G.CO.1







circular arc.

MP.3

MP.6

Pearson

Chapter 1

Text book

page #10-19

Web link for points,

lines and planes:

http://coachmetz.files.w

ordpress.com/2012/04/

geometry_point_lines_a

nd_planes_worksheet_a

.pdf


8-14 all, 65-80.

Problems 3-4

Exs. 15-26 all, 28-46 even, 51,

54-58 even


Exs. 9-13 odd, 65-80. Problems

3-4

Exs. 15-25 odd, 27-58


Exs.9-13 odd, 65-80. Problems

3-4

Exs. 15-25 odd, 27-64

30mn

Basic skills Review:

HSPA

PREP/PARCC/SAT

To identify parallel and

perpendicular lines.

Ex. How would you determine

whether two lines are parallel

G-C.O.1

See below

Pearson

Chapter 1

Web link for parallel

and perpendicular lines:

www.clackamasmiddlec

ollege.org/.../Parallel+a


(SAT/HSPA)


6

or

perpendicular?

Text book

page #10

nd+Perpendicular+lines.

pdf

1 day

1.

Measuring

Segments

Determine and compare

length of segments.

Example:

G.CO.1







circular arc.

G.GPE.6

Find the point on a directed line

segment between two given

points that partitions the

segment in a given ratio.

Pearson

Chapter 1

Text book

page #20-27

Web link for segments

and their measures:

www.kutasoftware.com

/FreeWorksheets/Geo

Worksheets/2-

Line%20Seg


8-22 all, 24-34 even, 35, 37-

39, 44-56


Exs. 9-21 odd, 23-41, 44-56


Exs. 9-21 odd, 23-56

7

MP.1, MP.3

30

mn

Basic skills

Review:

HSPA

PREP/PARCC/S

AT

To find translation image of

figures:

Example:

Consider parallelogram ABCD

with coordinates A(2,-2),

B(4,4), C(12,4) and D(10,-2).

Perform the following

transformations. Make

predictions about how the

lengths, perimeter, area and

angle measure will change

under each transformation.

a. A reflection over the x-axis.

b. A rotation of 270about the

origin. c. A dilation of scale

factor 3 about the origin. d. A

translation to the right 5 and

down 3.

Verify your predictions.

Compare and contrast which

transformations preserved the

size and/or shape with those

that did not preserve size

and/or shape. Generalize, how

could you determine if a

G-CO.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.

Pearson

Chapter 9-1

Text book

page #552

Weblink for practice

with translation in

coordinate geometry.

www.mathsisfun.com/g

eometry/translation.ht


(SAT/HSPA)

Text book page 552

Q. 36-39

Weblink for Video on

translation:

www.brightstorm.com/math/geo

metry/transformations/translatio

ns

8

transformation would maintain

congruency from the pre-image

to the image?

1 day

1.4 Measuring

Angles

1-5 Exploring

Angle Pairs

Determine and compare the

measures of angles.

Identify special angle pairs

and use their relationships to

find angle measures.

Example:

G.CO.1







circular arc.

G.CO.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

Pearson

Chapter 1

Text book

page # 28-47

Web link for angles and

their measures:

http://aggiejots.tripod.c

om/sitebuildercontent/s

itebuilderfiles/geo_0106

_ans.pdf

1. Basic: (1.4) problems 1-2

Exs 6-17 all, Exs. 6-17 all, 41-

49.

Problems 3-4 Ex. 18-23 all, 24-

28 even, 29, 31-34, 41-49

(1.5) problems 1-2 Exs. 7-23

all, 48-59. Problems 3-4

Exs. 7-26 all, 28-30 even,

31,34-38 even, 39-40

2. Average:

1) Section (1.4) problems 1-2

Exs. 7-17 odd, 41-49.

3. Problems 3-4 Exs. 19-23

odd, 24-32, 41-49. (1.5)

Problems 1-2 Exs. 7-23 odd,

48-59. Problems 3-4

Exs. 25, 27-41

4. Advanced:

9

point not on the line.

MP.1, MP.3

1) Section (1.4) Problems 1-4

Exs.7-23 odd, 24-49.

2) Section (1-5) Problems 1-4

Exs. 7-25 odd, 27-59

30mn

Basic skills

Review:

HSPA

PREP/PARCC/S

AT

Use the Pythagorean

Theorem to solve real life

problems:

Example:

A 16-ft ladder leans against

a building. To the nearest

foot, how far is the base of

the ladder from the

building? Sketch the

diagram.

G.SRT.8

Use trigonometric ratios and the

Pythagorean Theorem to solve

right triangles in applied

problems.

Pearson

Chapter 5

Text book

page # 291

Kuta software for

worksheet:


/FreeWorksheets/PreAlg

Worksheets/Pythagorea

n


(SAT/HSPA)


Interactive game link for

Pythagorean Theorem:

www.math-

play.com/Pythagorean-

Theorem-Game

1 day

1.6

Basic

Constructions

Perform basic constructions

using a straightedge and

compass.

Example:

Construct a circle

circumscribed about triangle

G.CO.12

Make formal geometric

constructions with a variety of

tools and methods (compass

and straightedge, string,

reflective devices, paper folding,

Pearson

Chapter 1

Text book

page # 48-56

Compass and

straightedge

construction worksheets

available on this site:

www.mathopenref.com

/worksheetlist

5. Basic:

1) problems 1-2

Exs 7-12 all, 20, 39-47.

2) Problems 3-4

10

ABC

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.

MP.1, MP.3, MP.5, MP.7

Exs. 13-16 all, 18, 19, 22,

24, 25, 26-30 even, 36-38

6. Average:

1) problems 1-2

Exs. 7-11 odd, 20, 39-47.

2) Problems 3-4

Exs. 13, 15, 17-19, 21-32,

36-38

7. Advanced:

1) Problems 1-2

Exs. 7-11 odd, 20,

39-47

2) Problems 3-4

Exs. 13, 15, 17-19,

21-38

30mn

Basic skills

Review:

HSPA

PREP/PARCC/S

AT

Use different scale to

solve real life

applications

Example:

Jan is building a scale

model of a house. If the

actual house is 86 feet

wide and 172 feet long,

G.GMD.3

Use volume formulas for

cylinders, pyramids, cones, and

spheres to solve problems.

Pearson

Chapter 10-1

Text book

page # 622

Web link for area and

parallelogram:

http://www.mathgoodie

s.com/lessons/vol1/area

_parallelogram.html


(SAT/HSPA)


Kutasoftware for worksheet:

www.kutasoftware.com/FreeW

orksheets/PreAlgWorksheets/

Area

11

what will be the length in

inches of the scale model if

it is 18 inches wide?

1 day

1.7 Midpoint

and Distance in

the Coordinate

Plane

Find the midpoint of a

segment.

Find the distance between

two points in the coordinate

plane.

Example:

The distance from the floor to

the ceiling of a rectangular

room is 8 ft. The diagonals of

two adjacent walls are 17 ft

and ft, respectively.

How long is a diagonal of the

floor?

G.GPE.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).

G.PE.7

Use coordinates to compute

perimeters of polygons and

areas of triangles and

rectangles, e.g., using the

distance formula.

MP.1, MP.3

Pearson

Chapter 1

Text book

page #49-66

Web link for

Pythagorean theorem

and the distance

formula:

http://users.manchester

.edu/Student/slmiller02

/ProfWeb/PythagoreanT

heoremNotes.pdf

8. Basic:

1) problems 1-2

Exs. 6-21 all, 62-67

2) Problems 3-4

Exs. 22-35all,

36-44 even, 45-47 all, 48-56

even

9. Average:

1) problems 1-2

Exs. 7-21 odd, 62-72

2) problems 3-4

Exs. 23-35 odd, 36-57

10. Advanced:

1) Problems 1-2

Exs. 7-21 odd, 62-72

2) Problems 3-4

12

Exs. 23-35 odd, 36-61

30

mn

Basic skills

Review:

HSPA

PREP/PARCC/S

AT

Apply trigonometric ratios.

Example:

Joshua is flying his kite at the

end of a100ft. string. The

angle of the string to the

ground is 50 degrees.

Find the

height, x,

of the kite

above

the ground.

G.SRT.8

Use trigonometric ratios and the

Pythagorean Theorem to solve

right triangles in applied

problems.

Pearson

Chapter 8-1

Text book

page # 498

Web link for

trigonometry ratios:

http://www.kutasoftwar

e.com/FreeWorksheets/

GeoWorksheets/9-

Trigonometric%20Ratios

.pdf

11. Standardized Test Prep

(SAT/HSPA)


12. Web link for video

tutorial on trigonometric

ratio

www.youtube.com/watch?

13

1 day

2.1

Patterns and

inductive

reasoning

Use inductive reasoning to

make conjectures.

Example:

Show the conjecture is false

by finding a counterexample.

Conjecture: The sum of two

numbers is always greater

than the larger of the two

numbers.

Prepare for: G.CO.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


segment are exactly those

qui i an fr g n ’

endpoints.

Pearson

Chapter 2-1

Text book

page # 82-88

Weblink for an

application of inductive

reasoning:

www.rohan.sdsu.edu/~i

tuba/math303s08/mathi

a i f

13. Basic:

1) problems 1-3

Exs. 6-30

2) Problems 4-5

Exs. 31-40, 50, 53,54, 59-

66

14. Average:

1) problems 1-3

Exs. 7-29, 38-49

2) problems 4-5

Exs. 31-37 odd,

50-55, 59-66

15. Advanced:

1) Problems 1-3

Exs. 7-29 odd,

38-49

2) Problems 4-5

Exs. 31-37 odd,

50-66

14

30

mn

Basic skills

Review:

HSPA

PREP/PARCC/S

AT

Apply the surface area and

the volume formulas:

Example:

Find the approximate surface

area of this can to the nearest

square inch. The diameter of

the top is about 6 inches and

the height of the cylinder is 8

inches.

G.GMD.3

Use volume formulas for

cylinders, pyramids, cones, and

spheres to solve problems.

Pearson

Chapter 11

Text book

page #695

Web link for surface

area and volume:

www.mathatube.com/c

ylinder-volume-surface-

area-worksheets


(SAT/HSPA)


17. Web link for video

tutorial on surface area

and volume:

www.khanacademy.org/.../c

ylinder-volume-and-surface-

area

15

1 day

2.2

Conditional

statements

Compose and distinguish

between the converse,

inverse, and contrapositive

of a conditional statement.

Example:

Your classmate claims that

the conditional and

contrapositive of the

following statement are both

true. Is he correct? Explain

If X = 2, then X2 = 4

1. Can you find a

counterexample of the

conditional?

2. Do you need to find a

counter example of the

contrapositive to know its

truth table?

Prepares for:

G.CO.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




qui i an fr g n ’

endpoints.

Pearson

Chapter 2-2

Text book

page #89-96

Web link for conditional

statement:

http://wwwregensprep.

org/Regents/n

Kuta software for

worksheet:

www.kutasoftware.co

m

you tube video tutorial:

www.youtube.com/wat

ch?v=undSZSratIA

3. Basic:

1) Problems 1-4

Exs. 5-24, 28-29, 35, 37

39-40, 47-58

4. Average:

1) problems 1-4

Exs. 5-23, 25-42, 47-58

5. Advanced:

1) Problems 1-4

Exs. 5-23 odd, 25-58

Math power point notes:

Google search:

ac r nric k va u … C n i

titionalStatement/LECTURE2-1.ppt

www a c rg … G ryPP

Ts/2.1%20Conditional%20Statement

www a a c … C a r%

20Powerpoints/2.2%20Intro%2

Math skills practice:

http://wwwregensprep.org/Regents/n

http://wwwregensprep.org/Regents/n



http://www.youtube.com/watch?v=undSZSratIA

http://www.youtube.com/watch?v=undSZSratIA

16

Intranet.asfa.k.12 a u … Law %

f%20Logic

17

30

mn

Basic skills

Review:

HSPA

PREP/PARCC/S

AT

To apply the Pythagorean

Theorem and the perimeter

formula:

Example:

The backyard behind Mr.

J n n’ u i a

rectangle. A sidewalk from

one corner of the backyard to

the opposite corner is 76 feet

long. Both the backyard and

the house are 40 feet wide.

What is the approximate

perimeter of the backyard? Sketch the figure.

G.SRT.8 Use trigonometric ratios

and the Pythagorean Theorem

to solve right triangles in applied

problems.

Pearson

Chapter 2-2

Text book

page #95

Kuta software for

worksheet:

www.kutasoftware.co

m


(SAT/HSPA)


7. Interactive game link for


www.math-

play.com/Pythagorean-

Theorem-Game.html



http://www.math-play.com/Pythagorean-Theorem-Game.html



18

1 day

2.3

Bi-conditionals

and Definitions

Illustrate bi-conditionals and

recognize good definitions.

Example:

What are the two conditional

statements that form this bi-

conditional?

A ray is an angle bisector if

and only if it divides an angle

into two congruent angles.

Prepares for

G.CO.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.

Pearson

Chapter 2-3

Text book

page #99-105

Web link for bi-

conditional statement:

http://www.mathgoodie

s.com/lesson/

Kuta software for

worksheet:

www.kutasoftware.co

m


www.youtube.com/wat

ch?v=12CeL-hFky8

8. Basic:

1) Problems 1-3

Exs. 7-30, 33, 35-36,

43, 45, 49-57

9. Average:

1) problems 1-4

Exs. 7-30, 33, 35-36,

43, 45, 49-57

10. Advanced:

1) Problems 1-4

Exs. 7-29 odd, 30-57


Google search:

teachers.henric k va u … C n

dititionalStatement/LECTURE2-

1.ppt

www a c rg … G ry-

f c fu i n u u …

/get_group_file.phtml?...

www.ohio.edu/people/melkonia/

math306/slides/logic2.ppt

http://www.mathgoodies.com/lesson/

http://www.mathgoodies.com/lesson/



http://www.youtube.com/watch?v=12CeL-hFky8

http://www.youtube.com/watch?v=12CeL-hFky8

http://www.ohio.edu/people/melkonia/math306/slides/logic2.ppt

http://www.ohio.edu/people/melkonia/math306/slides/logic2.ppt

19


In ran a fa k a u … Law %

0of%20Logic

PDF worksheet link:

http://mycoursecan.com/Files/Sub

jects/Ge

http://mycoursecan.com/Files/Subjects/Ge

http://mycoursecan.com/Files/Subjects/Ge

20

30

mn

Basic skills

Review:

HSPA

PREP/PARCC/S

AT

Apply reflections:

Example:

is the image when

point F is reflected over

the line and

then over the line

The location of

is Which of

the following is the

location of point F ?

a.

b.

c.

d.

G.CO.1

Use the undefined notion of a

point, line, distance, along a line

and distance around a circular

arc to develop definitions for

angles, circles, parallel lines,

perpendicular lines and line

segments.

Pearson

Chapter 2-3

Text book

page #104

Web link on reflection:

www.regentspre.org/Re

gents/math/geometry/G

T1/reflect.htm


(SAT/HSPA)




www.mangahigh.com/en_us

/games/translar

http://www.regentspre.org/Regents/math/geometry/GT1/reflect.htm



http://www.mangahigh.com/en_us/games/translar

http://www.mangahigh.com/en_us/games/translar

21

1 day

2-4

Deductive

reasoning

Apply the law of detachment

and the law of syllogism:

Example:

What can you conclude from

the given true statement?

If a u n g an “A” n a

final exam, then the student

will pass the course.

Prepares for:

G.CO.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.

Pearson

Chapter 2-4

Text book

page # 106-

112

Web links for

bi-conditional

statements:

rewww.khanacademy.or

g/.../geometry.../ca-

geometry--deductive-

www.sparknotes.com/...

/geometry3/inductivean

ddeductivereasoning/se

ct..

Kuta software for

worksheet:

www.gobookee.net/ded

uctive-reasoning-kuta/

www.mybookezz.org/ge

ometric-mean-kuta-

software-1344/


www.khanacademy.org/

.../geometry.../ca-

geometry--deductive-...

www.youtube.com/wat

ch?v=GluohfOedQE

13. Basic:

1) Problems 1-3

Exs. 6-21, 26, 28, 30,

33-39

14. Average:

1) problems 1-3

Exs. 7-17 odd, 18-30,

33-39

15. Advanced:

1) Problems 1-3 Exs. 7-

17 odd, 18-39


Google search:

www.cecs.csulb.edu/~mopkins/cecs100/D

eductInduct.pptx

www.taosschools.org/.../GeometryPPTs/2

.3Deductive%20Reasoning.ppt

http://www.khanacademy.org/.../geometry.../ca-geometry--deductive-



http://www.sparknotes.com/.../geometry3/inductiveanddeductivereasoning/sect




http://www.gobookee.net/deductive-reasoning-kuta/

http://www.gobookee.net/deductive-reasoning-kuta/

http://www.mybookezz.org/geometric-mean-kuta-software-1344/






http://www.youtube.com/watch?v=GluohfOedQE

http://www.youtube.com/watch?v=GluohfOedQE

http://www.cecs.csulb.edu/~mopkins/cecs100/DeductInduct.pptx

http://www.cecs.csulb.edu/~mopkins/cecs100/DeductInduct.pptx

http://www.taosschools.org/.../GeometryPPTs/2.3Deductive%20Reasoning.ppt

http://www.taosschools.org/.../GeometryPPTs/2.3Deductive%20Reasoning.ppt

22


www.csun.edu/~kme52026/Chapter4.pdf

www.brighthubeducation.com › › Math

Lessons: Grades 9-12

PDF worksheet link:

www.frapanthers.com/.../Geometry(

H)/worksheets/WorksheetDeductiv

e

www.matsuk12.us/cms/lib/AK010009

53/Centricity/.../geo2_1WS.pdf

http://www.csun.edu/~kme52026/Chapter4.pdf

http://www.brighthubeducation.com/

http://www.brighthubeducation.com/high-school-math-lessons/


http://www.frapanthers.com/.../Geometry(H)/worksheets/WorksheetDeductive



http://www.matsuk12.us/cms/lib/AK01000953/Centricity/.../geo2_1WS.pdf

http://www.matsuk12.us/cms/lib/AK01000953/Centricity/.../geo2_1WS.pdf

23

30

mn

Basic skills

Review:

HSPA

PREP/PARCC/S

AT

Apply transformations:

Triangle ABC is shown in the

coordinate plane below. Draw

the result of the

transformation when triangle

ABC is translated 6 units to

the right and then rotated

clockwise about the

origin.

G.CO.2-5

Develop and perform rigid

transformations that include

reflections, rotations,

translations and dilations using

geometric software, graph

paper, tracing paper, and

geometric tools and compare

them to non-rigid

transformations.

Pearson

Section

2-4

More HSPA

PREP Text

book page

#112

Q. 33-34

Kuta software for

worksheet


/FreeWorksheets/GeoW

orksheets/12-

All%20Tran


(SAT/HSPA)

Text book page 112 Q. 33,

34



www.kidsmathgamesonline.

com/geometry/transformati

on.html

http://www.kidsmathgamesonline.com/geometry/transformation.html



24

1 day

2-5

Reasoning in

Algebra and

Geometry

Connect reasoning in

algebra and

geometry.

Example:

What is the name of the

property of equality or

congruence that justify going

from the first statement to

the second statement?

1. 2x + 9 =19

2. and

so

3.

Prepares for:

G.CO.9











qui i an fr g n ’

endpoints.

Pearson

Chapter 2-5

Text book

page # 113-

119

Web link for reasoning

in algebra and

geometry:

www.mathplayground.c

om/games.html

www.xpmath.com

Kuta software for

worksheet:

www.gobookee.net/geo

metry-review-5-kuta-

answers/


www.youtube.com/wat

ch?v=xkTgnN5pOks

vimeo.com/49030863

4. Basic:

1) Problems 1-3

Exs. 5-17, 20, 22, 23

29-41

5. Average:

1) problems 1-3

Exs. 5-13 odd, 14-24,

29-41

6. Advanced:

1) Problems 1-3

Exs. 5-13 odd, 14-41


Google search:

www.cvsd.org/.../Geometry.../2-

5%20Reasoning%20in%20Algebra

%20a

jcs.k12.oh.us/.../Geometry/PH_G

eo_2-

a ning in A g ra


www.nhvweb.net/nhhs/math/ms

chuetz/files/.../Section-2-5-and-2-

http://www.mathplayground.com/games.html

http://www.mathplayground.com/games.html

http://www.xpmath.com/

http://www.gobookee.net/geometry-review-5-kuta-answers/



http://www.cvsd.org/.../Geometry.../2-5%20Reasoning%20in%20Algebra%20a



25

6.pdf

www.brighthubeducation.com ›

› Math Lessons: Grades 9-12

PDF worksheet link:

www.frapanthers.com/.../Geome

try(H)/worksheets/WorksheetDed

uctive

www.quia.com/files/quia/users/a

lamed/Geoguide/Geoguide2.5

http://www.brighthubeducation.com/





http://www.quia.com/files/quia/users/alamed/Geoguide/Geoguide2.5

http://www.quia.com/files/quia/users/alamed/Geoguide/Geoguide2.5

26

30

mn

Basic skills

Review:

HSPA

PREP/PARCC/S

AT

Use reflections, rotations, and

transformations:

Example:

Triangle ABC and triangle

LMN are shown in the

coordinate plane below.

Part A: Explain why triangle

ABC is congruent to triangle

LMN using one or more

reflections, rotations, and

translations.

Part B: Explain how you can

use the transformations

described in Part A to prove

triangle ABC is congruent to

triangle LMN by any of the

criteria for triangle

G.CO.6-8

Use rigid transformations to

determine, explain and prove

congruence of geometric

figures.

Pearson

Section

2-5

More HSPA

PREP Text

book page

#119

Q. 29-33

Kuta software for

worksheet:


/freeige.html


(SAT/HSPA)

Text book page 119

Q. 29- 33



www.mathplayground.com/

ShapeMods/ShapeMods.ht

ml

27

congruence (ASA, SAS, or

SSS).

28

2

day

2.6

Proving Angles

Congruent

Prove and apply theorems

about angles:

Example:

Write a paragraph proof:

Given:

are supplementary.

are

supplementary.

Prove:

3

1

2

G.CO.9











qui i an fr g n ’

endpoints.

Pearson

Chapter 2-6

Text book

page # 120-

127

Web link for proving

theorems about angles:

www.mathwarehouse.c

om/.../triangles/similar-

triangle-theorems.php


.../angles/v/angle-

bisector-theorem-proo

Kuta software for

worksheet:

www.letspracticegeome

try.com/free-geometry-

worksheets/


www.youtube.com/wat

ch?v=gq1B3ceW4TE

www.youtube.com/wat

ch?v=G_RsPC2dKHM

9. Basic:

1) problems 1-2

Exs. 6-12, 46-48

2) Problems 3

Exs. 13-14, 20-21, 25,

26, 28

10. Average:

1) problems 1-2

Exs. 7-11 odd, 36-48

2) problems 3

Exs. 13-30

11. Advanced:

1) Problems 1-2

Exs. 7-11 odd, 36-48

2) Problems 3

Exs. 13-35


Google search:

www.taosschools.org/.../GeometryP

PTs/4.4%20ASA%20AND%20AAS

www.dgelman.com/powerpoints/.../

2.6%20Proving%20Statements%20a.

.


http://www.mathwarehouse.com/.../triangles/similar-triangle-theorems.php



http://www.khanacademy.org/.../angles/v/angle-bisector-theorem-proo



http://www.letspracticegeometry.com/free-geometry-worksheets/



http://www.youtube.com/watch?v=gq1B3ceW4TE

http://www.youtube.com/watch?v=gq1B3ceW4TE

http://www.youtube.com/watch?v=G_RsPC2dKHM

http://www.youtube.com/watch?v=G_RsPC2dKHM

http://www.taosschools.org/.../GeometryPPTs/4.4%20ASA%20AND%20AAS

http://www.taosschools.org/.../GeometryPPTs/4.4%20ASA%20AND%20AAS

http://www.dgelman.com/powerpoints/.../2.6%20Proving%20Statements%20a

http://www.dgelman.com/powerpoints/.../2.6%20Proving%20Statements%20a

29

30

mn

Basic skills

Review:

HSPA

PREP/PAR

CC/SAT

Use transformations:

Quadrilateral PQRS is shown

below. Which of the following

transformations of triangle

PTS could be used to show

that

triangle PTS is congruent to

triangle QTR ?

1) A reflection over segment QS

2) A reflection over segment PR

G.CO.6, 7, 8

Use rigid transformations to

determine, explain and prove

congruence of geometric

figures.

Pearson

Section

2-6

More HSPA

PREP Text

book page

#127

Kuta software for

worksheet:

ww2.d155.org/.../Geom

etry%20363%20.../Ch%2

% % Pack


(SAT/HSPA)

Text book page 127

Q. 36- 39


transformation

www.onlinemathlearning.co

m/transformation-in-

geometry

30

3) A reflection over line m

4) A reflection over line l

31

1 day

3.1

Lines and

Angles

Identify relationships

between figures in space.

Identify angles formed by

two lines and a transversal.

Example:

Think of each segment in the

diagram as part of a line.

Which of the lines appears to

fit the description?

a. Parallel to line AB and

contains D

b. Perpendicular to line AB

and contains D

c. Skew to line AB and

contains D

d. Name the plane(s) that

contain D and appear to be

parallel to plane ABE.

G.CO.1

Use the undefined notion of a

point, line, distance, along a line

and distance around a circular

arc to develop definitions for

angles, circles, parallel lines,

perpendicular lines, and line

segments.

Pearson

Chapter 3-1

Text book

page # 140-

146

Web link for properties

and parallel lines:

www.nexuslearning.net/

.../ML%20Geometry%20

3-1%20Lines% an %


.../angles/v/angle-

bisector-theorem-proo

Kuta software for

worksheet:


/.../13-

Line%20Segment%20Co

n ruc n f



.../segments.../lines--

line-segments--and-ra..

www.youtube.com/wat

c v nv wI

14. Basic:

1) problems 1-3

Exs. 11-29 all, 30-44

Even, 49-60

15. Average:

1) problems 1-3

Exs. 11-23 odd, 25, 45, 49-60

16. Advanced:

1) Problems 1-3

Exs. 11-23 odd, 25 - 60


Google search:

www.eht.k12.nj.us/~Simmonsg/lines

%20ppt.ppt

www2.carrollk12.org/instruction/el

emcurric/.../line%20powerpoint.

ppt


www.mathwarehouse.com/.../triangles/si

milar-triangle-theorems.php

32

www.sanjuan.edu/webpages/john

higgins/files/8-

1%20Practice

PDF worksheet link:

tms6thgrade.weebly.com/uploads

/8/5/1/7/8517785/practice_8-

1

33

30

mn

Basic skills

Review:

HSPA

PREP/PAR

CC/SAT

Use perpendicular lines

Example:

Use paper folding to

construct the perpendicular

bisector of line segment

shown below. Trace and label

the line segment JK.

G. CO.12, 13

Generate formal constructions

with paper folding, geometric

software and geometric tools to

include, but not limited to, the

construction of regular polygons

inscribed in a circle.

Pearson

Section

3-1

More HSPA

PREP Text

book page

#146

Kuta software for

worksheet:


/FreeWorksheets/Geo

Worksheets/2-

Line%20Seg


(SAT/HSPA)

Text book page 146 Q. 49- 52


transformation

www.sheppardsoftware.com/

mathgames/geometry/.../line

_shoot.htm

http://www.sheppardsoftware.com/mathgames/geometry/.../line_shoot.htm



34

2

days

3.2 properties

of parallel lines


parallel lines.

Use properties of parallel

lines to find angle measures.

Example:

Complete the proof of the

Consecutive Interior Angles

Theorem.

GIVEN: p q

PROVE: 1 and 2 are

supplementary.

G.CO.9











qui i an fr g n ’

endpoint.

Pearson

Chapter 3-2

Text book

page # 147-

155

Web link for reasoning

in algebra and

geometry:

www.slideshare.net/1co

nejo/proving-lines-are-

parallel

web.mnstate.edu/peil/g

eometry/.../6ExteriorAn

gleR.htm

Kutasoftware for

worksheet:


fr ig


www.youtube.com/wat

c v L G

19. Basic:

1) problems 1-2

Exs. 7-11, 29-39

2) Problems 3-4

Exs. 12-18, 29-39

20. Average:

1) problems 1-2

Exs. 7-11 odd, 29-39

2) problems 3-4

Exs. 13-17 odd,18-26

21. Advanced:

1) Problems 1-2

Exs. 7-11 odd, 29-39

2) Problems 3-4

Exs. 13-17 odd,18-28


Google search:

teachers.henrico.k12.va.us/.../02Perp

endicularParallel/...5ProvingLinesP

a...

35

geometry-

f.mths.schoolfusion.us/modules/.../get_gro


www.nexuslearning.net/.../ML%20Ge

ometry%203-3%20Parallel%20Lin

PDF worksheet link:

www.bowerpower.net/geometry/ch03/

Wksh%203.2B.pdf

36

30

mn

Basic skills

Review:

HSPA

PREP/PAR

CC/SAT


parallel lines.

Example:

12. Using the figure above and

the fact that line is parallel

to segment prove that

the sum of the angle

measurements in a triangle is

Use as many or as

few rows in the table as

needed.

G.CO.9, 10, 11

Create proofs of theorems

involving lines, angles, triangles,

and parallelograms.* (Please

note G.CO.10 will be addressed

again in unit2 and G.CO.11 will

be addressed again in unit 4)

Pearson

Section

3-2

More HSPA

PREP Text

book page

#155

Kuta software for

worksheet:


fr ig


(SAT/HSPA)

Text book page 155

Q. 29- 32


transformation

www.onlinemathlearning.co

m/proving-parallel-

lines

37

2days

3.3

Proving Lines

are Parallel

To determine

whether two lines

are parallel.

Example:

In the diagram at the right,

each step is parallel to the

step immediately below it

and the bottom step is

parallel to the floor. Explain

why the top step is parallel to

the floor.

G.CO.9











qui i an fr g n ’

endpoint.

Pearson

Chapter 3-3

Text book

page # 156-

163


lines are parallel

https://dionmath.wikisp

aces.com/.../3.5+Showi

ng+Lines+are+Parallel.p

pt...

https://s3.amazonaws.c

om/engrade-

myfiles/.../03-05-

Kutasoftware for

worksheet:


24. Basic:

1) problems 1-2

Exs. 7-11, 18-28 even

2) Problems 3-4

Exs. 12-16 all, 30-34

Even, 35, 36,38, 47-57

25. Average:

1) problems 1-2

Exs. 7-11 odd, 17-28

2) problems 3-4

https://s3.amazonaws.com/engrade-myfiles/.../03-05-



38

/.../3-

Parallel%20Lines%20an

% ran v r a



.../parallel...lines/.../ide

ntifying-parallel-

Exs. 13-15 odd, 29-41,

47-57

26. Advanced:

1) Problems 1-2

Exs. 7-11 odd, 17-28

2) Problems 3-4

Exs. 13-15 odd, 28-57


Google search:

teachers.henrico.k12.va.us/.../02

PerpendicularParallel/...5Proving

LinesPa


www.regentsprep.org/Regents/

math/ALGEBRA/AC3/pracParallel

PDF worksheet link:

glencoe.mcgraw-

hill.com/sites/dl/free/007888484

5/634463/geohwp.pdf

39

30

mn

Basic skills

Review:

HSPA

PREP/PAR

CC/SAT

Proving that a

quadrilateral is a

parallelogram.

In In the quadrilateral below,

and

Prove that the quadrilateral is a

parallelogram.

Write an informal proof.

__________________________

__________________________

__________________________

__________________________

__________________________

__________________________

__________________________

__________________________

__________________________

__________________________

__________________________

__________________________

__________________________

___________________

G.CO.9











qui i an fr g n ’

endpoint

Pearson

Section

3-3

More HSPA

PREP Text

book page

#163

Kuta software for

worksheet:


/.../3-

Proving%20Lines%20Par

allel f


(SAT/HSPA)

Text book page 163

Q. 47- 51


transformation

www.math-

play.com/Angles-

Jeopardy/Angles-

Jeopardy.html

40

1day

4.4

Using

corresponding

parts of

congruent

triangles.

Apply triangle congruence

and corresponding parts of

congruent triangles.

Prove that parts of two

triangles are congruent.

Example:

G.SRT.5

Use congruence and similarity

criteria for triangles to solve


relationships in geometric

figures.

Pearson

Chapter 4-4

Text book

page # 244-

256


that two parts of two


www c a z n c ›

Geometry Concepts and

Skills › Chapter 5

salinesports.org/mr_fre

derick/GeomCS/Unit%2

g an f

Kutasoftware for

worksheet:


/.../4-

Congruence%20and%20

Triangles f


29. Basic:

1) problems 1-2

Exs. 5-8 all,

10-16 even

17, 20, 23-32

30. Average:

1) problems 1-2

Exs. 5, 7, 9-20,

23-32

31. Advanced:

1) Problems 1-2

Exs. 5-7, 9-32


Google search:

http://www.classzone.com/books/geometry_concepts/index.cfm


http://www.classzone.com/books/geometry_concepts/page_build.cfm?&ch=5

41


.../congruent-

triangles/...triangle/.../fi

n i

www.grossmont.edu/carylee/Ma

126/lectures/Chapter14.ppt


www.regentsprep.org/Regents/

math/geometry/GP4/PracCongTr

i

PDF worksheet link:

www.kutasoftware.com/FreeWo

rksheets/GeoWorksheets/4-

Congruence

http://www.grossmont.edu/carylee/Ma126/lectures/Chapter14.ppt

http://www.grossmont.edu/carylee/Ma126/lectures/Chapter14.ppt

42

30

mn

Basic skills

Review:

HSPA

PREP/PAR

CC/SAT

Prove vertical angles are

congruent:

U Using the figure above, prove

that vertical angles are

congruent. Use as many or as

few rows in the table as

needed.

G.CO.9











qui i an fr g n ’

endpoint

Pearson

Section

4-4

More HSPA

PREP Text

book page

#224

Kuta software for

worksheet:


/.../4-

Right%20Triangle%20Co

ngruence f


(SAT/HSPA)

Text book page 224 Q. 50-

53


transformation

www.mathsisfun.com/geom

etry/triangles-

congruent.html

http://www.mathsisfun.com/geometry/triangles-congruent.html



43

2

days

4.5

Isosceles and

Equilateral

Triangles

Apply properties of isosceles

and equilateral triangles.

Example:

Rock Climbing

In one type of rock climbing,

climbers tie themselves to a

rope that is supported by

anchors. The diagram shows a

red and a blue anchor in a

horizontal slit in a rock face.

G.CO.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.

Pearson

Chapter 4-5

Text book

page # 250-

257

Web link for

applying properties

of isosceles and

equilateral triangles.

www.math-

worksheet.org/isosceles

-and-equilateral-

triangles



orksheets/4-

Isosceles%

Kutasoftware for

34. Basic:

1) problems 1-2

Exs. 6-12 all, 37-44

2) Problems 3

Exs. 13-15,

16-24 even

28-32 even

35. Average:

1) problems 1-2

44

worksheet:



orksheets/4-

Isosceles%



...triangles/.../equilatera

l-and-isosceles-

Exs. 7-11 odd, 37-44

2) problem 3

Exs. 13-32

36. Advanced:

1) Problems 1-3

Exs. 7-13 odd, 14-44


Google search:

yourcharlotteschools.net/Schools

/PCHS/Dubbaneh_site/4.5a.ppt


library.thinkquest.org/20991/tex

tonly/quizzes g q

PDF worksheet link:



Isosceles%

45

30

mn

Basic skills

Review:

HSPA

PREP/PAR

CC/SAT

Prove that two angles or line

segments are congruent:

In isosceles ABC, the vertex

angle is A. What can you

prove?

1. AB = CB

2.

3.

4. BC = AC

G.CO.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.

Pearson

Section

4-5

More HSPA

PREP Text

book page

#256

Kuta software for

worksheet:



orksheets/4-

Isosceles%


(SAT/HSPA)

Text book page 256 Q. 37-

40


transformation

www.mathsisfun.com/trian

gle

INSTRUCTIONAL FOCUS OF UNIT

In previous grades, students were asked to draw triangles based on given measurements. Students also have prior experience with rigid motions:

translations, reflections, and rotations and have used these to develop notions about what it means for two objects to be congruent. In this unit,

students establish triangle congruence criteria, based on analyses of rigid motions and formal constructions. Students use triangle congruence as a

familiar foundation for the development of formal proof. Students prove theorems—using a variety of formats—and solve problems about lines,

angles, triangles, quadrilaterals, and other polygons. Students also apply reasoning to complete geometric constructions and explain why

constructions work.

PARCC FRAMEWORK/ASSESSMENT

7. PARCC EXEMPLARS: www.parcconline.org (copy & paste the URL or link into search engine)

8. Dollar Line: http://balancedassessment.concord.org/hs033.html

Example:

http://www.parcconline.org/

46

Think of a situation which could be represented by the graph below, Write a

full description of this situation (be sure to tell what each axis represents in your story.)

9. How would you determine whether two lines are parallel or perpendicular?

10. Consider parallelogram ABCD with coordinates A(2,-2), B(4,4), C(12,4) and D(10,-2). Perform the following transformations. Make predictions about how the

lengths, perimeter, area and angle measure will change under each transformation.

a. A reflection over the x-axis.

b. A rotation of 270about the origin.

c. A dilation of scale factor 3 about the origin.

d. A translation to the right 5 and down 3.

Verify your predictions. Compare and contrast which transformations preserved the size and/or shape with those that did not preserve size and/or shape. Generalize, how

could you determine if a transformation would maintain congruency from the pre-image to the image?

11. Prove that any point equidistant from the endpoints of a segment lies on the perpendicular bisector of the line.

47

12. A carpenter is framing a wall and wants to make sure his the edges of his wall are parallel. He is using a cross-brace. What are several different ways he could

verify that the edges are parallel? Can you write a formal argument to show that these sides are parallel? Pair up with another student who created a different

argument than yours, and critique their reasoning. Did you need to modify the diagram in anyway to help your argument?

13. Andy and Javier are designing triangular gardens for their yards. Andy and Javier want to determine if their gardens that they build will be congruent by looking

at the measures of the boards they will use for the boarders, and the angles measures of the vertices. Andy and Javier use the following combinations to build their

gardens. Will these combinations create gardens that enclose the same area? If so, how do you know?

a. Each garden has length measurements of 12ft, 32ft and 28ft.

b. Both of the gardens have angle measure of 110, 25and 45.

c. One side of the garden is 20ft another side is 30ft and the angle between those two boards is 40.

d. One side of the garden is 20ft and the angles on each side of that board are 60and 80.

e. Two sides measure 16ft and 18ft and the non-included angle of the garden measures 30.

Wiki page for Common Core Assessments:

http://maccss.ncdpi.wikispaces.net/file/view/Geometry%20Unpacking062512%20.pdf/359510147/Geometry%20Unpacking062512%20.pdf

PARCC Framework Assessment questions with Model Curriculum Website for all units:

http://www.parcconline.org/sites/parcc/files/PARCCMCFMathematicsNovember2012V3_FINAL.pdf



48

http://www.parcconline.org/sites/parcc/files/PARCCMCFMathematicsGeo_Nov2012V3_FINAL.pdf

http://www.nj.gov/education/assessment/hs/hspa_mathhb.pdf

21ST CENTURY SKILLS

(4Cs & CTE Standards)

1. Career Technical Education (CTE) Standards

1. 21st

Century Life and Career Skills: All students will demonstrate the creative, critical thinking, collaboration, the problem-solving skills needed to function

successfully as both global citizens and workers in diverse ethnic and organizational cultures.

9.1.12.B.1: Present resources and data in a format that effectively communicates the meaning of the data and its implications

for solving problems, using multiple perspectives.

2. Personal Financial Literacy: All students will develop skills and strategies that promote personal and financial responsibility related to financial planning,

savings, investment, and charitable giving in the global economy.

9.2.12.B.3: Construct a plan to accumulate emergency “rainy day” funds.

3. Career Awareness, Exploration, and Preparation: All students will apply knowledge about and engage in the process of career awareness, exploration, and

preparation in order to navigate the globally competitive work environment of the information age.

9.3.12.C.2: Characterize education and skills needed to achieve career goals, and take steps to prepare for postsecondary

options, including making course selections, preparing for and taking assessments, and participating in extra-curricular



http://www.state.nj.us/education/cccs/standards/9/9.pdf

49

activities.

4. Career and Technical Education: All students who complete a career and technical education program will acquire academic and technical skills for careers in

emerging and established professions that lead to technical skill proficiency, credentials, certificates, licenses, and/or degrees.

9.4.12.B.4: Perform math operations, such as estimating and distributing materials and supplies, to complete

classroom/workplace tasks.

Project Base Learning Activities:

http://www.achieve.org/files/CCSS-CTE-Task-FramingaHouse-FINAL.pdf

MODIFICATIONS/ACCOMMODATIONS

1. Group activity or individual activity

2. Review and copy notes from eno board/power point/smart board etc.

3. Group/individual activities that will enhance understanding.

4. Provide students with interesting problems and activities that extend the concept of the lesson

5. Help students develop specific problem solving skills and strategies by providing scaffolded guiding questions

http://www.achieve.org/files/CCSS-CTE-Task-FramingaHouse-FINAL.pdf

50

Peer tutoring

1. Team up stronger math skills with lower math skills

Use of manipulative

1. Eno or smart boards

2. Dry erase markers

3. Reference sheets created by special needs teacher

4. Pairs of students work together to make word cards for the chapter vocabulary

5. Use 3D shapes for visual learning

6. Reference sheets for classroom

7. Graphing calculators

APPENDIX

(Teacher resource extensions)

1. CCSS. Mathematical Practices:

MP1: Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry

points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and

51

meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try

special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change

course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window

on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations,

verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends.

Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students

check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the

approaches of others to solving complex problems and identify correspondences between different approaches.

MP2: Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary

abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it

symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the

ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved.

Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the

meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

MP3: Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing

arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze

situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others,

and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from

which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct

logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments

using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are

52

not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades

can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

MP4: Model with mathematics.

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the

workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply

proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a

design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply

what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision

later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables,

graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their

mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served

its purpose.

MP5: Use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and

paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry

software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of

these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school

students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using

estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the

results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels

are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems.

They are able to use technological tools to explore and deepen their understanding of concepts.

53

MP6: Attend to precision.

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in

their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are

careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately

and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give

carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of

definitions.

MP7: Look for and make use of structure.

Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and

seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have.

Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression

x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and

can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see

complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 –

3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

MP8: Look for and express regularity in repeated reasoning.

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper

elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have

a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope

3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x +

1), (x – 1)(x2 + x + 1), and (x – 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a

problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the

54

Notes to teacher (not to be included in your final draft):

reasonableness of their intermediate results.

2. Kuta G 1: Kuta Software – Geometry (Free Worksheets)

3. Teacher Edition: Geometry Common Core by Pearson

4. Student Companion: Geometry Common Core by Pearson

5. Practice and Problem Solving Workbook: Geometry Common Core by Pearson

6. Teaching with TI Technology: Pearson Mathematics by Pearson

7. Progress Monitoring Assessments: Geometry Common Core by Pearson

8. http://www.jmap.org/JMAP_RESOURCES_BY_TOPIC.htm#Geo

9. http://www.mathopenref.com/

10. http://www.mathisfun.com/

11. http://www.mathwarehouse.com/

12. http://www.regentsprep.org/Regents/math/geometry/math-GEOMETRY.htm

13. http://www.cpm.org/pdfs/state_supplements

14. http://www.cde.ca.gov/ta/tg/sr/documents/cstrtqgeomapr15.pdf

15. http://illuminations.nctm.org

16. http://www.state.nj.us/education/cccs/standards/9/

http://www.jmap.org/JMAP_RESOURCES_BY_TOPIC.htm#Geo

http://www.mathopenref.com/

http://www.mathisfun.com/

http://www.mathwarehouse.com/

http://www.regentsprep.org/Regents/math/geometry/math-GEOMETRY.htm

http://www.cpm.org/pdfs/state_supplements

http://www.cde.ca.gov/ta/tg/sr/documents/cstrtqgeomapr15.pdf

http://illuminations.nctm.org/

http://www.state.nj.us/education/cccs/standards/9/

55

4 Cs Three Parts Objective

Creativity: projects Behavior

Critical Thinking: Math Journal Condition

Collaboration: Teams/Groups/Stations Demonstration of Learning (DOL)

Communication – Power points/Presentations

UNIT 2

Similarity, Proof And Trigonometry



17. How do you identify corresponding parts of congruent

triangles?

23. If two triangles are congruent, then every pair of their corresponding parts is also

congruent.

56

18. How do you show that two triangles are congruent?

19. How do you use proportions to find side lengths in

similar polygons?

20. How do you show two triangles are similar?

21. How do you find a side length or angle measure in a

right triangle?

22. How do trigonometric ratios relate to similar right

triangles?

24. Two ways triangles can be proven to be congruent are by using three pairs of

corresponding sides or by using two pairs of corresponding sides and the pair of corresponding

angles included between those sides.

25. Two geometric figures are similar when corresponding lengths are proportional and

corresponding angles are congruent.

26. Ratios and proportions can be used to prove whether two polygons are similar and to

find unknown side lengths

27. If the lengths of any two sides of a right triangle are known, the length of the third side

can be found by using the Pythagorean Theorem.

28. Ratios can be used to find side lengths and angle measures of a right triangle when

certain combinations of the side lengths and angle measures are known

PACE CONTENT SKILLS STANDARDS

(CCSS/MP)

RESOURCES

LEARNING

ACTIVITIES/ASSESSMENTS Pearson

OTHER

(e.g., tech)

1 day

3.4

Parallel and

Perpendicular

lines

To Relate Parallel and Perpendicular

lines

Example:

G.MG.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).

Text book

page 164-

170

Teacher made power points

presentations.

http://www.summit.k12.co.

us/cms/lib04/CO01001195/

Centricity/Domain/565/cgp0

3gad.pdf

Page 170 Concept Byte –

Perpendicular Lines and Plane

Page 167: 1 - 5

29. Basic – Problems 1-2

Ex. 6 – 9, 12 – 16 even, 17 – 18, 31-

39

http://www.summit.k12.co.us/cms/lib04/CO01001195/Centricity/Domain/565/cgp03gad.pdf




57

MP 1

MP 3

http://www.mathsisfun.com

/algebra/line-parallel-

perpendicular.html

30. Average – Problems 1 – 2

Ex. 6 – 18 , 31 –39

31. Advanced – Problems 1-2

Ex 6 -26, 31 - 39

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To use properties of Parallel Lines

Question:

Using the given information, state the

theorem that allows you to conclude that

j || k

G.MG.3

See below

Text book

page 167

http://www.regentsprep.org

/Regents/math/ALGEBRA/A

C3/Lparallel.htm


/algebra/line-parallel-

perpendicular.html


Q. 27 - 30

http://www.regentsprep.org/Regents/math/ALGEBRA/AC3/Lparallel.htm



58

2 days

4.1 Congruent

Figures

Examine and identify that two

figures are congruent and identify

their corresponding parts

Example:

In the diagram of and

below, , and

.

G.SRT.5 Use

congruence and

similarity criteria

for triangles to

solve problems

and to prove

relationships in

geometric figures.

MP 1

MP 3

MP 4

MP 6

Text book

page 218 -

224

PowerGeometry.com

Interactive Practice games


Mathopenref.com/tocs/con

gruencetoc.html

http://jmap.org/htmlstandar

d/Geometry/Informal_and_

Formal_Proofs/G.G.28.htm

Page 221: 1 - 7

Building congruent triangles activity

page 225

Practice problem solving exercises

page 222 – 224.


Ex. 8 – 29, 50 – 61


Ex. 9 – 29 odd, 50 –61


Ex 9-29 odd, 50-61

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To find angle measures of a triangle

using Angle Sum Theorem

Question:

The measure of one angle In a triangle is

80˚ r w ang ar c ngru n

What is the measure of each?

G.SRT.5

See below

Text book

page 224

Mathopenref.com/tocs/con

gruencetoc.html

Page 224: Standardized Test

Prep – Q. 50 - 53

59

2 days

4.2 Triangle

Congruence by

SSS and SAS

Conclude and defend that two

triangles congruent using the SSS

and SAS Postulates

SSS stands for "side, side, side" and

means that we have two triangles

with all three sides equal.

SAS stands for "side, angle, side" and

means that we have two triangles

where we know two sides and the

included angle are equal.

G.SRT.5 Use

congruence and

similarity criteria

for triangles to

solve problems

and to prove

relationships in

geometric figures.

MP 1

MP 3

Text book

page 226 -

230

PowerGeometry.com


http://mathopenref.com/co

ngruentsss.html


/geometry/congruent.html

35. Page 230:1-7

36. Lesson Quiz

37. Practice and Problem

Solving Exercises page 230

38. Practice and Problem

Solving Exercises


Ex. 8 – 12, 35– 46


Ex. 9, 35 –46


Ex 9-13 odd, 15- 46

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To Find the coordinates of one

endpoint using the midpoint

formula.

Question:

A segment has a midpoint at (2, 2)

G.C0.1

G.GPE.6

Find the point on a

directed line

segment between

Text book

page 233

http://jmap.org/htmlstand

ard/Geometry/Coordinate

_Geometry/G.G.67.htm


Questions 35 – 38

http://mathopenref.com/congruentsss.html


http://jmap.org/htmlstandard/Geometry/Coordinate_Geometry/G.G.67.htm



60

and an endpoint at (-2, 4). What are

the coordinates of the other endpoint

of the segment?

two given points

that partitions the

segment in a given

ratio.

2 days

4.3 Triangle

Congruence by

ASA and AAS

Construct a proof defending that

two triangles congruent using the

ASA and AAS Postulates

ASA an f r "ang , i , ang ”

and means that we have two

triangles where we know two angles

and the included side are equal.

For example: the 2 triangles below

are congruent

AAS stands for "angle, angle, side"

and means that we have two

triangles where we know two angles

and the non-included side are equal.

G.SRT.5 Use

congruence and

similarity criteria

for triangles to

solve problems

and to prove

relationships in

geometric figures.

MP 1

MP 3

Text book

page 234 -

240

* PowerGeometry. Com

* Teacher made power

point presentations

43. http://www.mathsisf

un.com/geometry/congru

ent.html

44. Page 238: 1 - 7

45. Lesson Quiz page 241A

46. Basic – Problems 1-2: Ex. 8

– 12, 32- 39

47. Average – Problems 1 – 2:

Ex. 9 – 11 odd, 32-39

48. Advanced – Problems 1-2:

Ex 9-11 odd, 32 – 39

61

For example: the 2 triangles below

are congruent

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To write converses, inverses and

contrapositives of conditionals.

Question:

ri c nv r f “ If y u ar

than 18 years old, then you are too

y ung v in ni S a ”

Prepares for

G.CO.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.

Text book

page 241

http://www.cpm.org/pdfs/st

ate_supplements/Logical_St

atements.pdf

Standardized Test Prep Questions

32 - 35

1 day

4.6 Congruence

in Right

Triangles

To prove right triangles congruent

using the Hypotenuse Leg Theorem

Example:

G.SRT.5 Use

congruence and

similarity criteria

for triangles to

solve problems

Text book

page 258 -

264

http://www.finneytown.or

g/Downloads/GETE04062.p

df

Page 261: 1 - 7

http://www.cpm.org/pdfs/state_supplements/Logical_Statements.pdf



http://www.finneytown.org/Downloads/GETE04062.pdf



62

Solution

and to prove

relationships in

geometric figures.

MP 1

MP 3

http://www.mathopenref.co

m/congruenthl.html


/Regents/math/geometry/G

P4/Ltriangles.htm


Ex. 8 – 16, 20,22,25,32 - 36


Ex. 9 , 11– 28, 32 –36


Ex 9, 11-28, 32 - 36

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To determine whether given


Question:

Determine whether the triangles are

congruent. If they are, write a

congruent statement.

G.SRT.5

See above

Text book

page 264

http://www.regentsprep.o

rg/Regents/math/geometr

y/GP4/Ltriangles.htm


Questions 29 – 31

http://www.mathopenref.com/congruenthl.html

http://www.mathopenref.com/congruenthl.html

63

2days

4-7

Congruence in

Overlapping

Triangles

To identify congruent overlapping

triangles, prove two triangles

congruent using other congruent

triangles

For example:

Separate and redraw DFG and

EHG. Identify the common angle.

Solution

G.SRT.5 Use

congruence and

similarity criteria

for triangles to

solve problems

and to prove

relationships in

geometric figures.

MP 1

MP 3

Text book

page 265 –

271

http://www.finneytown.org

/Downloads/GETE04072.pdf

http://www.youtube.com/w

atch?v=wlEYuPhShig

Teacher made power point

presentation

http://www.sophia.org/over

lapping-

triangles/overlapping-

triangles--2-

tutorial?topic=congruent-

triangles

53. Page 268: 1 - 7

54. Basic – Problems 1-2:

Ex. 8 – 16, 17 – 20, 33 - 37


Ex. 9– 15 odd, 17 , 19 -26, 33 -

37


Ex 9-15 odd, 17, 19 – 28, 33 - 37

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To prove congruent segments in

overlapping triangles.

Question:

G.SRT.5

See above

Text book

page 271

http://www.sophia.org/over

lapping-

triangles/overlapping-

triangles--2-

tutorial?topic=congruent-

triangles


Questions 29 – 32



http://www.youtube.com/watch?v=wlEYuPhShig

http://www.youtube.com/watch?v=wlEYuPhShig

64

1

day

5-1

Midsegments of

Triangles

To use properties of midsegments to

solve problems

For example:

G.CO.10

G.CO.12

G.SRT.5 Use

congruence and

similarity criteria

for triangles to

solve problems

and to prove

relationships in

geometric figures.

MP 1

MP 3

MP 5

Text book

page 284 –

291

http://www.finneytown.org

/Downloads/GETE05012.pdf



P10/MidLineL.htm


m/trianglemidsegment.html

58. Page 284 Concept Byte –

Investigating Midsegments

59. Page 288: 1 - 6


Ex. 7 – 26, 28 – 30, 32 – 42 even


Ex. 7– 25 odd, 26 -45,


Ex 7-25 odd, 26 – 48, 53 - 57



http://www.regentsprep.org/Regents/math/geometry/GP10/MidLineL.htm



65

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To find the midsegment of a triangle

Question:

1. The triangular face of the rock and

Roll Hall of Fame in Cleveland, Ohio is

isosceles. The length of the base is

229ft 6in. What is the length of the

highlighted segment?

2. Explain your reasoning.

G.CO.10

G.CO.12

G.SRT.5

See above

Text book

page 291



P10/MidLineL.htm


Questions 49 - 52

66

1

day

5-2

Perpendicular

and Angle

Bisectors

To use properties of perpendicular

bisectors and angle bisectors

For example:

G.CO.9

G.SRT.5 Use

congruence and

similarity criteria

for triangles to

solve problems

and to prove

relationships in

geometric figures.

MP 1

MP 3

MP 5

Text book

page 292 –

299

http://163.150.89.242/YHS/

Faculty/AB/bagg/Geometry/

images/Geometry%20text%

20PDFs/5.6.pdf

http://www.youtube.com/w

atch?v=wxsr8egcq0M


m/bisectorperpendicular.ht

ml

64. Page 284 Concept Byte –

Investigating Midsegments

65. Page 288: 1 - 6


Ex. 7 – 26, 28 – 30, 32 – 42 even


Ex. 7– 25 odd, 26 -45,


Ex 7-25 odd, 26 – 48, 53 - 57

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To construct perpendicular bisector

of a triangle

Question:

G.CO.10

G.CO.12

G.SRT.5

See above

Text book

page 299


m/bisectorperpendicular.ht

ml


Questions 39 - 42

http://163.150.89.242/YHS/Faculty/AB/bagg/Geometry/images/Geometry%20text%20PDFs/5.6.pdf




http://www.youtube.com/watch?v=wxsr8egcq0M

http://www.youtube.com/watch?v=wxsr8egcq0M

67

A company plans to build a

warehouse that is equidistant from

each of its three stores, A, B, and C.

Where should the warehouse be

built?

2days

6-1

The Polygon

Angle-Sum

Theorems

Discriminate - interior and exterior

angles of polygons and their sums.

Determine and justify angle

measures using Polygon Angle-Sum

Theorems

For example:

Find the number of degrees

in each interior angle of a regular

dodecagon.

It is a regular polygon, so we can use

the formula.

In a dodecagon, n = 12.

G.SRT.5 Use

congruence and

similarity criteria

for triangles to

solve problems

and to prove

relationships in

geometric figures.

MP 1

MP 3

Text book

page 353 -

358

http://mathopenref.com/co

ngruentsss.html



G3/LPoly2.htm

Activity on Exterior Angles of

polygon page 352

70. Page 356: 1 - 6


Ex. 7 – 14, 49 - 54


Ex. 7 – 13 odd, 22 – 25, 49 -54


Ex 7-21 odd, 22 – 44, 49 -54



http://www.regentsprep.org/Regents/math/geometry/GG3/LPoly2.htm



68

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To find the sum of the measures of

interior and exterior angles of

polygon.

Question:

What is m∠ x ?

G.SRT.5 Use

congruence and

similarity criteria

for triangles to

solve problems

and to prove

relationships in

geometric figures.

Test boot

page 358

http://www.cde.ca.gov/ta/t

g/sr/documents/cstrtqgeom

apr15.pdf


45 - 48

2 days

6-2

Properties of Parallelograms

Determine and justify sides and

angles through relationships among

parallelograms

For example:

In the accompanying diagram of

G.SRT.5

G.CO.11 Prove

theorems about

parallelograms.

Theorems include:

opposite sides are

congruent,

Text book

page 359 -

366




74. Page 363: 1 - 8


Ex. 9 – 24, 38- 41, 49- 54


Ex. 9 – 23 odd, 25 - 41, 49 -54





http://jmap.org/htmlstandard/Geometry/Informal_and_Formal_Proofs/G.G.38.htm



69

parallelogram ABCD,

and . Find the number of

degrees in .

opposite angles are

congruent, the

diagonals of a

parallelogram

bisect each other,

and conversely,

rectangles are

parallelograms with

congruent

diagonals.

MP 1

MP 3

Ex 9-23 odd, 25 – 44, 49 -54

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To apply the relationship among

sides, angels and diagonals of

parallelograms.

Question:

What values of a and b make

quadrilateral MNOP a parallelogram?

G.CO.11 See above Text book

page 366



apr15.pdf


45 - 48




70

1 day

6-3

Proving that a

Quadrilateral Is

a Parallelogram

Justify that a quadrilateral is a

parallelogram using the properties of

parallelogram

For example:

The accompanying diagram shows

quadrilateral BRON, with diagonals

and , which bisect each other

at X.

Prove:

G.SRT.5

G.CO.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.

MP 1, MP 3

Test book

page 367 -

374




78. Page 372: 1 - 6


Ex. 7 – 16, 18- 20, 22- 28, 32-44


Ex. 7 – 15, odd, 17 - 28, 32 - 44


Ex 7-15 odd, 17 – 28, 32 -44

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To determine whether a

quadrilateral is a parallelogram

Question:

Based on the markings, determine if

the figure is a parallelogram. If so,

justify your answer.

G.SRT.5

G.CO.11 See above

Text book

page 374



apr15.pdf

http://www.jmap.org/Static

Files/PDFFILES/WorksheetsB

yPI/Geometry/Informal_and

_Formal_Proofs/Drills/PR_G.

G.38_2.pdf


29 - 31







http://www.jmap.org/StaticFiles/PDFFILES/WorksheetsByPI/Geometry/Informal_and_Formal_Proofs/Drills/PR_G.G.38_2.pdf





71

I day

6-4

Properties of

Rhombus,

Rectangle,

Square

Analyze parallelograms to determine

special types

For example:

Rectangle:

parallelogram

with 4 right angles

Rhombus:

parallelogram

with all 4 sides

congruent

Square:

a rectangle with

all 4 sides congruent

G.SRT.5

G.CO.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.

MP 1

MP 3

Text book

page 375 -

382



P9/LRectangle.htm

82. Page 379: 1 - 6


Ex. 7 – 23, 24 – 40 even, 41, 43,

46, 47, 60 -69.


Ex. 7 – 23, odd, 24 - 54, 60 - 69


Ex 7-23 odd, 24 – 54, 60-69

http://www.regentsprep.org/Regents/math/geometry/GP9/LRectangle.htm



72

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To find a side length of a

parallelogram

Question:

What is the height of this rectangle?

G.SRT.5

G.CO.11 See above

Text book

page 382



apr15.pdf





G.38_2.pdf


55 - 58

2 days

6-5

Conditions for

Rhombus,

Rectangle,

Square

Determine if a parallelogram is a

Rhombus, Rectangle or Square

For example:

Which reason could be used to prove

that a parallelogram is a rhombus?

G.SRT.5

G.CO.11 Prove

theorems about

parallelograms.

Theorems include:

opposite sides are

congruent,

opposite angles are

congruent, the

Text book

page 383 -

388

http://www.jmap.org/htmls

tandard/Geometry/Informal

_and_Formal_Proofs/G.G.39

.htm

86. Page 386: 1 - 7


Ex. 8 – 18, 24 – 31, 36 -43


Ex. 9 – 13, odd, 15 - 31, 36 - 43


Ex 9 -13 odd, 15 – 31, 36 - 43









http://www.jmap.org/htmlstandard/Geometry/Informal_and_Formal_Proofs/G.G.39.htm




73

1) Diagonals are congruent.

2) Opposite sides are parallel.

3) Diagonals are perpendicular.

4) Opposite angles are

congruent.

diagonals of a

parallelogram

bisect each other,

and conversely,

rectangles are

parallelograms with

congruent

diagonals.

MP 1

MP 3

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To determine whether a given

parallelogram is a rhombus or

rectangle

Question:

Each diagonal of a quadrilateral

bisects a pair of opposite angles of

the quadrilateral. What is the most

G.SRT.5

G.CO.11 See above

Text book

page 388



apr15.pdf






32- 35








74

precise name for the quadrilateral?

1. parallelogram

2. rhombus

3. rectangle

4. not enough information

G.38_2.pdf

2 days

6-6

Trapezoids and

Kites

To determine, verify and apply the

properties of trapezoids and Kite to

solve problems.

Example:

Exa : In the diagram below of isosceles

trapezoid DEFG, ,

, ,

, and . Find the value of

x.

G.SRT.5 Use

congruence and

similarity criteria

for triangles to

solve problems

and to prove

relationships in

geometric figures.

MP 1

MP 3

Text book

page 389 -

397

http://www.jmap.org/htmls

tandard/Geometry/Informal

_and_Formal_Proofs/G.G.40

.htm

5. Page 393: 1 - 6


Ex. 7 – 24, 26 – 34 even, 46 –

49, 71 - 76


Ex. 7 – 23, odd, 25 - 62, 71- 76


Ex 7 -23 odd, 25 – 66, 71 - 76





75

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To verify and apply properties of

trapezoids and kites

Question:

Figure ABCD is a kite.

What is the area of figure ABCD, in

square centimeters?

G.SRT.5

See above

Text book

page 397



apr15.pdf





G.38_2.pdf


67 - 70

2 days

7.1

Ratios and

Proportions

Conclude from evidence provided

which sides correspond in similar

triangles and identify appropriate

ratios to establish proportions and

solve for a missing side length

For example:

If ∆ABC ∼ ∆ E , n i n ify

appropriate ratios, establish a

G.SRT.5 Use

congruence and

similarity criteria

for triangles to

solve problems

and to prove

relationships in

geometric figures.

MP 1

Text book

page 432 -

438

9. PowerGeometry.Co

m

10. Teacher made

power points

presentations

11. Page 436: 1 - 8

12. Test prep page 438


Ex. 9 – 16, 61- 69


Ex. 9 – 15 odd, 33-34, 61-69


Ex 9-15 odd, 33- 34, 61-69









76

proportion and solve for side length

x.

MP 3

MP 7

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To apply ratio and proportion to

solve real life problem

Questions:

The ratio of the width to the height of

i ’ c u r ni r cr n i 6:

If the screen is 12 inches high, how

wide is it?

Prepares for

G.SRT.5 See below

Test book

page 438

Standardized Test Prep: Questions

61 - 65

77

2 days 7.2 Similar

Polygons

Examine similar polygons and utilize

traits of similar polygons to solve

problems

For example:

If , , ,

, and . What is the

length of ?

G.SRT.5 Use

congruence and

similarity criteria

for triangles to

solve problems

and to prove

relationships in

geometric figures.

MP 1

MP 3

Text book

page 440 -

446




http://mathopenref.com/si

milarpolygons.html

Teacher-made Power Point

presentation

16. Page 444: 1 - 8


Ex. 9 – 17, 51- 64


Ex. 9 – 17 odd, 51-64


Ex 9-17 odd, 51-64

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To apply scale factor to find the

length of a segment

Question:

∆P S ~ ∆JKL wi a ca fac r f

4:3, QR = 8cm. What is the value of KL?

G.SRT.5 Use

congruence and

similarity criteria

for triangles to

solve problems

and to prove

relationships in

geometric figures.

Text book

page 447




Standardized Test Prep: Questions

51 - 54




http://mathopenref.com/similarpolygons.html





78

2 days 7.3 Proving

Triangle Similar

To apply the AA Similarity Postulate and

the SAS and SSS Similarity Theorems.

To use the similarity to determine and

justify indirect measurements.

For example:

Given that the triangles below are similar

- If two of their angles are equal, then the

third angle must also be equal, because

angles of a triangle always add to 180. In

this case the missing angle is 180 - (72 +

35) = 73

G.SRT.5 Use

congruence and

similarity criteria

for triangles to

solve problems

and to prove

relationships in

geometric figures.

G.GPE.5

MP 1

MP 3

MP 3

Text book

page 450 -

458




http://mathopenref.com/si

milarpolygons.html

Teacher-made Power Point

presentations

20. Page 455: 1 - 6


Ex. 7 – 12, 37 - 52


Ex. 7 – 11 odd, 37 - 52


Ex 7-17 odd, 18 - 52






79

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To apply the Pythagorem Theorem

to find the missing side of a right

triangle

Question:

A 17 ft ladder leans against a wall, if

the ladder is 8ft from the base of the

wall, how far is it from the bottom of

the wall to the top of the ladder.

G.SRT.8 Use

trigonometric

ratios and the

Pythagorean

Theorem to solve

right triangles in

applied problems.

Text book

page 458




24. Standardized Test Prep:

Questions 37- 40

25. Worksheet from the stated

website

80

UNIT #3

Extending to three dimensions

81



26. How do you find the area of a polygon or

find the circumference and area of a

circle?

27. How can you determine the intersection

of a solid and a plane?

28. The area of a regular polygon is a function of the distance from the center to a side and the

perimeter.

29. A three-dimensional figure can be analyzed by describing the relationships among its vertices, edges,

and faces.

30. The surface area of a three-dimensional figure is equal to the sum of the areas of each surface of the

figure.

PACING CONTENT SKILLS

STANDARDS

(CCSS/MP)

RESOURCES

LEARNING ACTIVITIES and ASSESSMENTS

Pearson

OTHER

(e.g., tech)

2 days

10.1

Areas of parallelograms

and triangles

To find the area of

parallelograms and

triangles.

Example:

The piece of stained glass

at the bottom is made up

of eight congruent

parallelograms. Each

parallelogram has a base

of

8 centimeters and a height

of 3 centimeters. Find the

G.MG.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)

MP.3

Pearson

Chapter

#10.1 Get

Ready

Text book

page #616-

622

Web link for the area

of parallelograms and

triangles:

www.wyzant.com/help/math/.../a

reas/parallelograms_and_tria

ngles

www.virtualnerd.com/geometry/l

ength-area/parallelogram-

triangles-area

Kuta software for

worksheet:

www.kutasoftware.com/.../6-

1. Basic

1) problems 1-2

Exs 8-13 all, 47-62

2) Problems 3-4

Exs. 14-17 all, 19, 22, 23,

30-40 even, 37-38

2. Average:

82

area of the entire piece.

MP.5

Area%20of%20Triangles%20a

www.kutasoftware.com/.../Area

%20of%20Squares,%20Rectan


www.youtube.com/watch?v=Fac

www.youtube.com/watch?v=FG

LWKWcg0Vo

1) problems 1-2

Exs. 9-13 odd, 47-62.

2) Problems 3-4

Exs. 15-17 odd, 18-43

3. Advanced:

1) Problems 1-4

Exs. 9-17 odd, 18-62


Google search:

granicher.wikispaces.com/.../b)+Area+of+a+Parallelog

ram+%26+Triangl..


www.finneytown.org/Downloads/wk10.pdf

83

30 mn

Basic skills

Review:

HSPA

PREP/PAR

CC/SAT

Use Apply distance in

the coordinate

plane.

Ex Example:

Ex

On the directed line

segment from R to S on

the coordinate plane

above, what are the

coordinates of the point

that partitions the

segment in the ratio 2 to

3?

G.GPE.6

Find the point on a

directed line segment

between two given

points that partitions

the segment in a given

ratio.

Pearson

Chapter #10

Get Ready

Text book

page # 622

Kuta software for

worksheets

www.kutasoftware.co

m/.../Area%20of%20S

quares,%20Rectangles

Standardized Test Prep (SAT/HSPA) Text

book page 622 Q. 47-49

84

85

2 days

10.2

Areas of

trapezoids,

rhombuses,

and kites

Find the area of a

trapezoid,

rhombus, and kite.

Example:

The roof on the bridge

below consists of four

sides, two congruent

trapezoids and two

congruent triangles.

-Find the combined area of

the two trapezoids.

-Use the diagram above to

find the combined area of

the two triangles.

-What is the area of the

entire roof?

G.MG.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)

MP.1- 6

Pearson

Chapter

#10.2 Get

Ready

Text book

page #623-

628


of a trapezoid,

rhombus, and kite:

www.slideshare.net/.../112-

areas-of-trapezoids-

rhombuses-and-kites

www.khanacademy.org/.../area..

./areas_of_trapezoids_rhombi

_and_kites

Kuta software for

worksheet:


orksheets/.../Area%20of%20Tra

pezoids

www.mybookezz.org/kuta-

software-infinite-geometry-

finding-total-area


www.youtube.com/watch?v=1N

DXo8nnRUE

www.youtube.com/watch?v=V2x

-

1. Basic:

1) problems 1-2

Exs 11-19 all, 45-53

2) Problems 3-4

Exs. 20-25 all, 26-38 even

2. Average:

1) problems 1-2

Exs. 11-19 odd, 45-53.

2) Problems 3-4

Exs. 21-25 odd, 26-41

3. Advanced:

1) Problems 1-4

Exs. 11-25 odd, 26-53


Google search:

nehsmath.wikispaces.com/.../7-

4+PPT+Areas+of+Trapezoids,+Rhombus


http://www.slideshare.net/.../112-areas-of-trapezoids-rhombuses-and-kites



86

www.khanacademy.org/.../area.../areas_of_trapezoids

_rhombi_and_kites

87

30 mn

Basic skills

Review:

HSPA

PREP/PARCC/S

AT

Apply distance in

the coordinate

plane.

Example:

G.GPE.6

Find the point on a


between two given



ratio.

Pearson

Chapter #10

Get Ready

Text book

page # 628

Kuta software for

worksheets

www.kutasoftwar

e.com/FreeWorks

heets/GeoWorks

heets/3-

Points%20in...


(SAT/HSPA)


88

1 day

10.3

Areas of

Regular

Polygons

Find the area of a

regular polygon.

Example:

The gazebo in the photo is

built in the shape of a

regular octagon. Each side

is 8 ft long, and its

apothem is 9.7 ft. What is

the area enclosed by the

gazebo?

G.MG.1

Use geometric

shapes, their

measures, and their



a tree trunk or a

human torso as a

cylinder)

MP.1

MP.3

MP.4

MP.7

Pearson

Chapter

#10.3 Get

Ready

Text book

page #629-

634


of a regular polygon:

www.mathwords.com/a/area_re

gular_polygon.htm


Area%20of%20Regular%20Pol

ygons.pdf

Kuta software for

worksheet:


orksheets/.../Area%20of%20Tra

pezoids

www.gobookee.net/kuta-

software-area-of-regular-

polygons-answ


www.youtube.com/watch?v=eQ

hgozrRiYI

www.youtube.com/watch?v=Hlc

Hd-psOWs

4. Basic:

1) problems 1-3

Exs 8-25 all, 26-30 even

31-33 all, 35, 44-52

5. Average:

1) problems 1-3

Exs. 9-25 odd, 26-41, 44-52

6. Advanced:

1) Problems 1-3

Exs. 9-25 odd, 26-52 Math

power point notes:

Google search:

jcs.k12.oh.us/teachers/.../PH_Geo_10-

3_Areas_of_Regular_Polygons.pp


www.finneytown.org/Downloads/GETE1003.pdf

http://www.mathwords.com/a/area_regular_polygon.htm

http://www.mathwords.com/a/area_regular_polygon.htm


89

30 mn

Basic skills

Review:

HSPA

PREP/PARCC/S

AT

Partition line

segment given

ratio.

Example:

Point p lies on the

direct line segment

from A(2,3) to

B(8,0)and partitions

the segment in the

ratio 2 to 1. What

are the coordinates

of point P?

G.GPE.6

Find the point on a


between two given



ratio.

Pearson

Chapter #10

Get Ready

Text book

page # 634

Kuta software for

worksheets

schoolwires.henry.k12.

ga.us/.../4-

15_Partitioning%20a


(SAT/HSPA)


90

2 days

10.4

Perimeters

and areas of

similar figures

Find the

perimeters and

areas of similar

polygons.

Community Service During the

summer, a group of high school

students used a plot of city land

and harvested 13 bushels of

vegetables that they gave to a food

pantry. Their project was so

successful that next summer the

city will let them use a larger,

similar plot of land.

In the new plot, each dimension is

2.5 times the corresponding

dimension of the original plot.

How many bushels can they

expect to harvest next year?

G.MG.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).

MP.1

MP.5

MP.8

Pearson

Chapter

#10.3 Get

Ready

Text book

page #629-

634

Web link for finding

the perimeters and

areas of similar

polygons:

www.onemathematicalcat.org/M

ath/...obj/per_area_similar_figu

res.htm

www.kutasoftware.com/freeige.

Kuta software for

worksheet:

www.kutasoftware.com/freeige.


www.youtube.com/watch?v=ae-

www.youtube.com/watch?v=ML

AdoSrJfi0

7. Basic:

1) problems 1-2

Exs 9-16 all, 52-62

2) Problems 3-4

Exs. 17-24 all, 26-30 even

31-33 all, 34-44 even

8. Average:

1) problems 1-2

Exs. 9-15 odd, 52-62.

2) Problems 3-4

Exs. 17-23 odd, 25-47

9. Advanced:

1) Problems 1-4


power point notes:

Google search:

www.villagechristian.org/media/2322216/lesson%208-

6.ppt


91

www.mathwarehouse.com/.../similar/triangles/area-

and-perimeter-of-simi

92

30 mn

Basic skills

Review:

HSPA

PREP/PARCC/S

AT

Partition line

segment given

ratio.

Example:

Point R lies on the


from L(-8, -10) to

M(4, -2) and

partitions the

segment in the ratio

3 to 5. What are the

coordinates of point R?

G.GPE.6

Find the point on a


between two given



ratio.

Pearson

Chapter #10

Get Ready

Text book

page # 641

Kuta software for

worksheets

schoolwires.henry.k12.

ga.us/.../4-

15_Partitioning%20a


(SAT/HSPA)


93

2 days

11.1

Spaces Figures

and Cross

Section

Recognize

polyhedral and

their parts.

-To visualize cross

sections of space

figures.

Example:

Julie incorrectly identified

the solid below as a pyramid

with a square base.

1. Correctly identify the

solid.

2. What would you say to

Julie to help her tell the

difference between this

solid and a

pyramid?

G.GMD.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.

MP.1

MP.3

MP.4

MP.5

MP.7

Pearson

Chapter

#11.1 Get

Ready

Text book

page #688-

695

Web link for solid

figures:

www › Geometry

Concepts and Skills › Chapter 9

www.superteacherworksheets.

com/solid-shapes

Kuta software for

worksheet:


orksheets/GeoWorksheets/10-


www.youtube.com/watch?v=DB

S-8meBgZs

www.youtube.com/watch?v=q2

10. Basic:

1) problems 1-3

Exs 6-17 all, 51-62

2) Problems 4-5

Exs. 18-23 all, 24-34 even, 38

11. Average:

1) problems 1-3

Exs. 7-17 odd, 51-62.

2) Problems 4-5

Exs. 19-23 odd, 24-40

12. Advanced:

1) Problems 1-3


power point notes:

Google search:

www.clintweb.net/ctw/ppsspowerpointsolidshapes.pp

t


www.ixl.com/math/grade-5/identify-planar-and-solid-



http://www.classzone.com/books/geometry_concepts/page_build.cfm?&ch=9

http://www.ixl.com/math/grade-5/identify-planar-and-solid-figures

94

figures

95

30 mn

Basic skills

Review:

HSPA

PREP/PARCC/S

AT

Use the Pythagorean

theorem to solve

problems.

Example:

Triangle JKL above

represents the boundary

of a state wilderness

area. An access road

will be constructed that

intersects side JK at a

90 degrees angle and

extends to point L. The

road will intersect side

JK 24 miles from point

K, and the length of side

KL is 30 miles.

Part A:

What is the length, in

miles, of the access

road? Show your work.

G.SRT.8

Use trigonometric ratios

and the Pythagorean

Theorem to solve right

triangles in applied

problems.

Pearson

Chapter #11

Get Ready

Text book

page # 695

Kuta software for

worksheets

www.gobookee.net/kut

a-software-right-

triangles-and-

pythagorean-theor

Standardized Test Prep (SAT/HSPA)


96

Part B:

What is the length, in

miles, of side JK? Show

your work.

97

98

2 days

11.2

Surface Areas

of Prisms and

Cylinders

Find the surface

area of prism and

cylinder.

Example:

Architecture In this exercise

below use the following

information. Suppose a

skyscraper is a prism that

is 415 meters tall and each

base is a square that

measures 64 meters on a

side.

1. What is the lateral area

of this skyscraper? 2.

Challenge What is the

surface area of this

skyscraper? (Hint: The

ground is not part of the

surface area of the

skyscraper.)

G.MG.1

Use geometric

shapes, their

measures, and their



a tree trunk or a

human torso as a

cylinder).

MP.1

MP.3

MP.7

MP.8

Pearson

Chapter

#11.2 Get

Ready

Text book

page #699-

707


the surface area of

prism and cylinder:

hotmath.com/help/gt/genericpre

alg/section_9_4.html

www.virtualnerd.com/geometry/

surface-area.../prisms-

cylinders-area

Kuta software for

worksheet:


Surface%20Area%20of%20Pri

sms


www.youtube.com/watch?v=DB

S-8meBgZs

www.youtube.com/watch?v=q2

13. Basic:

1) problems 1-2

Exs 7-13 all, 44-45

2) Problems 3-4

Exs. 14-20 all, 22-30 even, 37

14. Average:

1) problems 1-2

Exs. 7-13 odd, 44-45.

2) Problems 3-4

Exs. 15-19 odd, 21-38

15. Advanced:

1) Problems 1-4


power point notes:

Google search:

https://www.madison.k12.al.us/.../Surface%20Area%2

0of%20Prisms


www.ixl.com/math/grade-8/surface-area-of-prisms-

http://www.ixl.com/math/grade-8/surface-area-of-prisms-and-cylinders

99

and-cylinders

100

30 mn

Basic skills

Review:

HSPA

PREP/PARCC/S

AT

Use proportions.

Example:

The figure above

represents a swing set.

The supports on each

side of the swing set are

constructed from two

12-foot poles connected

by a brace at their

midpoint. The distance

between the bases of

the two poles is 5 feet.

Part A:

What is the length of

each brace?

Part B:

Which theorem about

triangles did you apply

to find the solution in

Part A?

G.SRT.5

Use congruence and

similarity criteria for

triangles to solve


relationships in

geometric figures.

Pearson

Chapter #11

Get Ready

Text book

page # 707

Kuta software for

worksheets

www.gobookee.net/kut

a-software-right-

triangles-and-

pythagorean-theor



101

102

2 days

11.3

Surface areas

and pyramids

and cones

Find the surface

area of a pyramid

and cone.

Example:

Veterinary Medicine A cone-

shaped collar, called an

Elizabethan collar, is used to

prevent pets from

aggravating a healing wound.

1. Find the lateral area of

the entire cone shown

above.

2. Find the lateral area of

the small cone that has a

radius of 3 inches and a

G.MG.1

Use geometric

shapes, their

measures, and their



a tree trunk or a

human torso as a

cylinder).

MP.1

MP.3

MP.6

MP.7

Pearson

Chapter

#11.3 Get

Ready

Text book

page #708-

715


the surface area of a

pyramid and cone:

www.virtualnerd.com/geo

metry/surface-

area.../pyramids-codes-

area

Kuta software for

worksheet:

www.kutasoftware.com/.

../10-

Surface%20Area%20of

%20Pyramids%20a..


www.youtube.com/watch

3. Basic:

1) problems 1-4

Exs 9-15 all, 44-53

2) Problems 1-4

Exs. 16-21 all, 22, 25, 26-36

even

4. Average:

1) problems 1-4

Exs. 9-15 odd, 44-53.

2) Problems 1-4

Exs. 17-21 odd, 22-38

5. Advanced:

1) Problems 1-4


power point notes:

Google search:

www.marianhs.org/.../12.3%20Surface%20

Area%20of%20Pyramids

103

height of 4 inches.

Use your answers to

E rci “a” an “ ”

find the amount of material

needed to make the

Elizabethan collar shown.


www.ixl.com/math/grade-8/surface-area-of-

pyramids-and-cones

104

30 mn

Basic skills

Review:

HSPA

PREP/PARCC/S

AT

Apply trigonometric

ratios:

The figure above

represents a plan for a

wheelchair ramp to a

step that has a height of

10 inches. Jodi and

Kevin each used right-

triangle trigonometry to

determine the length of

the ramp. Both solutions

are shown below.

Explain why both

solutions resulted in the

same answer.

G.SRT.8


and the Pythagorean



problems.

Pearson

Chapter #11

Get Ready

Text book

page # 715

Kuta software for

worksheets

www.kutasoftware.co

m/.../10-

Surface%20Area%20o

f%20Pyramids



105

106

2 days

11.4

Volume of

prisms and

cylinders

Find the volume of a

prism and the volume

of a cylinder.

Example:

a. How do the radius and

height of the mug compare

to the radius and height of

the dog bowl?

b) How many times greater

is the volume of the bowl

than the volume of the

mug?

G.GMD.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.

MP.1

MP.3

MP.6

MP.7

Pearson

Chapter

#11.4 Get

Ready

Text book

page #717-

724


the volume of a prism

and the volume of a

cylinder.

hotmath.com/help/gt/gen

ericprealg/section_9_6.ht

Kuta software for

worksheet:

www.kutasoftware.com/...

/10-

Volume%20of%20Prism

s%20and%20Cyli


www.khanacademy.org/m

ath/.../volume.../solid-

geometry-volu

6. Basic:

1) problems 1-2

Exs 6-13 all, 46-53

2) Problems 3-4

Exs. 14-21 all, 24, 30- 32 all, 38

7. Average:

1) problems 1-2

Exs. 7-13 odd, 46-53.

2) Problems 3-4

Exs. 15-19 odd, 21-42

8. Advanced:

1) Problems 1-4

Exs. 17-19 odd, 21-53 Math

power point notes:

Google search:

www.lms.stjohns.k12.fl.us/.../8th%20Std%20

Chapter%209%20PowerPoi


107

www.ixl.com/math/grade-8/volume-of-

prisms-and-cylinders

108

30 mn

Basic skills

Review:

HSPA

PREP/PARCC/S

AT

Use trigonometric

ratios.

Example:

A 12-foot ladder that is

leaning against a wall

makes a 75.50

Angle with the level

ground. Which of the

equations below can be

used to determine the

height, y, above the

ground, in feet, that the

ladder touches the wall?

(Sketch the diagram)

G.SRT.8


and the Pythagorean



problems.

Pearson

Chapter #11

Get Ready

Text book

page # 724

Kuta software for

worksheets


Volume%20of%20Prisms%20a

nd%20Cyli



109

110

2 days

11.5

Volumes of

pyramids and

cones

Find the volume of a

pyramid and the

volume of a cone.

Example:

Popcorn A movie theater

serves a small size of

popcorn in a conical

container and a large size of

popcorn in a cylindrical

container.

a) What is the volume of the

small container? What is the

volume of the large

container?

b) How many small

containers of popcorn do you

have to buy to equal the

amount of popcorn in a large

container?

c) Which container gives you

more popcorn for your

money? Explain your

G.GMD.3

Use volume formulas

for cylinders,

pyramids, cones, and

spheres to solve

problems.

G.MG.1

Use geometric

shapes, their

measures, and their



a tree trunk or a

human torso as a

cylinder).

MP.1

MP.3

MP.7

Pearson

Chapter

#11.5 Get

Ready

Text book

page #726-

732


the volume of a

pyramid and cone:

www.glencoe.com/sec/m

ath/prealg/mathnet/pr01/p

Kuta software for

worksheet:

www.mybookezzz.com/k

uta-software-volume-of-

pyramids-and-cones



9. Basic:

1) problems 1-2

Exs 5-14 all, 39-46

2) Problems 3-4

Exs. 15-21 all, 24-32, even

10. Average:

1) problems 1-2

Exs. 5-13 odd, 39-46.

2) Problems 3-4

Exs. 15-19 odd, 20-34

11. Advanced:

1) Problems 1-4


power point notes:

Google search:

jcs.k12.oh.us/.../PH_Geo_11-

5_Volumes_of_Pyramids_and_Cones.ppt


111

reasoning hotmath.com/help/gt/genericprealg/section_

112

30 mn

Basic skills

Review:

HSPA

PREP/PARCC/S

AT

Use the Pythagorean

Theorem:

Example:

The figure above

represents a plot of land

that Susan has

measured to use as a

fenced garden. Before

she builds the fence,

she wants to make sure

that the plot is

rectangular. She

measures the length of

one of the diagonals. If

Susan's plot is

rectangular, what will be

the length, in feet, of the

diagonal she

measured?

G.SRT.8


and the Pythagorean



problems.

Pearson

Chapter #11

Get Ready

Text book

page # 732

Kuta software for

worksheets

www.kutasoftware.com/...

/10-

Volume%20of%20Pyram

ids%20and%20C..



113

114

2 days

11.6

Surface areas

and volume of

spheres

Find the surface area

and volume of a

sphere.

Example:

The entrance to the Civil

Rights Institute in

Birmingham, Alabama,

includes a hemisphere

that has a radius of 25.3

feet.

a) Find the volume of the

hemisphere.

b) Find the surface area

of the hemisphere, not

including its base.

c) The walls of the

hemisphere are 1.3 feet

thick. So, the rounded

surface inside the

building is a

hemisphere with a radius

of 24 feet. Find its

surface area, not

G.GMD.3

Use volume formulas

for cylinders,

pyramids, cones, and

spheres to solve

problems.

G.MG.1

Use geometric

shapes, their

measures, and their



a tree trunk or a

human torso as a

cylinder).

MP.1

MP.3

MP.6

MP.7

Pearson

Chapter

#11.6 Get

Ready

Text book

page #733-

740


the surface area and

volume of a sphere.

www.murrieta.k12.ca.us/c

ms/lib5/CA01000508/Cen

tricity/.../T9.6

Kuta software for

worksheet:

www.kutasoftware.com/Fr

eeWorksheets/GeoWork

sheets/10-Spheres.pdf


www.khanacademy.org/m

ath/.../volume.../v/volum

e-of-a-sphere

12. Basic:

1) problems 1-2

Exs 6-16 all, 60-71

2) Problems 3-4

Exs. 17-26 all, 29-31, 34-42

Even, 50

13. Average:

1) problems 1-2

Exs. 7-15 odd, 60-71.

2) Problems 3-4

Exs. 17-25 odd, 26-54

14. Advanced:

1) Problems 1-4


power point notes:

Google search:

www.dgelman.com/powerpoints/.../12.6%2

0Surface%20Area

115

including its base. Math skills practice:

www.ixl.com/math/grade-8/volume-and-

surface-area-of-spheres

116

30 mn

Basic skills

Review:

HSPA

PREP/PARCC/S

AT

Use the inverse of

trigonometric ratios.

Example:

The diagram below

shows a model of a

staircase in which all the

riser heights are equal

and all the tread lengths

are equal.

A carpenter wants to

build a staircase in

which each riser has a

height of 6 inches and

each tread has a length

of 11 inches. Which of

the following

expressions is equal to

the

stair

angle?

G.SRT.8


and the Pythagorean



problems.

Pearson

Chapter #11

Get Ready

Text book

page # 740

Kuta software for

worksheets



Spheres.pdf



117

118

2 days

11.7

Areas and

Volumes of

Similar Solids

Compare and find the

areas and volumes of

similar solids.

Example:

Spheres in Architecture In

Exercises a–d, refer to

the information below

about The Rose Center

for Earth and Space at

New York City’s

American Museum of

Natural History. The

sphere has a diameter of

87 feet. The glass cube

surrounding the sphere

is 95 feet long on each

edge.

a) Find the surface area

of the sphere.

G.MG.1

Use geometric

shapes, their

measures, and their



a tree trunk or a

human torso as a

cylinder).

G.MG.2

Apply concepts of

density based on area

and volume in

modeling situations

(e.g., persons per

square mile, BTUs per

cubic foot).

MP.3

MP.7

MP.8

Pearson

Chapter

#11.7 Get

Ready

Text book

page #742-

749

Web link for

comparing and

finding the areas and

volumes of similar

solids.

www.ck12.org/geometry/

Area-and-Volume-of-

Similar-Solids

Kuta software for

worksheet:

www.kutasoftware.com/Fr

eeWorksheets/.../10-

Similar%20Solids



-

15. Basic:

1) problems 1-2

Exs 5-14 all, 42-54

2) Problems 3-4

Exs. 15-26 all, 28-29, 34-38

Even

16. Average:

1) problems 1-2

Exs. 5-13 odd, 42-54.

2) Problems 3-4

Exs. 15-23 odd, 24-38

17. Advanced:

1) Problems 1-4


power point notes:

Google search:

cs.k12.oh.us/.../PH_Geo_11-

7_Areas_and_Volumes_of_Similar_Solid

s

119

b) Find the volume of

the sphere.

c) Find the volume of

the glass cube.

d) Find the approximate

amount of glass used to

make the cube. (Hint:

Do not include the

ground or roof in your

calculations)


www.ck12.org/geometry/Area-and-Volume-

of-Similar-Solids

120

30 mn

Basic skills

Review:

HSPA

PREP/PARCC/S

AT

Apply the formula to

find area of oblique

triangles.

Example:

The figure above shows

a triangle drawn over a

map of Honduras. Use

the measurements of

the triangle to

approximate the area, in

square kilometers, of

Honduras. Show your

work.

G.SRT.9

Derive and use the

formula for the area of

an oblique triangle (A =

1/2 ab sin (C)).

Pearson

Chapter #11

Get Ready

Text book

page # 749

Kuta software for

worksheets


rksheets/.../10-

Similar%20Solids




Students’ experience with two-dimensional and three-dimensional objects is extended to include informal explanations of circumference, area

and volume formulas. Additionally, students apply their knowledge of two-dimensional shapes to consider the shapes of cross-sections and the

result of rotating a two-dimensional object about a line.

121


Square and circles: http://balancedassessment.concord.org/hs012.html

Examples:

A cookie factory is making cookies in a pyramid shape with equilateral triangle as a base. We know that the lateral edge of the cookie is 2 cm long and the base edge of

the cookie is 3 cm long.

1. Prove that the height of the cookie is 1 cm.

2. Find the volume of the cookie.

3. Each cookie is wrapped totally in an aluminum foil. Prove that the minimum surface of foil necessary to wrap 100 cookies is greater than 960 cm2.

Example 2:

Diana’s Christmas present is placed into a cubic shaped box. The box is wrapped in a golden paper.

a. Are 3 m2 of golden paper enough for wrapping?

b. If 1 m2 of golden paper cost $3, how much would the wrapping material cost?

Could you pour 1 liter of juice in the box? (Know that 1 l=0.001 m3)

Wiki page for Common Core Assessments:


PARCC Framework Assessment questions with Model Curriculum Website for all units:

http://balancedassessment.concord.org/hs012.html


122




21ST CENTURY SKILLS


4. Career Technical Education (CTE) Standards

1. 21st

Century Life and Career Skills: All students will demonstrate the creative, critical thinking, collaboration, the problem-solving skills needed to function successfully

as both global citizens and workers in diverse ethnic and organizational cultures.

2. Personal Financial Literacy: All students will develop skills and strategies that promote personal and financial responsibility related to financial planning, savings,

investment, and charitable giving in the global economy.

3. Career Awareness, Exploration, and Preparation: All students will apply knowledge about and engage in the process of career awareness, exploration, and

preparation in order to navigate the globally competitive work environment of the information age.

4. Career and Technical Education: All students who complete a career and technical education program will acquire academic and technical skills for careers in emerging

and established professions that lead to technical skill proficiency, credentials, certificates, licenses, and/or degrees.





123

1. Career and Technical Education: All students who complete a career and technical education program will acquire academic and technical skills for careers in

emerging and established professions that lead to technical skill proficiency, credentials, certificates, licenses, and/or degrees.

9.4.12.B.4: Perform math operations, such as estimating and distributing materials and supplies, to complete

classroom/workplace tasks.


http://www.achieve.org/files/CCSS-CTE-Task-IvySmith-GrowsUp-FINAL.pdf


Group activity or individual activity

1. Review and copy notes from eno board/power point/smart board etc.

2. Group/individual activities that will enhance understanding.

3. Provide students with interesting problems and activities that extend the concept of the lesson

4. Help students develop specific problem solving skills and strategies by providing scaffolded guiding questions

http://www.achieve.org/files/CCSS-CTE-Task-IvySmith-GrowsUp-FINAL.pdf

124

Peer tutoring

1. Team up stronger math skills with lower math skills

Use of manipulative

2. Eno or smart boards

3. Dry erase markers

4. Reference sheets created by special needs teacher

5. Pairs of students work together to make word cards for the chapter vocabulary

6. Use 3D shapes for visual learning

7. Reference sheets for classroom

8. Graphing calculators

APPENDIX

125


9. CCSS. Mathematical Practices:

MP1: Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry

points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form

and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems,

and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress

and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the

viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences

between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for

regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem.

Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this

make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different

approaches.

MP2: Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two

complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and

represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their

referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the

symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units

involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations

126

and objects.

MP3: Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in

constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are

able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate

them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the

context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments,

distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can

construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct,

even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies.

Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve

the arguments.

MP4: Model with mathematics.

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the

workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply

proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a

design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply

what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision

later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables,

graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their

mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served

its purpose.

127

MP5: Use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil

and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic

geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when

each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high

school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using

estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the

results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade

levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve

problems. They are able to use technological tools to explore and deepen their understanding of concepts.

MP6: Attend to precision.

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and

in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are

careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately

and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give

carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of

definitions.

MP7: Look for and make use of structure.

Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and

seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have.

Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression

x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and

128

can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see

complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 –

3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

MP8: Look for and express regularity in repeated reasoning.

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper

elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they

have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with

slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x –

1)(x + 1), (x – 1)(x2 + x + 1), and (x – 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to

solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the

reasonableness of their intermediate results.

UNIT 4

Connecting Algebra And Geometry Coordinates



10. How do you prove that two lines are parallel or 14. A line can be graphed and its equation written when certain facts about the line

129

perpendicular?

11. How do you write an equation of a line in the coordinate

plane?

12. How can you classify quadrilaterals?

13. How can you use coordinate geometry to prove general

relationship?

such as the slope and a point on the line are known.

15. The equations of a line can be written in various forms such as the Slope-intercept

form and the Point-slope form.

16. Comparing the slopes of two lines can show whether the lines are parallel,

perpendicular, or neither.

17. The relationship between parallel or perpendicular lines can sometimes be used to

write the equation of a line.

18. The formulas for slope, distance and midpoint can be used to classify and to prove

geometric relationships for figures in the coordinate plane.

19. Using variables to name the coordinates of a figure allows relationships to be

shown to be true for a general case

20. Geometric relationships can be proven using variable coordinates for figures in the

coordinate plane.

PACING CONTENT SKILLS STANDARDS

(CCSS/MP)

RESOURCES LEARNING

ACTIVITIES/ASSESSMENTS

130

Pearson OTHER

(e.g., tech)

2 days

3.7 Equations

of Lines in the

Coordinate

Plane

Graph and write linear equations

Example:

The slope of a line is the rate of change

and is represented by m

When a line passes through the points

(x1, y1) and (x2, y2), the slope (m) is

Equations of line can take on several

forms:

Slope Intercept Form:

[used when you know, or can find, the

slope, m, and the y-intercept, b.]

y = mx + b

Point Slope Form:

[used when you know, or can find, a

point on the line (x1, y1), and the

slope, m.]

Prepares for

G.GPE.5 Prove

the slope criteria

for parallel and

perpendicular

lines and

uses 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).

MP 1

MP 3

Text book

page 189-

196

http://www.regentsprep

.org/Regents/math/geo

metry/GCG1/EqLines.ht

m

http://www.mathwareh

ouse.com/algebra/linear

_equation/slope-of-a-

line.php

Page 193: 1-7

Basic – Problems 1-2

Ex. 8 – 29, 50 – 63, 69 -77


Ex. 9 – 29 odd, 50 –63, 669 - 77


Ex 9-29 odd, 50-63, 69 - 77

http://www.regentsprep.org/Regents/math/geometry/GCG1/EqLines.htm




http://www.mathwarehouse.com/algebra/linear_equation/slope-of-a-line.php




131

y – y1 = m(x – x1)

30 mins

Basic Skills

Review

PARCC/

HSPA PREP

Write the equation of a line

Question:

What is the equation of the line in

slope-intercept form of the line parallel

to y = 5x + 2 that passes through the

point with coordinates (-2, 1)

G.GPE.5

See above

Text book

page 196

http://www.regentsprep.o

rg/Regents/math/geometr

y/GCG1/EqLines.htm

http://www.mathwarehou

se.com/algebra/linear_equ

ation/slope-of-a-line.php


Q 64 – 68

Worksheets from stated websites.







132

2 days

3.8

Slopes of

Parallel and

Perpendicular

Lines

Relate slope to parallel and

perpendicular lines

Example:

If we look at both equations, we notice that they both have slopes of 2. Since both lines "rise" two units for every one unit they "run," they will never intersect. Thus, they are parallel lines. The graph of these equations is shown below.

G.GPE.5 Prove

the slope

criteria for

parallel and

perpendicular

lines and

uses 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).

MP 1

MP2

Text book

page 197-

204

http://www.wyzant.com

/help/math/geometry/li

nes_and_angles/parallel

_and_perpendicular


.org/Regents/math/ALG

EBRA/AC3/Lparallel.htm

Kuta Software for

worksheets.

23. Page 201: 1-6


Ex. 7 – 14, 27, 53 - 62


Ex. 7 - 13 odd, 27, 53 - 62


Ex 7-21 odd, 27, 53 - 62

30 mins

Basic Skills

Review

PARCC/

HSPA PREP

Classify lines as parallel, perpendicular

or neither.

Question:

Classify each of the following pairs of

lines as parallel, perpendicular or

G.GPE.5

See above

Text book

page 204



metry/GCG1/EqLines.ht

m


Q 48 - 52

http://www.wyzant.com/help/math/geometry/lines_and_angles/parallel_and_perpendicular











133

neither

Lines

Parallel/

Perpendicular /Neither

3y= -5x -5

(y – 7) = 0.6(x – 5)

2x + 3y = 4

4x + 5y = 6

y = 4x + 1

(y – 2) = 4(x – 3)

y = -3x + 5

9x + 3y = 2


ouse.com/algebra/linear

_equation/slope-of-a-

line.php


27.





134

135

1 day

6.7

Polygons in

the

Coordinate

Plane

Classify polygons in the coordinate

plane applying the formulas for slope,

distance and midpoint.

Example:

Is parallelogram WXYZ a rhombus?

Explain

G.GPE.7

Use coordinates

to compute

perimeters of

polygons and

areas of

triangles and

rectangles, e.g.,

using the

distance

formula.

MP 1

MP 3

MP 8

Text book

page 400 –

405

Teacher made power

point presentations

28. Page 403: 1-4

29. Basic – Problems 1-3,

Ex. 5– 18, 21 - 24, 31, 35 – 44,

49 - 54

30. Average – Problems 1 – 3,

Ex. 5 - 15 odd, 17 – 44, 49 - 54

31. Advanced – Problems 1-3,

Ex 5-15 odd, 17 - 44, 49 - 54

136

30 mins

Basic Skills

Review

PARCC/

HSPA PREP

Determine if a given polygon is a

triangle, parallelogram or a

quadrilateral

Question:

In the coordinate plane, quadrilateral

ABCD has vertices with

coordinates

A(1, -1), B(-5, 3), C(-3, 6), and

D(3, 2).

1) Compute the lengths of the sides of

quadrilateral ABCD.

AB = ____ BC = ___

CD = ____ DA = ___

2) Compute the slopes of the sides

AB and AD .

Slope of AB = _____

Slope of AD = _____

G.GPE.5

G.GPE 7

Use coordinates

to compute

perimeters of

polygons and

areas of

triangles and

rectangles, e.g.,

using the

distance

formula.

Text book

page 405

Teacher made power

point presentations

Kuta software for

worksheets


Q 45 - 48


137

3. Indicate in the table below whether

ABCD is an example of each shape

listed. Explain why it is or is not.

Shape Yes or

No

Explain

Parallelogram

Rhombus

Rectangle

Square

138

2 days

6.8

Applying

Coordinate

Geometry

Name coordinates of special figures by

using their properties

Question

SQRE is a square where SQ = 2a. The

axes bisect each side, what are the

coordinates of the vertices of SQRE?

Prepares for

G.GPE.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).

Text book

page 402 -

412

Teacher made Power

point presentations

Kuta software

worksheets.

http://www.mathopenr

ef.com/coordsquare.ht

ml

http://www.youtube.co

m/watch?v=EZtXevirdes

32. Page 403: 1-3

33. Basic – Problems 1-3,

Ex. 7– 13, 14, 17, 19, 23, 24, 28,

42-49


Ex. 7- 13 odd, 14 – 31, 42 - 49


Ex 7-13 odd, 14 - 41, 42 - 49

30 mins

Basic Skills

Review

PARCC/

HSPA PREP

Find the coordinates of vertices of a

polygon given coordinates of two

vertices and a point of intersection of

the diagonals.

Question:

A parallelogram has two vertices at (1,

G.GPE.4

See above

Text book

page 412


ef.com/coordsquare.ht

ml


m/watch?v=EZtXevirdes


Q 38 - 41


http://www.mathopenref.com/coordsquare.html



http://www.youtube.com/watch?v=EZtXevirdes







139

1) and (0, 7) and its diagonals cross at

the point (4, 3). Where are the other

two vertices of the parallelogram

140

2 days

6.9

Proofs Using

Coordinate

Geometry

Prove theorems using figures in the

coordinate plane.

Example:

G.GPE.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).

MP 1

MP 3

MP 7

Text book

page 414-

418

http://www.youtube.com

/watch?v=EZtXevirdes

http://on.aol.com/video/

how-to-write-coordinate-

proofs-516909807

http://www.regentsprep.

org/Regents/math/geome

try/GCG4/CoordinatepRA

CTICE.htm

http://hotmath.com/hot

math_help/topics/coordin

ate-proofs.html

http://www.whiteplainsp

ublicschools.org/cms/lib5/

NY01000029/Centricity/D

omain/360/Coordinate%2

0Geometry%20Proofs%20

Packet%202012.pdf

36. Page 416: 1-3


Ex. 4, 6– 20 even, 21, 23, 33 -

40


Ex. 4 - 14, 15 – 26, 33 – 40.


Ex 4 – 28, 33 - 40



http://on.aol.com/video/how-to-write-coordinate-proofs-516909807



http://www.regentsprep.org/Regents/math/geometry/GCG4/CoordinatepRACTICE.htm




http://hotmath.com/hotmath_help/topics/coordinate-proofs.html



http://www.whiteplainspublicschools.org/cms/lib5/NY01000029/Centricity/Domain/360/Coordinate%20Geometry%20Proofs%20Packet%202012.pdf






141

30 mins

Basic Skills

Review

PARCC/

HSPA PREP

Use Coordinate Geometry to Prove

Right Triangles and Parallelograms

Question:

Daniel and Isaiah see a drawing of

quadrilateral ABCD, A(2,2), B(5,-2),

C(9,1) and D(6,5).

Daniel says the figure is a rhombus, but

not a square. Isaiah says the figure is a

square. Write a proof to show who is

making the correct observation.

G.G.PE 4

See above

Text book

page 418



metry/GCG4/Coordinate

pRACTICE.htm

http://www.whiteplains

publicschools.org/cms/li

b5/NY01000029/Centrici

ty/Domain/360/Coordin

ate%20Geometry%20Pr

oofs%20Packet%202012

.pdf


Q 29 - 32













142

1 day

12.5

Circles in the

Coordinate

plane

To write the equation of a circle and

find the center and radius of a circle.

Example:

Definition: A circle is a locus (set) of

points in a plane equidistant from a

fixed point.

Circle whose center is at the origin

Equation:

Example: Circle with center (0,0),

radius 4

G.GPE 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.

Text book

page 798 -

803


.org/Regents/math/algtr

ig/ATC1/circlelesson.ht

m


ouse.com/geometry/circ

le/equation-of-a-

circle.php

http://www.mathsisfun.

com/algebra/circle-

equations.html


ef.com/coordgeneralcirc

le.html

40. Page 800: 1-7


Ex. 8 – 30 all, 31 – 52 even, 58 -

65


Ex. 9 – 29 odd, 315– 56, 58 –

65.


Ex 9 – 29 odd, 31 - 65

http://www.regentsprep.org/Regents/math/algtrig/ATC1/circlelesson.htm




http://www.mathwarehouse.com/geometry/circle/equation-of-a-circle.php




http://www.mathsisfun.com/algebra/circle-equations.html



143

Graph:

Circle whose center is at (h, k)

( i wi r f rr a “c n r-

ra iu f r ”

I ay a r f rr a “ an ar

f r ” )

Equation:

144

Example: Circle with center (2,-5),

radius 3

Graph:

145

1 day

12.5

Circles in the

Coordinate

plane

To write the equation of a parabola.

Example

Definition: A parabola is a curve where

any point is at an equal distance from:

1. a fixed point (the focus), and

2. a fixed straight line

(the directrix)

G.GPE 2 Derive

the equation of

a parabola given

a focus and

directrix.

Text book

page 804 –

805


com/geometry/parabola

.html

http://www.purplemath

.com/modules/parabola.

htm

http://hotmath.com/hot

math_help/topics/findin

g-the-equation-of-a-

Concept Byte Page 804

Activity 1

Activity 2

Activity 3

Ex: 17 - 23

http://www.mathsisfun.com/geometry/parabola.html



http://www.purplemath.com/modules/parabola.htm



146

* the axis of symmetry (goes through

the focus, at right angles to the

directrix)

* the vertex (where the parabola

makes its sharpest turn) is halfway

between the focus and directrix.

parabola-given-focus-

and-directrix.html

147

30 mins

Basic Skills

Review

PARCC/

HSPA PREP

Find the equation of a circle

Question:

In the coordinate plane, the circle

with radius r centered at ,h k

consists of all the points ,x y that

are r units from , .h k Use the

Pythagorean theorem and the figure

below to find an equation of the circle

with radius r and center

Explain your answer.

G.GPE 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.

Text book

page 803



le/equation-of-a-

circle.php


com/algebra/circle-

equations.html


Q 58 - 60



3. Building on their knowledge and work with the Pythagorean theorem, students will find distances in the coordinate plane.

4. Students will use a rectangular coordinate system to verify geometric relationships, including properties of special triangles and quadrilaterals and

slopes of parallel and perpendicular lines.








148

5. Students will continue their study of quadratics by connecting the geometric and algebraic definitions of the parabola.


PARCC EXEMPLARS www.parcconline.org

1. The coordinates are for a quadrilateral, (3, 0), (1, 3), (-2, 1), and (0,-2). Determine the type of quadrilateral made by connecting these four points?

Identify the properties used to determine your classification. You must give confirming information about the polygon.

2. If Quadrilateral ABCD is a rectangle, where A(1, 2), B(6, 0), C(10,10) and D(?, ?) is unknown. a. Find the coordinates of the fourth vertex. b. Verify that

ABCD is a rectangle providing evidence related to the sides and angles.

3. Derive the equation of the parabola that has the focus (1, 4) and the directrix x=-5.

4. Derive the equation of the parabola that has the focus (2, 1) and the directrix y=-4.

5. Derive the equation of the parabola that has the focus (-3, -2) and the vertex (1, -2).

6. Given the midpoint of a segment and one endpoint. Find the other endpoint.

a. Midpoint: (6, 2) endpoint: (1, 3)

b. Midpoint: (-1, -2) endpoint: (3.5, -7)


149

7. Investigate the slopes of each of the sides of the rectangle ABCD (shown below). What do you notice about the slopes of the sides that meet at a right

angle? What do you notice about the slopes of the opposite sides that are parallel? Can you generalize what happens when you multiply slopes of

perperpendicular lines?

8. If general points N at (a,b) and P at (c,d) are given. Why are the coordinates of point Q (a,d)? Can you find the coordinates of point M?

150

9. Jennifer and Jane are best friends. They placed a map of their town on a coordinate grid and found the point at w ic ac f ir u i If J nnif r’

u i a ( , ) an Jan ’ u i a ( , ) an y wan in i , w a ar c r ina f ace they should meet?

10. John was visiting three cities that lie on a coordinate grid at (-4, 5), (4, 5), and (-3, -4). If he visited all the cities and ended up where he started, what is the

distance in miles he traveled?

11. Suppose a line k in a coordinate plane has slope c/d

a. What is the slope of a line parallel to k? Why must this be the case?

b. What is the slope of a line perpendicular to k? Why does this seem reasonable?

12. Two points A(0, -4) , B(2, -1) determines a line, AB.

a. What is the equation of the line AB?

b. What is the equation of the line perpendicular to AB passing through the point (2,-1)?

151

Wiki page for Common Core Assessments


PARCC Framework Assessment questions with Model Curriculum Website for all units




21ST CENTURY SKILLS


Career Technical Education (CTE) Standards

1. 21st Century Life and Career Skills: All students will demonstrate the creative, critical thinking, collaboration, the problem-solving skills needed to

function successfully as both global citizens and workers in diverse ethnic and organizational cultures.

9.1.12.B.1 Present resources and data in a format that effectively communicates the meaning of the data and its implications for solving problems,

using multiple perspectives.

2. Personal Financial Literacy: All students will develop skills and strategies that promote personal and financial responsibility related to financial






152

planning, savings, investment, and charitable giving in the global economy.

9.2.12.B.1 Prioritize financial decisions by systematically considering alternatives and possible consequences.

3. Career Awareness, Exploration, and Preparation: All students will apply knowledge about and engage in the process of career awareness,

exploration, and preparation in order to navigate the globally competitive work environment of the information age.

9.3.12.C.2 Characterize education and skills needed to achieve career goals, and take steps to prepare for postsecondary options, including making

course selections, preparing for and taking assessments, and participating in extra-curricular activities.

4. Career and Technical Education: All students who complete a career and technical education program will acquire academic and technical skills for

careers in emerging and established professions that lead to technical skill proficiency, credentials, certificates, licenses, and/or degrees.

9.4.12.B.2 Demonstrate mathematics knowledge and skills required to pursue the full range of postsecondary education and career

opportunities.


http://www.achieve.org/files/CCSS-CTE-Task-Stairway-FINAL.pdf



- Review and copy notes from eno board/power point/smart board etc.

- Group/individual activities that will enhance understanding.

- Provide students with interesting problems and activities that extend the concept of the l

153

- Help students develop specific problem solving skills and strategies by providing scaffolding guiding questions

Peer tutoring

- Team up stronger math skills with lower math skills

Use of manipulative

- Eno or smart boards

- Dry erase markers

- Reference sheets created by special needs teacher

- Pairs of students work together to make word cards for the chapter vocabulary

- Use 3D shapes for visual learning

- Reference sheets for classroom

- Graphing calculators

APPENDIX


MP1 Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than

154

simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continua y a k v , “ i ak n ” y can un r an a r ac f r ving c r an i ntify correspondences between different approaches.

MP 2 Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

MP 3 Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

MP 4 Model with mathematics.

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe

155

how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

MP 5 Use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts

MP 6 Attend to precision.

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

MP 7 Look for and make use of structure.

Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for

156

solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

MP 8 Look for and express regularity in repeated reasoning.

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x– 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x2 +x + 1), and (x – 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.















157

NOTE:

Standards alignment in accordance with Appendix A of Common Core State Standards and Pear n’ G ry C n C r ac r’ E i i n V u

1 and 2

Notes to teacher (not to be included in your final draft):

4 Cs Three Part Objective


* http://www.cpm.org/pdfs/state_supplements

* http://www.cde.ca.gov/ta/tg/sr/documents/cstrtqgeomapr15.pdf

* http://illuminations.nctm.org

* http://www.state.nj.us/education/cccs/standards/9/

*http://www.whiteplainspublicschools.org/cms/lib5/NY01000029/Centricity/Domain/360/Coordinate%20Geometry%20Proofs%20Packet%202012.pdf






158

Creativity: projects Behavior

Critical Thinking: Math Journal Condition

Collaboration: Teams/Groups/Stations Demonstration of Learning (DOL)

Communication – Powerpoints/Presentations

UNIT 5

Circles With and Without Coordinates

Total Number of Days: 11days Grade/Course: __Geometry 10th grade__


16. How do you solve problems that involve measurements of

triangles?

17. How do you find the area of a polygon or find the

circumference and area of a circle?

18. How can you prove relationships between angles and arcs

in a circle?

19. How do you find the equation of a circle in the coordinate

plane?

20. Angle bisectors and segment bisectors can be used in triangles to determine

various angle and segment measures.

21. ng f ar f a circ ’ circu f r nc can f un y r a ing i an ang

in the circle.

22. The ar a f ar f a circ f r y ra ii an arc can f un w n circ ’

radius is known

23. Angles formed by intersecting lines have a special relationship to the arcs the

intersecting lines intercept

159

24. The information in the equation of a circle allows the circle to be graphed. The

equation of a circle can be written if its center and radius are known.

PACING CONTENT SKILLS STANDARDS

(CCSS/MP)

RESOURCES

LEARNING

ACTIVITIES/ASSESSMENTS Pearson

OTHER

(e.g., tech)

1 day

5.3

Bisectors in

-To identify properties of

perpendicular bisectors and angles

G.C.3

Construct the

Text book

page 300-

www.pkwy.k12.mo.us/ho

mepage/ataylor1/file/2.2.

pdf

Page 300 - Concept Byte: Paper

160

Triangles bisectors.

Example:

Technology Use geometry software to

draw ABC. Construct the angle

bisector of BAC. Then find the

midpoint of . Drag any of the points.

Does the angle bisector always pass

through the midpoint of the opposite

side? Does it ever pass through the

midpoint?

inscribed and

circumscribed

circles of a

triangle, and

prove

properties of

angles for a

quadrilateral

inscribed in a

circle.

307


Files/PDFFILES/Workshee

tsByTopic/ANGLES/Drills

/PR_Measuring_Angles_3.

pdf

Folding Bisectors

Page 304: 1 - 6

Basic – Problems 1-3

Ex. 7– 20, 23, 26 – 29, 33 - 40


Ex. 7 – 17 odd, 18–29, 33 - 40


Ex 7-17 odd, 18-40.

http://www.jmap.org/StaticFiles/PDFFILES/WorksheetsByTopic/ANGLES/Drills/PR_Measuring_Angles_3.pdf





161

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To write an argument for the formulas

for the volume of a pyramid.

Question:

A cube in the xyz-coordinate system

(not shown) centered at the origin has

vertices at the points

and

G.GMD.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,

Text book

page 307

www.pkwy.k12.mo.us/ho

mepage/ataylor1/file/2.2.

pdf


Files/PDFFILES/Workshee

tsByTopic/ANGLES/Drills

/PR_Measuring_Angles_3.

pdf


Q 33 – 36







162

, where . If lines

are drawn from the center of the cube

to the 8 vertices of the cube, 6

pyramids are formed. Explain how

a pyramid with height a and square

base of side length 2a has a volume a3

Cava i ri’

principle, and

informal limit

arguments.

MP 1

MP 3

1 day

10.6

Circles and

Arcs

To find the measures of central angles

and arcs, find the circumference and

arc length

Example:

Challenge Engineers reduced the lean

of the Leaning Tower of Pisa. If they

moved it back 0.46�, what was the arc

length of the move? Round your

answer to the nearest whole number.

G.CO.1, G.C.1,

G.C.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

Text book

page 649-

658



metry/GP15/CircleArcs.

htm

www.cpm.org/pdfs/skillB

uilders/GC/GC_Extra_Pr

actice_Section18.pdf

www.robertfant.com/Geo

metry/PowerPoint/Chapt

er11.ppt

Page 658 - Concept Byte: Circle

Graphs

27. Page 654: 1-8


Ex. 9 – 35, 36 – 50 even, 64 - 71


Ex. 9- 35 odd, 36 – 56, 64 - 71


Ex 9-35 odd, 36 – 56, 64 - 71

http://www.regentsprep.org/Regents/math/geometry/GP15/CircleArcs.htm




163

radius intersects

the circle.

MP 1

MP 3

MP 8

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To find the measure of an angle in a

circle

Question:

In the figure below, is tangent to

the circle with center O at point A. If

has a measure of 68 degrees,

what is the measure, in degrees,

of

G.C.2

See above

Text book

page 657

163.150.89.242/yhs/F

aculty/AB/bagg/Geom

etry/images/.../11.3.pd

f


ef.com/arccentralanglet

heorem.html


Q 60 - 63


31.

164

165

1 day

10.7

Areas of

Circles and

Sectors

To find the areas of circles, sectors and

segments of circles.

Example:

Landscaping The diagram shows the

area of a lawn covered by a water

sprinkler. Round your answer to the

nearest whole number.

1. What is the area of the lawn that is

covered by the sprinkler?

2. Suppose the water pressure is

weakened so that the radius is 12 feet.

What is the area of lawn that will be

covered?

G.C.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.

MP 1

MP 3

MP 6

MP 8

Text book

page 659 –

667

Teacher made power

point presentations

Page 659 - Concept Byte: Exploring

the Area of a Circle

Page 667 – Concept Byte: Inscribed

and Circumscribed Figures

32. Page 663: 1-6


Ex. 7 – 25, 26 – 34 even, 35 –

36, 55 - 63


Ex. 7 - 25 odd, 26 – 44, 55 - 63


Ex 7-25 odd, 26 – 50, 55 - 63

166

167

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To find the length of a chord in a circle

Question:

A circle with center O and radius 5 has

central angle XOY. If mXY = 600, what is

the length of chord XY?

A circle w

G.C.5

See above

Text book

page 666


ef.com/chord.html



metry/GP14/CircleSegm

ents.htm


Q 51 - 54


2 days 12.1

Tangent Lines

To use properties of a tangent to a

circle

Example:

You are standing at C, 8 feet from a silo.

The distance to a point of tangency is

16 feet. What is the radius of the silo?

G.C.2

Identify and

describe

relationships

among inscribed

angles, radii,

and chords.

Include the

relationship

between

central,

inscribed, and

circumscribed

angles; inscribed

Text book

page 762 –

769

Teacher made power

point presentations

http://www.murrieta.k1

2.ca.us/cms/lib5/CA010

00508/Centricity/Domai

n/1830/T11.2.pdf

http://jmap.org/htmlsta

ndard/Geometry/Inform

al_and_Formal_Proofs/

G.G.50.htm

36. Page 766: 1-5


Ex. 6 – 22, 26 – 31, 36 – 44,


Ex. 7 - 19 odd, 20 – 31, 36 - 44


Ex 7-19 odd, 20 – 31, 36 - 44

http://www.mathopenref.com/chord.html

http://www.mathopenref.com/chord.html

http://www.regentsprep.org/Regents/math/geometry/GP14/CircleSegments.htm




http://www.murrieta.k12.ca.us/cms/lib5/CA01000508/Centricity/Domain/1830/T11.2.pdf








168

angles on a

diameter are

right angles; the

radius of a circle

is perpendicular

to the tangent

where the

radius intersects

the circle.

MP 1

MP 3

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To visualize the relation between two-

dimensional and three-dimensional

objects.

Question:

A three dimensional object is created

by rotating a circle about one of its

diameters. What is the shape of the

resulting object? Give as much detail as

possible.

G.GMD.4

Identify the

shapes of two-

dimensional

cross-sections of

three-

dimensional

objects, and

identify three-

dimensional

objects

generated by

rotations of

two-

Text book

page 769

Teacher made power

point presentation.


Q 32 - 35

169

A circle

dimensional

objects.

2 days

12.2

Chords And

Arcs

To use congruent chords, arcs and

central angles and also apply

perpendicular bisectors to chords.

Example:

Find the Length of a Chord

G.C.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

Text Book

page 771 -

779

http://163.150.89.242/y

hs/Faculty/AB/bagg/Geo

metry/images/Geometr

y%20text%20PDFs/11.4.

pdf

http://www.jmap.org/ht

mlstandard/Geometry/I

nformal_and_Formal_Pr

oofs/G.G.52.htm

Teacher made power

point presentation

Page 770 - Concept Byte: Paper

Folding With Circles

40. Page 776: 1-5


Ex. 6– 16, 18, 23 – 25, 29, 44 -

52


Ex. 7 - 15 odd, 16 – 34, 44 - 52


Ex 7-15 odd, 16 – 39, 44 - 52

http://163.150.89.242/yhs/Faculty/AB/bagg/Geometry/images/Geometry%20text%20PDFs/11.4.pdf









170

right angles; the

radius of a circle

is perpendicular

to the tangent

where the

radius intersects

the circle.

MP 1

MP 3

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To use the properties of tangent to

construct a line tangent to a circle.

Question:

Construct a line through point P that is

tangent to circle O below. Leave all

construction marks.

Construct a line through point.

G.C.4 Construct

a tangent line

from a point

outside a given

circle to the

circle.

Text book

page 779

Teacher made power

point presentation.


ef.com/consttangent.ht

ml

http://mathbits.com/Ma

thBits/GSP/TangentCircl

e.htm


Q 40 - 43

http://www.mathopenref.com/consttangent.html



http://mathbits.com/MathBits/GSP/TangentCircle.htm



171

A circle


m/watch?v=IT52gEoGe9

A

2 days

12.3

Inscribed

Angles

To find the measures of an inscribed

angle, measure of an angle formed by

a tangent and a chord.

Example:

Find the measure of the inscribed angle

or the intercepted arc.

G.C.2, G.C.3,

Construct the

inscribed and

circumscribed

circles of a

triangle, and

prove

properties of

angles for a

quadrilateral

inscribed in a

circle.

Text book

page 780 -

787

http://163.150.89.242/y

hs/Faculty/AB/bagg/Geo

metry/images/Geometr

y%20text%20PDFs/11.5.

pdf

Teacher made power

point presentations.




44. Page 784: 1-5


Ex. 6– 19, 18, 20 – 24 even, 28 -

29, 44 - 51


Ex. 7 - 17odd, 19 – 34, 44 - 51


Ex 7-17odd, 19 - 39, 44 - 51









172

MP 1

MP 3

oofs/G.G.51.htm


m/watch?v=DjgPtK0_Qh

0


ef.com/circleinscribed.h

tml

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To find the measure of an inscribed

angle.

Question:

Quadrilateral WXYZ is inscribed in a

circle. If radians

G.C.2, G.C.3

Above

Text book

page 787

Teacher made power

point presentation.


ef.com/circleinscribed.h

tml


Q 40 - 43

http://www.youtube.com/watch?v=DjgPtK0_Qh0



http://www.mathopenref.com/circleinscribed.html



173

and4

m5

X

radians, what are

the measures, in radians, of the other

two angles in the quadrilateral?

1 day

12.4

Angle

Measures and

Segment

Lengths

To find measures of angles formed by

chords, secants, tangents, and also

find the lengths of segments

associated with circles

Example:

G.C.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

Text book

page 789 -

797

Teacher made power

point presentation

http://www.finneytown.

org/Downloads/GETE12

042.pdf


m/watch?v=Ax33G6YdS

v0




oofs/G.G.51.htm

Page 789 - Concept Byte: Exploring

Chords and Secants

48. Page 794: 1-7


Ex. 8– 20, 22 = 26 even, 27 – 31

odd, 48 – 55


Ex. 9 - 19 odd, 21 – 39, 48 - 55


Ex 9-19 odd, 21 – 43, 48 - 55




http://www.youtube.com/watch?v=Ax33G6YdSv0







174

radius intersects

the circle.

MP 1

MP 3

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To find the measure of an angle.

Question:

In the figure below, ABC is

circumscribed about the circle centered

at O. If the measure of AOC is

radians, what is the measure, in

radians, of

G.C.2, Above Text book

page 797

Teacher made power

point presentation.




oofs/G.G.51.htm


Q 44- 47





175

1 day

12.5

Circles in the

Coordinate

Plane

To write the equation of a circle and to

find the center and radius of a circle.

Example:

Using the Center and a Point on a

Circle.

Write the standard equation of the

circle with center (1, -3) that passes

through the point (2, 2).

G.GPE.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.

MP 1

MP 3

MP 7

Text book

page 798 -

803

http://www.finneytown.

org/Downloads/GETE

12052.pdf


mlstandard/Geometry/

Coordinate_Geometry/

G.G.71.htm

http://www.ck12.org/g

eometry/Circles-in-the-

Coordinate-Plane/

52. Page 800: 1-7


Ex. 8– 30, 31 - 52 even, 61 – 65


Ex. 9 - 29 odd, 31 – 56, 61 - 65


Ex 9-29 odd, 31 – 56, 61 - 65




http://www.jmap.org/htmlstandard/Geometry/Coordinate_Geometry/G.G.71.htm




http://www.ck12.org/geometry/Circles-in-the-Coordinate-Plane/



176

30 mins

Basic Skills

Review

PARCC/HSPA

PREP

To find the equation of a circle

Question:

G.GPE 1 Derive

the equation of

a circle of given

center and

radius using the

Pythagorean

Theorem;

complete the

square to find

the center and

Text book

page 803



le/equation-of-a-

circle.php


com/algebra/circle-

equations.html


Q 58 - 60









177

In the coordinate plane, the circle with

radius r centered at ,h k consists

of all the points ,x y that are r

units from , .h k Use the

Pythagorean theorem and the figure

below to find an equation of the circle

with radius r and center

Explain your answer.

radius of a circle

given by an

equation.

178


56. In this unit, students will prove basic theorems about circles, with particular attention to perpendicularity and inscribed angles, in order to see

symmetry in circles and as an application of triangle congruence criteria.

57. They will study relationships among segments on chords, secants, and tangents as an application of similarity.

58. In the Cartesian coordinate system, students will use the distance formula to write the equation of a circle when given the radius and the coordinates

of its center. Given an equation of a circle, they will draw the graph in the coordinate plane, and apply techniques for solving quadratic equations to

determine intersections between lines and circles or parabolas and between two circles.


PARCC EXEMPLARS www.parcconline.org

1. An archeologist dug up an edge piece of a circular plate. He wants to know what the original diameter of the plate was before it broke. However, the

piece of pottery does not display the center of the plate. How could he find the original dimensions?

2. Jessica works at a daycare center and she is watching three rambunctious toddlers. One of the toddlers is in a crib at point A, another toddler is in her

high chair at point B and the third toddler is in a play-station at point C. Where can Jessica position herself so that she is equidistant from each of the

children? Construct an argument using concrete referents such as objects, drawing, diagrams and actions.

3. Since all circles are similar, the ratio of the will be the scale factor for any circle. Two students use different reasoning to find the length

of an arc with central angle measure of 45° in a circle with radius=3cm. Compare the effectiveness of these two plausible arguments:


179

Sv ana ay : “I kn w a 36 0 = 2 radians

Since = , the equivalent measure of the length of the arc will be (2 * 3) or c ”

ic a ay : “36 0 = 2 radians therefore 1 = radians. 45 =( ) radians. Therefore the measure of the arc will be 45 =( ) radians * 3cm = c ”

Can y u u Sv ana’ r a ning fin an arc ng a cia wi a c n ra ang f º f a circ wi a ra iu f f Can y u u ic a ’ r a ning

to find the arc length of a circle with a radius of 6m and a central angle of 120º? Which method do you prefer and why?

4. Given a coordinate and a distance from that coordinate develop a rule that shows the locus of points that is that given distance from the given point

(based on the Pythagorean theorem). If the coordinate of point H in the diagram below is (x,y) and the length of DH is 4 units. Can you write a rule that

represents the relationship of the x value, the y value and the radius? Why is this relationship true? As point H rotates around the circle, does this

relationship stay true?

5. In the diagram below, circle D translated 4 units to the right to create circle E. Why is the equation of this new circle (x − 4)2 + y2 = 42 . Why is the equation

for circle I x2 + (y − 4)2 = 42 . Using similar reasoning, could you right and equation for a circle with the center at

(-4, 0) and a radius of 4? Center of (0, -4) and radius of 4? What is the equation of a circle with center at (-8,11) and a radius of 5 ? Can you generalize this

equation for a circle with a center at (h,k) and a radius of r?

180

!

!

Add limitations for course 2 and 3.

G-GPE.2 Derive the equation of a

parabola given a focus and a directrix.

G-GPE.2 Given a focus and directrix, derive the equation of a parabola.

Parabola is defined as “the set of all points P in a plane equidistant from a fixed line and a fixed point in the plane.”

The fixed line is called the directrix, and the fixed point is called the focus.

(Level II)

Ex. Derive the equation of the parabola that has the focus (1, 4) and the directrix x=-5.

Ex. Derive the equation of the parabola that has the focus (2, 1) and the directrix y=-4.

Ex. Derive the equation of the parabola that has the focus (-3, -2) and the vertex (1, -2).

G-GPE.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.

G-GPE.3 Given the foci, derive the equation of an ellipse, noting that the sum of the distances from the foci to any

fixed point on the ellipse is constant, identifying the major and minor axis.

G-GPE.3 Given the foci, derive the equation of a hyperbola, noting that the absolute value of the differences of the

distances from the foci to a point on the hyperbola is constant, and identifying the vertices, center, transverse axis,

conjugate axis, and asymptotes.

!

!

!

!

Wiki page for Common Core Assessments


PARCC Framework Assessment questions with Model Curriculum Website for all units




21ST CENTURY SKILLS





181


Career Technical Education (CTE) Standards

5. 21st Century Life and Career Skills: All students will demonstrate the creative, critical thinking, collaboration, the problem-solving skills needed to

function successfully as both global citizens and workers in diverse ethnic and organizational cultures.

9.1.12.B.1 Present resources and data in a format that effectively communicates the meaning of the data and its implications for solving problems,

using multiple perspectives.

6. Personal Financial Literacy: All students will develop skills and strategies that promote personal and financial responsibility related to financial

planning, savings, investment, and charitable giving in the global economy.

9.2.12.B.1 Prioritize financial decisions by systematically considering alternatives and possible consequences.

7. Career Awareness, Exploration, and Preparation: All students will apply knowledge about and engage in the process of career awareness,

exploration, and preparation in order to navigate the globally competitive work environment of the information age.

9.3.12.C.2 Characterize education and skills needed to achieve career goals, and take steps to prepare for postsecondary options, including making

course selections, preparing for and taking assessments, and participating in extra-curricular activities.

8. Career and Technical Education: All students who complete a career and technical education program will acquire academic and technical skills for

careers in emerging and established professions that lead to technical skill proficiency, credentials, certificates, licenses, and/or degrees.

9.4.12.B.2 Demonstrate mathematics knowledge and skills required to pursue the full range of postsecondary education and career

opportunities.


http://www.achieve.org/files/CCSS-CTE-Spread-of-Disease-FINAL.pdf


182



- Review and copy notes from eno board/power point/smart board etc.

- Group/individual activities that will enhance understanding.

- Provide students with interesting problems and activities that extend the concept of the l

- Help students develop specific problem solving skills and strategies by providing scaffolding guiding questions

Peer tutoring

- Team up stronger math skills with lower math skills

Use of manipulative

- Eno or smart boards

- Dry erase markers

- Reference sheets created by special needs teacher

- Pairs of students work together to make word cards for the chapter vocabulary

- Use 3D shapes for visual learning

- Reference sheets for classroom

- Graphing calculators

183

APPENDIX


MP1 Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, an y c n inua y a k v , “ i ak n ” y can un r an a r ac f r ving c r an i n ify c rr n nc w en different approaches.

MP 2 Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

MP 3 Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there

184

is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

MP 4 Model with mathematics.

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

MP 5 Use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts

MP 6 Attend to precision.

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying

185

units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

MP 7 Look for and make use of structure.

Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

MP 8 Look for and express regularity in repeated reasoning.

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x– 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x2 +x + 1), and (x – 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.






186







* http://www.cpm.org/pdfs/state_supplements

* http://www.cde.ca.gov/ta/tg/sr/documents/cstrtqgeomapr15.pdf

* http://illuminations.nctm.org

* http://www.state.nj.us/education/cccs/standards/9/

*http://www.whiteplainspublicschools.org/cms/lib5/NY01000029/Centricity/Domain/360/Coordinate%20Geometry%20Proofs%20Packet%202012.pdf










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