Pitt County Schools 206322 Geometric Essentials

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Oct 10, 2013 (3 years and 11 months ago)

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Pitt County Schools

206322 Geometric Essentials

Instructional Guide


TIME FRAME: FIRST GRADING PERIOD






SCOS GOALS AND OBJECTIVES

ESSENTIAL QUESTIONS,
BENCHMARKS, AND SKILLS

ESSENTIAL TASKS,
STRATEGIES,
PROJECTS,
CONNECTIONS

RECOMMEND
ED
RESOURCES
AND
AS
SESSMENT

NC SCOS: Algebra 4.01
Use linear
functions or inequalities to model and
solve problems; justify results.

1.

Solve using tables, graphs, and
algebraic properties.

2.

Interpret constants and coefficients I
the context of the problem.

How can linear equ
ations model real
-
world
data?


What do the coefficients of the linear equation
mean in a real
-
world context?



Be able to use tables, graphs, equations

Collect real data and use it
to make a graph and find
the linear equation to
model.

Textbook:
Glencoe:
Alg
ebra I

(5 Days)


NCTM’s
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NC SCOS: Algebra 1.01

Write
equivalent forms of algebraic expressions
to solve problems.

1.

Apply the laws of exponents.

2.

Operate with polynomia
ls.

3.

Factor polynomials.

How can show that expressions that are
written in different forms are the same value?


What are the laws of exponents and why is
using exponents useful?


What is the relationship between the factoring
of a polynomial and the points
on the graph?

The Pyramid Problem
(Navigating through
Algebra
-
Grades 6
-
8 or call
Karen Vaughan)

Textbook:
Glencoe:
Algebra I

(5 Days)


NCTM’s
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瑨牯畧栠
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2

for Algebra I

NC SCOS: Algebra 4.02

G
raph, factor,
and evaluate quadratic functions to solve
problems.

How do the coefficients of the quadratic
equation affect the location of the parabola on
the coordinate graph?


How do you find the solutions of the
quadratic and how do they relate to the
points
on the graph of the parabola.

Use motion detector to
graph tossed ball.

Textbook:
Glencoe:
Algebra I

(4 Days)


NCTM’s
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Goal 1: The learner will perform
opera
tions with real numbers to solve
problems.

1.02 Use length, area, and volume of
geometric figures to solve problems.
Include arc length, area of sectors of
circles; lateral area, surface area, and
volume of three
-
dimensional figures; and
perimeter, area an
d volume of composite
figures.

Goal 2 The learner will use geometric
and algebraic properties of figures to
solve problems and write proofs.

2.02 Apply properties, definitions, and
theorems of angles and lines to solve
problems and write proofs.

DISCOVERI
NG POINTS, LINES,
PLANES, AND ANGLES

How can you apply segment measure to
coordinate graphing?



Find the midpoint and distance of a
segment



Glencoe:
Geometry

Chapter 1

(Sections 1
-
1 to
1
-
6)

(4 Days)



Goal 2: The learner will use geometric
and algebrai
c properties of figures to
solve problems and write proofs.

2.01 Use logic and deductive reasoning to
draw conclusions and solve problems.

2.02 Apply properties, definitions, and
CONNECTING REASONING AND
PROOF

How can you use logical reasoning to solve
mathematical prob
lems?



Develop a problem solving strategy



Identify and draw models of points,

Textbook:

Chapter 2

(Sections 2
-
1 to
2
-
5)

(4 Days)


3

theorems of angles and lines to solve
problems and write proofs.

2.03 Apply
properties, definitions, and
theorems of two
-
dimensional figures to
solve problems and write proofs:

(a) Triangles

(b) Quadrilaterals

(c) Other polygons

(d) Circles

lines, and planes



Goal 2: The learner will use geometric
and algebraic properties of figures to
solve problems and write p
roofs.

2.02 Apply properties, definitions, and
theorems of angles and lines to solve
problems and write proofs.

USING PERPENDICULAR AND
PARALLEL LINES


What are the relationships between segments,
lines, and planes?



Identify special angles formed by
paral
lel lines


How can you use the different types of angles
to solve real world problems



Identify angle addition postulate



Protractor use


Textbook:

Chapter 3

(Sections 3
-
1 to
3
-
7)

(6 Days)

Goal 2: The learner will use geometric
and algebraic properties of
figures to
solve problems and write proofs.

2.02 Apply properties, definitions, and
theorems of angles and lines to solve
problems and write proofs.

2.03 Apply properties, definitions, and
theorems of two
-
dimensional figures to
solve problems and write pr
oofs:

(a) Triangles

(b) Quadrilaterals

(c) Other polygons

(d) Circles

IDENTIFYING CONGRUENT
TRIANGLES

How can you determine what information is
necessary to identify congruent triangles?



Identify corresponding parts of
congruent triangles



Understand the an
gle sum theorem



Textbook:

Chapter 4

(Sections 4
-
1 to
4
-
6)

(5 Days)


TIME FRAME: SECOND GRADING PERIOD


SCOS GOALS AND OBJECTIVES

ESSENTIAL QUESTIONS,
ESSENTIAL TASKS,
RECOMMEND

4

BENCHMARKS, AND SKILLS

STRATEGIES,
PROJECTS,
CONNECTIONS

ED
RESOURCES
AND
A
SSESSMENT

Goal 2: The learner will use geometric
and algebraic properties of figures to
solve problems and write proofs.

2.03 Apply properties, definitions, and
theorems of two dimensional figures to
solve problems and write proofs:

(a) Triangles

(b) Qu
adrilaterals

(c) Other polygons

(d) Circles

APPLYING CONGRUENT TRIANGLES

What are the different ways to determine if
triangles are congruent?


Textbook:

Chapter 5

(Sections 5
-
1 to
5
-
6)

(6 Days)

Goal 2: The learner will use geometric
and algebraic proper
ties of figures to
solve problems and write proofs.

2.03 Apply properties, definitions, and
theorems of two dimensional figures to
solve problems and write proofs:

(a) Triangles

(b) Quadrilaterals

(c) Other polygons

(d) Circles

EXPLORING QUADRILATERALS

W
hat are the special properties of
quadrilaterals?



Properties of parallelograms and
trapezoids

Use The Geometer’s
p步瑣桰t搠瑯⁥d灬潲p
灲潰p牴楥猠潦⁦igu牥献

呥x瑢潯欺

C桡灴敲‶

⠶⁄ay猩


Goal 1: The learner will perform
operations with real numbers to so
lve
problems.

1.02 Use length, area, and volume of
geometric figures to solve problems.
Include arc length, area of sectors of
circles; lateral area, surface area, and
volume of three
-
dimensional figures; and
perimeter, area and volume of composite
figures
.

Goal 2: The learner will use geometric
and algebraic properties of figures to
solve problems and write proofs.

CONNECTING PROPORTION AND
SIMILARITY

How can you use proportional reasoning to
solve problems?



Identify proportional parts



Identify
similar figures


Use The Geometer’s
p步瑣桰t搠瑯⁥d灬潲p
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呥x瑢潯欺

C桡灴敲‷

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-
ㄠ瑯N
T
-


⠶⁄ay猩


5

2.02 Apply properties, definitions, and
theorems of angles and lines to solve
problems and write proofs.

2.03 Apply properties, definitions,
and
theorems of two
-
dimensional figures to
solve problems and write proofs:

(a)

Triangles

(b)

Quadrilaterals

(c)

Other polygons

(d)

Circles

Goal 1: The learner will perform
operations with real numbers to solve
problems.

1.02 Use length, area, and volume of
geomet
ric figures to solve problems.
Include arc length, area of sectors of
circles; lateral area, surface area, and
volume of three
-
dimensional figures;
and perimeter, area and volume of
composite figures.

Goal 2: The learner will use geometric
and algebraic pr
operties of figures to
solve problems and write proofs.

2.03 Apply properties, definitions, and
theorems of two dimensional figures to
solve problems and write proofs:

(a) Triangles

(b) Quadrilaterals

(c) Other polygons

(d) Circles

APPLYING RIGHT TRIANGL
ES AND
TRIGONOMETRY

How can you apply special segments in
solving problems involving triangles?



Understand the Pythagorean Theorem



Identify medians, altitudes, and
perpendicular bisectors



Construction of segments


How can you apply ratios to solve problems

with right triangles?



Identify parts of right triangles and
special right triangles


Flagpole shadow
demonstration


Use The Geometer’s
p步瑣桰t搠瑯⁥d灬潲p
灲潰p牴楥猠潦⁦igu牥献

呥x瑢潯欺

C桡灴敲‸

⡓Ec瑩潮猠o
-
ㄠ瑯N
U
-


⠶⁄ay猩†

Goal 2: The learner wi
ll use geometric
and algebraic properties of figures to
solve problems and write proofs.

2.02 Apply properties, definitions, and
theorems of angles and lines to solve
problems and write proofs.

2.03 Apply properties, definitions, and
ANALYZING CIRCLES

How can you solve problems using the
relationships between arcs, chords, and
diameters?



Identify relationships among arcs,

chords,
diameters



How can you apply segments to solving
Use The Geometer’s
p步瑣桰t搠瑯⁥d灬潲p
灲潰p牴楥猠潦⁦igu牥献

呥x瑢潯欺

C桡灴敲‹

⡓Ec瑩潮猠o
-
ㄠ瑯N
9
-


E
㔠䑡y猩†


6

theorems of two
-
dimen
sional figures
to solve problems and write proofs:

(a) Triangles

(b) Quadrilaterals

(c) Other polygons

(d) Circles


problems with circles?



Write the equation of a circle



Identify special segments in a circle



TIME FRAME: THIRD GRADING PERIOD

SCOS GOALS AND OBJECTIVES

ESSENTIAL QUESTIONS,
BENCHMARKS, AND SKILLS

ESSENTIAL TASKS,
STRATEGIES,
PROJECTS,
CONNECTIONS

RECOMMEND
ED
RESOURCES
AND
ASSESSMENT

Goal 1: The learner will perform
operations with rea
l numbers to solve
problems.

1.02 Use length, area, and volume to solve
problem. Include arc length, area of
sectors of circles; lateral area, surface
area, and volume of three
-
dimensional
figures; and perimeter, area, and volume
of composite figures.

1.03

Use length, area, and volume to
model and solve problems involving
probability.

Goal 2: The learner will use geometric
and algebraic properties of figures to
solve problems and write proofs.

2.03 Apply properties, definitions, and
theorems of two
-
dimens
ional figures to
solve problems and write proofs:

(a) Triangles

(b) Quadrilaterals

(c) Other polygons

(d) Circles

Goal 3: The learner will transform
EXPLORING POLYGONS AND AREA

How can you use angle relationships to solve
problems dealing with area?



Find areas of triangles and
quadrilaterals

Use The Geometer’s
Sket
chpad to explore
properties of figures.

Textbook:

Chapter 10

(Sections 10
-
1 to
10
-
6)

(7 Days)


Composition of
transformations

“Symmetry in
Motion”
Geometry to Go

p. 72


7

geometric figures in the coordinate
plane algebraically.

3.01 Describe transformations
(translation, reflec
tion, rotation, dilation)
of polygons in the coordinate plane in
simple algebraic terms.

Goal 1: The learner will perform
operations with real numbers to solve
problems.

1.03
Use length, area, and volume to
model and solve problems involving
probability.

Goal 2: The learner will use geometric
and algebraic properties of figures to
solve problems and write proofs.

2.04 Develop and apply properties of
solids to solve problems.

INVESTIGATING SURFACE AREA
AND VOLUME

How does surface area relate to volume?



Nets


How can you use the properties of solids to
connect the relationships between area and
volume?



Identify solid figures



Calculate area and volume


Textbook:

Chapter 11

(Secti
ons 11
-
1 to
11
-
6)

(7 Days)

Goal 2: The learner will use geometric
and algebraic properties of figures to
solve problems and write proofs.

2.03 Apply properties, definitions, and
theorems of two
-
dimensional figures to
solve problems and write proofs:

(a)
Triangles

(b) Quadrilaterals

(c) Other polygons

(d) Circles

2.04 Develop and apply properties of
solids to solve problems.

CONTINUING COORDINATE
GEOMETRY


Use The Geometer’s
p步瑣桰t搠瑯⁥d灬潲p
灲潰p牴楥猠潦⁦igu牥献



Coordinate Grid

Textbook:

Chapter 12

(
Sections 12
-
1 to
12
-
5)

(6 Days)

Goal 3: The learner will transform
geometric figures in the coordinate
plane algebraically.

3.01 Describe the transformation
(translation, reflection, rotation, dilation)
of polygons in the coordinate plane in
simple alge
braic terms.

3.02 Use matrix operations (addition,
INVESTIGATING LOCI AND
COORDINATE TRANSFORMATIONS

How do the coordinates of a point o
f a
polygon change after a transformation on the
coordinate plane?

Use The Geometer’s
p步瑣桰t搠瑯⁥d灬潲p
灲潰p牴楥猠潦⁦igu牥献


cer物猠r桥e氠l牯扬r洠m
⡓步瑣桰t搩

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-
ㄠ瑯N

-
㔩5

⠷⁄ay猩s


p異灬敭u湴n
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8

subtraction, multiplication, scalar
multiplication) to describe the
transformation of polygons in the
coordinate plane.


ADDITIONAL R
ECOMMENDED RESOURCES




Geometry To Go

, A Mathematics Handbook, Great Source Education Group, Houghton
-
Mifflin Company



Exploring Geometry With The Geometer’s Sketchpad
, Key Curriculum Press



Discovering Geometry
, Key Curriculum Press



Discovering Geometry Wit
h The Geometer’s Sketchpad
, Key Curriculum Press



Geometry Through The Circle
, Key Curriculum Press



Www. Nc.Geomconcepts.Com



Www.E
-
Zgeometry.Com


RECOMMENDED GRADING POLICY


10 %

Homework

10 %

Class work

10 %

Q
uizzes

70 %

Tests And Projects