Common Core State Standards GEOMETRY

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Oct 10, 2013 (3 years and 8 months ago)

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Mathematics
-

Geometry

201
0

KEY ELEMENTS

CONTENT


(What Students should know)

PERFORMANCE TARGETS


(What Students should
be able to do
)




16

Common Core State Standards

GEOMETRY



Congruence


Experiment with transformations in the plane


1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined not
ions of point, line, distance
alon
g a line, and distance around a circular arc.


2. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as func
tions that take points in
the plane as inputs and give other points as outputs. Compa
re transformations that preserve distance and angle to those that do not (e.g.,
translation versus horizontal stretch).


3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto

itself.


4.

Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel li
nes, and line segments.


5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using,

e.g., graph paper, tracing paper, or geometry
software. Specify a sequence of transformations that will carry a given figure onto another.

Understand congruence in terms of rigid motions


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.


7. Use the definition of congruence in terms of rigid motions to show that t
wo triangles are congruent if and only if corresponding pairs of sides and
corresponding pairs of angles are congruent.


8. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of
rigid motio
ns.

Prove geometric theorems


9. Prove theorems about lines and angles.
Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior


Mathematics
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Geometry

201
0

KEY ELEMENTS

CONTENT


(What Students should know)

PERFORMANCE TARGETS


(What Students should
be able to do
)




17

angles are congruent and corresponding angles are congruent; points on a p
erpendicular bisector of a line segment are exactly those equidistant
from the segment’s endpoints.


10. Prove theorems about triangles.
Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are
congruen
t; 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.


11. Prove theorems about parallelograms.
Theorems include: opposite sides are congruent, opposite angl
es are congruent, the diagonals of a
parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Make geometric constructions


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 s
egment; and constructing a line parallel to a given line through a point not on the line.


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


Similarity, Right Triangles, & Trigonometry



Understand similarity i
n terms of similarity transformations


1. Verify experimentally the properties of dilations given by a center and a scale factor:


A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through
th
e center unchanged.


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


2. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar;
explain using simil
arity
transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proporti
onality of all
corresponding pairs of sides.



Mathematics
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Geometry

201
0

KEY ELEMENTS

CONTENT


(What Students should know)

PERFORMANCE TARGETS


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be able to do
)




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3. Use the properties of similarity transformations to establish the AA criterio
n for two triangles to be similar.

Prove theorems involving similarity


4. Prove theorems about triangles.
Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the
Pythagorean Theorem proved using

triangle similarity.


5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Define trigonometric ratios and solve problems involving right triangles


6. Understand that by similarity, side

ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for
acute angles.


7. Explain and use the relationship between the sine and cosine of complementary angles.


8. Use trigonometric ratios a
nd the Pythagorean Theorem to solve right triangles in applied problems.


Apply trigonometry to general triangles


9. (+) Derive the formula
A

= 1/2
ab

sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.


10. (+) Prove the Laws of Sines and Cosines and use them to solv
e problems.


11. (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non
-
right triangles (e.g., surveying
problems, resultant forces).


Circles


Understand and apply theorems about circles


1. Prove th
at all circles are similar.



Mathematics
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Geometry

201
0

KEY ELEMENTS

CONTENT


(What Students should know)

PERFORMANCE TARGETS


(What Students should
be able to do
)




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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 ci
rcle is perpendicular to the tangent where the radius intersects the circle.


3. Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscri
bed in a circle.


4. (+) Construct a tangent line from
a point outside a given circle to the circle.

Find arc lengths and areas of sectors of circles

5. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and def
ine the radian measure of the
angle
as the constant of proportionality; derive the formula for the area of a sector.


Expressing Geometric Properties with Equations

Translate between the geometric description and the equation for a conic section


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.


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


3. (+) Derive the equations of ellipses and hyperbolas gi
ven the foci, using the fact that the sum or difference of distances from the foci is constant.

Use coordinates to prove simple geometric theorems algebraically


4. Use coordinates to prove simple geometric theorems algebraically.
For example, prove or disp
rove 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).


5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equ
ation of a line parallel or
perpendicular to a given

line that passes through a given point).



Mathematics
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Geometry

201
0

KEY ELEMENTS

CONTENT


(What Students should know)

PERFORMANCE TARGETS


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


7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g.,
using the distance formula.



Geometric Measurement & Dimension

Explain volume formulas and use them to solve problems


1. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyra
mid, and cone.
Use dissection
argumen
ts, Cavalieri’s principle, and informal limit arguments.


2. (+) Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figu
res.


3. Use volume formulas for cylinders, pyramids, cones, and spheres to

solve problems.


Visualize relationships between two
-
dimensional and three
-
dimensional objects

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.

Modeling with Geometry

Apply geometric concepts in modeling situations

1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human tor
so as a cylinder).


2. Apply concepts of density based on

area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).


3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints o
r minimize cost; working with
typogr
aphic grid systems based on ratios).




Mathematics
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Geometry

201
0

KEY ELEMENTS

CONTENT


(What Students should know)

PERFORMANCE TARGETS


(What Students should
be able to do
)




21


ESSENTIALS OF GEOMETRY



Identify Points, Lines, and Planes



Use Segments and Congruence




Use Midpoint and Distance Formulas
























Name and sketch geometric figures



Apply segment postulate to identify co
ngruent
segment



Students will model points, lines, and planes using
foam trays and uncooked spaghetti. They will explore
intersections of lines, and planes.



Find midpoint of segments in the coordinate plane



Find lengths of segments in the coordinate plane


FOLD A SEGMENT BISECTOR

Geometry McDougal Littell P. 15

Students will draw a line segment AB on paper, fold the
paper so that the two points fall on top of each other,
label the point M and compare the segments AM and
MB, and AB.


MODIFICATIONS

Using Geom
eter’s Sketch
-
pad students will:



Construct Acute, Right, Obtuse, and Straight angles



Explore Protractor Postulate



Explore The Angle Addition Postulate





Describe Angles Pair Relationship



Classify Polygons





Use special angle relationships to find angle
m
easures.



Classify polygons



CONSTRUCT REGULAR POLYGONS



U
se the compass tool of the Geometer’s Sketchpad
to construct a circle and an inscribed square.


Using Geometer’s Sketch
-
pad students will:

1.

Construct various polygons; triangle, square,
pentagon, etc

2.

Measure sum of interior angles

3.

Develop a formula for sum of angles in a polygon of


Mathematics
-

Geometry

201
0

KEY ELEMENTS

CONTENT


(What Students should know)

PERFORMANCE TARGETS


(What Students should
be able to do
)




22

a given




number of sides



Perimeter, Circumference, and
Area



Students will be able to:




Find dimensions of a polygon



Find Perimeter



Find Circumference



Find Area



Usi
ng a Graphing Calculator students will:

1.

Construct different rectangles of area 36 square
units but of different dimensions.

2.

Plot the various dimensions that produces the
same area and make observations.

PARALLEL AND PERPENDICULAR LINES



Identify Pairs o
f Lines and Angles



Parallel Lines and Transversals



Prove Lines are Parallel



Find and Use Slopes of Lines



Prove theorems about Perpendicular
lines







INVESTIGATE SLOPES

Use Geometer’s Sketchpad to verify the equality of slopes
of parallel lines


Students

will be able to:



Identify angle pairs formed by three intersecting
lines



Use angles formed by parallel lines and transversals



Using
Geometer’s Sketch
-
pad,
Students will draw
two parallel lines and a transversal and explore the
relationship among angles fo
rmed.



Use angle relationships to prove that lines are
parallel



Mathematics
-

Geometry

201
0

KEY ELEMENTS

CONTENT


(What Students should know)

PERFORMANCE TARGETS


(What Students should
be able to do
)




23



Students will review key vocabulary and theorems



Solve algebraic problems on geometry concepts



Find and compare slopes of lines



Find equations of lines



Students will review key vocabulary and t
heorems



Write equations of parallel lines and graph them



Write equations of perpendicular lines and graph
them



Students will review key vocabulary and theorems



Apply theorems learned in section to solve
algebraic problems

CONGRUENT TRIANGLES



Apply Congru
ence and Triangles



Prove Triangles Congruent



Use two more methods to prove
congruence



Congruent triangles



Isosceles and Equilateral Triangles




Classify triangles by side and by angles



Find measures of angles algebraically



Understand congruence transformat
ions


Students will be able to:



Identify congruent figures



Use side lengths to prove triangles are congruent



Classify triangles by side and by angles



Find measures of angles algebraically



Classify triangles by side and by angles



Find measures of angles alg
ebraically


DISCOVERING ASA CONGRUENCE

Students will use tracing paper and straightedge to
investigate congruence of triangles by Angle
-
Side
-
Angle


COMPARING CONGRUENT TRIANGLES

Students will use ruler and protractor to construct two
congruent triangles an
d compare corresponding parts


Students will be able to:



Use theorems about isosceles and equilateral
triangles



Create an image congruent to a given triangle


INVESTIGATE SLIDES AND FLIPS

Students will investigate reflection and rotation on a


Mathematics
-

Geometry

201
0

KEY ELEMENTS

CONTENT


(What Students should know)

PERFORMANCE TARGETS


(What Students should
be able to do
)




24

coordinate ax
is.

RELATIONSHIPS WITHIN TRIANGLES



Midsegment Theorem and
Coordinate Proof



Perpendicular Bisectors











Angle Bisectors of Triangles
















INVESTIGATE SEGMENTS IN TRIANGLES

Students will use Geometer’s Sketchpad to investigate
whether or not t
he midsegments of a triangle relates to
the sides of a triangles


Students will be able to
:



Use properties of midsegments and write
coordinate proofs



Use the midsegment theorem to find lengths



Place figure in a coordinate plane



Use perpendicular bisectors
to solve problems


EXPLORING PERPENDICULAR BISECTORS

Students will use tracing paper and straightedge to
investigate the relationship between the points on a
perpendicular bisector of a segment and the endpoint of
that segment


EXPLORING THE INCENTER

Stude
nts will use tracing paper, straightedge, and compass
to explore the relationship between the incenter and the
sides of a triangle


Students will be able to:



Use angle bisectors to find distance relationships



Use medians and altitudes of triangles



Use the
angle bisector theorem



Use the concurrency of angle bisectors



Medians and Altitudes



Inequalities in a Triangle




INVESTIGATING MEDIANS AND ALTITUDES

Students will use Cardboards to investigate the relationship
between segments formed by the medi
ans of a triangle


Students will be able to:



Mathematics
-

Geometry

201
0

KEY ELEMENTS

CONTENT


(What Students should know)

PERFORMANCE TARGETS


(What Students should
be able to do
)




25



Use medians and altitudes of triangles



Find possible side lengths of a triangle



Use the centroid of a triangle



Find centroid of a triangle



Inequalities in two Triangles and
Indirect Proof



DISCOVERING THE HING
E THEOREM

Students will use tracing paper and straightedge to
investigate triangles with two congruent sides


Students will be able to:



Use inequalities to make comparisons in two
triangles



Use the hinge theorem and its converse



Write an indirect proof

SI
MILARITY



Ratios, Proportions, and the
Geometric Mean



Proportions to solve Geometry
Problems



Similar Polygons



Prove Triangles Similar by AA



Prove Triangles Similar by SSS and
SAS



INVESTIGATING THE CROO PRODUCTS PROPERTY

Students will investigate the cross

product property by
equating the products of means and extremes


Students will be able to:



Solve problems by writing and solving proportions



Use the extended ratios and simplify ratios



Find geometric means



INVESTIGATE PROPERTIES OF PROPORTIONS

Students
will rearrange numbers to create proportions


Students will be able to:



Use proportions to solve geometry problems



Use proportions to identify similar polygons



Use properties of proportions



Find the scale of a drawing



SIMILAR POLYGONS



Mathematics
-

Geometry

201
0

KEY ELEMENTS

CONTENT


(What Students should know)

PERFORMANCE TARGETS


(What Students should
be able to do
)




26

Students will use G
eometer’s Sketchpad to compare sides
and angles of a figure and its reduced version


Students will be able to:



Use proportions to identify similar polygons



Use the AA Similarity Postulate



DISCOVERING TRIANGLE SIMILARITY SHORTCUTS

Students will use straws

and tape to show that
corresponding sides of similar triangles are proportional


Students will be able to:



Use the SSS and SAS Similarity Theorems



Use the similarity postulate



Use indirect measurement



Use Proportionality Theorems



INVESTIGATE TRIANGLES
& CONGRUENCE

Students will use a graphing calculator to compare segment
lengths in triangles


Students will be able to:



Use proportions with a triangle or parallel lines



Find the length of a segment



Determine whether line segments are parallel



Similarity
Transformations



PERFORM SIMILARITY TRANSFORMAIONS

Students will use Geometer’s Sketchpad perform
transformations



Draw a dilation



Find a point on a dilation

RIGHT TRIANGLES AND TRIGONOMETRY



Apply the Pythagorean Theorem



PYTHAGOREAN THOEREM

Students wil
l use graph paper to explore the relationship
among sides of a right triangles




Solve problems on side lengths in right triangles



Mathematics
-

Geometry

201
0

KEY ELEMENTS

CONTENT


(What Students should know)

PERFORMANCE TARGETS


(What Students should
be able to do
)




27



Converse of the Pythagorean
Theorem



Similar Right Triangles



CONVERSE OF THE PYTHAGOREAN THEOREM

Students will use graphing
calculator to explore
relationship between sides and angles of a triangle


Students will be able to:



Use the converse of the Pythagorean theorem to
determine if a triangle is a right triangle



Use properties of the altitude of a right triangle



Solve problem
s on similar right triangles



Similar Right Triangles



Special Right Triangles



SIMILAR RIGHT TRIANGLES

Students will explore how geometric means are related to
the altitudes of a triangle


Students will be able to:



Use properties of the altitude of a rig
ht triangle



Use the relationships among the sides in special
right triangle



Apply the Tangent Ratio



RIGHT TRIANGLE RATIO

Students will use Geometer’s Sketchpad establish formulas
for the trigonometric ratios


Students will be able to:



Use the relationsh
ips among the sides in special
right triangle



Use the tangent ratio for indirect measurement



Sine and Cosine Ratios



APPLY SINE AND COSINE RATIOS

Students will use Geometer’s Sketchpad explore the
relationship between sides of a triangle


Students will b
e able to:



Use the sine and cosine ratios



Right Triangles



SOLVING REAL


WORLD PROBLEMS USING
TRIGONOMETRY

Students will use a calculator to find an angle measure in a
right triangle given two sides



Mathematics
-

Geometry

201
0

KEY ELEMENTS

CONTENT


(What Students should know)

PERFORMANCE TARGETS


(What Students should
be able to do
)




28


Students will be able to:



Use inverse tangent, sine,

and cosine ratios

QUADRILATERALS



Angle Measures in Polygons



INVESTIGATE ANGLE SUMS IN POLYGONS

Generator CD

Activity 8.1

Students will derive a formula for the sum of the measures
of the interior angles of a convex n
-
gon


Students will be able to:



F
ind angle measures in polygons



Find the sum of angle measures in a polygon



Find the number of sides of a polygon



Ties of Parallelograms



Show that a quadrilateral is a
parallelogram



INVESTIGATE PARALLELOGRAMS

Students will use Geometer’s Sketchpad to inv
estigate
some of the properties of parallelograms


Students will be able to:



Find angle and side measures in parallelograms



Use properties to identify parallelograms



Use the properties of a parallelogram



Find the intersection of diagonals



Properties of rh
ombuses, rectangles,
and squares



EXPLORING PROPERTIES OF RHOMBUSES

Students will explore the properties of a rhombus


Students will be able to:



Use properties of rhombuses, rectangles, and
squares



Use Properties of Trapezoids and Kites



Use properties of
special quadrilaterals



Classify special quadrilaterals



Properties of Trapezoids and Kites



Special Quadrilaterals



MIDSEGMENT OF A TRAPEZOID

Students will use Geometer’s Sketchpad explore the
properties of the midsegment of a trapezoid



Mathematics
-

Geometry

201
0

KEY ELEMENTS

CONTENT


(What Students should know)

PERFORMANCE TARGETS


(What Students should
be able to do
)




29


Students will be a
ble to:



Use Properties of Trapezoids and Kites



Identify special quadrilaterals



Use a coordinate plane


PROPERTIES OF TRANSFORMATIONS



Translate Figures and Use Vectors



COMPARING TRANSLATED POLYGONS

Students will use Geometer’s Sketchpad to investigate
wh
at happens to a triangle when a constant is added to its
x and y coordinates

Students will be able to:



Use a vector to translate a figure.



Translate a figure in coordinate plane



Write a rule for transformation



Properties of Matrices



INVESTIGATING MATRIX

ADDITION & TRANSFORMATIONS

Students will use Geometer’s Sketchpad to investigate the
effect matrix addition has on the coordinates of a triangle


Students will be able to:



Perform translations using matrix operations



Add and subtract matrices



Represent
a transformation using matrices



Perform reflections



REFLECTION IN THE PLANE

Students will use Geometer’s Sketchpad to explore the
relationship between the line of reflection and the segment
connecting a point and its image


Students will be able to:



Re
flect a figure in any given line



Graph reflection in horizontal and vertical lines



Use matrix multiplication to reflect polygons



Perform Rotations



EXPLORING ROTATIONS ABOUT THE ORIGIN

Students will use Geometer’s Sketchpad to explore
rotations about or
igin



Mathematics
-

Geometry

201
0

KEY ELEMENTS

CONTENT


(What Students should know)

PERFORMANCE TARGETS


(What Students should
be able to do
)




30


Students will be able to:



Rotate figures about a point



Rotate a figure using the coordinate rules



Use matrices to rotate a figure



Compositions of Transformations



DOUBLE REFLECTION

Students will use a graphing calculator to reflect a figure in
tw
o lines in a plane


Students will be able to:



Perform combinations of two or more
transformations



Find the image of a glide reflection



Find image of a composition



Identify Symmetry



Identify and Perform Dilations



INVESTIGATE DILATIONS

Students will use G
eometer’s Sketchpad to construct
dilation of a figure


Students will be able to:



Identify line and rotational symmetries of a figure



Use drawing tools and matrices to draw dilations



Identify line of symmetry



Identify rotational symmetry

PROPERTIES OF CIRC
LES



Properties of Tangents





EXPLORE TANGENT SEGMENTS


Students will use Geometer’s Sketchpad to explore how the
lengths of tangent segments are related


Students will be able to:



Use properties of a tangent to a circle



Identify special segments and line
s



Find lengths in circles in a coordinate plane



Find Arc Measures



Apply Properties of Chords



UNDERSTANDING CIRCLE VOCABULARY

Students will play a geometry vocabulary game




Mathematics
-

Geometry

201
0

KEY ELEMENTS

CONTENT


(What Students should know)

PERFORMANCE TARGETS


(What Students should
be able to do
)




31

Students will be able to:



Use angle measures to find arc measures



Use relati
onships of arcs and chords in a circle



Find measures of arcs



Identify congruent arcs




Use Inscribed Angles and Polygons



EXPLORE INSCRIBED ANGLES

Students will use Geometer’s Sketchpad to explore how
inscribed angles relate to central angles


Students wi
ll be able to:



Use inscribed angles of circles



Use circumscribed circles



Other Angle Relationships in Circles



Segment Lengths in Circles



Students will be able to:



Find the measures of angles inside or outside a
circle



Find segment lengths in circles



Fin
d the angle and the arc measures



Find the angle measure inside a circle



Write and Graph Equations of Circles



DETERMINING EQUATIONS OF CIRCLES

Students will use Geometer’s Sketchpad to derive the
equation of a circle


Students will be able to:

Write equa
tions of circles in the coordinate plane

MEASURING LENGTH AND AREA



Areas of Triangles and
Parallelograms



Areas of Trapezoids, Rhombuses,
and Kites



DETERMINE PRECISION AND ACCURACY

Students will use Geometer’s Sketchpad to explore the
measuring distance
s in precision


Students will be able to:



Find areas of triangles and parallelograms



Find areas of other types of quadrilaterals




Mathematics
-

Geometry

201
0

KEY ELEMENTS

CONTENT


(What Students should know)

PERFORMANCE TARGETS


(What Students should
be able to do
)




32



Perimeter and Area of Similar
Figures



AREA OF TRAPEZOIDS AND KITES

Students will use graph paper to explore the use of a
pa
rallelogram to find other areas



Students will be able to:



Find areas of other types of quadrilaterals



Use ratios to find areas of similar figures



Find the area of a quadrilateral



Find an area in the coordinate plane




Circumference and Arc Length



EXPLO
RE CIRCUMFERENCE

Students will explore the ratio of circumference to
diameter and establish a formula for finding the
circumference of a circle when given diameter


Students will be able to:



Find arc lengths and other measures



Use the formula for circumfer
ence



Use arc length to find measures



Areas of Circles and Sectors



AREAS OF CIRCLES AND SECTORS

Students will explore the area of circles and sectors


Students will be able to:



Find areas of circles and sectors of circles



Use the formula for area of a c
ircle



Find the area of sectors



Areas of Regular Polygons



FINDING THE AREA OF REGULAR POLYGONS

Students will establish an equation for the area of a regular
polygon


Students will be able to:



Find areas of regular polygons inscribed in circles



Find angle
s measures in a regular polygon



Mathematics
-

Geometry

201
0

KEY ELEMENTS

CONTENT


(What Students should know)

PERFORMANCE TARGETS


(What Students should
be able to do
)




33



Find the perimeter and area of a regular polygon



Geometric Probability



INVESTIGATE GEOMETRIC PROBABILITY

Students explore how theoretical and experimental
probabilities compare


Students will be able to:



Use lengths and
areas to find geometric
probabilities


SURFACE AREA AND VOLUME OF SOLIDS



Explore Solids



INVESTIGATE SOLIDS

Students will investigate what solids can be made using
congruent regular polygons


Students will be able to:



Identify Solids



Identify and name
polyhedra



Use euler’s theorem with platonic solids



Surface Area of Prism and Cylinders



Surface Area of Pyramids and Cones



INVESTIGATE SURFACE AREA

Students will explore how you can find the surface area of
a polyhedron


Students will be able to:



Find t
he surface areas of prisms and cylinders



Find the surface areas of pyramids and cones




Volume of Prisms and Cylinders



SURFACE AREAS OF PYRAMIDS AND CONES

Students will use Geometer’s Sketchpad to prove triangles
are congruent by Side
-
Side
-
Angle


Student
s will be able to:



Find the surface areas of pyramids and cones



Find the volume of prisms and cylinders



Find the area of a lateral face of a pyramid



Mathematics
-

Geometry

201
0

KEY ELEMENTS

CONTENT


(What Students should know)

PERFORMANCE TARGETS


(What Students should
be able to do
)




34




Volume of Pyramids and Cones



VOLUME OF PRISMS AND CYLINDERS

Students will derive a formula for finding
the volume of
Prisms and Cylinders


Students will be able to:



Find the volume of prisms and cylinders



Find the volume of pyramids and cones



Use volume of prism



Volume of Pyramids and Cones



Surface Area and Volume of Spheres



INVESTIGATE TRIANGLES & CONGR
UENCE

Students will explore the surface area of a pyramid


Students will be able to:



Find the volume of pyramids and cones



Find the surface

area and volume of spheres



Find the volume of a solid



Use trigonometry to find the volume of a cone




Explore Simila
r Solids



Surface Area and Volume of Spheres

Students will play a game on surface area and volume of
spheres


Students will be able to:



Find the surface

area and volume of spheres



Use properties of similar solids