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

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

Geometry
201
0
KEY ELEMENTS
CONTENT
(What Students should know)
PERFORMANCE TARGETS
(What Students should
be able to do
)
18
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

Geometry
201
0
KEY ELEMENTS
CONTENT
(What Students should know)
PERFORMANCE TARGETS
(What Students should
be able to do
)
19
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

Geometry
201
0
KEY ELEMENTS
CONTENT
(What Students should know)
PERFORMANCE TARGETS
(What Students should
be able to do
)
20
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

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
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