Download Geometry CP Scope and Sequenc

Year at a Glance
First Semester
Geometry CP
Three Weeks
Topics/
Concepts
1st 3 weeks
Foundations
Vocabulary
2nd 3 weeks
Geometric Reasoning
Vocabulary
3rd 3 weeks
Lines and Planes
Vocabulary
4th 3 weeks
Triangles
Vocabulary
5th 3 weeks
More Triangles
Vocabulary
6th 3 weeks
Similar Triangles
Vocabulary
Mathematical Systems
Logical Reasoning
Parallel Lines and
Angles
Triangle Classification
Construction
Ratio and Proportion
Structure
Conjecture and
Justification
Congruence
Segments in a
Triangle
Similar Triangles
Measurement
Perpendicular Lines
and Angles
Applications
Applications
Applications
Resource:
HOLT
Geometry
Chapter 1
TEKS:
G1A, G2A, G3B, G7A,
G8A, G5C, G1B, G2B,
G7C, G8C
Lines in the Coordinate
Plane
Chapter 2
TEKS:
G3D, G3A, G3E,
G4A, G1A
Chapter 3
TEKS:
G9A, G3C, G1A, G8A,
G7B, G2A, G7A, G7C
Topics/
Concepts
Chapter 4
TEKS:
G1A, G9B, G2B,
G10B, G2A
Vocabulary
Vocabulary
Vocabulary
4th 3 weeks
Space
Measurement
Vocabulary
Pythagorean Theorem
and the Converse
Polygons
Perimeter and
Circumference
2-D/3-D
Representation
Area
Surface Area
1st 3 weeks
Right Triangles
Ratios in Right
Triangles
Special Right Triangles
Trigonometry
Applications
Resource:
HOLT
Geometry
Applications
Chapter 5
TEKS:
G3B, G2A, G7B, G9B,
G8C, G5D
Chapter 7
TEKS:
G11B, G5B, G11A,
G11D
Second Semester
Geometry CP
Three Weeks
Applications
Triangle Inequalities
Chapter 8
TEKS:
G11C, G2A, G7A,
G11A
2nd 3 weeks
Polygons
Special Types of
Quadrilaterals
rd
3 3 weeks
Planar Measurement
5th 3 weeks
Transformation
6th 3 weeks
Circles
Vocabulary
Vocabulary
Isometrics
Angles and Segments
Related to Circles
Dilations
Applications
Applications
Similarity of Polygons
Applications
Applications
Chapter 6
TEKS:
G2A, G5B, G9B, G3B
Volume
Applications
Chapter 9
TEKS:
G5A, G8A, G7A,
G11D
Chapter 10
TEKS:
G6A, G9D, G6B, G7C,
G8D, G11D, G1C
Chapter 12
TEKS:
G10A, G5C, G11A
Chapter 11
TEKS:
G9C, G1A, G8B, G5B,
G2A, G9C, G5A, G2B
First Semester
First Semester, 1st and 3rd 3 Weeks
Structure of a Mathematical System (Approximate Time: 3 weeks)
ELOs
TEKS
Topics (not in sequential order)
The student will:
-identify and model points, lines, and
planes.
-identify collinear and coplanar
points and intersecting lines and
planes in space.
-find segment and angle measures
using segment and angle postulates.
-describe relationships between
segments and angles (congruent,
midpoint, segment bisector, angle
bisector, perpendicular) and use the
relationships to solve problems.
-identify special pairs of angles
(vertical, linear pair, complementary,
supplementary) and use their
relationships to solve problems.
-develop midpoint and distance
formulas using the coordinate plane.
G1A
G2A
G3B
G7A
G8A
G5C
G1B
G2B
G7C
G8C
G9A
G3C
G7B
Mathematical Systems
Investigate the process and purpose of developing a
geometric system
Structure
Analyze the structure of a mathematical system,
connecting definitions, algebraic properties, postulates,
theorems, and corollaries
Lines and Planes
 Investigate properties of parallel and perpendicular
lines using exploration and concrete models
 Use coordinate systems by:
 deriving and using formulas to evaluate slope,
distance, and midpoint;
 evaluating slope, distance, and midpoint;
 investigating properties of lines using their slopes
and equations
Measurement
Measure segments and angles concretely, numerically,
and analytically
Suggested
Resources
Holt Geometry
Chapters 1 and
3
Suggested
Assessments
Teacher
Assessments
Geometry
Assessments
TAKS
Objectives
TAKS Obj. 6
TAKS Obj. 7
TAKS Obj. 8
First Semester, 2nd 3 Weeks
Logical Reasoning and Conjecture (Approximate Time: 3 weeks)
ELOs
TEKS
Topics (not in sequential order)
The student will:
-make conjectures based on inductive
reasoning.
-analyze statements in if-then form
(conditional statements).
-write the converse, inverse, and
contra positive of a conditional
statement and determine the truth
value of the statements.
-use properties of algebra and
congruence to make and justify
conclusions.
-use deductive reasoning with
different styles of proofs to verify
segment and angle relationships.
G3D
G3A
G3E
G4A
G1A
Logical Reasoning
Apply reasoning and logic by:
 testing validity of a conditional statement, its converse,
inverse, and contra positive,
 using inductive reasoning to formulate a conjecture,
 using deductive reasoning to prove a statement.,
 using logical reasoning to prove statements are true and
finding counter examples to disprove statements that
are false, and
 constructing and justifying statements about geometric
figures and their properties
Conjecture and Justifications
 Formulate conjectures based on investigations and
explorations
 Determine the validity of conjectures by using a
variety of approaches (coordinate, axiomatic) to
provide justification
Suggested
Resources
Chapter 2
Suggested
Assessments
Teacher
Assessments
Geometry
Resources
Geometry
Assessments
Holt Geometry
TAKS
Objectives
TAKS Obj. 2
TAKS Obj. 3
TAKS Obj. 6
TAKS Obj. 7
TAKS Obj. 8
First Semester, 4th 3 Weeks
Triangles (Approximate Time: 3 weeks)
ELOs
TEKS
The student will:
-identify and classify triangles by
side and angle measures.
-determine the relationships among
the measures of the interior and
exterior angles of a triangle and
apply these relationships.
-identify and use properties of
isosceles and equilateral triangles.
-identify congruent triangles and
their corresponding parts.
-identify methods (SSS, SAS, ASA,
AAS, HL) of proving triangles
congruent.
-find missing sides of triangles and
other figures based on congruence
relationships.
-use deductive reasoning to prove
corresponding parts of congruent
triangles congruent.
-use triangle congruence to solve
problems in real-life situations.
G1A
G9B
G2B
G10B
G2A
Topics (not in sequential order)
Suggested
Resources
Triangle Classification
 Classify triangles by angle and side measures
 Validate classification of triangles by using a variety
of approaches (coordinate, axiomatic) to provide
justification
Holt Geometry
Congruence
 Investigate properties of congruent triangles
 Construct statements related to triangle congruence
relationships
 Determine necessary and sufficient conditions in
order for triangles to be congruent
 Use logical reasoning to justify triangle congruence
from a variety of perspectives
 Formulate and test conjectures about the properties of
equilateral, equiangular, isosceles, and right triangles
based on explorations and concrete models
 Apply properties of congruent triangles to solve
meaningful problems by modeling, representing, and
analyzing relationships
Chapter 4
Suggested
Assessments
Teacher
Assessments
Geometry
Resources
Geometry
Assessments
TAKS
Objectives
TAKS Obj. 6
TAKS Obj. 7
TAKS Obj. 8
TAKS Obj. 10
First Semester, 5th 3 Weeks
Triangles (Approximate Time: 3 weeks)
ELOs
TEKS
The student will:
-identify and use properties of
perpendicular bisectors and angle
bisectors.
-identify special segments (angle
bisectors, perpendicular bisectors,
medians, altitudes, midsegments) of
a triangle, determine their
relationships and apply those
relationships to solve problems.
-recognize and apply properties of
inequalities to the relationships
between the sides and angles of a
triangle.
-recognize and apply properties of
inequalities between the sides and
angles of two triangles
G3B
G2A
G7B
G9B
G8C
G5D
Topics (not in sequential order)
Suggested
Resources
Construction
 Use a variety of techniques and tools (concrete,
graphical, technological) to recreate geometric
figures based on a given set of information
 Validate construction of geometric figures by using a
logical reasoning and a variety of approaches
(coordinate, axiomatic) to provide justification
Holt Geometry
Special Segments in a Triangle
 Identify bisectors, medians, altitudes and
midsegments of triangles
 Use a variety of techniques and tools to construct
special segments in triangles
 Identify points of concurrency for bisectors, medians,
and altitudes (circumcenter, incenter, centroid,
orthocenter)
 Make conjectures about the properties and
relationships of special segments and points of
concurrency in triangles
 Use logical reasoning to justify these properties from
a variety of perspectives
 Apply the properties of special segments and points
of concurrency to solve meaningful problems by
modeling, representing, and analyzing relationships
Triangle Inequalities
 Investigate situations involving inequalities within
and among triangles
 Compare and order sides and angles within one
triangle or among several triangles
 Apply triangle inequality properties to solve
meaningful problems by modeling, representing, and
analyzing relationships
Chapter 5
Suggested
Assessments
Teacher
Assessments
Geometry
Resources
Geometry
Assessments
TAKS
Objectives
TAKS Obj. 6
TAKS Obj. 7
TAKS Obj. 8
TAKS Obj. 10
First Semester, 6th 3 Weeks
Polygons (Approximate Time: 3 weeks)
ELOs
TEKS
The student will:
-compute ratios and use proportions
to solve problems.
-solve percent and probability
problems.
-identify the conditions that ensure
two polygons are similar.
-use properties of similar polygons to
solve problems.
-recognize the conditions that ensure
two triangles are similar.
-use similar triangles to solve reallife problems.
-identify proportional parts of a
triangle and use them to solve
problems.
-recognize and use proportional
relationships of perimeters and other
corresponding segments of similar
triangles.
G11B
G5B
G11A
G11D
Topics (not in sequential order)
Suggested
Resources
Ratio and Proportion
 Identify proportional and non-proportional
relationships in problem situations
 Use ratios as scale factors for similar figures
Holt Geometry
Similar Triangles
 Investigate properties of similar triangles
 Construct statements related to triangle similarity
relationships
 Determine necessary and sufficient conditions in
order for triangles to be similar
 Use logical reasoning to justify triangle similarity
from a variety of perspectives
 Apply properties of similar triangles to solve
meaningful problems by modeling, representing, and
analyzing relationships
Chapter 7
Suggested
Assessments
Teacher
Assessments
Geometry
Resources
Geometry
Assessments
TAKS
Objectives
TAKS Obj. 6
TAKS Obj. 7
TAKS Obj. 8
TAKS Obj. 9
TAKS Obj. 10
Second Semester
Second Semester, 1st 3 Weeks
Similar Triangles (Approximate Time: 3 weeks)
ELOs
TEKS
Topics (not in sequential order)
The student will:
-identify the geometric mean of two
numbers.
-solve problems involving
relationships between parts of a right
triangle and the altitude to the
hypotenuse.
-use the Pythagorean Theorem and
its converse to solve problems.
-use the Pythagorean theorem to
classify a triangle as acute, right, or
obtuse.
-identify a pattern in the side lengths
of special right triangles (45-4590, 30-60-90) and use special
right triangles to solve problems.
-find trigonometric ratios (sine,
cosine, tangent) using right triangles
and solve problems using these
trigonometric ratios.
-solve problems involving angles of
elevation and depression.
G11C
G2A
G7A
G11A
Pythagorean Theorem
 Review the simplification of and operations with
radical numbers
 Derive, extend and use the Pythagorean Theorem in
problem situations
 Apply the Pythagorean Theorem to investigate
Pythagorean Triples
 Apply the Converse of the Pythagorean Theorem to
determine, with justification, if a triangle is a right
triangle
Ratios in Right Triangles
 Apply the definition of geometric mean in situations
involving an altitude drawn to the hypotenuse of a
right triangle
Special Right Triangles (30-60-90 and 45-45-90)
 Investigate segment relationships in special right
triangles
 Derive statements defining segment relationships in
special right triangles
 Apply properties of special right triangles to solve
meaningful problems by modeling, representing, and
analyzing relationships
Trigonometry
 Use segment ratios to apply the definitions of sine,
cosine, and tangent
 Determine segment lengths and angle measures using
the trigonometric ratios sine, cosine, and tangent
 Identify angles of elevation or depression using
trigonometric ratios
Apply trigonometric ratios to solve meaningful problems
involving right triangle relationships
Suggested
Resources
Chapter 8
Suggested
Assessments
Teacher
Assessments
Geometry
Resources
Geometry
Assessments
Holt Geometry
TAKS
Objectives
TAKS Obj. 6
TAKS Obj. 7
TAKS Obj. 8
TAKS Obj. 9
TAKS Obj. 10
Second Semester, 2nd 3 Weeks
Right Triangles (Approximate Time: 3 weeks)
ELOs
TEKS
Topics (not in sequential order)
The student will:
-identify, name, and classify
polygons.
-find measures of interior and
exterior angles of polygons.
-recognize and apply properties of
the sides and angles of
parallelograms.
-use properties of parallelograms to
solve problems.
-recognize the conditions that ensure
a quadrilateral is a parallelogram.
-identify special
parallelograms(rectangle, rhombus,
square), identify their properties,
and apply the properties to solve
problems.
-recognize and apply properties of
trapezoids and special trapezoids.
-recognize the conditions that ensure
polygons are congruent.
G2A
G5B
G9B
G3B
Polygons
 Use appropriate terminology to identify polygons
based on the number of their sides or angles.
 Use a variety of methods to investigate the interior
and exterior angle relationships of polygons
 Make and justify conjectures about component parts
of polygons
 Investigate necessary conditions for polygons to be
identified as “regular”
 Make and justify conjectures about component parts
of regular polygons
 Use properties of polygons to make connections
between mathematics and the real world
Special Types of Quadrilaterals
 Use a variety of methods to investigate relationships
and make and justify conjectures about angles and
segments in a trapezoid
 Use a variety of methods to investigate relationships
and make and justify conjectures about angles and
segments in a kite
 Use a variety of methods to investigate relationships
and make and justify conjectures about the
component parts of a parallelogram
 Use the properties of parallelograms and the
definitions for rhombus, rectangle, and square to
investigate their related properties
 Make and justify conjectures about properties of
rhombi, rectangles, and squares
Similarity of Polygons
 Extend properties of similar triangles to investigate
properties of similar polygons
Apply these similarity properties to make connections
between mathematics and the real world
Suggested
Resources
Chapter 6
Suggested
Assessments
Teacher
Assessments
Geometry
Resources
Geometry
Assessments
Holt Geometry
TAKS
Objectives
TAKS Obj. 6
TAKS Obj. 7
TAKS Obj. 8
TAKS Obj. 9
TAKS Obj. 10
Second Semester, 3rd 3 Weeks
Perimeter and Area (Approximate Time: 3 weeks)
ELOs
TEKS
Topics (not in sequential order)
The student will:
-find perimeters and areas of
triangles and quadrilaterals
(including rectangles, squares,
parallelograms, trapezoids, rhombi,
and other quadrilaterals).
-identify regular polygons and find
their perimeters and areas.
-find circumference and area of a
circle and use them to find the length
of an arc or the area of a sector.
-find perimeters and areas of
composite figures.
-identify properties of areas of
similar polygons and use the
relationships to solve problems.
G5A
G8A
G7A
G11D
Perimeter and Circumference
 Use patterns and algebraic reasoning to derive
formulas for finding the perimeter of polygons and
the circumference of circles
 Apply formulas for perimeter and circumference to
make connections between mathematics and the real
world
 Use the formula for circumference of a circle and
proportional reasoning to determine arc lengths of
circles
 Use a variety of methods to investigate the
relationship between perimeters of similar geometric
figures
 Make and justify a conjecture describing the
proportionality of perimeters of similar figures
Area
 Use patterns and algebraic reasoning to derive
formulas for finding the area of polygons and circles
 Apply formulas for area to make connections
between mathematics and the real world
 Use the formulas for area of circles and triangles with
proportional reasoning to determine area of sectors
and segments of circles
 Use a variety of methods to investigate the
relationship between areas of similar geometric
figures
 Make and justify a conjecture describing the
proportionality of areas of similar figures
Suggested
Resources
Chapter 9
Suggested
Assessments
Teacher
Assessments
Geometry
Resources
Geometry
Assessments
Holt Geometry
TAKS
Objectives
TAKS Obj. 6
TAKS Obj. 7
TAKS Obj. 8
TAKS Obj. 9
TAKS Obj. 10
Second Semester, 4th 3 Weeks
Surface Area and Volume (Approximate Time: 3 weeks)
ELOs
TEKS
Topics (not in sequential order)
The student will:
-relate nets to different solids.
-identify three dimensional figures,
recognize different views of threedimensional figures, and investigate
cross sections of three-dimensional
figures.
-find surface areas of prisms,
pyramids, cylinders, cones, and
spheres.
-use surface areas to solve problems.
-find volumes of prisms, pyramids,
cylinders, cones, and spheres.
-use volumes to solve problems.
-identify properties of surface areas
and volumes of similar figures and
use the relationships to solve
problems.
G6A
G9D
G6B
G7C
G8D
G11D
G1C
2-D/3-D Representation
 Use concrete and pictorial representations to identify
three-dimensional objects such as prisms, cylinders,
pyramids, cones, cylinders, and composites of these
figures
 Use concrete objects, isometric and orthographic
paper, drawing tools, and/or technology to represent
three dimensional geometric figures
 Analyze, describe, and draw the intersection of a
plane with three-dimensional geometric figures
 Draw nets of three-dimensional objects and draw
three dimensional views of objects using their nets
Surface Area
 Make and justify conjectures about surface area using
concrete objects, measuring tools, patterns, and
algebraic reasoning
 Derive formulas for the surface area of various solid
geometric figures using area formulas for twodimensional figures
 Apply formulas for surface area to make connections
between mathematics and the real world
Volume
 Make and justify conjectures about volume using
concrete objects, measuring tools, patterns, and
algebraic reasoning
 Use formulas to find volume of various solid
geometric figures and composites of those figures
 Apply formulas for volume to make connections
between mathematics and the real world
 Use a variety of methods to investigate the
relationship between volumes of similar threedimensional geometric figures
 Make and justify a conjecture describing the
proportionality of volumes of similar threedimensional geometric figures
Suggested
Resources
Chapter 10
Suggested
Assessments
Teacher
Assessments
Geometry
Resources
Geometry
Assessments
Holt Geometry
TAKS
Objectives
TAKS Obj. 6
TAKS Obj. 7
TAKS Obj. 8
TAKS Obj. 9
TAKS Obj. 10
Second Semester, 5tht 3 Weeks
Transformations (Approximate Time: 3 weeks)
ELOs
TEKS
Topics (not in sequential order)
The student will:
-identify translation, reflection,
rotation, and dilation
transformations.
-use properties of reflections to find
reflection images and relate
reflections and line symmetry.
-use properties of rotations to find
rotation images and identify figures
with rotational symmetry.
-use properties of translations to find
translation images.
-use algebra notation to define
translations, reflections, and
rotations.
-identify tessellations.
-use compositions of transformations
and identify their properties.
-identify, use properties of, and
determine the scale factor of
dilations.
G10A
G5C
G11A
Isometrics
 Investigate the congruence transformations of
reflection, rotation, and translation of geometric
figures concretely and with technology
 Use coordinates to investigate reflection, rotation,
and translation of geometric figures, using
technology when appropriate
 Use patterns to derive symbolic representations of
geometric transformations
 Make conjectures about congruence transformations
of geometric figures and determine their validity
 Investigate composition of congruence
transformations, including tessellations, concretely
and symbolically
 Apply the properties of congruence transformations
to make connections between mathematics and the
real world
Dilations
 Use a center of dilation and scale factors to
investigate dilation of geometric figures using
appropriate concrete, coordinate and technological
methods
 Extend properties of similar figures, scale factors and
ratios to investigate properties of dilated geometric
figures analytically
 Make conjectures about dilated geometric figures and
determine their validity
 Apply similarity properties to dilated geometric
figures to make connections between mathematics
and the real world
Suggested
Resources
Chapter 12
Suggested
Assessments
Teacher
Assessments
Geometry
Resources
Geometry
Assessments
Holt Geometry
TAKS
Objectives
TAKS Obj. 6
TAKS Obj. 7
TAKS Obj. 8
TAKS Obj. 9
TAKS Obj. 10
Second Semester, 6th 3 Weeks
Circles (Approximate Time: 3 weeks)
ELOs
TEKS
The student will:
-identify and use parts of circles.
-recognize major arcs, minor arcs,
semicircles, and central angles, find
their measures and use their
measures to solve problems.
-recognize and use relationships
between arcs and chords to solve
problems.
-recognize inscribed angles and use
their properties to solve problems
including inscribed polygons.
-identify and use properties of
tangents to solve problems including
circumscribed polygons.
-find measures of angles formed by
segments or lines intersecting on a
circle, inside a circle, or outside a
circle (chords, secants, tangents).
-determine the equation of a circle.
G9C
G1A
G8B
G5B
G2A
G9C
G5A
G2B
Topics (not in sequential order)
Suggested
Resources
Chapter 11
Suggested
Assessments
Teacher
Assessments
Angles and Segments Related to Circles
 Describe and identify, using appropriate geometric
terms, the lines and segments that intersect circles
 Describe and identify, using appropriate geometric
terms, the angles formed by the intersection of lines
or segments when the intersection occurs in the
interior, exterior or on a circle
 Use exploration, concrete objects, drawing and
measuring tools, technology, patterns, and algebraic
reasoning to determine relationships between angles
and segments with circles
 Make and justify conjectures to describe angle and
segment relationships in circle situations
 Use symbolic notation to derive formulas describing
angle and segment relationships in circle situations
 Apply formulas to make connections between
mathematics and the real world
Holt Geometry
Geometry
Resources
Geometry
Assessments
TAKS
Objectives
TAKS Obj. 6
TAKS Obj. 7
TAKS Obj. 8
TAKS Obj. 9
TAKS Obj. 10