Download TEKS Content Topics

Geometry Year-at-a-Glance
Leander ISD
2nd six weeks
1st six weeks
2 weeks
Content Topics
Essential
Units of
Study
2 weeks
2 weeks
01
02
03 Parallel and
Essentials Reasoning Perpendicular
of Geometry and Proof
Lines
Points,
lines,
planes,
coplanar,
collinear,
segment
addition
postulate,
midpoint
and
distance
formulas.
Angle pair
relationship
s. Angle
addition
postulate.
Focus
G.1A,
G.7AC
Conjectures
from
patterns,
inductive
reasoning,
conditional
statements,
converse,
inverse,
contrapositi
ve,
deductive
reasoning.
Proofs and
angle
relationship
s.
Focus
G.1A,
G.3ACDE
Pairs of lines
and angles,
parallel lines
and
transversal,
def of
corresponding
, alternate
interior
angles, etc..,
perpendicular
lines, write
and graph
equations of
lines.
5 weeks
04
Triangles
3rd six weeks
3 weeks
06
05 Similarity Transformat
ions
Ratios,
Classifying
Translation,
proportions, reflections
triangles,
scale.
SSS,
on the
Similar
SAS,HL,
coordinate
ASA, &AAS, polygons,
plane.
proportionali Rotations
isosceles,
equilateral, ty
about origin
perpendicula theorems. or vertex of
r bisectors, Dilations
a figure.
and scale
angle
Line and
factor.
bisectors,
rotational
Similarity
medians,
symmetry.
transformati
altitudes,
inequalities in ons.
a triangle.
Focus
Focus G.7AB, Focus
G.9A
G.2A, G.3E, G.5B,
G.7B, G.10B G.11AB
TEKS
Support
Support
Support
G.1B, G.2B G.1B, G.2B, G.2B,G.4A,
G.3B
G.5A
Metal Tag
Geometry Assessment
Resources
McDougal
Text
Resources
1.1. to 1.5
Connjecture What's My Line
as Discovery Assessment
and Proof as
Explanantion
2.1, 2.2,
2.4, 2.3,
2.5 to 2.7
3.1 to 3.3,
3.6, 3.4, 3.5
2 weeks
Focus
G.5C,
G.10A,
G.11A
2007-08
4th six weeks
4 weeks
3 weeks
3 weeks
07 Right
Triangles
08
Quadrilaterals
09
Measuring
Length and Area
Angle
Radicals
measures in
review,
Pythagorean polygons.
Classifying
Thm,
Pythagoren polygons,
convex,
triples,
converse of concave,
Pyth Thm, 30- regular.
60-90, 45-45- Properties of
parallelogram
90, right
triangle trig. s, rhombuses,
rectangles,
squares,
trapezoids.
Focus
G.2A, G.5D,
G.8C,
G.11BC
Support
Support
Support
Support
G.2B, G.4A, G.2B, G.4A, G.4A, G.7A G.2B,G.4A,
G.5A
G.5AB
G.5A
Congruent
Triangles
Assessment
4.1 to 4.8
and
5.1 to 5.6
Focus
G.2A, G.5B,
G.9B
6th six
weeks
5th six weeks
3 weeks
3 weeks
10
Surface
11
Area and
Properties of
Volume of
Circles
Solids
Area of
triangles,
parallelograms,
trapezoids,
rhombuses,
regular
polygons.
Circumference,
arc length,
areas of circles
and sectors.
Effect of
dimension
changes.
Geometric
probability.
Surface
area, volume
of prisms,
cylinders,
pyramids,
cones,
spheres.
Include nets,
lateral and
total area,
composite
solids,
spherical
geometry.
Tangents ,
chords,
secants, arc
measures,
minor and
major arcs,
central
angles,
inscribed
angles,
equations
and graphs of
circles.
Focus
G.5B, G.8A,
G.9B, G.11D
Focus
G.1C,
G.5B,G.6AB
C, G.8BD,
G.9D,G.11D
Support
G.2B
Focus
G.5B, G.7B,
G.8AB, G.9C
Support G.2B, Support
G.2B, G.7A
G.4A
Support
G.2B, G.4A,
G.5A
Ancient Ruins Living Room Sightseeing
Assessment Transformatio Walk
Assessment
ns
Assessment
6.1 to 6.3,
6.6, 6.7,
9.1 and
9.3 to 9.6
7.1 to 7.7
8.1 to 8.6
11.1, 11.2, 11.4,
12.1 to 12.6
11.6, 11.5, 11.7
10.1 to 10.7
7 Aug 2007
Geometry Essential Units of Study 2007-08
01 EUS - Essentials of Geometry (2 Weeks)
Focus TEKS
Content Description
(G.1) Geometric structure: The student understands the
structure of, and relationships within, an axiomatic system.
The student is expected to:
(A) develop an awareness of the structure of a mathematical
system, connecting definitions, postulates, logical
reasoning, and theorems.
Identify points, lines , and planes and become familiar with the notation and
sketches to describe them. Know coplanar and collinnear.
1.1
Use segment addition postulates to identify congruent segments.
1.2
Find lengths of segments in the coordinate plane. Also use segment
bisector/midpoints to solve for lengths.
1.3
Name, measure, and classify angles. Understand the Angle addition
Postulate and angle bisectors.
1.4
Use special angle relationships like complementary, supplementary, and
vertical to find angle measures.
1.5
Support TEKS
(G.7) Dimensionality and the geometry of location: The
student understands that coordinate systems provide
convenient and efficient ways of representing geometric
figures and uses them accordingly. The student is expected
to:
(A) use one- and two-dimensional coordinate systems to
represent points, lines, ray, line segments, and figures.
(TAKS 7)
(C) derive and use formulas involving length, slope, and
midpoint. (TAKS 7)
Textbook
Key Vocabulary
- indefined term (points,
(G.1) Geometric structure: The student understands the structure of, and relationships within, an axiomatic system. The student lines, plane)
is expected to:
- defined terms
(B) recognize the historical development of geometric systems and know mathematics is developed for a variety of purposes.
- line segment
- endpoints
(G.2) Geometric structure: analyzes geometric relationships in order to make and verify conjectures.. The student is expected to:
- rays
(B) make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the
- opposite rays
conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.
- postulate, axiom
- congruent segments
- midpoint
- segment bisector
- acute, right, obtuse
- straight angles
- congruent angles
- angle bisector
- linear pair
- vertical angles
Resources
Common Assessment
Metal Tag Assessment
Aug 7, 2007
Geometry Essential Units of Study 2007-08
02 EUS - Reasoning and Proof (2 Weeks)
Focus TEKS
(G.1) Geometric structure: The student understands the
structure of, and relationships within, an axiomatic system.
The student is expected to:
(A) develop an awareness of the structure of a mathematical
system, connecting definitions, postulates, logical
reasoning, and theorems.
Support TEKS
(G.3) Geometric structure: applies logical reasoning to
justify and prove mathematical statements. The student is
expected to:
(A) determine the validity of a conditional statement, its
converse, inverse, and contrapositive.
(C) use logical reasoning to prove statements are true and
find counter examples to disprove statements that are false.
(D) use inductive reasoning to formulate a conjecture.
(E) use deductive reasoning to prove a statement.
Content Description
Textbook
Describe patterns and use inductive reasoning to make conjectures
2.1
Write definitions as conditional statements. Also include converse, inverse,
and contrapositive.
2.2
Use postulates involving points, lines, and planes.
2.4
Use deductive reasoning to form a logical argument. ( This is the beginning
of the proof section.)
2.3
Use algebraic properties in logical arguments. "Algebra Proofs"
2.5
Write proofs using geometric theorems such as the segment addition
property". Begin with fill in the blank.
2.6
Use properties of special pairs of angles (supplementary, complementary,
linear pair, vertical angles.)
2.7
(G.1) Geometric structure: The student understands the structure of, and relationships within, an axiomatic system. The student
Key Vocabulary
is expected to:
- conjecture
(B) recognize the historical development of geometric systems and know mathematics is developed for a variety of purposes.
- inductive reasoning
- counterexample
(G.2) Geometric structure: analyzes geometric relationships in order to make and verify conjectures.. The student is expected to: - conditional statement
(B) make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the
- converse
conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.
- inverse
- contrapositive
(G.3) Geometric structure: applies logical reasoning to justify and prove mathematical statements. The student is expected to:
- if-then form
(B) Construct and justify statements about geometric figures and their properties
- hypothesis
- conclusion
- negation
- equivalent statements
- if and only if (biconditional
statement)
- deductive reasoning
- proof
- two-column proof
- theorem
Resources
Common Assessment
Conjecture as Discovery
and Proof as
Explanantion Assessment
Aug 7, 2007
Geometry Essential Units of Study 2007-008
03 EUS - Parallel and Perpendicular Lines (2 Weeks)
Focus TEKS
Content Description
(G.7) Dimensionality and the geometry of location: The
student understands that coordinate systems provide
convenient and efficient ways of representing geometric
figures and uses them accordingly. The student is expected
to:
(A) use one- and two-dimensional coordinate systems to
represent points, lines, ray, line segments, and figures.
(TAKS 7)
(B) Use slopes and equations of lines to investigate
geometric relationships, including parallel lines,
perpendicular lines, and special segments of triangles and
other polygons. (TAKS 7)
Identify angle pairs formed by three intersecting lines. Include definitions of
corresponding angles, alternate interior and exterior angles, same side
interior and exterior.
3.1
Use angles formed by parallel lines and transversals.
3.2
Use angle relationships to prove that lines are parallel
3.3
Prove Theorems about perpendicular lines. (optional?)
3.6
Find and compare slopes of lines including the relationship between parallel
and perpendicular lines.
3.4
Support TEKS
(G.9) Congruence and the geometry of size: analyzes
properties and describes relationships in geometric figures. Write and graph the equations of lines
The student is expected to:
(A) formulate and test conjectures about the properties of
parallel and perpendicular lines based on explorations and
concrete models.
Textbook
Resources
3.5
(G.2) Geometric structure: analyzes geometric relationships in order to make and verify conjectures.. The student is expected to:
Vocabulary
(B) make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the
- parallel lines
conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.
- skew lines
- parallel planes
(G.4) Geometric structure: uses a variety of representations to describe geometric relationships and solve problems. The student - transversal
is expected to :
- corresponding angles
(A) select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems. (TAKS 6). - alternate interior angles
- alternate exterior angles
(G.5) Geometric patterns: uses a variety of representations to describe geometric relationships and solve problems. The student is - consecutive interior angles
expected to:
- paragraph proof
(A) use numeric and geometric patterns to develop algebraic expressions representing geometric properties.
- slope-intercept form
- standard form
Common Assessment
What's My Line
Assessment
Aug 7, 2007
Geometry Essential Units of Study 2007-08
04 EUS - Triangles (5 Weeks)
Focus TEKS
(G.2) Geometric structure: analyzes geometric relationships
in order to make and verify conjectures.. The student is
expected to:
(A) use constructions to explore attributes of geometric
figures and to make conjectures about geometric
relationships.
Content Description
4.1
Identify congruent figures. Use CPCTC.
4.2
4.3
4.4
4.5
4.6
4.7
Use side lengths to prove triangles congruent. SSS
Use side lengths and angles to prove congruence. SAS & HL
Use angles and side lengths to prove congruence. ASA & AAS
(G.3) Geometric structure: applies logical reasoning to
justify and prove mathematical statements. The student is
expected to:
(E) use deductive reasoning to prove a statement
Use congruent triangles to prove corresponding parts congruent. CPCTC
(G.7) Dimensionality and the geometry of location:
understands that coordinate systems provide convenient
and efficient ways of representing geometric figures and
uses them accordingly. The student is expected to:
(B) use slopes and equations of lines to investigate
geometric relationships, including parallel lines,
perpendicular lines, and special segments of triangles and
other polygons. (TAKS 7)
Use properties of midsegments and write coordinate proofs
Support TEKS
(G.10) Congruence and the geometry of size: applies the
concept of congruence to justify properties of figures and
solve problems. The student is expected to:
(B) justify and apply triangle congruence relationships.
Textbook
Classify triangles by side length and angles.
Use theorems about isosceles and equilateral triangles.
Create an image congruent to a given triangle. More congruence
transformations in Chap 6
Use perpendicular bisectors to solve problems.
Use angle bisectors to find distance relationships.
Use medians and altitudes of triangles
Find possible side lengths in a triangles.
Use inequalities to make comparisons in two triangles.
Resources
4.8
5.1
5.2
5.3
5.4
5.5
5.6
Key Vocabulary
- circumcenter
- scalene
- incenter
- isosceles
- median
- equilateral
- centroid
- equiangular
- altitude
- interior angles
(G.2) Geometric structure: analyzes geometric relationships in order to make and verify conjectures.. The student is expected to: - exterior angles
- orthocenter
(B) make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the
- congruent figures
conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.
- corresponding parts
- right triangle (legs, hypotenuse)
(G.4) Geometric structure: uses a variety of representations to describe geometric relationships and solve problems. The student - isosceles triangle (legs, vertex angle,
Common Assessment
is expected to :
base, base angles)
(A) select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems. (TAKS 6).
- congruence transformation
- midsegment
Congruent Triangles
(G.5) Geometric patterns: uses a variety of representations to describe geometric relationships and solve problems. The student is - coordinate proof
Assessment
expected to:
- perpendicular bisector
(A) use numeric and geometric patterns to develop algebraic expressions representing geometric properties.
- equidistant
(B) use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons,
- point of concurrency
ratios in similar figures and solids, and angle relationships in polygons and circles. (TAKS 6)
Aug 7, 2007
Geometry Essential Units of Study 2007-008
05 EUS - Similarity (3 Weeks)
Focus TEKS
Content Description
(G.5) Geometric patterns: uses a variety of representations Solve problems by writing and solving proportions. (No geometric mean.)
to describe geometric relationships and solve problems. The
student is expected to:
(B) use numeric and geometric patterns to make
Use proportions to solve geometry problems including scale.
generalizations about geometric properties, including
properties of polygons, ratios in similar figures and solids,
Use proportions to identify similar polygons.
and angle relationships in polygons and circles. (TAKS 6)
Support TEKS
(G.11) Similarity and the geometry of shape: applies the
Use proportions with a triangle or parallel lines.
concepts of similarity to justify properties of figures and
solve problems.. The student is expected to:
(A) use and extend similarity properties and transformations Perform dilations. Know how to use and determine scale factor in these
to explore and justify conjectures about geometric figures.
similarity transformations. Supplement with TAKS Objective 8.
(TAKS 8)
(B) use ratios to solve problems involving similar figures.
(TAKS 8)
Textbook
Resources
6.1
6.2
6.3
6.6
6.7
(G.2) Geometric structure: analyzes geometric relationships in order to make and verify conjectures.. The student is expected to:
Vocabulary
(B) make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the
conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.
- ratio
- proportion
(G.4) Geometric structure: uses a variety of representations to describe geometric relationships and solve problems. The student - scale factor
is expected to :
- scale drawing
(A) select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems. (TAKS 6).
- similar polygons
- dilation
(G.5) Geometric patterns: uses a variety of representations to describe geometric relationships and solve problems. The student is
- center of dilation
expected to:
- reduction
(A) use numeric and geometric patterns to develop algebraic expressions representing geometric properties.
- enlargement
Common Assessment
Ancient Ruins Assessment
Aug 7, 2007
Geometry Essential Units of Study 2007-008
06 EUS - Transformations (2 Weeks)
Focus TEKS
Content Description
Represent translations using coordinate geometry. (No vectors.)
(G.5) Geometric patterns: uses a variety of
representations to describe geometric relationships and
solve problems. The student is expected to:
(C) use properties of transformations and their compositions Reflect a figure in any given line on and off the coordinate plane (no
to make connections between mathematics and the real
matrices). Know line of reflection and symmetry.
world, such as tessellations. (TAKS 6)
Rotate a figure about a point concentrating on 90 , 180, 270, and 360
(G.10) Congruence and the geometry of size: applies the degrees, rotating about the origin or vertex of the figure.
concept of congruence to justify properties of figures and
solve problems. The student is expected to:
(A) use congruence transformations to make conjectures
and justify properties of geometric figures including figures
represented on a coordinate plane. (TAKS 6)
Textbook
Resources
Vocabulary
Common Assessment
9.1
9.3
9.4
Apply a combination of two or more transformations to form a composition
of transformations.
9.5
Identify line and rotational symmetry of a figure.
9.6
(G.11) Similarity and the geometry of shape: applies the
concepts of similarity to justify properties of figures and
solve problems.. The student is expected to:
(A) use and extend similarity properties and transformations
to explore and justify conjectures about geometric figures.
(TAKS 8)
Support TEKS
(G.4) Geometric structure: uses a variety of representations to describe geometric relationships and solve problems. The
student is expected to :
(A) select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems. (TAKS 6).
- image
- preimage
- isometry
(G.7) Dimensionality and the geometry of location: understands that coordinate systems provide convenient and efficient ways - line of reflection
of representing geometric figures and uses them accordingly . The student is expected to:
- center of rotation
(A) use one- and two-dimensional coordinate systems to represent points, lines, ray, line segments, and figures. (TAKS 7)
- angle of rotation
- line of symmetry
- rotational symmetry
- composition of transformations
- glide reflection
- tesselation
Living Room
Transformations
Assessment
Aug 7, 2007
Geometry Essential Units of Study 2007-08
07 EUS - Right Triangles (4 Weeks)
Focus TEKS
(G.2) Geometric structure: analyzes geometric relationships
in order to make and verify conjectures.. The student is
expected to:
(A) use constructions to explore attributes of geometric
figures and to make conjectures about geometric
relationships.
Content Description
7.1
Use the converse of the Pythagorean Theorem to determine if a triangle is a
right triangle.
7.2
Use similar right triangles to solve problems. (No geometric mean
theorems, use similarity of triangles to solve).
7.3
(G.5) Geometric patterns: uses a variety of representations
to describe geometric relationships and solve problems. The Use the relationships among the sides of a 30-60-90 and 45-45-90 special
student is expected to:
right triangles.
(D) identify and applies patterns from right triangles to solve
meaningful problems, including special right triangles (45-45- Apply the tangent ratio for indirect measurement of a right triangle.
90 and 30-60-90) and triangles whose sides are
Pythagorean triples. (TAKS 6)
Use the sine and cosine ratios to solve right triangle problems.
(G.8) Congruence and the geometry of size: uses tools to
determine measurements of geometric figures and extends Use inverse tangent, sine, and cosine ratios to solve right triangle problems.
measurement concepts to find perimeter, area, and volume
in problem situations. The student is expected to:
(C) G.8C Derive, extend, and use the Pythagorean
Theorem. (TAKS 8)
(G.11) Similarity and the geometry of shape: applies the concepts of similarity to justify properties of figures and solve problems.. The
student is expected to:
(B) use ratios to solve problems involving similar figures. (TAKS 8)
(C) develop, apply, and justify triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples
using a variety of methods. (TAKS 8)
(G.2) Geometric structure: analyzes geometric relationships in order to make and verify conjectures.. The student is expected to:
(B) make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the
conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.
Support TEKS
Textbook
Apply the Pythagorean Theorem to find side lengths in right triangles.
(Operations with radicals review).
(G.4) Geometric structure: uses a variety of representations to describe geometric relationships and solve problems. The student
is expected to :
(A) select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems. (TAKS 6).
Resources
7.4
7.5
7.6
7.7
Key Vocabulary
-Pythagorean triple
- trigonometric ratio
- opposite side
- adjacent side
- sine
- cosine
- tangent
- angle of elevation
- angle of depression
- inverse sine
- inverse cosine
- inverse tangent
Common Assessment
Sightseeing Walk
Assessment
(G.5) Geometric patterns: uses a variety of representations to describe geometric relationships and solve problems. The student is
expected to:
(A) use numeric and geometric patterns to develop algebraic expressions representing geometric properties.
Aug 7, 2007
Geometry Essential Units of Study 2007-08
08 EUS - Quadrilaterals (3 Weeks)
Focus TEKS
Content Description
(G.2) Geometric structure: analyzes geometric relationships
in order to make and verify conjectures.. The student is
expected to:
(A) use constructions to explore attributes of geometric
figures and to make conjectures about geometric
relationships.
Finding angle measures in polygons. (Review section 1.6 material - convex,
concave, classifying polygons, regular, interior, exterior, etc…)
8.1
Use properties of parallelograms to find angle and side measures in
parallelograms.
8.2
Use properties to identify/show that a quadrilateral is a parallelogram.
(G.5) Geometric patterns: uses a variety of representations
to describe geometric relationships and solve problems. The
Use properties of rhombuses, rectangles, and squares to solve problems.
student is expected to:
(B) use numeric and geometric patterns to make
generalizations about geometric properties, including
Use properties/characteristics (isosceles, midsegment) of trapezoids to
properties of polygons, ratios in similar figures and solids,
solve problems. (No kites).
and angle relationships in polygons and circles. (TAKS 6)
Identify special quadrilaterals.
(G.9) Congruence and the geometry of size: analyzes
properties and describes relationships in geometric figures.
The student is expected to:
(B) formulates and tests conjectures about the properties
and attributes of polygons and their component parts based
on explorations and concrete models.
Support TEKS
(G.2) Geometric structure: analyzes geometric relationships in order to make and verify conjectures.. The student is expected to:
(B) make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the
conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.
(G.4) Geometric structure: uses a variety of representations to describe geometric relationships and solve problems. The student
is expected to :
(A) select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems. (TAKS 6).
Textbook
Resources
Vocabulary
Common Assessment
8.3
8.4
8.5
8.6
- diagonal
- parallelogram
- rhombus
- rectangle
- square
- trapezoid
- bases
- base angles
- isosceles trapezoid
- midsegment of a trapezoid
Aug 7, 2007
Geometry Essential Units of Study 2007-08
09 EUS - Measuring Length and Area (3 Weeks)
Focus TEKS
Content Description
(G.5) Geometric patterns: uses a variety of representations Find areas of triangles and Parallelograms.
to describe geometric relationships and solve problems. The
student is expected to:
(B) use numeric and geometric patterns to make
Find areas of trapezoids and rhombuses. (No Area of kite).
generalizations about geometric properties, including
properties of polygons, ratios in similar figures and solids,
Find circumference and arc length of circles.
and angle relationships in polygons and circles. (TAKS 6)
(G.8) Congruence and the geometry of size: uses tools to
determine measurements of geometric figures and extends Find areas of regular polygons inscribed in circles.
measurement concepts to find perimeter, area, and volume
in problem situations. The student is expected to:
Find the areas of circles and sectors of circles.
(A) find areas of regular polygons, circles, and composite
figures. (TAKS 8).
Use lengths and areas to find geometric probability. Use this section as
(G.9) Congruence and the geometry of size: analyzes
springboard for review of probability TEKS of TAKS Objective 9.
properties and describes relationships in geometric figures.
The student is expected to:
(B) formulates and tests conjectures about the properties
and attributes of polygons and their component parts based
on explorations and concrete models.
Textbook
Resources
11.1
11.2
11.4
11.6
11.5
11.7
Key Vocabulary
Support TEKS
(G.11) Similarity and the geometry of shape: applies the concepts of similarity to justify properties of figures and solve problems. The
student is expected to:
(D) describe the effect on perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in
solving problems. (TAKS 8)
(G.2) Geometric structure: analyzes geometric relationships in order to make and verify conjectures.. The student is expected to:
(B) make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the
conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.
(G.7) Dimensionality and the geometry of location: The student understands that coordinate systems provide convenient and
efficient ways of representing geometric figures and uses them accordingly. The student is expected to:
(A) use one- and two-dimensional coordinate systems to represent points, lines, ray, line segments, and figures. (TAKS 7)
- bases of a parallelogram
- height of a parallelogram
- height of a trapezoid
- circumference
- arc length
- sector of a circle
- regular polygons
- center of a polygon
- radius of a polygon
- apothem
- central angle of a regular polygon
- probability
- geometric probability
Common Assessment
Aug 7, 2007
Geometry Essential Units of Study 2007-08
10 EUS - Surface Area and Volume of Solids (3 Weeks + 1 week TAKS review)
Focus TEKS
(G.1) Geometric structure: understands the structure of, and
relationships within, an axiomatic system. The student is
expected to:
(C) compare and contrast the structures and implications of
Euclidean and non-Euclidean geometries.
(G.5) Geometric patterns: uses a variety of representations
to describe geometric relationships and solve problems. The
student is expected to:
(B) use numeric and geometric patterns to make
generalizations about geometric properties, including
properties of polygons, ratios in similar figures and solids,
and angle relationships in polygons and circles. (TAKS 6)
Content Description
Textbook
Explore solids (definitions such as polyhedra, face, edge, base, vertex,
convex, concave, regular, etc…)
12.1
Find surface area of prisms and cylinders. Discuss nets and lateral versus
total surface area.
12.2
Find the surface area of pyramids and cones.
12.3
Find the volume of prisms and cylinders. Include composite solids. "B"
represents the area of the base.
12.4
Find the volume of pyramids and cones.
12.5
(G.6) Dimensionality and the geometry of location: analyzes Find the surface areas and volumes of spheres. Include definitions of great
the relationship between three-dimensional geometric
circle and hemisphere. Study of spherical geometry after TAKS.
figures and related two-dimensional representations and
uses these representations to solve problems. The student Use properties of similar solids. (optional)
is expected to:
Resources
12.6
12.7
Key Vocabulary
(A) describe and draw the intersection of a given plane with various three-dimensional geometric figures
(B) use nets to represent and construct three-dimensional objects. (TAKS 7)
(C) use orthographic and isometric views of three-dimensional geometric figures to represent and construct three-dimensional geometric
figures and solve problems. (TAKS 7)
Support
TEKS
- polyhedron
- face
- edge
- vertex of a solid
- cross section
- prism
(G.8) Congruence and the geometry of size: uses tools to determine measurements of geometric figures and extends measurement
- surface area
concepts to find perimeter, area, and volume in problem situations. The student is expected to:
- lateral area
(B) find areas of sectors and arc lengths of circles using proportional reasoning. (TAKS 8)
- net
(D) find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem
- right prism
situations. (TAKS 8)
- oblique prism
- cylinder
(G.9) Congruence and the geometry of size: analyzes properties and describes relationships in geometric figures. The student is
- pyramid
expected to:
(D) analyzes the characteristics of polyhedra and other three-dimensional figures and their component parts based on explorations and - regular pyramid
- cone
concrete models. (TAKS 7)
- volume
(G.11) Similarity and the geometry of shape: applies the concepts of similarity to justify properties of figures and solve problems. The stud - sphere
(D) describe the effect on perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving- great circle
- hemisphere
Common Assessment
(G.2) Geometric structure: analyzes geometric relationships in order to make and verify conjectures.. The student is expected to:
(B) make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the
conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.
Aug 7, 2007
Geometry Essential Units of Study 2007-08
11 EUS - Properties of Circles (3 Weeks)
Focus TEKS
(G.5) Geometric patterns: uses a variety of representations
to describe geometric relationships and solve problems. The
student is expected to:
(B) use numeric and geometric patterns to make
generalizations about geometric properties, including
properties of polygons, ratios in similar figures and solids,
and angle relationships in polygons and circles. (TAKS 6)
Content Description
Textbook
Use properties of a tangent to a circle. Include basic definitions, chords,
secants, etc..
10.1
Use angle measures to find arc measures. Include central angle, minor vs.
major arc.
10.2
Use relationships of arcs and chords in a circle.
10.3
(G.7) Dimensionality and the geometry of location: The
Use inscribed angles of circles and polygons.
student understands that coordinate systems provide
convenient and efficient ways of representing geometric
figures and uses them accordingly. The student is expected Find the measure of angles with vertices inside, outside, and on the circle.
to:
(B) Use slopes and equations of lines to investigate
geometric relationships, including parallel lines,
Find segment lengths in circles.
perpendicular lines, and special segments of triangles and
other polygons. (TAKS 7)
Write and graph equations of circles in a coordinate plane.
Resources
10.4
10.5
10.6
10.7
(G.8) Congruence and the geometry of size: uses tools to determine measurements of geometric figures and extends measurement
concepts to find perimeter, area, and volume in problem situations. The student is expected to:
(A) find areas of regular polygons, circles, and composite figures. (TAKS 8).
(B) find areas of sectors and arc lengths of circles using proportional reasoning. (TAKS 8)
Support TEKS
(G.9) Congruence and the geometry of size: analyzes properties and describes relationships in geometric figures. The student is
expected to:
(C) Formulate and test conjectures about the properties and attributes of circles and the lines that intersect them based on explorations
and concrete models.
Key Vocabulary
- circle
- center
- radius
- diameter
(G.2) Geometric structure: analyzes geometric relationships in order to make and verify conjectures.. The student is expected to:
- chord
(B) make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the
- secant
conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.
- tangent
- central angle
(G.4) Geometric structure: uses a variety of representations to describe geometric relationships and solve problems. The student
- minor arc
is expected to :
- major arc
(A) select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems. (TAKS 6).
- semicircles
- congruent circles
(G.5) Geometric patterns: uses a variety of representations to describe geometric relationships and solve problems. The student is
- congruent arcs
expected to:
- inscribed angle
(A) use numeric and geometric patterns to develop algebraic expressions representing geometric properties.
- intercepted arc
- standard equation of a circle
Common Assessment
Aug 7, 2007