Download Geneva Middle School/High School

Geneva CUSD 304
Content-Area Curriculum Frameworks
Grades 6-12
Mathematics
Mission Statement
The study of mathematics can be an exciting and interesting
challenge. Yet, the major reason to become proficient in this
discipline revolves around the use of mathematics as a tool to solve
problems from the areas of science, business, engineering,
economics, and all other areas which involve data collection and
analysis. The mathematics program is designed to establish
connections between the key concepts of math and the applications.
Theoretical structure of mathematics - Students will demonstrate
an understanding of the theoretical foundations of mathematics.
• Thought processes (intuition, deduction, induction)
• Logical arguments (two column, narrative, flow chart
proofs)
• Structure of axiomatic systems (Euclidian geometry, real
and complex number systems)
• Fundamental concepts (functions, sets, limits, infinity,
infinitesimals, statistics, probability)
Problem solving - Students will formulate problem solving
strategies.
• Establishment of relationships (numerical, geometric,
pictorial, graphic, symbolic)
• Recognition, collection, and analysis of pertinent data
• Development and evaluation of methods and algorithms
• Validation of results (estimation, approximation,
reasonableness)
Mechanics of mathematics - Students will symbolically manipulate
mathematical expressions and statements.
• Performance of operations and computational processes
(arithmetic, algebraic, graphic)
• Illustration of solution processes for equations and
inequalities
• Calculation using electronic devices (scientific and
graphing)
Appropriate use of emerging technology - Students will use
technology to improve and extend their understanding of
mathematics.
• Calculators at appropriate levels (scientific and graphing)
• Computer software (graphic, spread sheets, data bases,
Geometry and Geometry Honors.doc
August 1, 2008
Page 1 of 24
•
symbolic manipulators, simulations)
Information management systems (compact disk,
telecommunication, internet, video disk)
All students will experience an evolving curriculum designed to be a
rich tapestry of traditional mathematics skills intertwined with
problem solving, graphical analysis, measurement, probability, and
statistics. The use of manipulatives, calculators (scientific and
graphing), computers, writing assignments, and cooperative learning
activities will all be designed to achieve this mission.
Course Sequence
(Grades 6-12)
Geometry and Geometry Honors.doc
August 1, 2008
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6th Grade Mathematics
7th Grade Mathematics
Pre- Algebra
Integrated Mathematics I, II
Algebra I (4 semesters) A and B
Algebra I
Geometry /Concepts and Applications
Geometry (Regular & Honors)
Algebra II (Regular & Honors)
Algebra II 1/3-3/3
Pre-Calculus (Regular & Honors)
Trigonometry (Regular & Honors)
Calculus
AP Calculus
AP Statistics
Page 2 of 24
Course Title
Course Frameworks
Geometry
Grade Level
9, 10, 11, 12
Semesters
2
Prerequisite
Algebra I (C or higher)
Course Description
Geometry emphasizes the development of a formal, axiomatic
system. Students use inductive and deductive reasoning in the
process of writing formal and informal proofs. A continuous
review of algebra is included through geometry-related
problems. Geometry is a traditional course in the standard
college preparation sequence and serves as a prerequisite for
Algebra II (3 semesters) and Algebra II.
District-approved Materials
and/or Resources
Geometry
McDougal Littell
Larson Boswell and Stiff
ISBN# 0-395-97889-0
(H) Signifies material covered only in the honors course
Course Title
Geometry Honors
Grade Level
9, 10
Semesters
2
Prerequisite
Algebra I (Freshman Placement or Dept Approval)
This course in the honors sequence covers all of the topics of
regular Geometry with a strong emphasis placed upon deductive
and inductive reasoning skills. The course is open to students who
have been very successful in an Algebra I course. Geometry
Honors uses independent research projects, connections to mathrelated fields, increased problem-solving activities and an
emphasis on writing about the mathematical process. This course
is recommended for high ability mathematics students, especially
those who plan to pursue four, full years of high school
mathematics and math-related careers. Geometry Honors provides
the prerequisite for Algebra II and Algebra II Honors.
Geometry
District-approved
Materials and/or Resources McDougal Littell
Larson Boswell and Stiff
ISBN# 0-395-97889-0
Course Description
Geometry and Geometry Honors.doc
August 1, 2008
Page 3 of 24
Unit Frameworks
Resources that will support
instruction
Unit of Study:
Reasoning and Proof with the
Basics of Geometry
Illinois Learning
Standards,
Benchmarks,
6.A.4 Identify and apply the associative, commutative, distributive
and identity properties of real numbers, including special numbers
such as pi and square roots.
National Standards
Assessment
Frameworks, or other
standards that will be
taught in this unit
7.A.4b Apply formulas in a wide variety of theoretical and
practical real–world measurement applications involving
perimeter, area, volume, angle, time, temperature, mass, speed,
distance, density and monetary values.
7.B.4 Estimate and measure the magnitude and directions of
physical quantities (e.g., velocity, force, slope) using rulers,
protractors and other scientific instruments including timers,
calculators and computers.
7.C.4c Convert within and between measurement systems and
monetary systems using technology where appropriate.
8.A.4b Represent mathematical patterns and describe their
properties using variables and mathematical symbols.
9.B.4 Recognize and apply relationships within and among
geometric figures.
9.C.4a Construct and test logical arguments for geometric
situations using technology where appropriate.
9.C.4b Construct and communicate convincing arguments for
geometric situations.
9.C.4c Develop and communicate mathematical proofs (e.g., twocolumn, paragraph, indirect) and counter examples for geometric
statements.
Objectives
o Conceptual
o Factual
o Procedural
(H) Signifies material covered only in the honors course
1. Find and describe patterns
2. Use inductive reasoning to make real life conjectures
3. Understand and use the basic undefined terms and defined terms
Geometry and Geometry Honors.doc
August 1, 2008
Page 4 of 24
of geometry
4. Sketch the intersections of lines and planes
5. Use segment postulates
6. Use the Distance Formula to measure distances
7. Use angle postulates
8. Classify angles as acute, right, obtuse, or straight
9. Bisect a segment
10. Bisect an angle
11. Identify vertical angles and linear pairs
12. Identify complementary and supplementary angles
13. Recognize and analyze a conditional statement
14. Write postulates about points, lines and planes using
conditional statements
15. Recognize and use definitions
16. Recognize and use bi-conditional statements
17. Use symbolic notation to represent logical statements
18. Form conclusions by applying the laws of logic to true
statements
19. Use properties from algebra to justify algebraic manipulations
20. Use properties of length and measure to justify segment and
angle relationships
21. Justify statements about congruent segments
22. Write reasons for steps in a proof
23. Use angle congruence properties
24. Prove properties about special pairs of angles
25. Apply concepts to solve real-life application problems
Geometry and Geometry Honors.doc
August 1, 2008
Page 5 of 24
26. Generalize concepts and skills throughout unit to solve nonroutine rote and application problems (H)
Honors will devote significant time to the theoretical
development of concepts.
Performance tasks, chapter
Other Evidence:
quizzes, chapter tests, and
semester exams will be given.
Homework
They will include multiple choice
and /or free response problems.
Board/Class Work
Other learning activities that
may include:
• Cooperative Learning
Activities
• Technology Based
Discovery Activities
• Projects
Geometry and Geometry Honors.doc
August 1, 2008
Page 6 of 24
Unit Frameworks
Resources that will support
instruction
Unit of Study:
Parallel and Perpendicular
Lines
Illinois Learning
Standards,
Benchmarks,
7.A.4b Apply formulas in a wide variety of theoretical and practical
real–world measurement applications involving perimeter, area,
volume, angle, time, temperature, mass, speed, distance, density and
monetary values.
National Standards
Assessment
Frameworks, or other
standards that will be
taught in this unit
7.B.4 Estimate and measure the magnitude and directions of
physical quantities (e.g., velocity, force, slope) using rulers,
protractors and other scientific instruments including timers,
calculators and computers.
8.B.4a Represent algebraic concepts with physical materials, words,
diagrams, tables, graphs, equations and inequalities and use
appropriate technology.
8.D.4 Formulate and solve linear and quadratic equations and linear
inequalities algebraically and investigate nonlinear inequalities
using graphs, tables, calculators and computers.
9.B.4 Recognize and apply relationships within and among
geometric figures.
9.C.4a Construct and test logical arguments for geometric situations
using technology where appropriate.
9.C.4b Construct and communicate convincing arguments for
geometric situations.
Objectives
o Conceptual
o Factual
o Procedural
9.C.4c Develop and communicate mathematical proofs
(e.g., two-column, paragraph, indirect) and counter examples for
geometric statement.
(H) Signifies material covered only in the honors course
1. Identify relationships between lines
2. Identify angles formed by transversals
3. Perform compass and straight edge constructions (H)
4. Perform constructions using Geometer’s Sketchpad (H)
5. Write different types of proofs
Geometry and Geometry Honors.doc
August 1, 2008
Page 7 of 24
6. Write detailed algebraic proofs (H)
7. Prove results about perpendicular lines
8. Prove and use results about parallel lines and transversals
9. Prove that two lines are parallel
10. Use properties of parallel lines to solve real-life problems
11. Find slopes of lines and use slope to identify parallel lines in a
coordinate plane.
12. Write equations of parallel lines in a coordinate plane
13. Use slope to identify perpendicular lines in a coordinate plane
14. Write equations of perpendicular lines
15. Find the equation of a perpendicular bisector (H)
16. Find the distance between a point and a line (H)
17. Apply concepts to solve real-life application problems
15. Generalize concepts and skills throughout unit to solve nonroutine rote and application problems (H)
Assessments
Honors will devote significant time to the theoretical
development of concepts.
Performance tasks, chapter
Other Evidence:
quizzes, chapter tests, and
semester exams will be given.
Homework
They will include multiple choice
and /or free response problems.
Board/Class Work
Other learning activities that
may include:
• Cooperative Learning
Activities
• Technology Based
Discovery Activities
• Projects
Geometry and Geometry Honors.doc
August 1, 2008
Page 8 of 24
Unit Frameworks
Resources that will support
instruction
Unit of Study:
Congruent Triangles
Illinois Learning
Standards,
Benchmarks,
6.C.4 Determine whether exact values or approximations are
appropriate (e.g., bid a job, determine gas mileage for a trip).
National Standards
Assessment
Frameworks, or other
standards that will be
taught in this unit
6.D.4 Solve problems involving recipes or mixtures, financial
calculations and geometric similarity using ratios, proportions and
percents.
7.B.4 Estimate and measure the magnitude and directions of
physical quantities (e.g., velocity, force, slope) using rulers,
protractors and other scientific instruments including timers,
calculators and computers.
8.C.4b Apply algebraic properties and procedures with matrices,
vectors, functions and sequences using data found in business,
industry and consumer situations.
9.A.4b Make perspective drawings, tessellations and scale drawings,
with and without the use of technology.
9.B.4 Recognize and apply relationships within and among
geometric figures.
9.C.4b Construct and communicate convincing arguments for
geometric situations.
9.C.4c Develop and communicate mathematical proofs (e.g., twocolumn, paragraph, indirect) and counter examples for geometric
statements.
Objectives
o Conceptual
o Factual
o Procedural
9.D.4 Analyze and solve problems involving triangles (e.g.,
distances which cannot be measured directly) using trigonometric
ratios.
(H) Signifies material covered only in the honors course
1. Classify triangles by their sides and angles
2. Find angle measures in triangles
3. Identify congruent figures and corresponding parts
Geometry and Geometry Honors.doc
August 1, 2008
Page 9 of 24
4. Prove that two triangles are congruent
5. Prove that triangles are congruent using the SSS and SAS
Congruence Postulates
6. Prove that triangles are congruent using the ASA Congruence
Postulate and the AAS Congruence Theorem
7. Use congruence postulates and theorems in real-life problems
8. Use congruent triangles to plan and write proofs
9. Use properties of isosceles and equilateral triangles
10. Use properties of right triangles
11. Place geometric figures in a coordinate plane (H)
12. Write a coordinate proof (H)
13. Apply concepts to solve real-life application problems
14. Generalize concepts and skills throughout unit to solve nonroutine rote and application problems (H)
Assessments
Honors will devote significant time to the theoretical
development of concepts.
Performance tasks, chapter
Other Evidence:
quizzes, chapter tests, and
semester exams will be given.
Homework
They will include multiple choice
and /or free response problems.
Board/Class Work
Other learning activities that
may include:
• Cooperative Learning
Activities
• Technology Based
Discovery Activities
• Projects
Geometry and Geometry Honors.doc
August 1, 2008
Page 10 of 24
Unit Frameworks
Resources that will support
instruction
Unit of Study:
Quadrilaterals
Illinois Learning
Standards,
Benchmarks,
6.D.4 Solve problems involving recipes or mixtures, financial
calculations and geometric similarity using ratios, proportions and
percents.
National Standards
Assessment
Frameworks, or other
standards that will be
taught in this unit
7.A.4b Apply formulas in a wide variety of theoretical and practical
real–world measurement applications involving perimeter, area,
volume, angle, time, temperature, mass, speed, distance, density and
monetary values.
7.C.4c Convert within and between measurement systems and
monetary systems using technology where appropriate.
9.B.4 Recognize and apply relationships within and among
geometric figures.
9.C.4b Construct and communicate convincing arguments for
geometric situations.
Objectives
o Conceptual
o Factual
o Procedural
9.C.4c Develop and communicate mathematical proofs (e.g., twocolumn, paragraph, indirect) and counter examples for geometric
statements.
(H) Signifies material covered only in the honors course
1. Identify, name, and describe polygons
2. Use the sum of the measures of the interior angles of a
quadrilateral
3. Use properties of parallelograms in rote and real-life problems
4. Prove that a quadrilateral is a parallelogram
5. Use coordinate geometry with parallelograms
6. Use properties of sides and angles of rhombuses, rectangles, and
squares
7. Use properties of diagonals of rhombuses, rectangles, and squares
8. Use properties of trapezoids
Geometry and Geometry Honors.doc
August 1, 2008
Page 11 of 24
9. Use properties of kites
10. Identify special quadrilaterals based on limited information
11. Prove that a quadrilateral is a special type of quadrilateral
12. Apply concepts to solve real-life application problems
13. Generalize concepts and skills throughout unit to solve nonroutine rote and application problems (H)
Assessments
Honors will devote significant time to the theoretical
development of concepts.
Performance tasks, chapter
Other Evidence:
quizzes, chapter tests, and
semester exams will be given.
Homework
They will include multiple choice
and /or free response problems.
Board/Class Work
Other learning activities that
may include:
• Cooperative Learning
Activities
• Technology Based
Discovery Activities
Geometry and Geometry Honors.doc
August 1, 2008
Page 12 of 24
Unit Frameworks
Resources that will support
instruction
Unit of Study:
Similarity
Illinois Learning
Standards,
Benchmarks,
6.C.4 Determine whether exact values or approximations are
appropriate (e.g., bid a job, determine gas mileage for a trip).
National Standards
Assessment
Frameworks, or other
standards that will be
taught in this unit
6.D.4 Solve problems involving recipes or mixtures, financial
calculations and geometric similarity using ratios, proportions and
percents.
7.A.4a Apply units and scales to describe and compare numerical
data and physical objects.
7.C.4a Make indirect measurements, including heights and distances,
using proportions (e.g., finding the height of a tower by its shadow).
7.C.4b Interpret scale drawings and models using maps and
blueprints.
7.C.5b Determine how changes in one measure may affect other
measures (e.g., what happens to the volume and surface area of a cube
when the side of the cube is halved).
7.C.4c Convert within and between measurement systems and
monetary systems using technology where appropriate.
9.A.5 Use geometric figures and their properties to solve problems in
the arts, the physical and life sciences and the building trades, with
and without the use of technology.
9.B.4 Recognize and apply relationships within and among
geometric figures.
9.C.4a Construct and test logical arguments for geometric situations
using technology where appropriate.
9.C.5a Perform and describe an original investigation of a geometric
problem and verify the analysis and conclusions to an audience.
9.C.4b Construct and communicate convincing arguments for
geometric situations.
9.C.4c Develop and communicate mathematical proofs (e.g., twocolumn, paragraph, indirect) and counter examples for geometric
Geometry and Geometry Honors.doc
August 1, 2008
Page 13 of 24
statements.
9.D.4 Analyze and solve problems involving triangles (e.g., distances
which cannot be measured directly) using trigonometric ratios.
Objectives
o Conceptual
o Factual
o Procedural
(H) Signifies material covered only in the honors course
1. Find and simplify the ratio of two numbers
2. Use proportions to solve real-life problems
3. Use properties of proportions in rote and real-life problems
4. Identify similar polygons
5. Use similar polygons to solve rote and real-life problems
6. Identify similar triangles
7. Use similarity theorems to prove that two triangles are similar
8. Use similar triangles to solve rote and real-life problems
9. Use proportionality theorems to solve rote and real-life problems
10. Generalize concepts and skills throughout unit to solve nonroutine rote and application problems (H)
Assessments
Honors will devote significant time to the theoretical development
of concepts.
Performance tasks, chapter
Other Evidence:
quizzes, chapter tests, and
semester exams will be given.
Homework
They will include multiple choice
and /or free response problems.
Board/Class Work
Other learning activities that may
include:
• Cooperative Learning
Activities
• Technology Based
Discovery Activities
Geometry and Geometry Honors.doc
August 1, 2008
Page 14 of 24
Unit Frameworks
Resources that will support
instruction
Unit of Study:
Properties of Triangles
Illinois Learning
Standards,
Benchmarks,
6.C.4 Determine whether exact values or approximations are
appropriate (e.g., bid a job, determine gas mileage for a trip).
National Standards
Assessment
Frameworks, or other
standards that will be
taught in this unit
7.A.4a Apply units and scales to describe and compare numerical
data and physical objects.
7.C.4a Make indirect measurements, including heights and distances,
using proportions (e.g., finding the height of a tower by its shadow).
7.C.5b Determine how changes in one measure may affect other
measures (e.g., what happens to the volume and surface area of a cube
when the side of the cube is halved).
7.C.4c Convert within and between measurement systems and
monetary systems using technology where appropriate.
9.A.5 Use geometric figures and their properties to solve problems in
the arts, the physical and life sciences and the building trades, with
and without the use of technology.
9.B.4 Recognize and apply relationships within and among
geometric figures.
9.C.4a Construct and test logical arguments for geometric situations
using technology where appropriate.
9.C.5a Perform and describe an original investigation of a geometric
problem and verify the analysis and conclusions to an audience.
9.C.4b Construct and communicate convincing arguments for
geometric situations.
9.C.4c Develop and communicate mathematical proofs (e.g., twocolumn, paragraph, indirect) and counter examples for geometric
statements.
9.D.4 Analyze and solve problems involving triangles (e.g., distances
which cannot be measured directly) using trigonometric ratios.
Geometry and Geometry Honors.doc
August 1, 2008
Page 15 of 24
Objectives
o Conceptual
o Factual
o Procedural
(H) Signifies material covered only in the honors course
1. Use properties of perpendicular bisectors
2. Use properties of perpendicular bisectors to identify equal distances
3. Use properties of perpendicular bisectors of a triangles
4. Use properties of angle bisectors of a triangle
5. Use properties of medians of a triangle
6. Use properties of altitudes of a triangle
7. Identify the mid-segments of a triangle
8. Use properties of mid-segments of a triangle
9. Use triangle measurements to decide which side is longest or which
angle is largest
10. Use the Triangle Inequality
11. Read and write indirect proof (H)
12. Use the Hinge Theorem and its converse to compare side lengths
and angle measures (H)
13. Apply concepts to solve real-life application problems
14. Generalize concepts and skills throughout unit to solve nonroutine rote and application problems (H)
Assessments
Honors will devote significant time to the theoretical development
of concepts.
Performance tasks, chapter
Other Evidence:
quizzes, chapter tests, and
semester exams will be given.
Homework
They will include multiple choice Board/Class Work
and /or free response problems.
Other learning activities that may
include:
• Cooperative Learning
Activities
• Technology Based
Discovery Activities
• Projects
Geometry and Geometry Honors.doc
August 1, 2008
Page 16 of 24
Unit Frameworks
Resources that will support
instruction
Unit of Study:
Transformations
(Honors Only Unit)
Illinois Learning
Standards,
Benchmarks,
7.A.4a Apply units and scales to describe and compare numerical
data and physical objects.
National Standards
Assessment
Frameworks, or other
standards that will be
taught in this unit
7.C.4c Convert within and between measurement systems and
monetary systems using technology where appropriate.
9.A.4b Make perspective drawings, tessellations and scale drawings,
with and without the use of technology.
9.A.5 Use geometric figures and their properties to solve problems in
the arts, the physical and life sciences and the building trades, with
and without the use of technology.
9.B.4 Recognize and apply relationships within and among
geometric figures.
9.C.4b Construct and communicate convincing arguments for
geometric situations.
Objectives
o Conceptual
o Factual
o Procedural
(H) Signifies material covered only in the honors course
1. Identify the three basic rigid transformations (isometries) (H)
2. Identify and use reflections in a plane (H)
3. Draw a reflection of an object over a given line using manual and
technology assisted methods (H)
4. Find lines of symmetry in a given object (H)
5. Identify rotations in a plane (H)
6. Construct a rotation using manual and technology assisted methods
(H)
7. Identify and use rotational symmetry (H)
8. Identify and use translations in the plane (H)
9. Use vectors to represent translations (H)
Geometry and Geometry Honors.doc
August 1, 2008
Page 17 of 24
10. Find the component form of the vector that can be used to
represent a given translation (H)
11. Find the image of a glide reflections (H)
12. Describe the result of a composition of transformations (H)
13. Generalize concepts and skills throughout unit to solve nonroutine rote and application problems (H)
Assessments
Honors will devote significant time to the theoretical development
of concepts.
Performance tasks, chapter
Other Evidence:
quizzes, chapter tests, and
semester exams will be given.
Homework
They will include multiple choice
and /or free response problems.
Board/Class Work
Other learning activities that may
include:
• Cooperative Learning
Activities
• Technology Based
Discovery Activities
• Projects
Geometry and Geometry Honors.doc
August 1, 2008
Page 18 of 24
Unit Frameworks
Resources that will support instruction
Unit of Study:
Properties of Right Triangles and
Right Triangle Trigonometry
Illinois Learning
Standards,
Benchmarks,
9.B.4 Recognize and apply relationships within and among geometric figures.
National Standards
Assessment
Frameworks, or
other standards that
will be taught in this
unit
9.B.5 Construct and use two- and three-dimensional models of objects that have
practical applications (e.g., blueprints, topographical maps, scale models).
9.C.4a Construct and test logical arguments for geometric situations using
technology where appropriate.
9.C.4b Construct and communicate convincing arguments for geometric
situations.
9.C.5b Apply physical models, graphs, coordinate systems, networks and vectors
to develop solutions in applied contexts (e.g., bus routing, areas of irregular
shapes, describing forces and other physical quantities).
9.C.4c Develop and communicate mathematical proofs (e.g., two-column,
paragraph, indirect) and counter examples for geometric statements.
9.D.4 Analyze and solve problems involving triangles (e.g., distances which
cannot be measured directly) using trigonometric ratios.
Objectives
o Conceptual
o Factual
o Procedural
(H) Signifies material covered only in the honors course
1. Solve problems involving similar right triangles formed by the altitude drawn
to the hypotenuse of a right triangle.
2. Write radicals in standard radical form
3. Prove the Pythagorean Theorem
4. Use the Pythagorean Theorem to solve real-life problems
5. Use the Converse of the Pythagorean Theorem to solve problems
6. Use side lengths to classify triangles by their angle measures
7. Find the side lengths of special right triangles
8. Use special right triangles to solve rote and real-life problems
Geometry and Geometry Honors.doc
August 1, 2008
Page 19 of 24
9. Define the trigonometric ratios
10. Find the sine, cosine, and tangent of an acute angle
11. Use simple trigonometric identities
12. Use trigonometric ratios to solve real-life problems involving angle of
elevation and angle of depression
13. Solve right triangles
14. Use right triangles to solve real-life problems
15. Solve oblique triangles using the Law of Sines (H)
16. Solve oblique triangles using the Law of Cosines (H)
17. Generalize concepts and skills throughout unit to solve non-routine rote and
application problems (H)
Assessments
Honors will devote significant time to the theoretical development of
concepts.
Performance tasks, chapter quizzes,
Other Evidence:
chapter tests, and semester exams will
be given. They will include multiple
Homework
choice and /or free response problems.
Board/Class Work
Other learning activities that may
include:
• Cooperative Learning Activities
• Technology Based Discovery
Activities
• Projects
Geometry and Geometry Honors.doc
August 1, 2008
Page 20 of 24
Unit Frameworks
Resources that will support instruction
Unit of Study:
Circles
Illinois Learning
Standards,
Benchmarks,
7.A.4b Apply formulas in a wide variety of theoretical and practical real–world
measurement applications involving perimeter, area, volume, angle, time,
temperature, mass, speed, distance, density and monetary values.
National Standards
Assessment
Frameworks, or
other standards that
will be taught in this
unit
7.C.4c Convert within and between measurement systems and monetary systems
using technology where appropriate.
9.B.4 Recognize and apply relationships within and among geometric figures.
9.C.4a Construct and test logical arguments for geometric situations using
technology where appropriate.
9.C.4b Construct and communicate convincing arguments for geometric
situations.
9.C.5b Apply physical models, graphs, coordinate systems, networks and vectors
to develop solutions in applied contexts (e.g., bus routing, areas of irregular
shapes, describing forces and other physical quantities).
9.D.4 Analyze and solve problems involving triangles (e.g., distances which
cannot be measured directly) using trigonometric ratios.
Objectives
o Conceptual
o Factual
o Procedural
(H) Signifies material covered only in the honors course
1. Identify segments and lines related to circles
2. Use properties of a tangent to a circle
3. Use properties of arcs of circles
4. Use properties of chords of circles
5. Use inscribed angles to solve problems
6. Use properties of inscribed polygons
7. Use angles formed by tangents and chords to solve problems
8. Use angles formed by lines that intersect a circle to solve problems
Geometry and Geometry Honors.doc
August 1, 2008
Page 21 of 24
9. Find the lengths of segments of chords
10. Find the lengths of segments of tangents and secants
11. Write the equation of a circle
12. Use the equation of a circle and its graph to solve problems
13. Apply concepts to solve real-life application problems
14. Generalize concepts and skills throughout unit to solve non-routine rote and
application problems (H)
Assessments
Honors will devote significant time to the theoretical development of
concepts.
Performance tasks, chapter quizzes,
Other Evidence:
chapter tests, and semester exams will
be given. They will include multiple
Homework
choice and /or free response problems.
Board/Class Work
Other learning activities that may
include:
• Cooperative Learning Activities
• Technology Based Discovery
Activities
• Projects
Geometry and Geometry Honors.doc
August 1, 2008
Page 22 of 24
Unit Frameworks
Resources that will support instruction
Unit of Study:
Area, Surface Area, and Volume
Illinois Learning
Standards,
Benchmarks,
6.D.4 Solve problems involving recipes or mixtures, financial calculations and
geometric similarity using ratios, proportions and percents.
National Standards
Assessment
Frameworks, or
other standards that
will be taught in this
unit
7.A.4b Apply formulas in a wide variety of theoretical and practical real–world
measurement applications involving perimeter, area, volume, angle, time,
temperature, mass, speed, distance, density and monetary values.
7.C.4c Convert within and between measurement systems and monetary systems
using technology where appropriate.
9.A.4a Construct a model of a three–dimensional figure from a two–dimensional
pattern.
Objectives
o Conceptual
o Factual
o Procedural
9.B.4 Recognize and apply relationships within and among geometric figures.
(H) Signifies material covered only in the honors course
1. Find the measures of interior and exterior angles of polygons
2. Find the area of an equilateral triangle
3. Find the area of a regular polygon
4. Compare perimeters and areas of similar figures
5. Find the circumference of a circle and the length of a circular arc
6. Find the area of a circle and a sector of a circle
7. Find geometric probability and apply geometric probability to real-life
application problems (H)
8. Use properties of polyhedra
9. Apply Euler’s Theorem in real-life application problems
12. Find the surface area of a prism
13. Find the surface area of a cylinder
14. Find the surface area of a pyramid
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15. Find the surface area of a cone
16. Use volume postulates
17. Find the volume of pyramids and cones
18. Find the surface area of a sphere
19. Use volume and surface area to solve real-life application problems
20. Find the scale factor of similar solids
21. Use similar solids to solve real-life problems
22. Apply concepts to solve real-life application problems
23. Generalize concepts and skills throughout unit to solve non-routine rote and
application problems (H)
Assessments
Honors will devote significant time to the theoretical development of
concepts.
Performance tasks, chapter quizzes,
Other Evidence:
chapter tests, and semester exams will
be given. They will include multiple
Homework
choice and /or free response problems.
Board/Class Work
Other learning activities that may
include:
• Cooperative Learning Activities
• Technology Based Discovery
Activities
• Projects
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