I. COURSE DESCRIPTION
Geometry is the study of measurement of zero , one, two, and three
dimensional objects. In studying geometry, students will see and understand how
patterns occur in the construction of geometric shapes. Students will use
similarity, congruence, transformations, and both formal and informal reasoning
to compare and construct given geometric shapes, and shapes found in both art
and the world around them. In studying geometry, students will add to their
knowledge of mathematical reasoning by formulating , investigating, analyzing,
and defending geometric conjectures. This knowledge of geometry will enhance
their understanding of algebra and prepare them for higher levels of
mathematics. It will also enrich their view and understanding of the vast
universe around them.
II. PREREQUISITE KNOWLEDGE
Students entering high school geometry should know and be able to use:
A. Visualization
1. names/definitions of shapes (2D and 3D)
2. properties of shapes
3. basic geometric construction (building blocks)
4. spatial reasoning
5. connect shapes and figures to mathematical situations
B. Analysis
1. relationships between properties (make conjectures
about properties)
2. measurement (perimeter, area, volume)
3. categorization using attributes (compare and contrast attributes of 2D and 3D
figures, make conjectures about relationships of triangles, quadrilaterals and
circles )
4. proportional reasoning
5. Pythagorean theorem
C. Informal Deduction
1. visual proofs
2. introduction to Cartesian coordinate plane
3. transformational geometry
D. Algebra
1. solve linear equations
2. evaluate algebraic expressions
3. Pythagorean theorem
III. CONTENT
After taking high school geometry, students should know, understand, and be
able to use:
A. Formal proofs in geometry
1. logical reasoning
2. formal justification
3. proportional reasoning
B. Rigor in geometry
1. axiomatic system
2. construct figures
3. introduction to non-Euclidean geometries (e.g. spherical geometry)
4. introduction to trigonometry
5. coordinate geometry
6. formal use of similarity, transformations, congruence
C. Application of geometry
1. determine, use, and estimate measurements of 2D and 3D
figures
2. use geometry to make decisions about living and work space
3. extract geometric information from real life
IV. ASSESSMENT
A. It is suggested that a variety of methods be used to assess student
learning. This includes assessments that show student work as well as student
explanations of their work. These assessments might include both traditional and
alternative methods such as:
1. Performance based tasks
2. Open book (including homework)
3. Technology-based presentations
4. Interviews
5. Observations
6. Portfolios
7. Projects with rubrics (individual and group)
8. Warm-up quizzes
9. Multiple choice
10. Open response
11. Comprehensive, multi- step problems
12. Final Exam – The final exam should be a comprehensive exam standardized by
campus with future plans to standardize by district, city, and/or state. Having
all students taking a final exam will prepare students for college final exams.
The final exam should count approximately 25% of the grade.
B. Recommended Course Grade – Each district has guidelines
for course grades and, whenever possible, it is suggested that final course
grades for students be guided by the following:
1. Formative assessments 25% (daily tools: warm-ups,
quizzes, teacher observations and interviews, group work )
2. Closed book assessments 25% (Open response, multiple choice, quantitative
comparisons, SAT, multi-step problems)
3. Open book assessments 25% (homework, projects, presentations, portfolios)
4. Final Comprehensive Exam 25%
V. INFORMATION/RESOURCES
A. FOR STUDENTS
1. Course description
2. Teacher information (conference period, office hours)
3. Work, projects, homework, exams, etc., to be produced by the students
including grading
policy for each
4. Rubrics for projects/presentations/portfolios
5. Resources – tutoring, lab, Internet web sites specific to the course,
computer programs,
teacher conference period, other outside support available
6. Weekly calendar
7. Materials: It is recommended that a textbook/ calculator package be issued to
each student
B. FOR TEACHERS
1. Labs: math and computer
2. Materials: textbooks, calculators with view screens, charts, transparencies,
etc.
3. Computer: hardware, software, and multi-media resources
4. Professional Networks: provisions for teacher teaming during conference time,
professional
development/credits or endorsements to increase salaries, peer coaching
5. References: instructor manuals, journals, Educational Resource Information
Clearinghouse,
Internet websites
6. CBL- Computer Based Lab and CBR – Computer Based Range
7. Vertical alignment information on K-16 alignment initiatives
8. Suggested course calendar
VI. MATRIX MAPPING GEOMETRY TO COGNITIVE DEMANDS
A. Attached is a matrix that matches cognitive demands to knowledge and
skills in Geometry. The
work on cognitive demands has been guided by the work of Andrew Porter, Norman
Webb, and
John Smithson. The cognitive demands identified by Porter, Webb, and Smithson
were used as models and modified by the working group to fit the work in
Geometry. These identify thinking levels that incorporate five (5) levels of
cognitive demands. They are listed in order on the matrix from higher order to
lower order as you read from left to right. The matrix also maps the textbook
and materials being used in each of the major independent school districts, and
the state and national mathematics standards.
B. Cognitive Demands for Mathematics
Cognitive demands assist teachers in distinguishing what a student is expected
to know and be able to do with mathematics content and what level of thinking a
student must be engaged in while learning content. This mapping of topics of
cognitive demands describes content knowledge that will not merely be stored,
but also understood, represented, organized, connected, and structured in ways
that facilitate retrieval and application of knowledge. With knowledge and
skills mapped to cognitive demands, teachers know how to get students to use,
represent, and connect pieces of content knowledge in coherent ways that will
determine whether students understand knowledge deeply and can use it to solve
new problems. The cognitive demands are not linear , nor are they sequential. In
many instances they overlap and are not clearly separated. They are to:
1. Generalize - make and prove conjectures, prove
statements, generate questions
2. Make Connections – transfer knowledge, connect two of more concepts to
solve non-routine problems
3. Understand Concepts – communicate “big ideas”, justify and explain
solutions to problems, use and select multiple representations to model
mathematical ideas and select the most appropriate for given situations
4. Perform Procedures – do computations, make observations, measure and
compare, solve routine problems
5. Memorize – facts, definitions, formulas, properties, rules
C. Format and Further Information on Matrix Structure
1. All TEKS are included in the framework.
2. Items in the matrix appearing in regular fonts are actual TEKS and are placed
within the appropriate cognitive demand column.
3. Italicized items are used:
a. to support the teaching and learning of a topic; these do not reference a
TEKS;
b. to paraphrase a TEKS to address the different levels of cognitive demands;
these will
have a referenced TEKS and are placed under multiple cognitive demands
4. Strands/topics in matrices overlap and may be integrated.
5. Cognitive demands overlap and are not linear.
6. The framework is not intended to be sequential.
7. Other topics supporting the study of geometry may be included in the matrix.
