TAMALPAIS UNION HIGH SCHOOL DISTRICT
Larkspur, California

COURSE OF STUDY 

I. INTRODUCTION

Honors Geometry 1H-2H is part of the basic foundation sequence in college preparatory mathematics.  This honors option is designed to parallel the regular Geometry 1-2 course of study.  The course covers that content at a more rapid pace, allowing time to further explore more challenging applications of the concepts and enrichment topics.  Homework, projects, and other supplemental work will require on average 45 minutes to 1 hour per night.

Geometry 1H-2H is intended for students who have shown strong mastery of the concepts presented in Algebra 1-2 and who meet the admissions requirements for this honors course.  These very competent, successful mathematics students will be provided with extra challenges in addition to standard course work.

This course addresses the following Tam 21st Century Mission, Beliefs, and Goals in the following ways:  

The learning environment provides opportunities for students to:

I.	Acquire, manage, and use knowledge of geometry concepts and skills; 
II.	Think critically and creatively when developing a conceptual understanding of the concepts
III.	       Acquire methods of creating and completing geometric proofs;
IV.       Practice self-directed learning, decision making, and problem solving;
V.        Use and further develop skills to effectively articulate geometric concepts in small group and whole group discussions.
VI.      Develop skills needed for effective teamwork

This course contributes to attainment of the following district outcomes:
Outcome1	Communicate articulately, effectively, and persuasively when speaking and writing.
Outcome 2	Students will read and analyze material in a variety of disciplines
Outcome 3	     Use technology as a tool to access information, analyze and solve problems, and communicate ideas.
Outcome 5	Apply mathematical knowledge and skills to analyze and solve problems.

II. STUDENT LEARNING OUTCOMES

The students will:

1.	become an active learner by investigating, conjecturing, verifying, applying, evaluating, and communicating mathematical ideas both collaboratively and individually in solving problems;
  	develop awareness of their own thinking and explain and justify their work and thinking both in oral and written form;
  	develop consistent study habits and organizational skills and personal responsibility for learning;
  	develop confidence, perseverance, and an appreciation of mathematics; and
  	use appropriate technology including calculators and computers as an integral part of student work.

In support of the California State Content Standards and the mathematics framework, more emphasis will be placed on proof while making reasonable arguments and problem solving; emphasis on geometry from only a synthetic viewpoint will be shifted to the use of transformations, coordinates, and modeling.  Re-enforcing concepts from a three-dimensional standpoint should be used whenever possible. 

This course covers all the student learning outcomes of Geometry 1-2  and, in addition, explores enrichment topics not included in Geometry 1-2.  The following list is intended to be illustrative, not definitive, and indicates the minimum exposure level, not the level of student competence.  (Note: These student learning outcomes are referenced by the State Content Standards for Geometry. The Standard is indicated by the number in parentheses.)

A.  There are several unsolved problems that have haunted mathematicians for years.  Some have been solved after years or even centuries of work, some have had solutions suggested but not proven.  Find out about the conjectures of Goldbach and Fermant and their attempts to solve the conjectures.  (Standards 2.0 and 3.0)

B.  What would life be like in a two dimensional world?  Read Flatland: A romance of Many Dimensions by Edwin A. Abbott and report on the book.  You might extend the adventure to the fourth dimension or you might investigate the social and historical intent of the author.  (Standard 3.0)

C.  Dutch artist M.C. Escher made use of the theory of tessellations.  Research the artist and his works or tessellation and create your own tessellations.  (Standard 22.0)

D.  Investigate the Golden Ratio and its applications.  (Standard 4.0)

E.  What are snowflake curves?  What is their significance in dealing with fractals? (Standard 4.0)

F.  Write a computer program that will generate fractals.  (Standard 4.0)

G.	The triangular numbers are 1, 3, 6, 10, 15, 21, 28...where t=n(n+1)/2.  If the triangular numbers are divided by two, the sequence of remainders is 1,1,0,0,1,1,0,0...; for division by three, the sequence of remainders is 1,0,0...  Find the sequence for remainders for divisors four through ten.  Conjecture a rule for the lengths of the periods of the remainders on the basis of your evidence.  (The period length is the number of quantities in the sequence before it begins repeating.  Thus for 2, the period length is 4; for 3, the period length is 3.  

H.  Calculate any apply vectors to a three-dimensional situation.

I.  Look at graph theory.

J.	Explore Archimedean Solids.  (Standard 8.0)

K.  Compare and contrast Euclidean and Non-Euclidean Geometry.  What realm is it more appropriate to use a certain platform?  (Standard 20.0)

K.	Explore topology and describe its utility.  (Standard 4.0)

M.  Measure distances indirectly using similarity/trigonometry.  Students may construct their own clinometer or other indirect measuring tool to do this.  (Standard 4.0, 12.0)

N.  Create an animation using graphing calculators.  (Standard 22.0)

III.  ASSESSMENT	

		
Assessment should be made on the basis of a variety of means such as quizzes and tests, projects, investigations, writing samples, and daily work.  Given that this is an honors course, more emphasis will be placed on performance assessment rather than completion of homework.

Students will be given the grading criteria at the beginning of the course, preferably in writing.

B. Course Assessment 

Results of the State Content Standards in Geometry, the High School Exit Exam, and college entrance standardized tests will be monitored to determine the effectiveness of this course.	

XII.	 METHODS AND MATERIALS

The instructional strategies used by teachers of the course will enable students to 

1.  work collaboratively and individually in solving problems;

2.  use calculators and computers as a supplemental part of their work;

3.  explain and justify their work and thinking both in oral and written form;

4.  develop confidence and perseverance in tackling mathematics;

5.  develop an appreciation of mathematics;

6.  develop consistent study habits, organizational skills and personal responsibility for        learning. 

As an honors course, instruction should incorporate “best practices” for working with high performing students (see Gifted and Talented program descriptions).

This course will use the Board-adopted textbook (see approved textbook list) and ancillary materials selected by the teacher.

Manipulatives, compasses, graphing calculators, and computers should be utilized in conjunction with the textbook and resource materials.

C.  School to Career Goals

Whenever possible, the concepts learned in this course will be tied to career applications.  Guest speakers will be brought in to represent how the concepts taught are used in the professional world.  Students are encouraged to investigate  how to apply geometry in their community by interviewing professionals, community service, etc.

V.  GENERAL INFORMATION

Honors Geometry 1H-2H is a two-semester sequence, which carries five credits per semester open to students who meet the prerequisites. As an honors course, it carries a weighted grade point.

A or better in Algebra 1 and Algebra 2 (to date of qualifying exam) and a satisfactory score on the qualifying exam.  

Students must earn a C- or better in Honors Geometry 1H in order to continue into Honors Geometry 2H.

This course can be used in partial fulfillment of the district’s graduation requirement of 30 credits in mathematics. 

This course is accepted in partial fulfillment of the UC/CSU “c” admissions requirement in mathematics.

Revised: 8/17/01
Revised: 11/24/03
Revised:  01/09/04

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