Foundations of Geometry

 

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"The value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would be solver."

-- I.N. Herstein
 

Why do the angles of a triangle add up to 180°?

How can I cut a line in half without using a ruler?

Course Description

This course is an exploration of geometric concepts.  Students will become aware of geometrical ideas and be exposed to many hands-on activities to help them discover geometric principles and relationships, as well as gain better understanding of how geometry relates to the world.  Topics include points, lines, planes, angles, segments, and their relationships; triangles and congruency, inequalities, similarity,; parallel lines and quadrilaterals, polygons, circles, and area relationships.  Emphasis will be placed on how geometry can be applied in the real world.  Foundations of Geometry will focus on the following:

Chapter 1

Points, lines and planes

Chapter 2

Segments and their relations

Chapter 3

Angles and their relations

Chapter 4

Triangles and congruency

Chapter 5

Special segments of triangles

Chapters 9+10

Similarity and its applications

Chapter 7

Parallel lines

Chapter 8

Quadrilaterals, polygons and circles

Chapter 11

Area relationships

Chapter 12

Pythagorean Theorem

 

Instructional Outcomes

Students who successfully complete this course should be able to:
 

·         Use proper geometric notation to describe various relations among terms.

·         Identify congruent triangles and apply this concept.

·         Identify and apply special segments within a triangle.

·         Identify similar polygons and apply this concept to solve for unknown lengths.

·         Identify special angles that are formed between parallel lines and a transversal.

·         Categorize quadrilateral based on characteristics.

·         Apply basic area formulas.

·         Apply the Pythagorean Theorem.

 

My expectations

I expect every student to come to class on time, prepared with all necessary materials and completed assignments, and most importantly, a positive attitude and an open mind.  Each day a student comes to class unprepared a point will be deducted from their class participation grade (see ‘Grading Policy’ below).  Every student has something unique to offer our class and is, therefore, a valuable member of our learning community.  Coming to class unprepared reduces everyone’s experience.  I expect students to respect each fellow student, their property, the classroom and the teacher.  Finally, I count on students to be persistent.  It takes effort to grasp some mathematical concepts.  Anyone can show effort when something is easy; what defines one’s character is how hard one tries when things get tough.  With persistence and a solid effort, everyone can succeed in this course.

 

What you can expect from me

You can expect me to come to class prepared each day with a positive attitude and an open mind.  Each student learns differently and I will make every effort to accommodate these differences through a variety of instructional methods.  You can expect me to grade fairly and to return assignments in a timely manner.  If additional help is needed outside the classroom, I will typically be available in Room 5 before school starting at 7am and after school Monday through Thursday.  Appointments are appreciated.

 

Grading Policy

Student grades take into account several aspects of the learning experience:
 

Semester Grade

Quarter Grade

Element

Percentage of Grade

Quarter 1
Grade

40%

Quarter 2
Grade

40%

 

 

Final Exam

20%

*Passing grade is 65%

 

Element

Percentage of Grade

Class work

10%

Homework

10%

Collins

10%

Quizzes

25%

Tests

35%

Class Participation

5%

Portfolio

5%

 

The elements comprising the quarter grades are defined below.  Final Exam formats and content will be discussed in class prior to the exams.

 

Class work (10%) – Any in class work (i.e. bell work, worksheets) will fall under this category.  All class work should be documented in the student portfolio. 

Each assignment is worth 1 point and will be graded as credit or no credit.  Full credit is given if an effort is made to complete the assignment.  There is no partial credit given.

 

Homework (10%) – Homework is necessary to practice learned math concepts and will be assigned most nights.  I understand that students will have homework from more than one class a night, and some students also have part-time jobs.  Therefore, the homework assignments will typically be short and every effort will be made not to give homework on Fridays.

Each homework assignment is worth 2 points and is graded on effort.  It will be common for there to be 2 homework assignments from which to choose.  Completing either assignment will earn full credit.  Full credit (2 points) is given if the student has put in an honest effort to complete the full assignment in a legible fashion.  Half credit (1 point) is given if the assignment is not complete or illegible.  Every time a student fails to turn in assigned homework, they must submit a written reason for not having the homework.  These will be kept on file and will be shared with parents if the problem persists.

 

Collins (10%) – The journal will contain the following types of entries:

  • Daily Thoughts (1 point each)
    • At the end of most classes, the last 5 minutes will be spent writing daily thoughts on an assigned topic to get the students to relate to the material covered in class that day.  These will be worth 1 point each and are graded on effort.  There are no wrong answers to daily thought assignments.
  • Type 1 Writing (1 point each)
    • Type 1 writing simply gets ideas on paper and is analogous to brainstorming.  There are no wrong answers, but students must meet the specific quantity of ideas.  Each assignment will be graded as full or no credit.
  • Type 2 Writing (5 points each)
    • Type 2 writing is similar to Type 1 writing in format, but with definite right and wrong answers. 
  • Type 3 Writing (25 points each)
    • Type 3 writing assignments are short essays, usually 3-5 paragraphs, on topics we cover.  Students are graded on criteria specified for that particular assignment.

 

Portfolio (5%) – This course requires the maintenance of a dedicated portfolio of all class work, including class notes, homework, class work, Collins writing, quizzes and tests.  Each quarter, the student portfolios will be evaluated based on the level of organization and completeness.  This is where it is important to ensure dated class notes, class work, homework, quizzes, tests, and Collins assignments are present in the correct sections of the portfolio.  If a student is unhappy with the assigned grade, they will be given one additional opportunity to resubmit their portfolio for review.  Second reviews must occur within 2 days.  Only the highest grade will be logged.

 

Quizzes (25%) – Quizzes will be given on a regular basis to ensure the concepts are understood before moving forward.  This is where students have the opportunity to demonstrate their knowledge of the topics covered.  If a student is unhappy with their performance on a quiz, they have the opportunity to resubmit it with documented corrections for the missed problems.  Students must correctly solve the problem and legibly document the step or concept originally missed.  Corrected quizzes are due within 2 days.  The submitted problems, if correct, earn 50% of the original credit.  For example, if a student earned a 50% on a quiz, but then correctly answered all questions on the resubmission, they would receive a 75% for the quiz.  There will be no unannounced quizzes.

 

Class Participation (5%) – All students are expected to attend class daily, respect each individual in the community and actively participate in each class. I truly believe each one of us has something unique to offer the class.  Only through working together can we make the largest strides.  Student contributions in these areas are rewarded here.

 

Tests (35%) – Tests will be given at the end of each chapter to ensure the concepts are understood before moving forward.  This is where students have the opportunity to demonstrate their knowledge of the topics covered. If a student is unhappy with their performance on a test, they have the opportunity to resubmit it with documented corrections for the missed problems.  Students must correctly solve the problem and legibly document the step or concept originally missed.  Corrected tests are due within 2 days.  The submitted problems, if correct, earn 50% of the original credit.  For example, if a student earned a 50% on a quiz, but then correctly answered all questions on the resubmission, they would receive a 75% for the quiz.

 

Extra Credit – Students will be given opportunities throughout the course to earn extra credit.  All extra credit assignments are optional.

 

Late Work Policy

The following policy will be strictly adhered to regarding late work for Foundations of Geometry.  Please refer to the Student Handbook for definitions of excused and unexcused absences.  In some situations, extensions may be granted for extended excused absences. 

Absences

Excused Absences

Unexcused Absences

Class work

Students missing class for an excused absence may receive full credit for any missed bell work activities (1 point each).  These must be completed as homework.

 

Student missing class for an unexcused absence will receive zero credit for any bell work and class work activities while they were absent.

Homework

If the student was present when the homework was assigned, the homework is due within 1 day of the return to class.

If the student was not present when the homework was assigned, the homework is due within 3 days of returning to class.

If the assignment was due when the student was out for an unexcused absence, zero credit is given.

If the assignment was given while the student was out for an unexcused absence, it is due on the original due date or will result in zero credit.

 

Quizzes
&
Tests

Students missing a quiz or test due to an excused absence must make it up within 3 days of returning to class.

Students missing a quiz or test due to an unexcused absence will receive zero credit.

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