Download Course Prerequisites - Birmingham City Schools

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GEOMETRY SYLLABUS
Ms. M. Lake
2014-2015
Course Description
The Geometry course builds on Algebra I concepts and increases students’ knowledge
of shapes and their properties through geometry-based applications, many of which are
observable in aspects of everyday life. This knowledge helps develop visual and spatial
sense and strong reasoning skills. The Geometry course requires students to make
conjectures and to use reasoning to validate or negate these conjectures. The use of
proofs and constructions is a valuable tool that enhances reasoning skills and enables
students to better understand more complex mathematical concepts. Technology will be
used to enhance students’ mathematical experience, not replace their reasoning
abilities.
Course Prerequisites
Algebra I
Course Objectives
The course will cover: congruence; similarity, right triangles, and trigonometry; circles;
expressing geometric properties with equations; geometric measurement and
dimension; modeling with geometry; conditional probability and the rules of probability;
and using probability to make decisions
Course Standards
1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line
segment based on the undefined notions of point, line, distance along a line, and
distance around a circular arc. [G-CO1]
2. Represent transformations in the plane using, e.g., transparencies and geometry
software; describe transformations as functions that take points in the plane as inputs
and give other points as outputs. Compare transformations that preserve distance and
angle to those that do not (e.g., translation versus horizontal stretch). [G-CO2]
3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations
and reflections that carry it onto itself. [G-CO3]
4. Develop definitions of rotations, reflections, and translations in terms of angles,
circles, perpendicular lines, parallel lines, and line segments. [G-CO4]
5. Given a geometric figure and a rotation, reflection, or translation, draw the
transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify
a sequence of transformations that will carry a given figure onto another. [G-CO5]
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6. Use geometric descriptions of rigid motions to transform figures and to predict the
effect of a given rigid motion on a given figure; given two figures, use the definition of
congruence in terms of rigid motions to decide if they are congruent. [G-CO6]
7. Use the definition of congruence in terms of rigid motions to show that two triangles
are congruent if and only if corresponding pairs of sides and corresponding pairs of
angles are congruent. [G-CO7]
8. Explain how the criteria for triangle congruence, angle-side-angle (ASA), side-angleside (SAS), and side-side-side (SSS), follow from the definition of congruence in terms
of rigid motions. [G-CO8]
9. Prove theorems about lines and angles. [G-CO9]
10. Prove theorems about triangles. [G-CO10]
11. Prove theorems about parallelograms. [G-CO11]
12. Make formal geometric constructions with a variety of tools and methods such as
compass and straightedge, string, reflective devices, paper folding, and dynamic
geometric software. [G-CO12]
13. Construct an equilateral triangle, a square, and a regular hexagon inscribed in a
circle. [G-CO13]
14. Verify experimentally the properties of dilations given by a center and a scale factor.
[G-SRT1]
a. A dilation takes a line not passing through the center of the dilation to a
parallel line and leaves a line passing through the center unchanged. [G-SRT1a]
b. The dilation of a line segment is longer or shorter in the ratio given by the
scale factor. [G-SRT1b]
15. Given two figures, use the definition of similarity in terms of similarity transformations
to decide if they are similar; explain using similarity transformations the meaning of
similarity for triangles as the equality of all corresponding pairs of angles and the
proportionality of all corresponding pairs of sides. [G-SRT2]
16. Use the properties of similarity transformations to establish the angle-angle (AA)
criterion for two triangles to be similar. [G-SRT3]
17. Prove theorems about triangles. [G-SRT4]
18. Use congruence and similarity criteria for triangles to solve problems and to prove
relationships in geometric figures. [G-SRT5]
19. Understand that by similarity, side ratios in right triangles are properties of the angles
in the triangle leading to definitions of trigonometric ratios for acute angles. [G-SRT6]
20. Explain and use the relationship between the sine and cosine of complementary
angles. [G-SRT7]
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21. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in
applied problems.* [G-SRT8]
Apply trigonometry to general triangles.
22. (+) Derive the formula A = ( 1/2)ab sin(C) for the area of a triangle by drawing an
auxiliary line from a vertex perpendicular to the opposite side. [G-SRT9]
23. (+) Prove the Law of Sines and the Law of Cosines and use them to solve problems.
[G-SRT10]
24. (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown
measurements in right and non-right triangles (e.g., surveying problems, resultant
forces). [G-SRT11]
25. Prove that all circles are similar. [G-C1]
26. Identify and describe relationships among inscribed angles, radii, and chords. [G-C2]
27. Construct the inscribed and circumscribed circles of a triangle, and prove properties
of angles for a quadrilateral inscribed in a circle. [G-C3]
28. (+) Construct a tangent line from a point outside a given circle to the circle. [G-C4]
29. Derive, using similarity, the fact that the length of the arc intercepted by an angle is
proportional to the radius, and define the radian measure of the angle as the constant of
proportionality; derive the formula for the area of a sector. [G-C5]
30. Derive the equation of a circle of given center and radius using the Pythagorean
Theorem; complete the square to find the center and radius of a circle given by an
equation. [G-GPE1]
31. Use coordinates to prove simple geometric theorems algebraically. [G-GPE4]
32. Prove the slope criteria for parallel and perpendicular lines, and use them to solve
geometric problems. [G-GPE5]
33. Find the point on a directed line segment between two given points that partitions the
segment in a given ratio. [G-GPE6]
34. Use coordinates to compute perimeters of polygons and areas of triangles and
rectangles.* [G-GPE7]
35. Determine areas and perimeters of regular polygons, including inscribed or
circumscribed polygons, given the coordinates of vertices or other characteristics.
36. Give an informal argument for the formulas for the circumference of a circle; area of
a circle; and volume of a cylinder, pyramid, and cone. [G-GMD1]
37. Use volume formulas for cylinders, pyramids, cones, and spheres to solve
problems.* [G-GMD3]
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38. Determine the relationship between surface areas of similar figures and volumes of
similar figures.
39. Identify the shapes of two-dimensional cross-sections of three-dimensional objects,
and identify three-dimensional objects generated by rotations of two-dimensional
objects. [G-GMD4]
40. Use geometric shapes, their measures, and their properties to describe objects (e.g.,
modeling a tree trunk or a human torso as a cylinder).* [G-MG1]
41. Apply concepts of density based on area and volume in modeling situations (e.g.,
persons per square mile, British Thermal Units (BTUs) per cubic foot).* [G-MG2]
42. Apply geometric methods to solve design problems (e.g., designing an object or
structure to satisfy physical constraints or minimize cost, working with typographic grid
systems based on ratios).* [G-MG3]
43. Understand the conditional probability of A given B as P(A and B)/P(B), and interpret
independence of A and B as saying that the conditional probability of A given B is the
same as the probability of A, and the conditional probability of B given A is the same as
the probability of B. [S-CP3]
44. Construct and interpret two-way frequency tables of data when two categories are
associated with each object being classified. Use the two-way table as a sample space
to decide if events are independent and to approximate conditional probabilities. [S-CP4]
45. Recognize and explain the concepts of conditional probability and independence in
everyday language and everyday situations. [S-CP5]
46. Find the conditional probability of A given B as the fraction of B’s outcomes that also
belong to A, and interpret the answer in terms of the model. [S-CP6]
47. Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the
answer in terms of the model. [S-CP7]
48. (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) =
P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. [S-CP8]
49. (+) Use permutations and combinations to compute probabilities of compound events
and solve problems. [S-CP9]
50. (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random
number generator). [S-MD6]
51. (+) Analyze decisions and strategies using probability concepts. [S-MD7]
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Teaching Methods
The following types of teaching methods will be used:
 Lectures
 Individual presentations
 Group presentations
 Demonstrations
 Project(s)
Expectations
Students are expected to be strong academically, highly motivated and be able to work
independently. Extra emphasis will be placed on the students to learn on their own and
to initiate the process of getting extra help when required. The student is expected to
exhibit the behavior of a good citizen at all times in the classroom. Hence, the
classroom will be an environment conducive to learning. Two of the major goals are to
prepare the student for both the American College Testing (ACT) and a post-secondary
education.
Required Course Materials
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Textbook
Workbook
Three ring binder
Plenty of loose leaf paper
Plenty of pencils and erasers
Scientific Calculator (Note: a graphing calculator is highly recommended)
Colored pencils
Evaluation
 Daily grades
o Classwork
o Homework
 Quizzes
o Bell Ringer
o Daily Quiz
o Book Check
 Tests
o In-Class Test
o Take Home Test
o Midterm Test
o Notebook Check
 9 Weeks Exam
Policies
 Classroom Rules
o Come to class with all necessary materials.
o Be in your seat when the tardy bell rings.
o Use the restroom between classes.
o Personal grooming is to take place before class.
o Refrain from talking while the teacher is conducting class.
o Leave your seat only when permitted.
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Cheating or helping others to cheat will not be tolerated.
Profanity will not be permitted verbally or visually.
No food or drink is allowed in class.
Do not leave trash on the floor or mark on the furniture
Be dismissed from the class only by the teacher.
Electronic devices, cell phones, handheld games, mp3’s WILL NOT be
used during class.
ALL daily assignments and test MUST be completed in PENCIL.
 Absentee Policy
o Keep a record of your own absences in your student planner.
o You will see updates of your absences and tardies on your progress
report and on your report card.
o Bring an excuse to me within three days of your absence.
o Making up missed assignments, quizzes, and/or test
 Assignments
 Ask/call a classmate for their notes.
 If you still don’t understand the assignment, come to
afternoon tutoring.
 Upon your return, you have up to 3 class days to turn in a
missed assignment. At the end of the 3rd class day a 0 will
be given for that assignment.
 Quizzes and Tests
 Upon your return, all tests must be completed within 3
class days before or after school.
 A 0 will take the place of any test not completed within 3
class days of your return.
 Uniform Dress Policy
1. All students will wear the designated school system attire. The clothing may
not be altered by slits, cuts, holes, shredded hems, slashes, etc.
2. All students in grades K-12 are required to use clear or mesh book bags/back
packs only.
3. ID cards issued by the school are part of the required uniform and must be
worn in a visible location above the waist at all times.
4. The designated uniform for all Birmingham City Schools students when in a
school-owned building for any school related business shall be:
 Tops
o Solid white, blue, black and khaki shirt with collar. The shirt must
be uniform style. This must be a collared shirt, dress shirt,
turtleneck, or mock turtleneck. The shirt must be buttoned. No
logos, symbols, pictures or writing on the shirt other than the
approved school logo.
o Sweaters/Sweatshirts - V-neck style pullover, crew neck style
pullover, cardigan or sweater vest in the solid uniform colors.
o Hoods, Masks, or Coverings over the face MUST not be worn in
the school building at all.
o No logos, symbols, pictures or writing on the sweaters/sweatshirts
other than approved school logo
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 Bottoms
o Navy blue, khaki, or black pants, skirts, Capri pants, jumpers,
“walking” length shorts limited to 2” above the knee.
o No jeans/denim.
 Shoes
o Any shoe can be worn except: shoes with open toes, boots with
chains, steel toes, or metal reinforcement or decorations, shoes
with wheels or lights, or any other shoes the principal deems
unsafe.
o Socks and a belt must be worn at all times.
 Coats and Jackets
o Gloves, coats and hooded jackets worn to school must be stored
in lockers or other designated locations during the normal school
day.
o Students sensitive to cold temperatures may include a sweater or
sweatshirt as part of the uniform as described above.
 Strictly Forbidden Articles of Clothing or Styles
o Jeans/denim.
o Cargo style pants; overalls or coveralls.
o Over-sized pants or shirts; pants worn below the waist or
“sagging”.
o Pajamas, athletic wear (sweat suits, gym shorts, etc.,); knit, nylon,
spandex or skin tight/tightly fitted clothes (dresses, tops, bottoms
and etc.).
o Visible cleavage.
o Sleeveless/tank tops, tube tops, halter tops, mesh tops, midriff
tops.
o Tee-shirts or tall tees hooded jackets or sweatshirts inside the
building.
o Sunglasses.
o Buttons, jewelry, accessories, or any clothing with offensive, lewd,
vulgar, obscene language, slogans or pictures which
advocate/advertise use of drugs or alcohol or depict weapons or
acts of violence.
o Secret society, fraternity or sorority symbols or lettering.
o Rollers, combs, or cosmetology clamps.
o Scarves/head-rags/doo-rags/bandannas/sweatbands/hats/caps or
other head coverings.
o Visible undergarments clothing altered by cuts, slits or holes or
that in any way exposes the skin.
o Gold teeth or fangs (unless required by a dentist with written
documentation on file).
o Anything else the principal or designee deems inappropriate or
disruptive of the educational environment.
 Guidelines for Enforcement of Student Uniform Regulations
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First Offense:
 The classroom teacher shall contact the parent.
 The parent shall be contacted for a conference.
 The parent shall be required to bring the student appropriate
uniform attire/ID or take the student home to change clothes and
return the student to school.
Second Offense:
 The student shall be taken to the school office or administrative
designee.
 The parent shall be contacted for a conference.
 The parent shall be required to bring the student appropriate
uniform attire/ID or take the student home to change clothes and
return the student to school.
Third Offense:
 The student shall be taken to the school office or administrative
designee.
 The student shall be suspended from school in accordance with
this Code of Conduct, Section 1.03.
 The principal or his/her designee shall determine appropriate
ways to enforce the dress code policy utilizing alternatives listed in
the Code of Student Conduct.
Fourth Offense:
 The student shall be taken to the school office or administrative
designee.
 The student shall be suspended from school in accordance with
this Code of Conduct, Section 2.03.
 The parent must return to school with the student following the
suspension for a conference.
Fifth and All Subsequent Offenses:
 The student shall be taken to the school office or administrative
designee.
 The student shall be suspended from school in accordance with
this Code of Conduct, Section 3.24.
 The Hearing Officer, as outlined under Class III offenses, will
schedule a hearing for the student.
Repeated violations of the Uniform Dress Policy may result in suspension
for noncompliance or expulsion
Parental Involvement
It is essential to get involve with your child’s education. There are
several parent tools that are incorporated into my class.
1. If you have questions, comments, and/or concerns, feel free to set up a
parent/teacher/student conference via your child’s designated
counselor.
2. If you need to get in contact with your child during the educational
process, please call 231-2370.
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Important Dates to Remember
DATE
EVENT
FALL SEMESTER 2014
Thursday, August 14
First Day for Students
Monday, September 1
Labor Day(No School)
Friday, September 12
Progress Reports Go Home
Wed. – Wed., October 15 - 22
PLAN
Tuesday, October 23
Report Cards Picked Up
Friday, October 24
Teacher Work Day (No Students)
Tuesday, November 11
Veterans’ Day(No School)
Tuesday, November 18
Progress Reports Go Home
Wednesday – Friday November 26-28
Thanksgiving Holidays (No School)
Monday, December 15
Final Exam(1st, 3rd, and 5th Periods)
Tuesday, December 16
Final Exam(2nd, 4th, and 6th Periods)
Wednesday, December 17
Final Exam(7th and 8th Periods)
Friday, December 19
End of First Semester
Tues.-Fri., December 23-January 2
Christmas Holidays
SPRING SEMESTER 2015
Tuesday, January 6
Second Semester Begins
Friday, January 9
Report Cards Go Home
Monday, January 19
Martin Luther King, Jr. Day (No School)
Tuesday, February 10
Progress Reports Go Home
Friday, February 13
Professional Development Day (No Students)
Monday, February 16
President Day(No School)
Friday, March 27
Report Cards Go Home
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Monday – Friday, March 30 – April 3
Spring Break
Friday, April 24
Progress Reports Go Home
Thursday, May 21
Final Exam(1st, 3rd, and 5th Periods)
Friday, May 22
Final Exam(2nd, 4th, and 6th Periods)
Monday, May 25
Memorial Day(No School)
Tuesday, May 26
Final Exam(7th and 8th Periods)
Wednesday, May 27
Report Cards Go Home/Last Day for Students
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Ms. M. Lake
Geometry
Class Syllabus Consent
I understand the information given in this class syllabus. Should I fail to achieve
the expectations or fail to uphold the rules and procedures, I understand and
accept the consequences that I face.
___________________________________
Date
_____________________________________________________
Student’s Signature
I have read and discussed the syllabus with my child. I understand what is
expected of him/her in this course. I will provide my full cooperation to
encourage my child’s success in this class. I also know that I am encouraged to
contact the teacher if I have any additional questions or concerns.
______________________________________
Parent’s/Guardian’s Signature
_____________________
Date
Phone Number: ___________________________
E-mail address (optional): ___________________________________________
*******A copy of this syllabus will be sent to you**********
Comments:
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