Download Geometry MYP Course Syllabus

Summit International Preparatory
Geometry MYP Course Syllabus
School Year: 2014-2015
Instructor:
Cristina Niver
Room 219
Email: [email protected]
Tutoring Hours: Monday, Tuesday, Thursday 4:15-5:15pm, or by appointment
I believe all scholars can be successful at math – it takes perfect practice, but it can be done!
“I've missed 3000 shots. Twenty-six times the game-winning shot has been trusted to me, and I've missed. I've lost over
300 games. I've failed over and over and over again, and that is why I've succeeded.”- Michael Jordan
"A person who never made a mistake never tried anything new." – Albert Einstein
The Course: Geometry
In this course, scholars will cover the fundamentals of geometry while reviewing algebra principles in
preparation for one of the IB Diploma Program math courses. The study of geometry and trigonometry
enhances scholars’ spatial awareness and provides them with the tools for analyzing, measuring and
transforming geometric quantities in two and three dimensions. Key concepts from other MYP subjects that
could be used within the geometry branch include aesthetics (geometric shapes, transformations), change
(identities, transformations), communities (angle properties, triangle properties), creativity (transformations,
similarity and congruency), identity (unit circle, identities), perspective (coordinate geometry, similarity and
congruency), and time, place and space (three-dimensional coordinate geometry, transformations). Geometry
is meant to lead students to an understanding that reasoning and proof are fundamental aspects of
mathematics and something that sets it apart from the other sciences.
Nature of MYP Math
“An MYP mathematics programme should be tailored to the needs of students, seeking to intrigue and motivate
them to want to learn its principles. Students should see authentic examples of how mathematics is useful and
relevant to their lives and be encouraged to apply it to new situations. Mathematics provides the foundation for
the study of sciences, engineering and technology. However, it is also evident in the arts and is increasingly
important in economics, the social sciences and the structure of language. Students in the MYP are encouraged
to use tools to represent information, to explore and model situations, and to find solutions to various
problems. These are skills that are useful in a wide range of arenas. MYP mathematics aims to equip all
students with the knowledge, understanding and intellectual capabilities to address further courses in
mathematics, as well as to prepare those students who will use mathematics in their studies, workplaces and
lives in general.”
-From MYP Mathematics Subject Guide, 2014
Scope and Sequence:
Unit
1: Foundations of
Geometry
Description
 Fundamentals of geometry (points, lines, planes, segments, rays, opposite rays,
etc.)
 Use proper written geometric notation to represent segments, line, rays,
angles, measure of angles, arrays, etc.
 Basic angle vocabulary and calculations (supplementary, complementary,
straight, right, acute, obtuse, etc.)
 Segment addition
2: Logic
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3: Lines and Angles
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4: Triangle
Congruence
5: Triangle
Similarity
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6: Advanced
Triangles
7: Quadrilaterals
8: Transformations
9: 2D Geometry
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Coordinate plane
Solving algebraic equations with variables on both sides
Solving algebraic equations requiring distribution and combining like terms
Inductive reasoning
Deductive reasoning
Conditionals, converse, inverse and contrapositive
Use inductive reasoning to make conjectures and counter examples to disprove
conjectures
Writing and graphing equations of lines
Slopes
Distance Formula – using Pythagorean Theorem as well as the distance
formula
Midpoint
Remediate radicals (for connection to Pythagorean Theorem)
Identify patterns and solve problems involving parallel lines cut by a
transversal.
Relate slope to parallel and perpendicular lines
Explore line postulates incorporating linear equations (point intercept formula
and systems of linear equations)
Properties and classifications of triangles
Use triangle congruence and corresponding parts of congruent triangles to
prove that parts of two triangles are congruent
Executing 2 column proofs: SAS, SSS, AAS, ASA, Hypotenuse leg
Right triangle similarity
Applications with ratios and proportions
Dilations
Identify and apply properties of similar polygons
Justify triangles are similar by applying the AA, SAS, and SSS similarity
theorems
Find and compare the perimeters and areas of similar polygons
Simplify radicals
Apply the Pythagorean Theorem and its converse including in problem solving
situations
Recognize the Pythagorean triples 3-4-5 and 5-12-13
Investigate and apply trigonometric ratios in a right triangle to solve problems
with missing sides
Apply the trigonometry of right triangles to solve problems including angles of
depression and angles of elevation
Special right triangles (30-60-90, 45-45-90)
SOH CAH TOA
Angle of depression
Angle of elevation
Properties of parallelograms
Trapezoids (Right, isosceles, and scalene)
Kites
Quadrilaterals in the coordinate plane
Reflections over either axis as well as the line y=x.
Translations – following a rule and/or writing the rule.
Rotations – in Multiples of 90 degrees
Interior angle sum and exterior angle sum
Perimeter and area formulas
Composite figures
Effect of changing dimensions (on perimeter and area)
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10: 3D Geometry
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11: Circles
12: Algebra 2 Prep
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Apothem
Nets
Isometric and orthographic views
Volume of prisms, cylinders, pyramids, cones and spheres
Surface area (and lateral surface area) of prisms, cylinders, pyramids, cones
and spheres
Composite figures
Effect of changing dimensions (on surface area and volume)
Describe and draw the intersection of a given plane with various threedimensional figures
Use orthographic and isometric views of three-dimensional figures to represent
and construct three-dimensional figures and solve problems
Parts of a circle Including - Radii, diameter, circumference, major/minor arcs,
chords, secants, tangents, etc.
Calculating circumference and area
Proportional reasoning to find arc length and sector area
Find measures of central angles, inscribed angles, exterior angles, and arcs
Formulate and test conjectures about the properties of tangents to circles
Use the properties of congruent chords, arcs, and central angles
Use perpendicular bisectors to chords
Find the measure of an inscribed angle and an angle formed by a tangent and a
chord
Find the measures of angles formed by chords, secants, and tangents
Fluency with solving equations
Fluency with simplifying radicals
Graphing and solving systems of equations
Quadratics review of solving, graphing, and factoring
Prerequisite:
Algebra 1
Textbook: Bass, L. and Charles, R., Texas Geometry, Boston, Massachusetts: Pearson Prentice Hall, 2008
Supplies:
1.5’’ -2’’ Binder, binder dividers (5), loose leaf paper, pencils, blue or black ink pens, protractor, compass, Casio
calculator
Classroom Behavior:
Each scholar should attend class with all class materials including their textbook and homework. Each scholar
will be expected to abide by all school rules and regulations as outlined in the Code of Conduct. In addition,
each student should demonstrate courtesy, respect and consideration to their peers and adults. No food, drink,
or gum permitted. Each scholar is expected to be fully engaged in all class activities, to maintain the highest
level of integrity and honesty in their work, and to ask for help when needed.
Cell Phone Policy:
Classroom disruption by cell phones is prohibited. Cell phones may be used for specific lessons, but only at the
discretion of the instructor.
Assessment:
Grades are calculated based on daily exit tickets (quizzes), homework, class projects, and exams. Each grade
component will be weighed as follows: homework 10%, exit tickets 10%, quizzes 20%, class projects 20%, and
exams 40%
Course grades will use the following scale:
Letter
A
Numerical
90 – 100
B
80 – 89
C
70 – 79
F
69 and below
Grading Policy:
If scholars do not submit assigned homework or projects, they will receive a 10% deduction per class period
until the graded assignment is returned. (i.e., once the homework has been graded, the scholar can no longer
make up those points). If a scholar misses work due to an excused absence, they may submit their work within
two business days of returning to school.
Scholars will have the opportunity to redo work in an effort to demonstrate mastery. If a scholar requests a
redo opportunity, they will be required to schedule and attend a tutorial with the instructor prior to redoing the
assessment (common assessments, homework and exit tickets do not fall under this category). The scholar will
have two options to redo an assessment:
1. Retake assessment: scholar may choose to retake an assessment with the understanding that the rigor
will be increased to ensure content mastery; scholar will receive a new grade that will replace their
previous grade
2. Correct mistakes: scholar may choose to correct their mistakes on a separate sheet on paper showing all
their work to receive half of the points missed on their first assessment; for example, if the scholar
receives a 70% on a unit test, they may correct their mistakes with the understanding that the new
highest grade possible is 85%
In order to receive credit for any and all assessments, the scholar must show their work. The instructor may
reference scholar work to understand where the scholar needs additional practice to gain mastery.
Disabilities:
The teachers of scholars requiring accommodations or modifications are notified by the administration when
the scholar enters the class; however, parents should feel free to alert their child’s teachers of any such
requirements and discuss any concerns they may have.
Course Grades:
Parents and scholars are encouraged to view grades via POWER SCHOOL on a regular basis. Official grades
are provided via report cards and/or transcripts.
Important Dates:
These are subject to change with adequate notice from the instructor; unit tests may also come in the form of a
project dependent upon the topic and testing schedule
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Unit 1 Exam/Project – August 25th and 26th
Unit 2 Exam/Project – September 9th and 10th
Unit 3 Exam/Project – September 29th and 30th
Math Common Assessment – October 6th
Unit 4 Exam/Project – October 28th and 29th
Unit 5 Exam/Project – November 13th and 14th
Math Common Assessment – December 15th
Unit 6 Exam/Project – January 12th and 13th
Unit 7 Exam/Project – January 23rd and 26th
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Unit 8 Exam/Project – February 6th and 9th
Unit 9 Exam/Project – February 23rd and 24th
Math Common Assessment – March 2nd
Unit 10 Exam/Project – April 1st and 2nd
Unit 11 Exam/Project – April 22nd and 23rd
A paper version of parent and student signatures is required to show that you have read the syllabus and
understand the contents therein. If you have any questions, please feel free to contact me. I look forward to
working with you and your child as we explore various aspects of Geometry.
C.Niver
Cut along line and return the bottom.
Mrs. Niver,
I have read and understand the contents of your syllabus for Geometry.
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Parent/Guardian signature
Date
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Student signature
Date