Course Title: Geometry
School Year: 2013-2014
School: Pueblo East High School
Instructor: Mrs. Rochelle Maes
Email: rochelle.maes@pueblocityschools.us
Phone: 423-3918
I.
Course Description:
Although there are many types of geometry, school mathematics is devoted primarily
to plane Euclidean geometry, studied both synthetically (without coordinates) and
analytically (with coordinates). Euclidean geometry is characterized most importantly
by the Parallel Postulate, that through a point not on a given line there is exactly one
parallel line. (Spherical geometry, in contrast, has no parallel lines.)
During high school, students begin to formalize their geometry experiences from
elementary and middle school, using more precise definitions and developing careful
proofs.
The aim of all IB programmes is to develop internationally minded people who, recognizing their
common humanity and shared guardianship of the planet, help to create a better and more peaceful
world. Students in this course will be encouraged to develop the attributes of the IB Learner Profile
through various activities including collaboration, inquiry based lessons and reflection.
II.
Common Core Standards Addressed
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Congruence
Similarity and Right Triangle Trigonometry
Circles
Expressing Geometric Properties with Equations
Geometric Measuring and Dimension
Modeling with Geometry
MYP Aims and Objectives:
The aims of any MYP subject state in a general way what the teacher may expect to teach or do, and
what the student may expect to experience or learn. In addition, they suggest how the student may be
changed by the learning experience.
The aims of the teaching and study of MYP mathematics are to encourage and enable students to:
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enjoy mathematics and to develop curiosity as well as an appreciation of its elegance and power
develop an understanding of the principles and nature of mathematics
communicate clearly and confidently in a variety of contexts
develop logical, critical and creative thinking, and patience and persistence in problem solving
develop power of generalization and abstraction
apply and transfer skills to a wide range of situations including real life, other areas of knowledge and
future developments
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appreciate how developments in technology and mathematics have influenced each other
appreciate the moral, social and ethical implications arising from the work of mathematicians and the
applications of mathematics
appreciate the international dimension in mathematics through an awareness of the universality of
mathematics and its multicultural and historical perspectives
appreciate the contribution of mathematics to other areas of knowledge
develop the knowledge, skills and attitudes necessary to pursue further studies in mathematics
develop the ability to reflect critically upon their own work and the work of others.
The objectives of any MYP subject state the specific targets that are set for learning in the subject. They
define what the student will be able to accomplish as a result of studying the subject.
These objectives relate directly to the assessment criteria found in the “Mathematics assessment criteria”
section.
A. Knowledge and understanding
Knowledge and understanding are fundamental to studying mathematics and form the base from which
to explore concepts and develop problem-solving skills. Through knowledge and understanding,
students develop mathematical reasoning to make deductions and solve problems.
At the end of the course, students should be able to:
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know and demonstrate understanding of the concepts from the five branches of mathematics (number,
algebra, geometry and trigonometry, statistics and probability, and discrete mathematics)
use appropriate mathematical concepts and skills to solve problems in both familiar and unfamiliar
situations, including those in real-life contexts
select and apply general rules correctly to make deductions and solve problems, including those in reallife contexts.
B. Investigating patterns
Investigating patterns allows students to experience the excitement and satisfaction of mathematical
discovery. Working through investigations encourages students to become risk-takers, inquirers and
critical thinkers.
The ability to inquire is invaluable in the MYP and contributes to lifelong learning.
Through the use of mathematical investigations, students are given the opportunity to apply
mathematical knowledge and problem-solving techniques to investigate a problem, generate and/or
analyse information, find relationships and patterns, describe these mathematically as general rules, and
justify or prove them.
At the end of the course, students should be able to:
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select and apply appropriate inquiry and mathematical problem-solving techniques
recognize patterns
describe patterns as relationships or general rules
draw conclusions consistent with findings
justify or prove mathematical relationships and general rules.
C. Communication in mathematics
Mathematics provides a powerful and universal language. Students are expected to use mathematical
language appropriately when communicating mathematical ideas, reasoning and findings—both orally
and in writing.
At the end of the course, students should be able to communicate mathematical ideas, reasoning and
findings by being able to:
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use appropriate mathematical language in both oral and written explanations
use different forms of mathematical representation
communicate a complete and coherent mathematical line of reasoning using different forms of
representation when investigating problems.
Students are encouraged to choose and use information and communication technology (ICT) tools as
appropriate and, where available, to enhance communication of their mathematical ideas. Some of the
possible ICT tools used in mathematics include spreadsheets, graph plotter software, dynamic geometry
software, computer algebra systems, mathematics content-specific software, graphic display calculators
(GDC), word processing, desktop publishing, graphic organizers and screenshots.
D. Reflection in mathematics
MYP mathematics encourages students to reflect upon their findings and problem-solving processes.
Students are encouraged to examine different problem-solving strategies and share their thinking with
teachers and peers. Critical reflection in mathematics helps students gain insight into their strengths and
weaknesses as learners and to appreciate the value of errors as powerful motivators to enhance learning
and understanding.
At the end of the course, students should be able to:
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explain whether their results make sense in the context of the problem
explain the importance of their findings in connection to real life where appropriate
justify the degree of accuracy of their results where appropriate
suggest improvements to the method when necessary.
MYP Areas of Interaction
Teaching mathematics through the areas of interaction enhances the learning experience in mathematics.
The use of the areas of interaction introduces a new dimension to the inquiry and allows for a richer and
in-depth exploration of concepts and topics. The areas of interaction can be used as starting points to
develop units of work in mathematics, or as bridges to explore connections with other disciplines and
real-world issues.
IV.
MYP Unit Sequence and Duration
Example
Unit Sequence
Introducing Geometry:
Students develop rigorous definitions of
geometric terms to include: congruence
Duration
Approximately 4 weeks
transformations reflections translations and
rotations and use these to discover and prove
geometry properties
V.
Angles, Lines and Constructions:
Students begin to see the structure of math
systems as they make conjectures and then
prove statements involving lines and angles.
Students learn basic constructions and use
these to explore basic geometric properties
Approximately 4 weeks
Triangle Congruence
Students formulize the definition of congruent
triangles using the properties form unit 1 &
unit 3
Polygons
Students use triangle congruence to prove
theorems about parallelograms
Similarities
Students prove theorems involving similarity
and apply dilations and similarity
Right Triangle Relationships and
Trigonometry
Students develop and apply properties of
similar triangles and trigonometric ratios
Circles
Students exploring properties of circles and
deriving equation of circle
Area
Apply prior learning to real world situations
Volume
Explore situations with 3-Dimensional figures
and calculate volume and surface area.
Approximately 3 weeks
Approximately 3 weeks
Approximately 3 weeks
Approximately 5 weeks
Approximately 4 weeks
Approximately 4 weeks
Approximately 5 weeks
Texts and resources
Discovering Geometry: An Investigative Approach, Key Curriculum Press
Additional Supplementary Resources as deemed appropriate
VI.
Assessment
Students will be assessed using the following MYP Criteria which allows the instructor as well as the
student an opportunity to better interpret student understanding in Mathematics.
Criterion A: Knowledge and understanding
Knowledge and understanding are fundamental to studying mathematics and form the base from which
to explore concepts and develop skills. This criterion expects students to use their knowledge and to
demonstrate their understanding of the concepts and skills of the prescribed framework in order to make
deductions and solve problems.
Criterion B: Investigating patterns
Through the use of mathematical investigations, students are given the opportunity to apply
mathematical knowledge and problem-solving techniques to investigate a problem, generate and/or
analyse information, find relationships and patterns, describe these mathematically as general rules, and
justify or prove them.
Criterion C: Communication in mathematics
Students are expected to use mathematical language appropriately when communicating mathematical
ideas, reasoning and findings—both orally and in writing.
Criterion D: Reflection in mathematics
MYP mathematics encourages students to reflect upon their findings and problem-solving processes.
Grading Scale and Policies
90-100% = A 80-89% = B
70-79% = C
60-69% = D
Below 60% = F
Your students grade will be weighted as follows:
Summative Tasks = 40% (Tests, Finals, End of Unit Assessments, Performance Based Projects)
Formative Tasks = 60% (Class work, Home work, Projects, etc.)
This is an interactive course. Class discussions and student presentations will enable us to explore
various methods in problem solving and the reasons they work. Whole group instruction as well as
small group investigation will be used regularly with the expectation that all students will participate
equally.
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CHEATING OF ANY KIND WILL NOT BE TOLERATED AND WILL RESULT IN A GRADE
OF ZERO AND LOSS OF CHANCE TO RE-TEST/SUBMIT.
VII.
ATTENDANCE AND TARDIES
Attendance is required. There is a direct correlation between high student achievement and good
attendance.
Absences: Please refer to the East High School Handbook for school policy regarding absences from
school. Extended absences will be reviewed on an individual basis. In the case of an excused absence
on a test day, the student must take the missing test the day of return to school. Make-up work will only
be allowed for excused absences.
Tardies: St:udents are expected to be in their seat when the tardy bell rings. In the event that they are
late in excess of 5 times during a semester, they will be referred to the Assistant Principal.
VIII. Behavior
Respect is expected at all times for the instructor, substitute instructor, all students and their ideas.
Please refer to the Pueblo City Schools Student Conduct Code.