September 2014
York Region District School Board
Newmarket High School
Mathematics Department Course Outline
Subject Head: Mr te Bokkel
Prepared/revised by: J.Grove Sept 2014
Principles of Mathematics, Gr 10 Gifted /Enriched – MPM2DG/3
Credit Value:
1.0
Prerequisites:
MPM1D1/MPM1DG Grade 9 Academic or Gifted/Enriched Mathematics
Teacher:
Mrs Grove
Office location: Math Office, Room 306
Telephone: 905 895 5159 voice mail 422
Curriculum
Document:
The Ontario Curriculum Grades 9 and 10 Mathematics (2005) Revised
Text:
Principles of Mathematics 9, McGraw-Hill Ryerson, 2006
Mathematics 11, Knill, et al., McGraw-Hill Ryerson, 2001
Rationale:
Overall
Expectations
This course enables students to broaden their understanding of relationships and extend their
problem-solving and algebraic skills through investigation, the effective use of technology, and
abstract reasoning. Students will explore quadratic relations and their applications; solve and apply
linear systems; verify properties of geometric figures using analytic geometry; and investigate the
trigonometry of right and acute triangles. Students will reason mathematically and communicate their
thinking as they solve multi-step problems.
By the end of this course, students will:
• determine the basic properties of quadratic relations;
• relate transformations of the graph of 𝑦 = 𝑥 2 to the algebraic representation 𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘
• solve quadratic equations and interpret the solutions with respect to the corresponding
relations;
• solve problems involving quadratic relations.
• model and solve problems involving the intersection of two straight lines;
• solve problems using analytic geometry involving properties of lines and line segments;
• verify geometric properties of triangles and quadrilaterals, using analytic geometry
• use their knowledge of ratio and proportion to investigate similar triangles and solve
problems related to similarity;
• solve problems involving right triangles, using the primary trigonometric ratios and the
Pythagorean theorem;
• solve problems involving acute triangles, using the sine law and the cosine law.
Mark are posted on line through TEACH ASSIST
Website
Please visit the Grade 10 Gifted/Enriched Mathematics website regularly to keep up to date on
assigned homework, assignments and tests. To enter the website:
1. Go to the Newmarket High School Website: www.newmarket.hs.yrdsb.edu.on
2. Click on mathematics (right hand side of the page), Department Home Page, Mrs Grove,
Grade 10 Gifted/Enriched Daybook.
Topics:
Content
Unit Title
1
Equivalent
Algebraic
Expressions
 Expand and simplify second-degree polynomial expressions
 Factor polynomial expressions involving common factors, trinomials,
and differences of squares
 Distributive Property
Factoring
2
Operations with
Exponents
 Power laws
 Zero and Negative Exponents
3
Linear Systems
4
Analytic Geometry
5
Quadratic Functions
& Equations
 Solve systems of two linear equations involving two variables using
graphing and the algebraic method of substitution or elimination
 Solve problems that arise from realistic situations described in words
or represented by linear systems of two equations involving two
variables.
 Solve problems using midpoint,
 Solve problems involving the equation of a circle:
𝑥 2 + 𝑦2 = 𝑟 2
 Verify using algebraic techniques and analytic geometry some
characteristics of geometric figures.
 Verify through a multi-step strategy that uses analytic geometry and
algebraic techniques to verify a geometric property
 Explore the properties of a quadratic relation
 Identify the key features of a graph of a parabola
 Compare the graphs of 𝑦 = 𝑥 2 and 𝑦 = 2 𝑥
 Graph a quadratic from: 𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘
 Determine the roots of a quadratic algebraically
 Distinguish between real and non-real roots.
 Convert 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 to 𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘
 Solve quadratics using the quadratic formula:
−𝑏±√𝑏2 −4𝑎𝑐
2𝑎
 Solve quadratics that have real roots using a variety of methods.
Teaching
strategies:
6
Similar Triangles &
Trigonometry
 Prove two triangles are similar using equality of corresponding
angles and the proportionality of corresponding sides.
 Solve problems involving similar triangles in realistic situations
 Using Trigonometry solve problems involving right triangles using the
primary trigonometric ratios: SOH CAH TOA
 Solving problems involving acute triangles using the Sine Law or
Cosine Law
*
Extension Topics
 Exploration of Matrices and Probability if time permits.
Students will have opportunities to learn in a variety of ways – individually, cooperatively,
independently, with teacher direction, through hands-on experience, and through examples followed
by practice. The approaches and strategies used in the classroom to help students meet the
expectations of this curriculum will vary according to the object of the learning and the needs of the
students, and will include instructions and modelling of preferred ways of working in mathematics,
extensive use of pictures, diagrams, graphic organizers, and manipulatives, key specialized
vocabulary; collaborative learning and class discussion and opportunities to investigate initial
understandings, identify and develop relevant supporting skills, and gain experience with varied and
interesting applications of the new knowledge.
Evaluation:
Evaluation is based on the four Ministry of Education achievement categories: Knowledge and
Understanding, Thinking, Communication, and Application. A single evaluation may include one or
more of the above categories. Evaluation in this course will be continuous throughout the year and
will include a variety of assessment methods (e.g. assignments, projects, quizzes, practical exercises,
presentations, tests, summative activities, final exam).
Learning Skills: (Responsibility, Organization, Independent Work, Collaboration, Initiative, SelfRegulations) will be reported separately from the Achievement of Expectations.
Term
Final
Knowledge and Understanding
25%
Application
20%
Thinking
15%
Communication
10%
Final Examination/Final Culminating
Activity
30%
Total
Equipment:
Expectations:
Be prepared with pen and pencil, 3-ringed binder with dividers, paper (lined and graph), textbook,
ruler, a scientific calculator and your enthusiasm.
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Extra Help
100%
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Bring the proper equipment
Do your homework (expect 30-40 min daily); don’t fall behind.
If you do not understand a lesson please ask questions the next day or arrange a time with
me to get extra help.
If you or your parents have concerns about your progress, please discuss them with me right
away.
Inform me ahead of time if you know you will be absent for a class or classes.
Any student missing a test will have an opportunity to write a make up test upon their return to
school, provided that: (a) I have been informed of a school related absence before the test or
(b) in case of illness I have been informed by phone before your class on the day of the test.
No test marks will be dropped. See department policy.
Available from me. Please speak to me to arrange a time and place.
Peer tutors are available. Go to the Guidance Dept to arrange a tutor.
There is an extra help after school programme at NHS.
Classroom
Guidelines:
There are a number of positive ways in which to contribute to the learning environment of the
classroom:
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Listen attentively and take proper notes, mathematics builds on previous concepts
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Provide answers orally and/or put solutions on the board
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Ask questions! Don’t be afraid to take a risk
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Help others – both in your group and with individual problems
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Keep your mind open – each semester is a fresh start and a new opportunity, this course is
different from other mathematics courses that you have taken
Steps for
Success:
To continue in the academic stream students should achieve a Level 3. Level 3 (which corresponds to
70-80%) is the provincial standard. Students achieving a Level 3 at the end of the course can be
confident that they will be prepared for work in the next grade.
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Student’s Signature
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