NSS Course Overview MPM 2D • Page XXX
Northern Secondary School
Course Overview
Principles of Mathematics, Grade 10, Academic
Note 1: All Ontario Ministry of Education curriculum documents with full course content information can be located at http://www.edu.gov.on.ca/eng/curriculum/secondary/subjects.html
Note 2: Detailed information on Ministry of Education assessment, evaluation, and reporting policy is provided in The Ontario Curriculum, Grades 9 to 12: Program Planning and Assessment, 2000, located at http://www.edu.gov.on.ca/eng/curriculum/secondary/progplan912curr.pdf
1. Course Details
• Program Area: Mathematics
• Date of Revision: June 2011
• Course title: Principles of Mathematics, Grade 10, Academic (MPM2D). Credit Value 1.0
• Prerequisites(s): Mathematics, Grade 9, Gifted, Enriched, Academic or Applied with Transfer Course
• Textbook(s) and resource materials that are essential to the course: Math Power 10, McGraw-Hill Ryerson, 2000
2. Overall Goals
• Course Description:
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.
• Overall Expectations are in the areas of Quadratic Relations of the Form y = ax2 + bx + c; Analytic Geometry; and Trigonometry. By the end of the course, students will:
• in Quadratic Relations of the Form y = ax2 + bx + c
* determine the basic properties of quadratic relations;
* relate transformations of the graph of y = x2 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.
• in Analytic Geometry
* 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.
• in Trigonometry
* 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.
• Specific Curriculum Expectations
Please refer to Ontario Ministry of Education curriculum document for details of Overall and Specific Expectations, found at http://www.edu.gov.on.ca/eng/curriculum/secondary/math.html
• Course content: unit titles in the sequence in which the material will be studied and a suggested time frame as best as known at the time of printing
Linear Systems / 13 periodsPolynomials / 12 periods
Quadratic Equations / 9 periods
Cumulative Review and Test / 4 periods
Functions / 15 periods
Trigonometry / 12 periods
Analytic Geometry / 14 periods
3. Learning Skills
Learning Skills are skills and habits are essential to success in school and in the workplace. The Learning Skills evaluated are: Responsibility, Organization, Individual Work, Collaboration, Initiative, and Self Regulation. Teachers report achievement on the six Learning Skills using letter symbols: E = Excellent, G = Good, S = Satisfactory, N = Needs Improvement.
Learning Skills clearly affect levels of achievement, but they are not part of the evaluation of achievement and are not included in the midterm mark or final course mark.
4. Academic Honesty: Cheating and Plagiarism
Students are expected to submit only their own original work on evaluations done in class or out of class. Plagiarism the passing off the ideas or writings of another as one's own. Cases of academic dishonesty (cheating and/or plagiarism) will be dealt with on a case-by-case basis, but each case will involve an investigation, communication with the student and his/her parent/guardian, and a mark of zero for the plagiarized work. Whether the student has an opportunity to demonstrate his/her learning in another assignment will be at the discretion of the teacher and/or Principal.
5. Assessment and Evaluation Strategies
Assessment and Evaluation of Student Achievement
The primary purpose of assessment and evaluation is to improve student learning. Assessment is the process of gathering information from assignments, demonstrations, projects, performances, and tests that accurately reflects how well a student is achieving the curriculum expectations in a course. As part of assessment, teachers provide students with feedback that guides their efforts towards improvement.
Evaluation refers to the process of judging the quality of student work on the basis of established criteria, and assigning a value to represent that quality. In Ontario secondary schools, the value assigned will be in the form of a percentage grade.
• In this course, the following evaluation strategies will be used:
70% Course Work / Tests/Quizzes/Assignments30% Culminating Activities / Final Exam and/or Rich Assessment Task
6. Achievement Chart
The achievement chart provides a standard, province-wide method for teachers to use in assessing and evaluating their students’ achievement. Students are evaluated according to the major categories or strands in each course. Ministry curriculum documents provide detailed description of student achievement levels.
In this course, students are evaluated in four strands, according to the weightings shown:
Knowledge/Understanding / Thinking/Inquiry / Communication / Application35 / 15 / 15 / 35
7. 70% Mark on Course Work
• Students need to demonstrate achievement of all the overall expectations of the course. 70% of the final mark in the course will be based on work done prior to the culminating activities. Evaluations that are late, missing, and/or incomplete will affect a student’s 70% grade. See the NSS Evaluation Policy as printed in the Student Agenda Book for information about late, missed, and/or incomplete assignments.
Quizzes and Assignments will be scheduled during each unit. A unit test will be written at the end of each unit. A cumulative test will be written during December.
8. 30% Grade Based on Course Culminating Activities
• All students must take part in the culminating activities for each course at every grade and level of study. The steps to follow when a student is absent from one or more culminating activities is included in the NSS evaluation policy as printed in the Student Agenda Book.
• Culminating activities that occur in class are held within the last six weeks of classes. Culminating activities that are formal examinations occur within the June exam period.
9. Determining Marks for the Provincial Reports
November Report / 100% course workJanuary Report / 80% course work, 20% cumulative test
April Report / 80% course work, 20% cumulative test
June Report / 60% course work, 30% final exam, 10% cumulative test
This grade will be based on the evaluations that have been conducted up to that point in the course. Some of the Overall Expectations, categories/strands, and units will not have been addressed by the report deadline, and the students’ grades will most likely change when the students’ entire work is evaluated by the end of the course.
10. Determining the Mark for the Final Report Card
The mark for the final report card will be the sum of the 70% mark and the 30% mark.
11. Missed tests/quizzes policy
Unit tests will be announced at least one week in advance.
It is expected that all students will write all tests and cumulative tests as a class group. If a student is unable to write the evaluation with the class because of
a) previously scheduled appointments;
b) school-sanctioned excursions or sporting events;
c) recognized religious events;
d) a death in the family, or
e) a court date,
then the student must inform the teacher at least two school days in advance of the test so that alternate arrangements can be made.
Students who are absent on the day of the test due to illness or a family emergency must have their parents phone the math office at 416 393-0284 x20080 on the day of the test explaining why they will be absent. [Doctor’s notes will be required from students who miss more than one scheduled test.] Alternate arrangements will be made for these students to write the test.
If these procedures are not followed, it is possible that a mark of zero will be assigned.
12. Teacher Contact: 416-393-0284 Ext. 20080/20081
13. Extra Help: To be determined depending on individual teacher schedules.
Math help is available daily at lunch in the Math Homework Club in Room 121.
UNIT 1 / Linear Systems (13 periods) / Textbook ExercisesReview Simplifying Expressions, Solving Equations, Graphing Lines
(y =mx+b and intercepts) / p. 3 # 1–9
1.2 / Solving Linear Systems Graphically / p. 12 # 3, 4, 8, 10, 12
1.2 / Solving Linear Systems Graphically / p. # 4, 5, 13–17 p. 14 Modelling Math
p. 15 Achievement Check
1.3 / Solving Linear Systems by Substitution / p. 21 #3, 4, 6, 8, 10, 11, 12
1.5 / Solving Linear Systems by Elimination
Integer Coefficients / p. 30 # 4–7
1.5 / Solving Linear Systems by Elimination
Rational Coefficients / p. 31 # 8–21,
Achievement Check
Review / p. 50 # 1–3, 6, 7, 9–12
Mini-TEST
1.7 / Measurement and Interest Problems / p. 44 # 4, 5, 8, 9, 12, 14, 16
Distance and Current Problems / p. 44 # 6, 7, 13, 15, 17, 19 Math p. 53 # 14–18
Word problems on 1.7 and handouts / p. 50 # 4, 5, 8, 13–18
“Number and Measurement Problems” “Money Problems”, “Interest and Mixture Problems” and “Distance Currency Problems”
Unit Review
Unit-Test
UNIT 2 / Polynomials (12 periods) / Textbook Exercises
3.1 / Polynomials / p. 127 # 3, 5, 6 p. 131 # 1–3, 5–12, 14–22
3.2 / Multiplying Binomials / p. 137 # 3, 4acfg, 5bdgh, 8, 11–16
3.3 / Special Products / p. 142 # 4–8, 10, 14, 18–20, 22
Mini-test
3.4 / Common Factors / p. 150 # 1–9
3.5 / Factoring x2+bx+c / p. 156 # 2–6, 11–14
3.5 / Factor using Algetiles
3.6 / Factoring ax2+bx+c / p. 163 #1–5, 8, 9
3.6 / Factor using Algetiles
3.7 / Factoring Special Quadratics / p. 167 #1–12
Review / p. 174
Test
UNIT 3 / Quadratic Equations (9 periods) / Textbook Exercises
5.1 / Solving Quadratic Equations by Graphing (by hand and TI-83+) / p. 275 # 1–15
5.2 / Solving Quadratic Equations by Factoring / p. 282 # 4–10 (bdfh)
5.2 / Solving Quadratic Equations by Factoring (Applications) / p. 283 # 11–35
Radicals / Simplifying radicals for use in Quadratic Formula / Radicals worksheet
5.4 / The Quadratic Formula / p. 292 # 1–3
5.4 / The Quadratic Formula (Applications) / p. 292 # 5bfj, 6bf, 7, 9, 10, 13–19, 22, 23
Extra Handouts for 5.4 / “The quadratic Formula” “Applications Quadratic Equations” and “Optimization Problems”
Review
Unit-Test
Cumulative Test and Review (4 periods)
1 / Review Linear Systems and Polynomials
2 / Review Polynomials and Quadratic Formula
3 / Cumulative Test Review (all three chapters
4 / Cumulative Test
UNIT 4 / Functions (15 periods) / Textbook Exercises
4.1 / Functions / p. 197 #1,3, 5, 7–12, 15–22
4.2 / Quadratic Functions – Vertical Transformations / p. 213 # 1–5
4.2 / Quadratic Functions – Vertical Transformations (Applications) / p. 213 # 6–18, Modelling Math
4.3 / Quadratic Functions – Horizontal Transformations / p. 223 # 1–7, 9, 10
4.3 / Quadratic Functions – Horizontal Transformations (Applications) / p. 224 # 11–26
Extra Handouts for 4.1 - 4.3 / Graphing y = x2 + k
Review
Mini-Test
4.4 / Completing the Square / p. 234 # 3, 5, 8
4.4 / Completing the Square (Applications) / p. 235 # 10, 11, 14–22
4.5 / Partial Factoring / p. 241 # 1, 2
4.6 / Finite Differences (TI-83+) / p. 242–245
4.7 / Equations of Parabola of Best Fit (TI-83+) / p. 246–247
Review
Unit Test
UNIT 6 / Trigonometry (12 periods) / Textbook Exercises
Proportions, Congruent Triangles, Angle Properties Review / p. 315 # 1–4
6.2 / Similar Triangles / p. 322 # 1–15
6.3-6.5 / Sine/Cosine/Tangent Ratio (2 periods) / p. 338 # 1–16 p. 344 # 1–15
p. 330 # 1–20 Pizzazz # 227, 229, 230
6.6 / Solving Right Triangles / p. 348 #1–13
6.7 / Problems with Two Right Angles / p. 355 # 1–20
Review / p. 380 # 1-19
Test
6.9 / The Sine Law / p. 366 # 1–14
6.10 / The Cosine Law / p. 373 # 1–16
Review / p. 387 # 20-31
Test
UNIT 7 / Analytic Geometry (6 periods) / Textbook Exercises
2.1 / Length of Line Segment / p. 71 # 1bdfg, 5ad, 6bd, 18
2.1 / Length of a Line Segment
Circle – centre (0, 0) / p. 71 # 2–4, 8, 9, 11, 13, 15, 16, 19
2.3 / Midpoint of a Line Segment / p. 77 # 1, 7, 10, 13, 16, 19, 20, 24, 25
Review Equations of Lines (point – slope form) / p. 82–87 select
Review
Test