MPM2D Course Outline
Course Outline
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Course Title: | Principles of Mathematics Grade 10 Academic |
Department: | Mathematics |
Grade Level: | 10 |
Course Code: | MPM2D |
Developed from: | Mathematics, Ontario Secondary School Curriculum, Grades 9 and 10, 2005, Revised |
Prerequisite: | MPM1D or MFM1P |
Credits: | 1.0 |
Developed by: | George Vanderkuur |
Development Date: | Mar 2021 |
Reviewed/Revised By: | Ella Hou |
Review/Revise Date: | March 2021 |
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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.
Units: Titles, Time and Sequence
Unit 0 | Grade 9 Review | 3 hours |
Unit 1 | Linear Systems | 15 hours |
Unit 2 | Analytical Geometry | 15 hours |
Unit 3 | Quadratic Expressions | 15 hours |
Unit 4 | Quadratic Relations | 21 hours |
Unit 5 | Quadratic Equations | 18 hours |
Unit 6 | Trigonometry | 17 hours |
| Final Summative Assessment | 6 hours |
| Total | 110 hours |
Overall Curriculum Expectations:
By the end of this course, students will:
Quadratic Relations Of The Form Y=Ax2 + Bx + C
× 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.
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.specific expectations
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.
Teaching / Learning Strategies:
There are seven mathematical processes that support effective learning in mathematics. Attention to the mathematical processes is considered to be essential to a balanced mathematics program. The processes are to be applied in all strands of the mathematics course and are part of the evaluation of student achievement.
The seven mathematical processes are:
Communicating: To improve student success there will be several opportunities for students to share their understanding both in oral as well as written form.
Problem solving: Scaffolding of knowledge, detecting patterns, making and justifying conjectures, guiding students as they apply their chosen strategy, directing students to use multiple strategies to solve the same problem, when appropriate, recognizing, encouraging, and applauding perseverance, discussing the relative merits of different strategies for specific types of problems.
Reasoning and proving: Asking questions that get students to hypothesize, providing students with one or more numerical examples that parallel these with the generalization and describing their thinking in more detail.
Reflecting: Modeling the reflective process, asking students how they know.
Selecting Tools and Computational Strategies: Modeling the use of tools and having students use technology to help solve problems.
Connecting: Activating prior knowledge when introducing a new concept in order to make a smooth connection between previous learning and new concepts, and introducing skills in context to make connections between particular manipulations and problems that require them.
Representing: Modeling various ways to demonstrate understanding, posing questions that require students to use different representations as they are working at each level of conceptual development - concrete, visual or symbolic, allowing individual students the time they need to solidify their understanding at each conceptual stage.
These seven learning strategies are used throughout the course to support strategies including:
× Guided Exploration × Problem Solving × Graphing Applications × Visuals | × Direct Instruction × Independent Reading × Graphing | × Independent Study × Ideal Problem Solving × Model Analysis |
Assessment and Evaluation Strategies
Diagnostic Assessment (For) is the process of gathering evidence of student learning prior to commencing instruction. This information is useful for planning instruction, and in particular for individualizing program delivery. It is not used to determine student achievement levels. |
Implementation × Pre-test for each section of the Course × Interview with teacher × Mathematics Language competency test
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Formative assessment (As) is the process of gathering information during the learning process. It involves constructive and specific feedback to students aimed to improve learning. This evidence may be used for determining a grade/level when there is insufficient evidence from summative assessments. |
Implementation × Learning expectations and criteria for assessment are communicated to students in advance. × Frequent use of Quizzes with feedback to student × Class room observation with teacher feedback to student × ESL students express problems in their own words (English) and verbally describe the steps they use to solve a problem × Assignments with rubrics written in simple English. × Discussion of achievement chart relation to a specific expectations × Teachers provide students with ongoing and descriptive feedback on their learning to help them establish goals for improvement × Peer assessment is used for formative feedback may take the form of marking each other’s quizzes and making suggestions for improvement. × Students periodically assess their own work and set goals for improvement. × Student portfolios to demonstrate growth over time × Exemplars that illustrate achievement levels inform students about their own achievement level.
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Summative assessment (Of) may occur throughout a course. Summative assessment is designed to allow students to demonstrate achievement toward the expectations of a course. It forms the primary basis for establishing the report card levels of achievement and the final mark. Determination of grading levels for formal reporting purposes should primarily reflect student performance on summative tasks. Students’ level grades will reflect their most consistent level of achievement with an eye to their most recent levels of achievement at the time of reporting. |
Implementation × Summative tests throughout term × Rich project × Final exam that covers the overall expectations of the course. |
Student Achievement of the Learning Expectations
Evaluation will be based on the provincial curriculum expectations and the achievement levels outlined in the curriculum document and will be evaluated according to the following breakdown.
Categories of the Achievement Chart | Description | Term | Final |
Knowledge/Understanding | × understanding concepts × performing algorithms | 25% | 25% |
Thinking /Inquiry / Problem Solving | × reasoning × applying the steps of an inquiry/ problem-solving process (e.g., formulating questions; selecting strategies, resources, technology, and tools; representing in mathematical form; interpreting information and forming conclusions; reflecting on the reasonableness of results) | 25% | 25% |
Communication | × communicating reasoning orally, in writing, and graphically × using mathematical language, symbols, visuals, and conventions | 25% | 25% |
Application | × applying concepts and procedures relating to familiar and unfamiliar settings | 25% | 25% |
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| 100% | 100% |
Final Mark
The percentage grade represents the quality of the student's overall achievement of the expectations for the course and reflects the corresponding level of achievement as described in the achievement chart for mathematics.
70% of the grade will be based upon evaluations conducted throughout the course. This portion of the grade will reflect the student's most consistent level of achievement throughout the course, although special consideration will be given to more recent evidence of achievement.
30% of the grade will be based on a final evaluation. At least 20% of the evaluation will be a formal examination. The other 10% may be any one of a variety of appropriate rich assessment tools.
Program Planning Considerations for Mathematics
The Role of Technology in the Curriculum: Information technology is considered a learning tool that must be accessed by Mathematics students when the situation is appropriate. As a result, students will develop transferable skills through their experience with applications like word processing, search engines for internet research, presentation software, equation editors, and graphing tools. By using ICT tools, the students will be able to reduce the time required to perform mundane or repetitive tasks thus creating more time to be spent on higher order tasks such as thinking or concept development.
English as a Second Language and English Literacy Development (ESL/ELD): This Mathematics course can provide a wide range of options to address the needs of ESL/ELD students. Assessment and evaluation exercises will help ESL students in mastering the English language and all of its idiosyncrasies. Many ESL students are mathematically competent in their native language. Teachers should take advantage of this competency to place emphasis on developing the students’ ability to comprehend and do math in English through strategies like:
Oral Language × Individual communication whenever possible × Encourage students to repeat orally × Review and repetition × Regular checking of understanding (content & instructions) × Simultaneous oral and visual presentation × Pacing of instruction × Chunking presentation of new skills/concepts | Environment × Working in pairs and small groups × Charts, pictures of real-life examples × Space in class room to do hands-on work × Peer tutoring × Connect first and second language × Ongoing modelling |
Orientation × Reassurance that first language is valued and important × Buddy to assist with routines, orientation and instructions × First language instruction by other students × Start with what students know – make connections to new learning experiences
| Organization × Patterning (to slow sequencing, procedures, rules) × Colour coding, labelling, picture clues × Numbering of sequential steps × Consistent learning routines similar from one subject to the next × Graphic organizers × Use of charts and other methods of organizing what students have learned × Lists of vocabulary for topics studied
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Curriculum × Flexible testing procedures (e.g., take home, more time allowed) × Visual clues and use of real-life links × Brainstorming × Modification of amount of work expected × Extra time allowed × Use of technology × Word wall as well as picture dictionary × Set up centers × Write in first language and have higher English proficiency student translate × Simplify language when teaching new skills/contents × Provide frequent review (peers, tutors, teachers)
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Literacy and Inquiry/Research Skills: Mathematics course encourages communication among the students through a variety of modes. It also encourages students to communicate with precision in order to communicate effectively. Students are encouraged to ask questions to their peers and teacher and, as well, to become proactive in the solving of their own questions through investigations using a variety of resources such as the internet, textbooks and libraries.
Career Education: Mathematics definitely helps prepare students for employment in a huge number of diverse areas - Engineering, Science, Business, etc. The skills, knowledge and creativity that students acquire through this course are essential for a wide range of careers. Being able to express oneself in a clear concise manner without ambiguity, solve problems, make connections between this Mathematics course and the larger world, etc., would be an overall intention of this Mathematics course, as it helps students prepare for success in their working lives.
× Principles of Mathematics Grade 10, McGraw- Hill Ryerson
× computer software
× manipulatives
× calculator
× various internet websites
× video lessons
The Ontario Skills Passport and Essential Skills:
http://www.skills.edu.gov.on.ca/OSP2Web/EDU/Welcome.xhtml
Teachers planning programs in Mathematics studies need to be aware of the purpose and benefits of the Ontario Skills Passport (OSP). The skills described in the OSP are the essential skills that the Government of Canada and other national and international agencies have identified and validated, through extensive research, as the skills needed for work, learning, and life. Essential skills provide the foundation for learning all other skills and enable people to evolve with their jobs and adapt to workplace change.
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Categories | 50-59% Level 1 | 60-69% Level 2 | 70-79% Level 3 | 80-100% Level 4 | |||
Knowledge/Understanding | The student: | ||||||
understanding | demonstrates limited understanding | demonstrates some understanding | demonstrates considerable understanding | demonstrates thorough understanding | |||
performing algorithms | performs only simple algorithms accurately by hand and using technology | performs algorithms with inconsistent accuracy by hand, mentally, and using technology | performs algorithms accurately by hand, mentally, and using technology | selects the most efficient algorithm and performs it accurately by hand, mentally, and using technology | |||
Thinking/ Inquiry/Problem Solving | The student: | ||||||
reasoning | follows simple mathematical arguments | follows arguments of moderate complexity and makes simple arguments | follows arguments of considerable complexity, judges the validity of arguments, and makes arguments of some complexity | follows complex arguments, judges the validity of arguments, and makes complex arguments | |||
applying the steps of an inquiry/problem- solving process (e.g., formulating questions; selecting strategies, resources, technology, and tools; representing in mathematical form; interpreting information and forming conclusions; reflecting on reasonableness of results) | applies the steps of an inquiry/problem- solving process with limited effectiveness | applies the steps of an inquiry/problem- solving process with moderate effectiveness | applies the steps of an inquiry/problem- solving process with considerable effectiveness | applies the steps of an inquiry/problem- solving process with a high degree of effectiveness and poses extending questions | |||
Communication | The student: | ||||||
communicating reasoning orally, in writing, and graphically | communicates with limited clarity and limited justification of reasoning | communicates with some clarity and some justification of reasoning | communicates with considerable clarity and considerable justification of reasoning | communicates concisely with a high degree of clarity and full justification of reasoning | |||
use of mathematical language, symbols, visuals, and conventions | infrequently uses mathematical language, symbols, visuals, and conventions correctly | uses mathematical language, symbols, visuals, and conventions correctly some of the time | uses mathematical language, symbols, visuals, and conventions correctly most of the time | routinely uses mathematical language, symbols, visuals, and conventions correctly and efficiently | |||
Application | The student: | ||||||
applying concepts and procedures relating to familiar and unfamiliar settings | applies concepts and procedures to solve simple problems relating to familiar settings | applies concepts and procedures to solve problems of some complexity relating to familiar settings | applies concepts and procedures to solve complex problems relating to familiar settings; recognizes major mathematical concepts and procedures relating to applications in unfamiliar settings | applies concepts and procedures to solve complex problems relating to familiar and unfamiliar settings | |||