Login User Name: Password: Login Help

COURSE OUTLINE

Course Title: Mathematics Transfer Course, Grade 9, Applied to Academic
Course Code: MPM1H
Grade: 9
Course Type:Transfer
Credit Value: 0.5
Prerequisite: Foundations of Mathematics, Grade 9, Applied, MFM1P
Curriculum Policy Document: The Ontario Curriculum, Mathematics, Mathematics Transfer Course, Grade 9 Applied to Academic, 2006
Department: Mathematics
Course Developer: Deb Homuth
Development Date: Spring 2008
Course Revised by: -
Revision Date: -

Course Description:

This transfer course will provide students who have successfully completed Foundations of Mathematics, Grade 9, Applied with an opportunity to achieve the expectations not covered in that course but included in Principles of Mathematics, Grade 9, Academic. On successful completion of this transfer course, students may proceed to Principles of Mathematics, Grade 10, Academic (MPM 2D).

This transfer course focuses on developing number sense and algebra, linear relations, analytic geometry, and measurement and geometry through investigation, the effective use of technology, and abstract reasoning. Students will reason mathematically, and communicate their thinking as they solve multi-step problems.

Unit	Titles and Descriptions	Time and Sequence
Unit 1	Exponents When two variables have the same base, but different exponents, they cannot be added or subtracted. However, as long as the base is the same, they can be multiplied and divided. Terms such as y6, x12 and 45 are called powers and are made up of a base and an exponent. Laws for exponents have been developed to aid in calculations involving powers. In this first unit students will study the exponent laws.	10 hours
Unit 2	Algebra Algebraic expressions are made up of terms. These terms are often different. Terms include variables, coefficients, constants and like terms. Students will develop an understanding of all of these and be able to add and subtract algebraic expressions as well as how to divide and factor polynomial expressions.	10 hours
Unit 3	Equations When a linear equation containing one variable is given and you are asked to find the solution, you are solving a linear relation. This involves isolating for the variable and finding the unique solution for the variable that satisfies the relation. With more complicated linear equations, the usual process involves a series of steps that rely on students’ ability to work with numbers algebraically. The general method of solving using specific steps will be taught. When a sentence is given and you are asked to convert the sentence into a mathematical equation, we interpret these words into operations and develop an equation from the given statement. Once the words have been converted into a mathematical equation, the equation can be solved. Practice doing so will be the focus of the second half of this unit.	10 hours
Unit 4	Relations Some relations are given in equation form, rather than just as data. One form of an equation is one that is written as y = mx + b. To graph this type of relation, several techniques can be used. To determine if a set of data will display a relationship, we could graph the relation and look at the graph. However, a second method also exists that does not require us to display the data on a graph. Which steps to follow for this method will be taught. When two relations are graphed on the same set of axes and when the two lines have different rates of change they will intersect (or cross) at one point somewhere on the Cartesian plane. The many applications to this style of intersection problem will be investigated.	10 hours
Unit 5	Analytical Geometry This unit begins with the concept of slope and how it relates to the equation of the line. From here students will find the x and y intercepts. As we have seen linear equations can be written in the form y = mx + b, but they can also be written in the form ax + by = c. This form of a linear equation will be studied in detail in this unit. When the equation is in the form y = mx + b, it is said to be in slope y-intercept form and when it is in the form Ax + By + C = 0, it is said to be in standard form. There are advantages and disadvantages to each way of writing a linear relation and these will be explored.	10 hours
Unit 6	Area / Perimeter / Volume In this unit students will study surface area and volume of three dimensional shapes such as right prisms, pyramids and cylinders.	5 hours
	Final Evaluation The final assessment task is a proctored ninety minute exam worth 30% of the student’s final mark.	2 hours
	Total	110 hours

Teaching / Learning Strategies:

Seven mathematical processes will form the heart of the teaching and learning strategies used.

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 your 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.

Since the over-riding aim of this course is to help students use language skillfully, confidently and flexibly, a wide variety of instructional strategies are used to provide learning opportunities to accommodate a variety of learning styles, interests and ability levels. These include:

Computer Software Use	Problem Solving	Investigations
Visuals	Direct Instruction	Independent Reading
Logical Mathematical Intelligence	Ideal Problem Solving	Problem Posing
Model Analysis	Graphing Applications	Self-Assessments
Manipulatives	Modelling

Assessment and Evaluation Strategies of Student Performance:

Assessment is a systematic process of collecting information or evidence about a student’s progress towards meeting the learning expectations. Assessment is embedded in the instructional activities throughout a unit. The expectations for the assessment tasks are clearly articulated and the learning activity is planned to make that demonstration possible. This process of beginning with the end in mind helps to keep focus on the expectations of the course. The purpose of assessment is to gather the data or evidence and to provide meaningful feedback to the student about how to improve or sustain the performance in the course. Scaled criteria designed as rubrics are often used to help the student to recognize their level of achievement and to provide guidance on how to achieve the next level. Although assessment information can be gathered from a number of sources (the student himself, the student’s course mates, the teacher), evaluation is the responsibility of only the teacher. For evaluation is the process of making a judgment about the assessment information and determining the percentage grade or level.

Strategy	Purpose	Who	Assessment Tool
Self Assessment Quizzes	Diagnostic	Self/Teacher	Marking scheme
Problem Solving	Diagnostic	Self/Peer/Teacher	Marking scheme
Problem Solving	Assessment	Peer/teacher	Marking scheme
Research	Assessment	Peer/teacher	Anecdotal records
Graphing	Assessment	Teacher	Checklist
Problem Solving	Evaluation	Teacher	Marking scheme
Graphing	Evaluation	Teacher	Checklist
Investigations	Evaluation	Teacher	Checklist
Unit Tests	Evaluation	Teacher	Marking scheme
Final Exam	Evaluation	Teacher	Checklist

Assessment is embedded within the instructional process throughout each unit rather than being an isolated event at the end. Often, the learning and assessment tasks are the same, with formative assessment provided throughout the unit. In every case, the desired demonstration of learning is articulated clearly and the learning activity is planned to make that demonstration possible. This process of beginning with the end in mind helps to keep focus on the expectations of the course as stated in the course guideline. The evaluations are expressed as a percentage based upon the levels of achievement.

Overall Expectations - MPM1H

Number Sense and Algebra
Overall Expectations
MNS.01	demonstrate an understanding of the exponent rules of multiplication and division, and apply them to simplify expressions;
MNS.02	manipulate numerical and polynomial expressions, and solve first-degree equations.
Analytic Geometry
Overall Expectations
MAG.01	demonstrate an understanding of the characteristics of a linear relation;
MAG.02	determine the relationship between the form of an equation and the shape of its graph with respect to linearity and non-linearity;
MAG.03	determine, through investigation, the properties of the slope and y-intercept of a linear relation;
MAG.03	solve problems involving linear relations.
Measurement and Geometry
Overall Expectations
MMG.01	solve problems involving surface areas and volumes of three-dimensional figures;
MMG.02	verify through investigation facilitated by dynamic geometry software, geomteric properties and relationships involving two-dimensional shapes, and apply the results to solving prblems.

The Final Grade:

The evaluation for this course is based on the student's achievement of curriculum expectations and the demonstrated skills required for effective learning.

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 the discipline.

A credit is granted and recorded for this course if the student's grade is 50% or higher. The final grade for this course will be determined as follows:

• 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 examination administered at the end of the course. This exam will be based on an evaluation of achievement from all four categories of the Achievement Chart for the course and of expectations from all units of the course. This exam includes well-formulated multiple-choice questions.

The report card will focus on two distinct but related aspects of student achievement; the achievement of curriculum expectations and the development of learning skills. The report card will contain separate sections for the reporting of these two aspects.

A Summary Description of Achievement in Each Percentage Grade Range and Corresponding Level of Achievement
Percentage Grade Range	Achievement Level	Summary Description
80-100%	Level 4	A very high to outstanding level of achievement. Achievement is above the provincial standard.
70-79%	Level 3	A high level of achievement. Achievement is at the provincial standard.
60-69%	Level 2	A moderate level of achievement. Achievement is below, but approaching, the provincial standard.
50-59%	Level 1	A passable level of achievement. Achievement is below the provincial standard.
below 50%	Level R	Insufficient achievement of curriculum expectations. A credit will not be granted.

Achievement Chart: Mathematics, Grades 9-12

Categories	50-59% (Level 1)	60-69% (Level 2)	70-79% (Level 3)	80-100% (Level 4)
Knowledge and Understanding - Subject-specific content acquired in each course (knowledge), and the comprehension of its meaning and significance (understanding)
	The student:
Knowledge of content (e.g., facts, terms, definitions)	demonstrates limited knowledge of content	demonstrates some knowledge of content	demonstrates considerable knowledge of content	demonstrates thorough knowledge of content
Understanding of content (e.g., concepts, ideas, theories, procedures, processes, methodologies, and/or technologies)	demonstrates limited understanding of content	demonstrates some understanding of content	demonstrates considerable understanding of content	demonstrates thorough and insightful understanding of content
Thinking - The use of critical and creative thinking skills and/or processes
	The student:
Use of planning skills (e.g., focusing research, gathering information, organizing an inquiry, asking questions, setting goals)	uses planning skills with limited effectiveness	uses planning skills with moderate effectiveness	uses planning skills with considerable effectiveness	uses planning skills with a high degree of effectiveness
Use of processing skills (e.g., inquiry process, problem-solving process, decision-making process, research process)	uses processing skills with limited effectiveness	uses processing skills with some effectiveness	uses processing skills with considerable effectiveness	uses processing skills with a high degree of effectiveness
Use of critical/creative thinking processess (e.g., oral discourse, research, critical analysis, critical literacy, metacognition, creative process)	uses critical / creative thinking processes with limited effectiveness	uses critical / creative thinking processes with some effectiveness	uses critical / creative thinking processes with considerable effectiveness	uses critical / creative thinking processes with a high degree of effectiveness
Communication - The conveying of meaning through various forms
	The student:
Expression and organization of ideas and information (e.g., clear expression, logical organization) in oral, graphic, and written forms, including media forms	expresses and organizes ideas and information with limited effectiveness	expresses and organizes ideas and information with some effectiveness	expresses and organizes ideas and information with considerable effectiveness	expresses and organizes ideas and information with a high degree of effectiveness
Communication for different audiences (e.g., peers, adults) and purposes (e.g., to inform,to persuade) in oral, written, and visual forms	communicates for different audiences and purposes with limited effectiveness	communicates for different audiences and purposes with some effectiveness	communicates for different audiences and purposes with considerable effectiveness	communicates for different audiences and purposes with a high degree of effectiveness
Use of conventions (e.g., conventions of form, map conventions), vocabulary, and terminology of the discipline in oral, written, and visual forms	uses conventions, vocabulary, and terminology of the discipline with limited effectiveness	uses conventions, vocabulary, and terminology of the discipline with some effectiveness	uses conventions, vocabulary, and terminology of the discipline with considerable effectiveness	uses conventions, vocabulary, and terminology of the discipline with a high degree of effectiveness
Application - The use of knowledge and skills to make connections within and between various contexts
	The student:
Application of knowledge and skills (e.g., concepts, procedures, processes, and/or technologies) in familiar contexts	applies knowledge and skills in familiar contexts with limited effectiveness	applies knowledge and skills in familiar contexts with some effectiveness	applies knowledge and skills in familiar contexts with considerable effectiveness	applies knowledge and skills in familiar contexts with a high degree of effectiveness
Transfer of knowledge and skills (e.g., concepts, procedures, methodologies, technologies) to new contexts	transfers knowledge and skills to new contexts with limited effectiveness	transfers knowledge and skills to new contexts with some effectiveness	transfers knowledge and skills to new contexts with considerable effectiveness	transfers knowledge and skills to new contexts with a high degree of effectiveness
Making connections within and between various contexts (e.g., past, present, and future; environmental; social; cultural; spatial; personal; multidisciplinary)	makes connections within and between various contexts with limited effectiveness	makes connections within and between various contexts with some effectiveness	makes connections within and between various contexts with considerable effectiveness	makes connections within and between various contexts with a high degree of effectiveness

Resources:

• calculator
• various internet websites

Program Planning Considerations for Mathematics:

Teachers who are planning a program in Mathematics must take into account considerations in a number of important areas. Essential information that pertains to all disciplines is provided in the companion piece to this document, The Ontario Curriculum, Grades 9 to 12: Program Planning and Assessment, 2000. The areas of concern to all teachers that are outlined there include the following:

• types of secondary school courses
• education for exceptional students
• the role of technology in the curriculum
• English as a second language (ESL) and English literacy development (ELD)
• career education
• cooperative education and other workplace experiences
• antidiscrimination
• health and safety

Considerations relating to the areas listed above that have particular relevance for program planning in Mathematics are noted here.

Education for Exceptional Students: In planning courses in Mathematics, teachers should take into account the needs of exceptional students as set out in their Individual Education Plan. All Mathematics courses reflect the real world very closely, which offers a vast array of opportunities for exceptional students. Students who use alternative techniques for communication may find a venue for their talents in this online mathematics course as they go about researching the nature of their world.

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 word processing, internet research, presentation software, and equation editors as would be expected in any environment.

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. In addition, since all occupations require employees with a wide range of English skills and abilities, many students will learn how the operation of their own physical world can contribute to their success in their social world.

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.

Cooperative Education and Other Workplace Experiences: By applying the skills they have developed, students will readily connect their classroom learning to real-life activities in the world in which they live. Cooperative education and other workplace experiences will broaden their knowledge of employment opportunities in a wide range of fields. In addition, students will increase their understanding of workplace practices and the nature of the employer-employee relationship. Teachers of Mathematics should maintain links with community-based workers to ensure that students have access to hands-on experiences that will reinforce the knowledge they have gained in school.

Antidiscrimination: The mathematics curriculum in this online course attempts to be unbiased with respect to culture, experiences, interests and learning styles. Where possible, the content reflects a diverse range of cultures and backgrounds. Attempts are made to make to embrace all students in the learning process. In addition, girls are encouraged to consider careers involving mathematics and boys are encouraged to become involved in the learning of mathematics through the inclusion of content that would be of high interest for boys.

Health and Safety: The Mathematics program provides the reading and analytical skills for the student to be able to explore the variety of concepts relating to health and safety in the workplace. Teachers who provide support for students in workplace learning placements need to assess placements for safety and ensure that students can read and understand the importance of issues relating to health and safety in the workplace.