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COURSE OUTLINE

Course Title: Foundations of Mathematics
Course Code: MFM1P
Grade: 9
Course Type: Applied
Credit Value: 1
Prerequisite: None
Curriculum Policy Document: Mathematics, Ontario Secondary School Curriculum, Grades 9 and 10, 2005, Revised
Department: Mathematics
Course Developer: Mr. Ken Stewart
Development Date: October 2004
Course Revised by: Mr. Ken Stewart
Revision Date: 2005

Course Description:

This course enables students to develop an understanding of mathematical concepts related to introductory algebra, proportional reasoning, and measurement and geometry through investigation, the effective use of technology, and hands-on activities. Students will investigate real-life examples to develop various representations of linear relations, and will determine the connections between the representations. They will also explore certain relationships that emerge from the measurement of three-dimensional figures and two-dimensional shapes. Students will consolidate their mathematical skills as they solve problems and communicate their thinking.

Unit	Titles and Descriptions	Time and Sequence
Unit 1	Number Sense and Algebraic Review Today, there are a variety of number systems that mathematicians use for a variety of applications. The unit begins by reviewing these. Number sense is not the ability to count, but the ability to recognize that something has changed in a small collection and this is the second topic for review. Applying the rules for order of operations as well as those for manipulating fractions, changing decimals to percents and vice-versa, ratios and laws for exponents are all reviewed in this unit.	20 hours
Unit 2	Analyzing Relationships with Data The unit begins with practical problems regarding ratios, rates, percents, proportions; scale drawings are used to target proportional reasoning. Then kinds of surveys, their graphs and terminology like interpolation and extrapolation are explained. The final topics involve determining if a set of data will display a relationship, generating a table of values so we can graph it and the variations.	22 hours
Unit 3	Linear Equations and Word Problems This unit takes time to develop a step by step procedure to solve linear equations. This procedure uses the concept of opposite operations to isolate for the given variable. Addition and subtraction are opposite operations and multiplication and division are the second set of opposite operations. We will always use the opposite operation to that which is given in the linear equation to solve for the variable. We review the distributive law then attack word problems for solving linear equations.	22 hours
Unit 4	Slopes and Equations of a Line Three topics comprise this unit. Students will look at distance time graphs to find data, they will deal with the concept of a slope of a line and talk about the points of intersection of two lines.	22 hours
Unit 5	Measurement and Geometry This unit opens with problems involving the Pythagorean Theorem then after reviewing areas and perimeters of polygons we will move right into calculated areas of composite shapes where the total area of the shape is equal to the combination of the individual areas of the shapes that make up the composite shape. Determining surface areas of right prisms and pyramids, cylinders cones and spheres concludes the unit.	22 hours
	Final Evaluation The final assessment task is a proctored two hour exam worth 30% of the student’s final mark.	2 hours
	Total	110 hours

Teaching / Learning Strategies:

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:

e-Textbook Use	Problem Solving	Graphing
Visuals	Direct Instruction	Independent Reading
Logical Mathematical Intelligence	Ideal Problem Solving	Problem Posing
Model Analysis	Graphing Applications	Self-Assessments

Assessment and Evaluation Strategies of Student Performance:

Assessment is a systematic process of collecting information or evidence about student learning. Evaluation is the judgment we make about the assessments of student learning based on established criteria. The purpose of assessment is to improve student learning. This means that judgments of student performance must be criterion-referenced so that feedback can be given that includes clearly expressed next steps for improvement. Tools of varying complexity are used by the teacher to facilitate this. For the more complex evaluations, the criteria are incorporated into a rubric where levels of performance for each criterion are stated in language that can be understood by students.

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 - MFM1P

Number Sense and Algebra
Overall Expectations
MNS.01	solve problems involving proportional reasoning;
MNS.02	simplify numerical and polynomial expressions in one variable, and solve simple first-degree equations.
Linear Relations
Overall Expectations
MLR.01	apply data-management techniques to investigate relationships between two variables;
MLR.02	determine the characteristics of linear relations;
MLR.03	demonstrate an understanding of constant rate of change and its connection to linear relations;
MLR.04	connect various representations of a linear relation, and solve problems using the representations.
Measurement and Geometry
Overall Expectations
MMG.01	determine, through investigation, the optimal values of various measurements of rectangles;
MMG.02	solve problems involving the measurements of two-dimensional shapes and the volumes of three-dimensional figures;
MMG.03	determine, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems.

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, procedural skills, use of tools)	demonstrates limited knowledge of content	demonstrates some knowledge of content	demonstrates considerable knowledge of content	demonstrates thorough knowledge of content
Understanding of matematical concepts	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 -understanding the problem (e.g., formulating and interpreting the problem, making conjectures) -making a plan for problem solving	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 -carrying out a plan (e.g., collecting data, questioning, testing, revising, modelling, solving, inferring, forming conclusions) -looking back at the solution (e.g., evaluating reasonableness, making convincing arguments, reasoning, justifying, proving, reflecting)	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., problem solving, inquiry)	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 mathematical thinking (e.g., clarity of expression, logical organization), using oral, visual, and written forms (e.g., pictorial, graphic, dynamic, numeric, algebraic forms; concrete materials)	expresses and organizes mathematical thinking with limited effectiveness	expresses and organizes mathematical thinking with some effectiveness	expresses and organizes mathematical thinking with considerable effectiveness	expresses and organizes mathematical thinking with a high degree of effectiveness
Communication for different audiences (e.g., peers and teachers) and purposes (e.g., to present data, justify a solution, express a mathematical argument) in oral, visual, and written 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, vocabulary, and terminology of the discipline (e.g., terms, symbols) in oral, visual, and written 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 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 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., connections between concepts, representations, and forms within mathematics; connections involving use of prior knowledge and experience; connections between mathematics, other disciplines, and the real world))	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:

• MFM1P online course of study
• visuals
• videos
• calculator
• various internet websites

Reference Texts:

• Addison Wesley Applied Mathematics 9; Robert Alexander, Lynda Conan, Peter J. Harrison, Rob McLeish, et al.; Pearson Education Canada, 2003
• Mathematics: Applying the Concepts 9; Chris Dearling, Wayne Erdman, Brian McCudden, Roland W. Meisel, Tess Miller, et al.; McGraw-Hill Ryerson, 2003

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
• 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 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.

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.