Foundation of Mathematics (MFM 1P)

Course Overview

Course Title: Foundations of Mathematics, Grade 9
Course Code: MFM 1P
Grade: 9
Course Type: Applied
Credit Value: 1.0
Prerequisite: None required
Department: Mathematics
Tuition Fee (CAD): $529

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.

Overall Curriculum Expectations

By the end of the course, students will gain proficiency in the following areas:

Number Sense and Algebra
  • Solve problems involving proportional reasoning;
  • Simplify numerical and polynomial expressions in one variable, and solve simple first-degree equations.

Linear Relations
  • apply data-management techniques to investigate relationships between two variables;
  • determine the characteristics of linear relations;
  • demonstrate an understanding of constant rate of change and its connection to linear relations;
  • connect various representations of a linear relation, and solve problems using the representations.
Measure and Geometry
  • determine, through investigation, the optimal values of various measurements of rectangles;
  • solve problems involving the measurements of two-dimensional shapes and the volumes of three-dimensional figures;
  • determine, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems

Unit Overview

Unit 1: 2D & 3D Measurement
In this unit, you will explore volume relationships for pyramids, cones and spheres. You will solve a variety of perimeter and area problems involving composite shapes, as well as problems dealing with the Pythagorean Theorem.
5 hours
Unit 2: Measurement Optimization
In this unit, you will solve optimization problems that require either maximizing the area or minimizing the perimeter of 2D shapes.
5 hours
Unit 3: Exploring Relationships
In this unit, you will explore linear and non-linear relations. By examining trends in data you will identify if a relation is linear or not. You will model linear relations with a line of best fit. You will have an opportunity to conduct an investigation, explore first differences and create models to make predictions.
15 hours
Unit 4: Proportional Reasoning
In this unit, you will be given opportunities to reason proportionally. Connections will be made between linear relations and proportional relationships. You will work with ratios, percents, scale factors, and rates using practical examples.
15 hours
Unit 5: Linear Relationships
This is the culminating unit for this course. This unit will provide a In this unit, you will create stories from information conveyed by graphs. You will make connections between pictorial, numeric, algebraic and graphical representations of linear relationships, and give meaning to the rate of change and initial value. You will identify linear relations as being direct or partial variations.
15 hours
Unit 6: Solving Equations
In this unit, you will solve equations a variety of ways. You will be given opportunities to represent practical examples of pairs of linear relations graphically then use the graph to determine and give meaning to the point of intersection.
15 hours
Unit 7: Algebraic Models
In this unit, you will examine the need for working with polynomials. You will investigate techniques to add, subtract and multiply polynomials. Problems are posed that can be solved algebraically. You will make connections between the volume formulas for cones, cylinders and spheres.
20 hours
Unit 8: Geometry
In this unit, you will investigate angle properties of 2-D shapes. You will explore angles formed by parallel lines cut by a transversal as well as exterior and interior angles of polygons to develop further angle properties. You will apply angle properties to solve geometric problems including those involving algebra.
10 hours
Unit 9: Culminating Unit
10 hours
Total Hours110 hours
Teaching and Learning Strategies

Enthusiastic teachers and instructors bring unique teaching and assessment methods to the classroom because students learn best when they are engaged in a range of different learning techniques. The activities allow students to apply learned concepts to current world social, economic, and environmental issues which impact daily life. Opportunities to relate knowledge and skills to these wider contexts will motivate students to learn in a meaningful way and to become life-long learners. Instructors also inspire students to become successful problem solvers by investigating, providing alternative reasoning and solutions to problems as well as dedicating time and energy to the tasks at hand.

Effective instructional techniques utilize students’ existing knowledge and by capturing their interest and engaging in meaningful participation. Students will be engaged when they are able to see the correlation between the learned concepts and their ability to apply them to the world around them and in real-life situations. Students will have the chance to learn using a wide range of methods which include self-learning, cooperative learning as well as learning through teacher guidance as well has hands-on experiences. The methods and strategies teachers implement will be tailored to the learning requirements and the individual needs of the students. Teachers will achieve effective instruction in an online environment by using videos, interactive animations and virtual labs and discussion forums and video conferencing/live chat.

Individualized Accommodations for Students

Our methodology for student assessment follows the Growing Success Assessment, Evaluation and Reporting in Ontario Schools First Edition, Covering Grades 1 to 12 (2010) manual published by the Ontario Ministry of Education. Assessment is the process of gathering information that accurately reflects how well a student is achieving the curriculum expectations in a subject or course. Assessment tools are designed to improve student learning which includes descriptive feedback, coaching, observations and self-assessments. In addition, student can be independent and set individual goals, monitor progress against these goals, determine next steps and reflect on their thinking and learning.

For a student with special education needs who requires modified or alternative expectations, assessment and evaluation of his or her achievement will be based on the modified curriculum expectations or alternative expectations outlined in the student’s Individual Education Plan (IEP). Accommodations required to facilitate the student’s learning may be identified by the teacher, however recommendations from a School Board generated in the form of an Individual Education Plan (IEP) should be used, if available. 

For a student with special education needs who requires “accommodations only”, as described in his or her IEP, assessment and evaluation of achievement will be based on the appropriate subject/ grade/course curriculum expectations and the achievement levels outlined in the curriculum documents.

A student’s Individual Education Plan (IEP) describes his or her educational program and any accommodations that may be required. The IEP specifies whether the student requires:
accommodations only; or
modified learning expectations, with the possibility of accommodations;

Assessment accommodations are changes in procedures that enable the student to demonstrate his
or her learning. These may include:
visual supports to clarify verbal instructions, assistive devices, or some form of human support;
alternative methods for the student to demonstrate his or her achievement of expectations (e.g., allowing the student to take tests orally) or the allowance of extra time to complete the assessment;
alternative settings that may be more suitable for the student to demonstrate his or her learning.

If accommodations are required to assess and evaluate student learning, the strategies to be used are outlined in the student’s IEP.
For further details about the different types of accommodations, modified learning expectation and alternative programs please refer to Growing Success Assessment, Evaluation and Reporting in Ontario Schools First Edition, Covering Grades 1 to 12 (2010)

Materials Required

Standard Computer Requirements for all courses:
-Processor speed of 2 GHz or faster
-Memory of 4 GB RAM or greater
-A high speed internet connection with a connection speed of 10 MB/s or better.
-Monitor and video card with 1024×768 or greater resolution
-Keyboard and Mouse is recommended