Principles of Mathematics (MPM 2D)

Course Overview

Course Title: Principles of Mathematics, Grade 10
Course Code: MPM 2D
Grade: 10
Course Type: Academic
Credit Value: 1.0
Prerequisite: MPM 1D, Principles of Mathematics, Grade 9, Academic br>Department: Mathematics
Tuition Fee (CAD): $529

This course enables students to broaden their understanding of relationships and extend their problem-solving and algebraic skills through investigation, their 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 Curriculum Expectations

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

Problem Solving
  • Develop, select, apply, and compare a variety of problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding;

Reasoning and Proving
  • Develop and apply reasoning skills (e.g., recognition of relationships, generalization through inductive reasoning, use of counter-examples) to make mathematical conjectures, assess conjectures, and justify conclusions, and plan and construct organized mathematical arguments;
  • Demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem (e.g., by assessing the
  • Effectiveness of strategies and processes used, by proposing alternative approaches, by judging the reasonableness of results, by verifying solutions);

Selecting Tools and Computational Strategies
  • Select and use a variety of concrete, visual, and electronic learning tools and Select and use a variety of concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems;
  • Make connections among mathematical concepts and procedures, and relate mathematical ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas, daily life, current events, art and culture, sports);
  • Create a variety of representations of mathematical ideas (e.g., numeric, geometric, algebraic, graphical, pictorial representations; onscreen dynamic representations), connect and compare them, and select and apply the appropriate representations to solve problems;
  • Communicate mathematical thinking orally, visually, and in writing, using mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.

Unit Overview

Unit 1: Linear Systems
You will be introduced to a Peace and Development fundraising initiative, which will provide the context for using Linear Systems to solve problems. At the beginning of the unit, you will complete an on-line tutorial for using Geometers’ Sketchpad, a tool that can provide graphical solutions for this unit and other units in this course. You will solve Linear Systems algebraically and connect their solutions with graphical representations. You will keep their own notes in a journal, which will be submitted periodically for assessment.
10 hours
Unit 2: Analytic Geometry
In this unit you will use analytical geometry to form a relationship between these three shapes. These shapes will also form the basis of some key formulas that are used in calculations.
15 hours
Unit 3: Properties of Quadratic Relations
You will begin this unit by collecting and fitting data that is non-linear and then move into graphing simple quadratic equations using appropriate technology. Through investigation, you will learn some key features of parabolas. You will calculate the first and second differences of quadratic equations. This leads to a study of some transformations of quadratics, and sketching by hand. You will learn to find the equation of a quadratic from a graph. You will begin to explore the exponential function by comparing its graph to that of the parabola. Throughout the unit, you will complete summary notes for each activity, in preparation for the summative test at the end of the unit.
20 hours
Unit 4: Applications of Quadratic Relations
The process of expanding and simplifying algebraic expressions is explored using polynomial tiles. The exploration leads to the development of an algorithm that will permit algebraic expansions to be performed more efficiently. The algorithm is reversed to introduce the concept of factoring as well as the need for a variety of techniques of factoring. The ability to express the same expression in different ways leads to the various forms in which a quadratic relation may be written. Algebraic manipulation is used to change between forms of a quadratic relation. The graphical representation is connected to the various algebraic representations of a quadratic relation. Interpreting the information from the graph introduces the need to be able to solve quadratic equations. A variety of techniques to solve quadratic equations are applied to a variety of situations that can be modeled by quadratic relations.
20 hours
Unit 5: Similar Triangles
You will undertake an investigation to determine the basic properties of similar triangles. The study continues with a further look at similar triangles, this time using different orientations and perspectives. The unit study then moves into an activity on congruence versus similarity. You will learn how to solve for unknown sides and angles in similar triangles. They further develop their skills with similar triangles by examining the ratio of areas of similar triangles. You will apply their learning by solving realistic problems with similar triangles.
15 hours
Unit 6: Trigonometry
Trigonometry is a branch of mathematics that studies the relationship between sides and angles in a triangle. This unit will focus on discovering some of these relationships and using them as a method for finding the missing measurements of triangles. Surveyors, architects and engineers, as well as navigators and astronomers to name but a few, use trigonometry to find solutions to their problems.
20 hours
Unit 7: Culminating
The summative project and final exam will be a culmination of everything you have learned throughout the course units.
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