Course Title: Principles of Mathematics, Grade 10
Course Code: MPM 2D
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:
- 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 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.
|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.
|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.
|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.
|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.
|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.
|Unit 7: Culminating |
The summative project and final exam will be a culmination of everything you have learned throughout the course units.
|Total Hours||110 hours|