Mathematics: Principles of Mathematics (MPM1D)
Course Description
This course enables students to develop generalization of mathematical ideas and methods through the exploration of applications, the effective use of technology, and abstract reasoning. Students will investigate relationships to develop equation of the lines in analytic geometry, explore relationship between volume and surface area of objects in measurement, and apply extended algebraic skills in problem solving. Students will engage in abstract extensions of core learning that will deepen their mathematical knowledge and enrich their understanding.This course enables students to develop an understanding of mathematical concepts related to algebra, analytic geometry, and measurement and geometry through investigation, the effective use of technology, and abstract reasoning. Students will investigate relationships, which they will then generalize as equations of lines, and will determine the connections between different representations of a linear relation. They will also explore relationships that emerge from the measurement of three-dimensional figures and two-dimensional shapes. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
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| Units | Descriptions | Length (Approximately) |
|---|---|---|
| 1. | Essential Skills Algebra 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. Algebraic expressions and how to add, subtract, multiply and divide them are the substance of Unit Two as students acquire the skills for simplifying algebraic expressions |
33 hours |
| 2. | Linear Relations We begin by developing strategies to solve linear equations. We investigate different ways in which relationships can be expressed, and how to translate between these different means. We look at several involved situations related to our everyday lives and consider the many different ways in which linear equations help us to find solutions. The unit begins with Cartesian planes and the graphing of ordered pairs; the two quantities (x and y) are related in some way and form a relationship. The values that change in this relationship are called variables. Next, we look at the relation y = mx + b. To graph this type of relation, several techniques are used. We investigate relationships through a data management project, considering how we might determine whether relationships exist between different factors. We decide what data must be collected and how it must be processed in order to reliably make a conclusion. |
35 hours |
| 3. | Analytical Geometry We further our discussion of slope with distance time graphs. The concepts of slope, x and y intercepts, the slopes of parallel, perpendicular, horizontal, and vertical lines will prepare students for the important concept of the equation of a line and the forms in which it can be written. After a review of areas and perimeters of shapes, students take part in several interactive activities that encourage the investigation of internal and external angles, optimization of area, dimensional analysis, and patterns created by shapes’ diagonals |
32 hours |
| The final assessment task is to provide students to do Exam Review (4 Hrs) +Formative Exam (2 Hrs) +Culminating Task (2 Hrs) + Final Exam (2 Hrs) + | 10 hours | |
| Total | 110 hours | |
Overall Curriculum Expectations
By the end of this course, students will:
- Demonstrate an understanding of the exponent rules of multiplication and division and apply them to simplify expressions.
- Manipulate numerical and polynomial expressions and solve first-degree equations.
By the end of this course, students will:
- Apply data-management techniques to investigate relationships between two variables.
- Demonstrate an understanding of the characteristics of a linear relation.
- Connect various representations of a linear relation.
By the end of this course, students will:
- Determine the relationship between the form of an equation and the shape of its graph with respect to linearity and non-linearity.
- Determine, through investigation, the properties of the slope and y-intercept of a linear relation.
- Solve problems involving linear relations.
By the end of this course, students will:
- Determine, through investigation, the optimal values of various measurements.
- Solve problems involving the measurements of two-dimensional shapes and the surface areas and volumes of three-dimensional figures.
- Verify, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems.
Assessment & Evaluation of student performance
Formative assessments are learning practices that provide important feedback to student progress. Examples include homework and quizzes.
Summative assessments form a foundation for final mark allotment at the end of the unit, term and final evaluation.
An achievement chart will be given to students at regular intervals and the purpose of the charts is to provide feedback to students in relation to content and performance strands.
| Knowledge and understanding | Communication | Thinking Inquiry and Problem solving | Application |
|---|---|---|---|
| 25% | 25% | 25% | 25% |
Unit Tests, Written assignments, presentations, Classroom Observations and Classroom conversations.
Pass Percentage