Grade: Grade 9
Course Name: mathematical principles
Course Code: mpm1d
Course type: Academic
Credit value: 1.0
Pilot course: None
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.
Unit Titles and Descriptions
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 percentages 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.
Linear Equations and Word Problem
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 a number of 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 or not 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.
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 a number of interactive activities that encourage the investigation of internal and external angles, optimization of area, dimensional analysis, and patterns created by shapes' diagonals.
This is a proctored exam worth 30% of your final grade.
Overall Curriculum Expectations
A. Number Sense and Algebra
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.
B. Linear Relations
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.
C. Analytic Geometry
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.
D. Measurement and Geometry
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.
Teaching and Learning Strategies:
The over-riding aim of this course is to help students use the language of mathematics 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. The following mathematical processes are used throughout the course as strategies for teaching and learning the concepts presented:
● Communicating: Through the use of discussions, this course offers students the opportunity to share their understanding both in oral as well as written form.
● Problem solving: This course scaffolds learning by providing students with opportunities to review and activate prior knowledge, and build off of this knowledge to acquire new skills. The course guides students toward recognizing opportunities to apply knowledge they have gained to solve problems.
● Connecting: This course connects the concepts taught to real-world applications (e.g. connecting linear equations to problems such as splitting a bill or manufacturing a product).
● Representing: Through the use of examples and practice problems, and solution videos, the course models various ways to demonstrate understanding, poses questions that require students to use different representations as they are working at each level of conceptual development - concrete, visual or symbolic, and allows individual students the time they need to solidify their understanding at each conceptual stage.