MPM1D(9年级数学)

Unit Titles and Descriptions

Essential Skills

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.

Algebra

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.

Relations

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.

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.

Area/Perimeter/Volume

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.

Final Assessment

Exam

This is a proctored exam worth 30% of your final grade.

A. Number Sense and Algebra

A1

demonstrate an understanding of the exponent rules of multiplication and division, and apply them to simplify expressions;

A2

manipulate numerical and polynomial expressions, and solve first-degree equations.

B. Linear Relations

B1

apply data-management techniques to investigate relationships between two variables;

B2

demonstrate an understanding of the characteristics of a linear relation;

B3

connect various representations of a linear relation.

C. Analytic Geometry

C1

determine the relationship between the form of an equation and the shape of its graph with respect to linearity and non-linearity;

C2

determine, through investigation, the properties of the slope and y-intercept of a linear relation;

C3

solve problems involving linear relations.

D. Measurement and Geometry

D1

determine, through investigation, the optimal values of various measurements;

D2

solve problems involving the measurements of two-dimensional shapes and the surface areas and volumes of three-dimensional figures;

D3

verify, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems.