1: Mathematical process expectations

1.2: Reasoning and Proving

1.2.1: 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;

Biconditional Statements
Conditional Statements

1.5: Connecting

1.5.1: 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);

Estimating Population Size
Unit Conversions

1.7: Communicating

1.7.1: communicate mathematical thinking orally, visually, and in writing, using mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions.

Using Algebraic Expressions

MPM1H.1: Number Sense and Algebra

MPM1H.1.1.1: demonstrate an understanding of the exponent rules of multiplication and division, and apply them to simplify expressions;

MPM1H.1.2.2: extend the multiplication rule to derive and understand the power of a power rule, and apply it to simplify expressions involving one and two variables with positive exponents.

Simplifying Algebraic Expressions II

MPM1H.1.1.2: manipulate numerical and polynomial expressions, and solve first-degree equations.

MPM1H.1.3.1: add and subtract polynomials with up to two variables [e.g., (3x²y + 2xy²) + (4x²y – 6xy²)], using a variety of tools (e.g., computer algebra systems, paper and pencil);

Addition and Subtraction of Functions
Addition of Polynomials

MPM1H.1.3.3: expand and simplify polynomial expressions involving one variable [e.g., 2x(4x + 1) – 3x(x + 2)], using a variety of tools (e.g., algebra tiles, computer algebra systems, paper and pencil);

Addition of Polynomials
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations I

MPM1H.1.3.4: solve first-degree equations, including equations with fractional coefficients, using a variety of tools (e.g., computer algebra systems, paper and pencil) and strategies (e.g., the balance analogy, algebraic strategies);

Modeling One-Step Equations
Solving Two-Step Equations

MPM1H.1.3.6: solve problems that can be modelled with first-degree equations, and compare algebraic methods to other solution methods (Sample problem: Solve the following problem in more than one way: Jonah is involved in a walkathon. His goal is to walk 25 km. He begins at 9:00 a.m. and walks at a steady rate of 4 km/h. How many kilometres does he still have left to walk at 1:15 p.m. if he is to achieve his goal?).

Modeling One-Step Equations
Modeling and Solving Two-Step Equations

MPM1H.2: Linear Relations

MPM1H.2.1: Most of the expectations in the Linear Relations strand of the Grade 9 applied and academic courses are common to the two courses. Some of these expectations may require review since the concepts and skills in this strand are critical for student success in the Analytic Geometry strand of this transfer course.

Linear Functions

MPM1H.4: Measurement and Geometry

MPM1H.4.1.1: solve problems involving the surface areas and volumes of three-dimensional figures;

MPM1H.4.2.2: determine, through investigation, the relationship for calculating the surface area of a pyramid (e.g., use the net of a square-based pyramid to determine that the surface area is the area of the square base plus the areas of the four congruent triangles);

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

MPM1H.4.2.3: solve problems involving the surface areas of prisms, pyramids, cylinders, cones, and spheres, including composite figures (Sample problem: Break-bit Cereal is sold in a single-serving size, in a box in the shape of a rectangular prism of dimensions 5 cm by 4 cm by 10 cm. The manufacturer also sells the cereal in a larger size, in a box with dimensions double those of the smaller box. Compare the surface areas and the volumes of the two boxes, and explain the implications of your answers.);

Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

MPM1H.4.2.4: identify, through investigation with a variety of tools (e.g. concrete materials, computer software), the effect of varying the dimensions on the surface area [or volume] of square-based prisms and cylinders, given a fixed volume [or surface area];

Surface and Lateral Areas of Prisms and Cylinders

MPM1H.4.2.5: explain the significance of optimal surface area or volume in various applications (e.g., the minimum amount of packaging material; the relationship between surface area and heat loss);

Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

MPM1H.3: Analytic Geometry

MPM1H.3.1.1: demonstrate an understanding of the characteristics of a linear relation;

MPM1H.3.2.3: determine the equation of a line of best fit for a scatter plot, using an informal process (e.g., using a movable line in dynamic statistical software; using a process of trial and error on a graphing calculator; determining the equation of the line joining two carefully chosen points on the scatter plot).

Correlation
Determining a Spring Constant
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

MPM1H.3.1.2: determine the relationship between the form of an equation and the shape of its graph with respect to linearity and non-linearity;

MPM1H.3.3.1: determine, through investigation, the characteristics that distinguish the equation of a straight line from the equations of nonlinear relations (e.g., use a graphing calculator or graphing software to graph a variety of linear and non-linear relations from their equations; classify the relations according to the shapes of their graphs; connect an equation of degree one to a linear relation);

Absolute Value with Linear Functions
Exponential Functions
Graphs of Polynomial Functions
Quadratics in Vertex Form

MPM1H.3.3.2: identify, through investigation, the equation of a line in any of the forms y = mx + b, Ax + By + C = 0, x = a, y = b;

Linear Inequalities in Two Variables
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

MPM1H.3.3.3: express the equation of a line in the form y = mx + b, given the form Ax + By + C = 0.

Linear Inequalities in Two Variables
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

MPM1H.3.1.3: determine, through investigation, the properties of the slope and y-intercept of a linear relation;

MPM1H.3.4.1: determine, through investigation, various formulas for the slope of a line segment or a line (e.g., m = rise/run, m = the change in y/the change in x or m = delta y/delta x, m = (y2 - y1)/(x2 - x1), and use the formulas to determine the slope of a line segment or a line;

Cat and Mouse (Modeling with Linear Systems) - Metric
Slope
Slope-Intercept Form of a Line

MPM1H.3.1.4: solve problems involving linear relations.

MPM1H.3.5.1: graph lines by hand, using a variety of techniques (e.g., graph y = 2/3x - 4 using the y-intercept and slope; graph 2x + 3y = 6 using the x- and y-intercepts);

Slope-Intercept Form of a Line

MPM1H.3.5.2: determine the equation of a line from information about the line (e.g., the slope and y-intercept; the slope and a point; two points) (Sample problem: Compare the equations of the lines parallel to and perpendicular to y = 2x – 4, and with the same x-intercept as 3x – 4y = 12. Verify using dynamic geometry software.);

Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

MPM1H.3.5.3: describe the meaning of the slope and y-intercept for a linear relation arising from a realistic situation (e.g., the cost to rent the community gym is $40 per evening, plus $2 per person for equipment rental; the y-intercept, 40, represents the $40 cost of renting the gym; the value of the slope, 2, represents the $2 cost per person);

Cat and Mouse (Modeling with Linear Systems) - Metric
Slope-Intercept Form of a Line