N9: Number

N9.1: Demonstrate (concretely, pictorially, and symbolically) understanding of powers with integral bases (excluding base 0) and whole number exponents including:

N9.1.3: powers with an exponent of zero

Dividing Exponential Expressions
Multiplying Exponential Expressions

N9.1.h: Apply the exponent laws to expressions involving powers, and determine the quantity represented by the expression, with or without the use of technology.

Compound Interest

N9.1.k: Analyze a simplification of an expression involving powers for errors

Dividing Exponential Expressions
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

N9.2: Demonstrate understanding of rational numbers including:

N9.2.1: comparing and ordering

Comparing and Ordering Decimals
Rational Numbers, Opposites, and Absolute Values

N9.2.2: relating to other types of numbers

Rational Numbers, Opposites, and Absolute Values

N9.2.3: solving situational questions.

Estimating Population Size

N9.2.a: Order a given set of rational numbers, in fraction and decimal form, by placing them on a number line and explaining the reasoning used (e.g., 3/5, - 0.666, 4,? , 0.5,-5/8).

Comparing and Ordering Decimals
Rational Numbers, Opposites, and Absolute Values

N9.3: Extend understanding of square roots to include the square root of positive rational numbers.

N9.3.a: Develop a generalization about what type of number results from the squaring of a rational number.

Square Roots

N9.3.c: Determine the square root of a rational number that is a perfect square.

Simplifying Radical Expressions
Square Roots

N9.3.d: Determine the rational number for which a given rational number is its square root (e.g., is the square root of what rational number?).

Square Roots

N9.3.e: Explain and apply strategies involving benchmarks for determining an estimate of the square root of a rational number that is not a perfect square.

Square Roots

N9.3.f: Determine, with the use of technology, an approximate value for the square root of a rational number that is not a perfect square.

Square Roots

N9.3.g: Explain why the value shown by technology may only be an approximation of the square root of a rational number.

Square Roots

P9: Patterns and Relations

P9.1: Demonstrate understanding of linear relations including:

P9.1.1: graphing

Linear Functions

P9.1.4: solving situational questions.

Linear Functions

P9.1.b: Sort a set of graphs into representations of linear and nonlinear relations.

Linear Functions

P9.1.d: Generalize strategies for determining if a given linear relation will have a graph that is horizontal, vertical, increasing, or decreasing.

Linear Functions
Point-Slope Form of a Line
Standard Form of a Line

P9.1.i: Solve situational questions by graphing linear relations and interpreting the resulting graphs.

Linear Functions

P9.2.1: ax = b

Solving Equations by Graphing Each Side
Standard Form of a Line

P9.2.2: x/a= b, a ≠ 0

Solving Equations by Graphing Each Side
Standard Form of a Line

P9.2.3: ax + b = c

Solving Equations by Graphing Each Side
Solving Two-Step Equations
Standard Form of a Line

P9.2.4: x/a + b = c, a ≠ 0

Solving Equations by Graphing Each Side
Solving Two-Step Equations
Standard Form of a Line

P9.2.5: ax = b + cx

Solving Equations by Graphing Each Side

P9.2.6: a(x + b) = c

Solving Equations by Graphing Each Side

P9.2.7: ax + b = cx + d

Solving Equations by Graphing Each Side

P9.2.8: a(bx + c) = d(ex + f)

Solving Equations by Graphing Each Side

P9.2.9: a/x = b, x ≠ 0

Solving Equations by Graphing Each Side
Solving Two-Step Equations
Standard Form of a Line

P9.2.c: Write a linear equation to represent a particular situation.

Linear Inequalities in Two Variables
Solving Equations by Graphing Each Side
Standard Form of a Line

P9.2.d: Observe and describe a situation relevant to self, family, or community which could be represented by a linear equation.

Absolute Value with Linear Functions
Solving Equations by Graphing Each Side
Standard Form of a Line

P9.2.e: Write a linear equation representing the pattern in a given table of values and verify the equation by substituting values from the table.

Direct and Inverse Variation
Points, Lines, and Equations

P9.2.i: Solve a linear equation symbolically.

Solving Equations by Graphing Each Side

P9.2.j: Analyze the given solution for a linear equation that has resulted in an incorrect solution, and identify and explain the error(s) made.

Modeling and Solving Two-Step Equations

P9.2.k: Provide examples from the modern world in which linear equations are used and solved.

Absolute Value with Linear Functions
Solving Equations by Graphing Each Side
Solving Two-Step Equations
Standard Form of a Line

P9.3: Demonstrate understanding of single variable linear inequalities with rational coefficients including:

P9.3.1: solving inequalities

Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Solving Linear Inequalities in One Variable
Systems of Linear Inequalities (Slope-intercept form)

P9.3.3: comparing

Systems of Linear Inequalities (Slope-intercept form)

P9.3.4: graphing.

Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Solving Linear Inequalities in One Variable
Systems of Linear Inequalities (Slope-intercept form)

P9.3.a: Observe and describe situations relevant to self, family, or community, including First Nations and Métis communities, that involve inequalities and classify the inequality as being less than, greater than, less than or equal to, or greater than or equal to.

Systems of Linear Inequalities (Slope-intercept form)

P9.3.b: Verify whether or not a given rational number is part of the solution set for a linear inequality.

Solving Linear Inequalities in One Variable

P9.3.f: Compare and explain the process for solving a linear equation to the process for solving a linear inequality.

Linear Inequalities in Two Variables

P9.3.i: Graph the solution of a linear inequality on a number line.

Compound Inequalities
Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable

P9.3.l: Solve a situational question involving a single variable linear inequality and graph the solution.

Compound Inequalities
Linear Inequalities in Two Variables
Systems of Linear Inequalities (Slope-intercept form)

P9.4: Demonstrate understanding of polynomials (limited to polynomials of degree less than or equal to 2) including:

P9.4.2: generalizing strategies for addition, subtraction, multiplication, and division

Addition and Subtraction of Functions
Addition of Polynomials
Dividing Polynomials Using Synthetic Division
Modeling the Factorization of x²+bx+c

P9.4.5: comparing for equivalency.

Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

P9.4.d: Identify the variables, degree, number of terms, and coefficients, including the constant term, of a given simplified polynomial expression and explain the role or significance of each.

Addition of Polynomials
Dividing Polynomials Using Synthetic Division
Simplifying Algebraic Expressions II

P9.4.e: Identify the type of expression that is represented by a polynomial of degree 1.

Graphs of Polynomial Functions

P9.4.g: Critique the statement ?A binomial can never be a degree 2 polynomial?.

Dividing Polynomials Using Synthetic Division

P9.4.h: Write equivalent forms of a polynomial expression by interchanging terms or by decomposing terms, and justify the equivalence.

Simplifying Algebraic Expressions II

SS9: Shape and Space

SS9.1: Demonstrate understanding of circle properties including:

SS9.1.2: inscribed angles subtended by the same arc have the same measure

Chords and Arcs
Inscribed Angles

SS9.1.3: the measure of a central angle is twice the measure of an inscribed angle subtending the same arc

Chords and Arcs
Inscribed Angles

SS9.1.a: Observe and describe situations relevant to self, family, or community that involve circles, chords, central angles, inscribed angles, radii, arcs, and/or points of tangency.

Circles

SS9.1.c: Generalize, from personal explorations, the relationship between the measures of inscribed angles subtended by the same arc.

Chords and Arcs
Inscribed Angles

SS9.1.d: Generalize, from personal explorations, the relationship between the measure of a central angle and the measure of inscribed angles subtended by the same arc.

Chords and Arcs
Inscribed Angles

SS9.1.g: Describe examples of where First Nations and Métis, past and present, lifestyles and worldviews demonstrate one or more of the circle properties (e.g., tipi and medicine wheel).

Circles

SS9.1.h: Solve a situational question involving the application of one or more of the circle properties.

Circles

SS9.2: Extend understanding of area to surface area of right rectangular prisms, right cylinders, right triangular prisms, to composite 3-D objects.

SS9.2.b: Analyze a composite 3-D object to identify areas of overlap and explain the impact of these areas on determining the surface area of the composite 3-D object.

Surface and Lateral Areas of Prisms and Cylinders

SS9.2.c: Critique the statement ?To find the surface area of a composite 3-D object, add together the surface areas of the individual 3-D objects from which the composite 3-D object is comprised?.

Surface and Lateral Areas of Prisms and Cylinders

SS9.2.d: Determine the surface area of composite 3-D objects.

Surface and Lateral Areas of Prisms and Cylinders

SS9.2.f: Give dimensions for a single 3-D object that will have the same surface area as a composite 3-D object.

Surface and Lateral Areas of Prisms and Cylinders

SS9.3.d: Explain how ratios and proportionality are related to similarity of polygons.

Similar Figures

SS9.3.e: Draw a polygon similar to a given polygon and explain the strategies used.

Similar Figures

SS9.3.f: Solve situational questions involving the similarity of polygons.

Similar Figures

SS9.3.h: Explain how scale diagrams are related to similarity, ratios, and proportionality.

Dilations
Similar Figures

SS9.3.i: Draw a diagram to scale that represents an enlargement or reduction of a given 2-D shape and explain the strategies used.

Dilations
Similar Figures

SS9.3.j: Explain how to determine the scale factor for a given 2-D shape and an enlargement or reduction of the shape.

Dilations
Similar Figures

SS9.3.k: Verify whether or not a given diagram is a scale diagram of a 2-D shape and, if it is, identify the scale factor for the diagram.

Dilations
Similar Figures

SS9.3.l: Solve situational questions involving scale diagrams and scale factors.

Dilations
Similar Figures

SP9: Statistics and Probability

SP9.1: Demonstrate understanding of the effect of:

SP9.1.8: population or sample on data collection.

Polling: City
Polling: Neighborhood

SP9.1.b: Provide examples to illustrate how bias, use of language, ethics, cost, time and timing, privacy, or cultural sensitivity may influence the data collected.

Polling: Neighborhood
Populations and Samples

SP9.1.c: Identify situations relevant to self, family, or community where a set of data was collected and classify each situation as involving a sample or the population.

Describing Data Using Statistics
Polling: City
Polling: Neighborhood

SP9.1.e: Provide an example of a question where a limitation precludes the use of a population and describe the limitation (e.g., too costly, not enough time, limited resources).

Polling: Neighborhood

SP9.2: Demonstrate an understanding of the collection, display, and analysis of data through a project.

SP9.2.a: Devise a project plan related to a situation relevant to self, family, or community, that involves:

SP9.2.a.1: formulating a question for investigation

Correlation
Describing Data Using Statistics
Real-Time Histogram

SP9.2.a.2: choosing a data collection method that includes social considerations

Describing Data Using Statistics
Estimating Population Size

SP9.2.a.3: electing a population or a sample, and justifying the choice

Polling: City
Polling: Neighborhood

SP9.2.a.4: collecting the data

Describing Data Using Statistics
Estimating Population Size

SP9.2.a.5: displaying the collected data in an appropriate manner

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Estimating Population Size
Stem-and-Leaf Plots

SP9.2.a.6: drawing conclusions to answer the question.

Estimating Population Size
Reaction Time 1 (Graphs and Statistics)

SP9.2.b: Create and apply a rubric to assess a project that includes the assessment of all requirements for the project.

Polling: City
Real-Time Histogram

SP9.2.c: Complete the project according to the plan, draw conclusions, and communicate findings to an audience.

Correlation
Reaction Time 1 (Graphs and Statistics)

SP9.3: Demonstrate an understanding of the role of probability in society.

SP9.3.b: Analyze the meaningfulness of a probability against the limitations of assumptions associated with that probability.

Probability Simulations
Theoretical and Experimental Probability

SP9.3.c: Provide examples of how a single probability could be used to support opposing positions.

Estimating Population Size
Theoretical and Experimental Probability

SP9.4: Research and present how First Nations and Métis peoples, past and present, envision, represent, and make use of probability and statistics.

SP9.4.b: Compare the significance, representation, and use of probability and statistics for different First Nations and Métis peoples, and other cultures.

Estimating Population Size
Probability Simulations
Theoretical and Experimental Probability