A: Mathematical Models

A.1: make connections between the numeric, graphical, and algebraic representations of quadratic relations, and use the connections to solve problems;

A.1.1: construct tables of values and graph quadratic relations arising from real-world applications (e.g., dropping a ball from a given height; varying the edge length of a cube and observing the effect on the surface area of the cube)

Addition and Subtraction of Functions
Quadratics in Polynomial Form

A.1.3: determine, through investigation using technology, the roles of a, h, and k in quadratic relations of the form y = a(x – h)² + k, and describe these roles in terms of transformations on the graph of y = x² (i.e., translations; reflections in the x-axis; vertical stretches and compressions to and from the x-axis)

Exponential Functions
Quadratics in Vertex Form
Translations
Zap It! Game

A.1.4: sketch graphs of quadratic relations represented by the equation y = a(x – h)² + k (e.g., using the vertex and at least one point on each side of the vertex; applying one or more transformations to the graph of y = x²)

Quadratics in Vertex Form

A.1.7: factor trinomials of the form ax² + bx + c , where a = 1 or where a is the common factor, by various methods

Factoring Special Products

A.1.9: solve problems, using an appropriate strategy (i.e., factoring, graphing), given equations of quadratic relations, including those that arise from real-world applications (e.g., break-even point)

Quadratics in Polynomial Form

A.2: demonstrate an understanding of exponents, and make connections between the numeric, graphical, and algebraic representations of exponential relations;

A.2.1: determine, through investigation using a variety of tools and strategies (e.g., graphing with technology; looking for patterns in tables of values), and describe the meaning of negative exponents and of zero as an exponent

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

A.2.4: graph simple exponential relations, using paper and pencil, given their equations [e.g., y = 2 to the x power, y = 10 to the x power, y = (½) to the x power]

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

A.3: describe and represent exponential relations, and solve problems involving exponential relations arising from real-world applications.

A.3.2: describe some characteristics of exponential relations arising from real-world applications (e.g., bacterial growth, drug absorption) by using tables of values (e.g., to show a constant ratio, or multiplicative growth or decay) and graphs (e.g., to show, with technology, that there is no maximum or minimum value)

Introduction to Exponential Functions

B: Personal Finance

B.1: compare simple and compound interest, relate compound interest to exponential growth, and solve problems involving compound interest;

B.1.2: determine, through investigation (e.g., using spreadsheets and graphs), and describe the relationship between compound interest and exponential growth

Compound Interest

B.1.4: calculate the total interest earned on an investment or paid on a loan by determining the difference between the amount and the principal [e.g., using I = A – P (or I = FV – PV)]

Compound Interest

B.1.6: determine, through investigation using technology (e.g., a TVM Solver on a graphing calculator or on a website), the effect on the future value of a compound interest investment or loan of changing the total length of time, the interest rate, or the compounding period

Compound Interest

B.2: compare services available from financial institutions, and solve problems involving the cost of making purchases on credit;

B.2.4: gather, interpret, and compare information about current credit card interest rates and regulations, and determine, through investigation using technology, the effects of delayed payments on a credit card balance

Compound Interest

B.2.5: solve problems involving applications of the compound interest formula to determine the cost of making a purchase on credit

Compound Interest

C: Geometry and Trigonometry

C.1: represent, in a variety of ways, two-dimensional shapes and three-dimensional figures arising from real-world applications, and solve design problems;

C.1.4: solve design problems that satisfy given constraints (e.g., design a rectangular berm that would contain all the oil that could leak from a cylindrical storage tank of a given height and radius), using physical models (e.g., built from popsicle sticks, cardboard, duct tape) or drawings (e.g., made using design or drawing software), and state any assumptions made

Segment and Angle Bisectors

C.2: solve problems involving trigonometry in acute triangles using the sine law and the cosine law, including problems arising from real-world applications.

C.2.1: solve problems, including those that arise from real-world applications (e.g., surveying, navigation), by determining the measures of the sides and angles of right triangles using the primary trigonometric ratios

Sine, Cosine, and Tangent Ratios

D: Data Management

D.1: solve problems involving one-variable data by collecting, organizing, analysing, and evaluating data;

D.1.3: explain the distinction between the terms population and sample, describe the characteristics of a good sample, and explain why sampling is necessary (e.g., time, cost, or physical constraints)

Polling: City
Polling: Neighborhood
Populations and Samples

D.1.6: identify and describe properties associated with common distributions of data (e.g., normal, bimodal, skewed)

Mean, Median, and Mode
Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions

D.1.7: calculate, using formulas and/or technology (e.g., dynamic statistical software, spreadsheet, graphing calculator), and interpret measures of central tendency (i.e., mean, median, mode) and measures of spread (i.e., range, standard deviation)

Box-and-Whisker Plots
Describing Data Using Statistics
Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

D.1.8: explain the appropriate use of measures of central tendency (i.e., mean, median, mode) and measures of spread (i.e., range, standard deviation)

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

D.1.9: compare two or more sets of one-variable data, using measures of central tendency and measures of spread

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Real-Time Histogram

D.1.10: solve problems by interpreting and analysing one-variable data collected from secondary sources

Describing Data Using Statistics

D.2: determine and represent probability, and identify and interpret its applications.

D.2.1: identify examples of the use of probability in the media and various ways in which probability is represented (e.g., as a fraction, as a percent, as a decimal in the range 0 to 1)

Probability Simulations
Theoretical and Experimental Probability

D.2.2: determine the theoretical probability of an event (i.e., the ratio of the number of favourable outcomes to the total number of possible outcomes, where all outcomes are equally likely), and represent the probability in a variety of ways (e.g., as a fraction, as a percent, as a decimal in the range 0 to 1)

Binomial Probabilities
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

D.2.3: perform a probability experiment (e.g., tossing a coin several times), represent the results using a frequency distribution, and use the distribution to determine the experimental probability of an event

Binomial Probabilities
Polling: City

D.2.4: compare, through investigation, the theoretical probability of an event with the experimental probability, and explain why they might differ

Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

Correlation last revised: 9/24/2019

This correlation lists the recommended Gizmos for this province's curriculum standards. Click any Gizmo title below for more information.