Ontario Curriculum

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;

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

2.1.1: represent, compare, and order decimals to hundredths and fractions, using a variety of tools (e.g., number lines, Cuisenaire rods, base ten materials, calculators);

Comparing and Ordering Decimals

Fraction Garden (Comparing Fractions)

Rational Numbers, Opposites, and Absolute Values

Toy Factory (Set Models of Fractions)

2.1.2: generate multiples and factors, using a variety of tools and strategies (e.g., identify multiples on a hundreds chart; create rectangles on a geoboard) (Sample problem: List all the rectangles that have an area of 36 cm² and have whole-number dimensions.);

Chocomatic (Multiplication, Arrays, and Area)

2.1.3: identify and compare integers found in real-life contexts (e.g., –10°C is much colder than +5°C);

Integers, Opposites, and Absolute Values

2.1.6: represent perfect squares and square roots, using a variety of tools (e.g., geoboards, connecting cubes, grid paper);

2.2.2: use a variety of mental strategies to solve problems involving the addition and subtraction of fractions and decimals (e.g., use the commutative property: 3 x 2/5 x 1/3 = 3 x 1/3 x 2/5, which gives 1 x 2/5 = 2/5; use the distributive property: 16.8 ÷ 0.2 can be thought of as (16 + 0.8) ÷ 0.2 = 16 ÷ 0.2 + 0.8 ÷ 0.2, which gives 80 + 4 = 84);

Estimating Sums and Differences

2.2.6: evaluate expressions that involve whole numbers and decimals, including expressions that contain brackets, using order of operations;

Equivalent Algebraic Expressions I

Order of Operations

2.2.9: add and subtract integers, using a variety of tools (e.g., two-colour counters, virtual manipulatives, number lines).

Adding and Subtracting Integers

Adding and Subtracting Integers with Chips

Adding on the Number Line

Addition of Polynomials

2.3.1: determine, through investigation, the relationships among fractions, decimals, percents, and ratios;

Part-to-part and Part-to-whole Ratios

Percents, Fractions, and Decimals

2.3.2: solve problems that involve determining whole number percents, using a variety of tools (e.g., base ten materials, paper and pencil, calculators) (Sample problem: If there are 5 blue marbles in a bag of 20 marbles, what percent of the marbles are not blue?);

Percent of Change

Percents and Proportions

2.3.3: demonstrate an understanding of rate as a comparison, or ratio, of two measurements with different units (e.g., speed is a rate that compares distance to time and that can be expressed as kilometres per hour);

2.3.4: solve problems involving the calculation of unit rates (Sample problem: You go shopping and notice that 25 kg of Ryan’s Famous Potatoes cost $12.95, and 10 kg of Gillian’s Potatoes cost $5.78. Which is the better deal? Justify your answer.).

Beam to Moon (Ratios and Proportions) - Metric

Household Energy Usage

3.1.1: research and report on real-life applications of area measurements (e.g., building a skateboard; painting a room).

Area of Parallelograms

Perimeter and Area of Rectangles

3.2.2: solve problems that require conversion between metric units of measure (e.g., millimetres and centimetres, grams and kilograms, millilitres and litres) (Sample problem: At Andrew’s Deli, cheese is on sale for $11.50 for one kilogram. How much would it cost to purchase 150 g of cheese?);

3.2.5: solve problems involving the estimation and calculation of the area of a trapezoid;

3.2.6: estimate and calculate the area of composite two-dimensional shapes by decomposing into shapes with known area relationships (e.g., rectangle, parallelogram, triangle) (Sample problem: Decompose a pentagon into shapes with known area relationships to find the area of the pentagon.);

Area of Parallelograms

Area of Triangles

3.2.7: determine, through investigation using a variety of tools and strategies (e.g., decomposing right prisms; stacking congruent layers of concrete materials to form a right prism), the relationship between the height, the area of the base, and the volume of right prisms with simple polygonal bases (e.g., parallelograms, trapezoids), and generalize to develop the formula (i.e., Volume = area of base x height) (Sample problem: Decompose right prisms with simple polygonal bases into triangular prisms and rectangular prisms. For each prism, record the area of the base, the height, and the volume on a chart. Identify relationships.);

3.2.8: determine, through investigation using a variety of tools (e.g., nets, concrete materials, dynamic geometry software, Polydrons), the surface area of right prisms;

Surface and Lateral Areas of Prisms and Cylinders

4.1.1: construct related lines (i.e., parallel; perpendicular; intersecting at 30º, 45º, and 60º), using angle properties and a variety of tools (e.g., compass and straight edge, protractor, dynamic geometry software) and strategies (e.g., paper folding);

Constructing Parallel and Perpendicular Lines

Parallel, Intersecting, and Skew Lines

4.1.2: sort and classify triangles and quadrilaterals by geometric properties related to symmetry, angles, and sides, through investigation using a variety of tools (e.g., geoboard, dynamic geometry software) and strategies (e.g., using charts, using Venn diagrams) (Sample problem: Investigate whether dilatations change the geometric properties of triangles and quadrilaterals.);

Classifying Quadrilaterals

Classifying Triangles

Special Parallelograms

4.1.3: construct angle bisectors and perpendicular bisectors, using a variety of tools (e.g., Mira, dynamic geometry software, compass) and strategies (e.g., paper folding), and represent equal angles and equal lengths using mathematical notation;

Concurrent Lines, Medians, and Altitudes

Constructing Parallel and Perpendicular Lines

Segment and Angle Bisectors

4.2.1: identify, through investigation, the minimum side and angle information (i.e., side-side-side; side-angle-side; angle-sideangle) needed to describe a unique triangle (e.g., “I can draw many triangles if I’m only told the length of one side, but there’s only one triangle I can draw if you tell me the lengths of all three sides.”);

Classifying Triangles

Concurrent Lines, Medians, and Altitudes

Isosceles and Equilateral Triangles

Triangle Inequalities

4.2.3: demonstrate an understanding that enlarging or reducing two-dimensional shapes creates similar shapes;

4.2.4: distinguish between and compare similar shapes and congruent shapes, using a variety of tools (e.g., pattern blocks, grid paper, dynamic geometry software) and strategies (e.g., by showing that dilatations create similar shapes and that translations, rotations, and reflections generate congruent shapes) (Sample problem: A larger square can be composed from four congruent square pattern blocks. Identify another pattern block you can use to compose a larger shape that is similar to the shape of the block.).

Dilations

Reflections

Rock Art (Transformations)

Rotations, Reflections, and Translations

Similar Figures

4.3.1: plot points using all four quadrants of the Cartesian coordinate plane;

City Tour (Coordinates)

Points in the Coordinate Plane

4.3.2: identify, perform, and describe dilatations (i.e., enlargements and reductions), through investigation using a variety of tools (e.g., dynamic geometry software, geoboard, pattern blocks, grid paper);

4.3.3: create and analyse designs involving translations, reflections, dilatations, and/or simple rotations of two-dimensional shapes, using a variety of tools (e.g., concrete materials, Mira, drawings, dynamic geometry software) and strategies (e.g., paper folding) (Sample problem: Identify transformations that may be observed in architecture or in artwork [e.g., in the art of M.C. Escher].);

Dilations

Holiday Snowflake Designer

Reflections

Rock Art (Transformations)

Rotations, Reflections, and Translations

Similar Figures

5.1.1: represent linear growing patterns, using a variety of tools (e.g., concrete materials, paper and pencil, calculators, spreadsheets) and strategies (e.g., make a table of values using the term number and the term; plot the coordinates on a graph; write a pattern rule using words);

Arithmetic Sequences

Arithmetic and Geometric Sequences

Finding Patterns

Function Machines 1 (Functions and Tables)

Function Machines 2 (Functions, Tables, and Graphs)

Geometric Sequences

Introduction to Functions

Points, Lines, and Equations

5.1.4: compare pattern rules that generate a pattern by adding or subtracting a constant, or multiplying or dividing by a constant, to get the next term (e.g., for 1, 3, 5, 7, 9, …, the pattern rule is “start at 1 and add 2 to each term to get the next term”) with pattern rules that use the term number to describe the general term (e.g., for 1, 3, 5, 7, 9, …, the pattern rule is “double the term number and subtract 1”, which can be written algebraically as 2 x n – 1) (Sample problem: For the pattern 1, 3, 5, 7, 9,…, investigate and compare different ways of finding the 50th term.).

Arithmetic and Geometric Sequences

Finding Patterns

5.2.1: model real-life relationships involving constant rates where the initial condition starts at 0 (e.g., speed, heart rate, billing rate), through investigation using tables of values and graphs (Sample problem: Create a table of values and graph the relationship between distance and time for a car travelling at a constant speed of 40 km/h. At that speed, how far would the car travel in 3.5 h? How many hours would it take to travel 220 km?);

Compound Interest

Direct and Inverse Variation

5.2.4: evaluate algebraic expressions by substituting natural numbers for the variables;

Equivalent Algebraic Expressions I

5.2.6: solve linear equations of the form ax = c or c = ax and ax + b = c or variations such as b + ax = c and c = bx + a (where a, b, and c are natural numbers) by modelling with concrete materials, by inspection, or by guess and check, with and without the aid of a calculator (e.g., “I solved x + 7 = 15 by using guess and check. First I tried 6 for x. Since I knew that 6 plus 7 equals 13 and 13, is less than 15, then I knew that x must be greater than 6.”).

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

6.1.1: collect data by conducting a survey or an experiment to do with themselves, their environment, issues in their school or community, or content from another subject and record observations or measurements;

Correlation

Describing Data Using Statistics

Estimating Population Size

Polling: City

Polling: Neighborhood

Reaction Time 2 (Graphs and Statistics)

Real-Time Histogram

Time Estimation

6.1.2: collect and organize categorical, discrete, or continuous primary data and secondary data (e.g., electronic data from websites such as E-Stat or Census At Schools) and display the data in charts, tables, and graphs (including relative frequency tables and circle graphs) that have appropriate titles, labels (e.g., appropriate units marked on the axes), and scales (e.g., with appropriate increments) that suit the range and distribution of the data, using a variety of tools (e.g., graph paper, spreadsheets, dynamic statistical software);

Box-and-Whisker Plots

Graphing Skills

Histograms

Stem-and-Leaf Plots

6.1.4: distinguish between a census and a sample from a population;

6.2.1: read, interpret, and draw conclusions from primary data (e.g., survey results, measurements, observations) and from secondary data (e.g., temperature data or community data in the newspaper, data from the Internet about populations) presented in charts, tables, and graphs (including relative frequency tables and circle graphs);

6.2.3: determine, through investigation, the effect on a measure of central tendency (i.e., mean, median, and mode) of adding or removing a value or values (e.g., changing the value of an outlier may have a significant effect on the mean but no effect on the median) (Sample problem: Use a set of data whose distribution across its range looks symmetrical, and change some of the values so that the distribution no longer looks symmetrical. Does the change affect the median more than the mean? Explain your thinking.);

Describing Data Using Statistics

Mean, Median, and Mode

Movie Reviewer (Mean and Median)

6.2.4: identify and describe trends, based on the distribution of the data presented in tables and graphs, using informal language;

Solving Using Trend Lines

Trends in Scatter Plots

6.2.5: make inferences and convincing arguments that are based on the analysis of charts, tables, and graphs (Sample problem: Use census information to predict whether Canada’s population is likely to increase.).

Polling: City

Real-Time Histogram

6.3.1: research and report on real-world applications of probabilities expressed in fraction, decimal, and percent form (e.g., lotteries, batting averages, weather forecasts, elections);

Estimating Population Size

Probability Simulations

Theoretical and Experimental Probability

6.3.2: make predictions about a population when given a probability (Sample problem: The probability that a fish caught in Lake Goodfish is a bass is 29%. Predict how many bass will be caught in a fishing derby there, if 500 fish are caught.);

6.3.3: represent in a variety of ways (e.g., tree diagrams, tables, models, systematic lists) all the possible outcomes of a probability experiment involving two independent events (i.e., one event does not affect the other event), and determine the theoretical probability of a specific outcome involving two independent events (Sample problem: What is the probability of rolling a 4 and spinning red, when you roll a number cube and spin a spinner that is equally divided into four different colours?);

Independent and Dependent Events

Theoretical and Experimental Probability

6.3.4: perform a simple probability experiment involving two independent events, and compare the experimental probability with the theoretical probability of a specific outcome (Sample problem: Place 1 red counter and 1 blue counter in an opaque bag. Draw a counter, replace it, shake the bag, and draw again. Compare the theoretical and experimental probabilities of drawing a red counter 2 times in a row.).

Independent and Dependent Events

Probability Simulations

Theoretical and Experimental Probability

Correlation last revised: 9/16/2020

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