Ontario Curriculum
2.1.1: represent, compare, and order equivalent representations of numbers, including those involving positive exponents;
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents, Fractions and Decimals
2.1.2: solve problems involving whole numbers, decimal numbers, fractions, and integers, using a variety of computational strategies;
Adding Real Numbers
Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals
2.1.3: solve problems by using proportional reasoning in a variety of meaningful contexts.
Beam to Moon (Ratios and Proportions)
Estimating Population Size
Proportions and Common Multipliers
2.2.3: represent, compare, and order rational numbers (i.e., positive and negative fractions and decimals to thousandths);
Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Rational Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
2.2.4: translate between equivalent forms of a number (i.e., decimals, fractions, percents) (e.g., 3/4 = 0.75);
Improper Fractions and Mixed Numbers
Percents, Fractions and Decimals
2.2.5: determine common factors and common multiples using the prime factorization of numbers (e.g., the prime factorization of 12 is 2 x 2 x 3; the prime factorization of 18 is 2 x 3 x 3; the greatest common factor of 12 and 18 is 2 x 3 or 6; the least common multiple of 12 and 18 is 2 x 2 x 3 x 3 or 36).
Finding Factors with Area Models
2.3.2: solve problems involving percents expressed to one decimal place (e.g., 12.5%) and whole-number percents greater than 100 (e.g., 115%) (Sample problem: The total cost of an item with tax included [115%] is $23.00. Use base ten materials to determine the price before tax.);
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents and Proportions
2.3.3: use estimation when solving problems involving operations with whole numbers, decimals, percents, integers, and fractions, to help judge the reasonableness of a solution;
Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Percents and Proportions
Sums and Differences with Decimals
2.3.4: represent the multiplication and division of fractions, using a variety of tools and strategies (e.g., use an area model to represent 1/4 multiplied by 1/3);
Dividing Fractions
Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
2.3.5: solve problems involving addition, subtraction, multiplication, and division with simple fractions;
Adding Fractions (Fraction Tiles)
Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
2.3.7: solve problems involving operations with integers, using a variety of tools (e.g., twocolour counters, virtual manipulatives, number lines);
Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Comparing and Ordering Integers
Real Number Line - Activity A
2.3.8: evaluate expressions that involve integers, including expressions that contain brackets and exponents, using order of operations;
Dividing Exponential Expressions
Order of Operations
2.3.9: multiply and divide decimal numbers by various powers of ten (e.g.,"To convert 230 000 cm_ to cubic metres, I calculated in my head 230 000 Ö 106 to get 0.23 m_.") (Sample problem: Use a calculator to help you generalize a rule for dividing numbers by 1 000 000.);
2.3.10: estimate, and verify using a calculator, the positive square roots of whole numbers, and distinguish between whole numbers that have whole-number square roots (i.e., perfect square numbers) and those that do not (Sample problem: Explain why a square with an area of 20 cm_ does not have a whole-number side length.).
2.4.1: identify and describe real-life situations involving two quantities that are directly proportional (e.g., the number of servings and the quantities in a recipe, mass and volume of a substance, circumference and diameter of a circle);
Circle: Circumference and Area
Measuring Trees
2.4.3: solve problems involving percent that arise from real-life contexts (e.g., discount, sales tax, simple interest) (Sample problem: In Ontario, people often pay a provincial sales tax [PST] of 8% and a federal sales tax [GST] of 7% when they make a purchase. Does it matter which tax is calculated first? Explain your reasoning.);
Percent of Change
Percents and Proportions
Simple and Compound Interest
3.1.1: research, describe, and report on applications of volume and capacity measurement;
Prisms and Cylinders - Activity A
3.1.2: determine the relationships among units and measurable attributes, including the area of a circle and the volume of a cylinder.
Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
3.2.1: research, describe, and report on applications of volume and capacity measurement (e.g., cooking, closet space, aquarium size) (Sample problem: Describe situations where volume and capacity are used in your home.).
Prisms and Cylinders - Activity A
3.3.2: measure the circumference, radius, and diameter of circular objects, using concrete materials (Sample Problem: Use string to measure the circumferences of different circular objects.);
Circle: Circumference and Area
Measuring Trees
3.3.3: determine, through investigation using a variety of tools (e.g., cans and string, dynamic geometry software) and strategies, the relationships for calculating the circumference and the area of a circle, and generalize to develop the formulas [i.e., Circumference of a circle = pi x diameter; Area of a circle = pi x (radius)_] (Sample problem: Use string to measure the circumferences and the diameters of a variety of cylindrical cans, and investigate the ratio of the circumference to the diameter.);
Circle: Circumference and Area
Measuring Trees
Perimeter, Circumference, and Area - Activity B
3.3.4: solve problems involving the estimation and calculation of the circumference and the area of a circle;
Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B
3.3.5: determine, through investigation using a variety of tools and strategies (e.g., generalizing from the volume relationship for right prisms, and verifying using the capacity of thin-walled cylindrical containers), the relationship between the area of the base and height and the volume of a cylinder, and generalize to develop the formula (i.e.,Volume = area of base x height);
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
3.3.6: determine, through investigation using concrete materials, the surface area of a cylinder (Sample problem: Use the label and the plastic lid from a cylindrical container to help determine its surface area.);
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones
3.3.7: solve problems involving the surface area and the volume of cylinders, using a variety of strategies (Sample problem: Compare the volumes of the two cylinders that can be created by taping the top and bottom, or the other two sides, of a standard sheet of paper.).
Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders
4.1.1: demonstrate an understanding of the geometric properties of quadrilaterals and circles and the applications of geometric properties in the real world;
Chords and Arcs
Inscribing Angles
Parallelogram Conditions
Special Quadrilaterals
4.1.2: develop geometric relationships involving lines, triangles, and polyhedra, and solve problems involving lines and triangles;
4.1.3: represent transformations using the Cartesian coordinate plane, and make connections between transformations and the real world.
City Tour (Coordinates)
Dilations
Points in the Coordinate Plane - Activity A
Reflections
Translations
4.2.1: sort and classify quadrilaterals by geometric properties, including those based on diagonals, through investigation using a variety of tools (e.g., concrete materials, dynamic geometry software) (Sample problem: Which quadrilaterals have diagonals that bisect each other perpendicularly?);
Classifying Quadrilaterals - Activity A
Parallelogram Conditions
Special Quadrilaterals
4.2.3: investigate and describe applications of geometric properties (e.g., properties of triangles, quadrilaterals, and circles) in the real world.
Parallelogram Conditions
Triangle Inequalities
4.3.1: determine, through investigation using a variety of tools (e.g., dynamic geometry software, concrete materials, geoboard), relationships among area, perimeter, corresponding side lengths, and corresponding angles of similar shapes (Sample problem: Construct three similar rectangles, using grid paper or a geoboard, and compare the perimeters and areas of the rectangles.);
Isosceles and Equilateral Triangles
Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area
4.3.2: determine, through investigation using a variety of tools (e.g., dynamic geometry software, concrete materials, protractor) and strategies (e.g., paper folding), the angle relationships for intersecting lines and for parallel lines and transversals, and the sum of the angles of a triangle;
Investigating Angle Theorems - Activity A
Triangle Angle Sum - Activity A
4.3.3: solve angle-relationship problems involving triangles (e.g., finding interior angles or complementary angles), intersecting lines (e.g., finding supplementary angles or opposite angles), and parallel lines and transversals (e.g., finding alternate angles or corresponding angles);
Investigating Angle Theorems - Activity A
Triangle Angle Sum - Activity A
4.3.4: determine the Pythagorean relationship, through investigation using a variety of tools (e.g., dynamic geometry software; paper and scissors; geoboard) and strategies;
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
4.3.5: solve problems involving right triangles geometrically, using the Pythagorean relationship;
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
4.3.6: determine, through investigation using concrete materials, the relationship between the numbers of faces, edges, and vertices of a polyhedron (i.e., number of faces + number of vertices = number of edges + 2) (Sample problem: Use Polydrons and/or paper nets to construct the five Platonic solids [i.e., tetrahedron, cube, octahedron, dodecahedron, icosahedron], and compare the sum of the numbers of faces and vertices to the number of edges for each solid.).
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones
4.4.1: graph the image of a point, or set of points, on the Cartesian coordinate plane after applying a transformation to the original point(s) (i.e., translation; reflection in the x-axis, the y-axis, or the angle bisector of the axes that passes through the first and third quadrants; rotation of 90¡, 180¡, or 270¡ about the origin);
City Tour (Coordinates)
Points in the Coordinate Plane - Activity A
Reflections
Rock Art (Transformations)
Rotations, Reflections and Translations
Translations
4.4.2: identify, through investigation, real-world movements that are translations, reflections, and rotations.
Quilting Bee (Symmetry)
Reflections
Rock Art (Transformations)
Rotations, Reflections and Translations
Translations
5.1.1: represent linear growing patterns (where the terms are whole numbers) using graphs, algebraic expressions, and equations;
Arithmetic Sequences
Arithmetic and Geometric Sequences
Linear Functions
5.1.2: model linear relationships graphically and algebraically, and solve and verify algebraic equations, using a variety of strategies, including inspection, guess and check, and using a "balance" model.
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Modeling and Solving Two-Step Equations
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side
Solving Two-Step Equations
Using Tables, Rules and Graphs
5.2.1: represent, through investigation with concrete materials, the general term of a linear pattern, using one or more algebraic expressions (e.g.,"Using toothpicks, I noticed that 1 square needs 4 toothpicks, 2 connected squares need 7 toothpicks, and 3 connected squares need 10 toothpicks. I think that for n connected squares I will need 4 + 3(n - 1) toothpicks, because the number of toothpicks keeps going up by 3 and I started with 4 toothpicks. Or, if I think of starting with 1 toothpick and adding 3 toothpicks at a time, the pattern can be represented as 1 + 3 to the n power.");
Arithmetic Sequences
Arithmetic and Geometric Sequences
Linear Functions
5.2.2: represent linear patterns graphically (i.e., make a table of values that shows the term number and the term, and plot the coordinates on a graph), using a variety of tools (e.g., graph paper, calculators, dynamic statistical software);
Arithmetic Sequences
Defining a Line with Two Points
Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line
Using Tables, Rules and Graphs
5.2.3: determine a term, given its term number, in a linear pattern that is represented by a graph or an algebraic equation (Sample problem: Given the graph that represents the pattern 1, 3, 5, 7,..., find the 10th term. Given the algebraic equation that represents the pattern, t = 2n - 1, find the 100th term.).
Arithmetic Sequences
Arithmetic and Geometric Sequences
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Linear Functions
5.3.2: model linear relationships using tables of values, graphs, and equations (e.g., the sequence 2, 3, 4, 5, 6,... can be represented by the equation t = n + 1, where n represents the term number and t represents the term), through investigation using a variety of tools (e.g., algebra tiles, pattern blocks, connecting cubes, base ten materials) (Sample problem: Leah put $350 in a bank certificate that pays 4% simple interest each year. Make a table of values to show how much the bank certificate is worth after five years, using base ten materials to help you. Represent the relationship using an equation.);
Arithmetic Sequences
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Modeling Linear Systems - Activity A
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs
5.3.3: translate statements describing mathematical relationships into algebraic expressions and equations (e.g., for a collection of triangles, the total number of sides is equal to three times the number of triangles or s = 3n);
Using Algebraic Equations
Using Algebraic Expressions
5.3.5: make connections between solving equations and determining the term number in a pattern, using the general term (e.g., for the pattern with the general term 2n + 1, solving the equation 2n + 1 = 17 tells you the term number when the term is 17);
Modeling and Solving Two-Step Equations
Solving Two-Step Equations
5.3.6: solve and verify linear equations involving a one-variable term and having solutions that are integers, by using inspection, guess and check, and a "balance" model (Sample problem: What is the value of the variable in the equation 30x - 5 = 10?).
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations
6.1.1: collect and organize categorical, discrete, or continuous primary data and secondary data and display the data using charts and graphs, including frequency tables with intervals, histograms, and scatter plots;
Graphing Skills
Histograms
Scatter Plots - Activity A
6.2.2: organize into intervals a set of data that is spread over a broad range (e.g., the age of respondents to a survey may range over 80 years and may be organized into ten-year intervals);
Box-and-Whisker Plots
Describing Data Using Statistics
Reaction Time 1 (Graphs and Statistics)
6.2.3: 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 histograms and scatter plots) 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);
Describing Data Using Statistics
Graphing Skills
Histograms
Reaction Time 1 (Graphs and Statistics)
Scatter Plots - Activity A
6.2.4: select an appropriate type of graph to represent a set of data, graph the data using technology, and justify the choice of graph (i.e., from types of graphs already studied, including histograms and scatter plots);
Graphing Skills
Histograms
Scatter Plots - Activity A
6.2.5: explain the relationship between a census, a representative sample, sample size, and a population (e.g.,"I think that in most cases a larger sample size will be more representative of the entire population.").
6.3.1: read, interpret, and draw conclusions from primary data (e.g., survey results, measurements, observations) and from secondary data (e.g., election data or temperature data from the newspaper, data from the Internet about lifestyles), presented in charts, tables, and graphs (including frequency tables with intervals, histograms, and scatter plots);
Correlation
Graphing Skills
Histograms
Reaction Time 1 (Graphs and Statistics)
Scatter Plots - Activity A
Solving Using Trend Lines
6.3.2: determine, through investigation, the appropriate measure of central tendency (i.e., mean, median, or mode) needed to compare sets of data (e.g., in hockey, compare heights or masses of players on defence with that of forwards);
Describing Data Using Statistics
Line Plots
Mean, Median and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
6.3.3: demonstrate an understanding of the appropriate uses of bar graphs and histograms by comparing their characteristics (Sample problem: How is a histogram similar to and different from a bar graph? Use examples to support your answer.);
Graphing Skills
Histograms
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
6.3.4: compare two attributes or characteristics (e.g., height versus arm span), using a scatter plot, and determine whether or not the scatter plot suggests a relationship (Sample problem: Create a scatter plot to compare the lengths of the bases of several similar triangles with their areas.);
Correlation
Populations and Samples
Scatter Plots - Activity A
Similar Polygons
Solving Using Trend Lines
6.3.5: identify and describe trends, based on the rate of change of data from tables and graphs, using informal language (e.g., "The steep line going upward on this graph represents rapid growth. The steep line going downward on this other graph represents rapid decline.");
Correlation
Graphing Skills
Reaction Time 1 (Graphs and Statistics)
Solving Using Trend Lines
6.3.6: make inferences and convincing arguments that are based on the analysis of charts, tables, and graphs (Sample problem: Use data to make a convincing argument that the environment is becoming increasingly polluted.);
Graphing Skills
Histograms
Reaction Time 1 (Graphs and Statistics)
6.3.7: compare two attributes or characteristics, using a variety of data management tools and strategies (i.e., pose a relevant question, then design an experiment or survey, collect and analyse the data, and draw conclusions) (Sample problem: Compare the length and width of different-sized leaves from a maple tree to determine if maple leaves grow proportionally. What generalizations can you make?).
Correlation
Populations and Samples
6.4.1: compare, through investigation, the theoretical probability of an event (i.e., the ratio of the number of ways a favourable outcome can occur compared to the total number of possible outcomes) with experimental probability, and explain why they might differ (Sample problem:Toss a fair coin 10 times, record the results, and explain why you might not get the predicted result of 5 heads and 5 tails.);
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability
6.4.2: determine, through investigation, the tendency of experimental probability to approach theoretical probability as the number of trials in an experiment increases, using class-generated data and technology-based simulation models (Sample problem: Compare the theoretical probability of getting a 6 when tossing a number cube with the experimental probabilities obtained after tossing a number cube once, 10 times, 100 times, and 1000 times.);
Geometric Probability - Activity A
Polling: City
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability
6.4.3: identify the complementary event for a given event, and calculate the theoretical probability that a given event will not occur (Sample problem: Bingo uses the numbers from 1 to 75. If the numbers are pulled at random, what is the probability that the first number is a multiple of 5? is not a multiple of 5?).
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability
Correlation last revised: 8/18/2015