2: Number Sense and Numeration

2.1: Overall Expectations

2.1.1: represent, compare, and order numbers, including integers;

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Comparing and Ordering Rational Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1

2.1.2: demonstrate an understanding of addition and subtraction of fractions and integers, and apply a variety of computational strategies to solve problems involving whole numbers and decimal numbers;

Adding Fractions (Fraction Tiles)
Adding Real Numbers
Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Fractions with Unlike Denominators
Multiplying with Decimals
Sums and Differences with Decimals

2.1.3: demonstrate an understanding of proportional relationships using percent, ratio, and rate.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part:Part and Part:Whole Ratios
Percents and Proportions
Polling: Neighborhood
Proportions and Common Multipliers

2.2: Quantity Relationships

2.2.1: 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
Comparing and Ordering Fractions
Comparing and Ordering Rational Numbers
Fraction Garden (Comparing Fractions)
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1

2.2.2: 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 cm_ and have whole-number dimensions.);

Finding Factors with Area Models

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

Comparing and Ordering Integers

2.2.4: represent and order integers, using a variety of tools (e.g., two-colour counters, virtual manipulatives, number lines);

Comparing and Ordering Integers
Real Number Line - Activity A

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

Square Roots

2.3: Operational Sense

2.3.1: divide whole numbers by simple fractions and by decimal numbers to hundredths, using concrete materials (e.g., divide 3 by 1/2 using fraction strips; divide 4 by 0.8 using base ten materials and estimation);

Dividing Fractions

2.3.2: 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 Ö 0.2 can be thought of as (16 + 0.8) Ö 0.2 = 16 Ö 0.2 + 0.8 Ö 0.2, which gives 80 + 4 = 84);

Adding Fractions (Fraction Tiles)
Chocomatic (Multiplication, Arrays, and Area)
Fractions with Unlike Denominators
Sums and Differences with Decimals

2.3.3: solve problems involving the multiplication and division of decimal numbers to thousandths by one-digit whole numbers, using a variety of tools (e.g., concrete materials, drawings, calculators) and strategies (e.g., estimation, algorithms);

Multiplying with Decimals

2.3.5: use estimation when solving problems involving operations with whole numbers, decimals, and percents, to help judge the reasonableness of a solution (Sample problem: A book costs $18.49. The salesperson tells you that the total price, including taxes, is $22.37. How can you tell if the total price is reasonable without using a calculator?);

Multiplying with Decimals
Percents and Proportions
Sums and Differences with Decimals

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

Multiplying with Decimals
Order of Operations
Sums and Differences with Decimals

2.3.7: add and subtract fractions with simple like and unlike denominators, using a variety of tools (e.g., fraction circles, Cuisenaire rods, drawings, calculators) and algorithms;

Adding Fractions (Fraction Tiles)
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators

2.3.8: demonstrate, using concrete materials, the relationship between the repeated addition of fractions and the multiplication of that fraction by a whole number (e.g., 1/2 + 1/2 + 1/2 = 3 x 1/2);

Adding Fractions (Fraction Tiles)
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers

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

Adding Real Numbers
Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Comparing and Ordering Integers
Real Number Line - Activity A

2.4: Proportional Relationships

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

Part:Part and Part:Whole Ratios
Percents and Proportions
Polling: Neighborhood

2.4.2: 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
Polling: Neighborhood

2.4.3: 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);

Distance-Time Graphs
Part:Part and Part:Whole Ratios
Polling: Neighborhood

2.4.4: 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.).

Road Trip (Problem Solving)

3: Measurement

3.1: Overall Expectations

3.1.2: determine the relationships among units and measurable attributes, including the area of a trapezoid and the volume of a right prism.

Prisms and Cylinders - Activity A

3.3: Measurement Relationships

3.3.1: sketch different polygonal prisms that share the same volume (Sample problem: The Neuman Company is designing a new container for its marbles. The container must have a volume of 200 cm_. Sketch three possible containers, and explain which one you would recommend.);

Prisms and Cylinders - Activity A

3.3.4: determine, through investigation using a variety of tools (e.g., concrete materials, dynamic geometry software) and strategies, the relationship for calculating the area of a trapezoid, and generalize to develop the formula [i.e., Area = (sum of lengths of parallel sides x height) Ö 2] (Sample problem: Determine the relationship between the area of a parallelogram and the area of a trapezoid by composing a parallelogram from congruent trapezoids.);

Area of Parallelograms - Activity A
Rectangle: Perimeter and Area

3.3.6: 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 - Activity A
Fido's Flower Bed (Perimeter and Area)

3.3.7: 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.);

Area of Parallelograms - Activity A
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

3.3.8: 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 Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

3.3.9: solve problems that involve the surface area and volume of right prisms and that require conversion between metric measures of capacity and volume (i.e., millilitres and cubic centimetres) (Sample problem: An aquarium has a base in the shape of a trapezoid. The aquarium is 75 cm high. The base is 50 cm long at the front, 75 cm long at the back, and 25 cm wide. Find the capacity of the aquarium.).

Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

4: Geometry and Spatial Sense

4.1: Overall Expectations

4.1.1: construct related lines, and classify triangles, quadrilaterals, and prisms;

Classifying Quadrilaterals - Activity A
Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders

4.1.2: develop an understanding of similarity, and distinguish similarity and congruence;

Similar Figures - Activity A

4.1.3: describe location in the four quadrants of a coordinate system, dilatate two-dimensional shapes, and apply transformations to create and analyse designs.

Dilations

4.2: Geometric Properties

4.2.1: construct related lines (i.e., parallel; perpendicular; intersecting at 30¼, 45¼, and 60¼), using angle properties and a variety of tools (e.g., compass and straight edge, protractor, dynamic geometry software) and strategies (e.g., paper folding);

Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles

4.2.2: 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 - Activity A
Classifying Triangles
Isosceles and Equilateral Triangles
Pythagorean Theorem - Activity B
Quilting Bee (Symmetry)
Special Quadrilaterals

4.2.4: investigate, using concrete materials, the angles between the faces of a prism, and identify right prisms (Sample problem: Identify the perpendicular faces in a set of right prisms.).

Prisms and Cylinders - Activity A

4.3: Geometric Relationships

4.3.1: 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
Isosceles and Equilateral Triangles
Pythagorean Theorem - Activity B
Triangle Angle Sum - Activity A

4.3.2: 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 congruent shapes (Sample problem: Do you agree with the conjecture that triangles with the same area must be congruent? Justify your reasoning.);

Rectangle: Perimeter and Area

4.3.4: 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 - Activity A

4.4: Location and Movement

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

City Tour (Coordinates)
Points in the Coordinate Plane - Activity A

4.4.2: 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);

Dilations

4.4.3: 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
Quilting Bee (Symmetry)
Reflections
Rock Art (Transformations)
Rotations, Reflections and Translations

4.4.4: determine, through investigation using a variety of tools (e.g., pattern blocks, Polydrons, grid paper, tiling software, dynamic geometry software, concrete materials), polygons or combinations of polygons that tile a plane, and describe the transformation(s) involved.

Dilations
Quilting Bee (Symmetry)
Rock Art (Transformations)
Rotations, Reflections and Translations

5: Patterning and Algebra

5.1: Overall Expectations

5.1.1: represent linear growing patterns (where the terms are whole numbers) using concrete materials, graphs, and algebraic expressions;

Arithmetic Sequences
Arithmetic and Geometric Sequences
Linear Functions

5.1.2: model real-life linear relationships graphically and algebraically, and solve simple algebraic equations using a variety of strategies, including inspection and guess and check.

Function Machines 2 (Functions, Tables, and Graphs)
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 Two-Step Equations
Using Tables, Rules and Graphs

5.2: Patterns and Relationships

5.2.1: 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
Linear Functions
Using Tables, Rules and Graphs

5.2.2: make predictions about linear growing patterns, through investigation with concrete materials (Sample problem: Investigate the surface area of towers made from a single column of connecting cubes, and predict the surface area of a tower that is 50 cubes high. Explain your reasoning.);

Arithmetic Sequences
Arithmetic and Geometric Sequences
Linear Functions

5.2.3: develop and represent the general term of a linear growing pattern, using algebraic expressions involving one operation (e.g., the general term for the sequence 4, 5, 6, 7, ... can be written algebraically as n + 3, where n represents the term number; the general term for the sequence 5, 10, 15, 20, ... can be written algebraically as 5n, where n represents the term number);

Arithmetic Sequences
Arithmetic and Geometric Sequences
Linear Functions

5.2.4: 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 Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

5.3: Variables, Expressions, and Equations

5.3.1: 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?);

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Elevator Operator (Line Graphs)
Linear Functions
Quadratic and Absolute Value Functions
Using Tables, Rules and Graphs

5.3.2: model real-life relationships involving constant rates (e.g., speed, heart rate, billing rate), using algebraic equations with variables to represent the changing quantities in the relationship (e.g., the equation p = 4t represents the relationship between the total number of people that can be seated (p) and the number of tables (t), given that each table can seat 4 people [4 people per table is the constant rate]);

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Elevator Operator (Line Graphs)

5.3.3: translate phrases describing simple mathematical relationships into algebraic expressions (e.g., one more than three times a number can be written algebraically as 1 + 3x or 3x + 1), using concrete materials (e.g., algebra tiles, pattern blocks, counters);

Using Algebraic Equations
Using Algebraic Expressions

5.3.6: 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 and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

6: Data Management and Probability

6.1: Overall Expectations

6.1.1: collect and organize categorical, discrete, or continuous primary data and secondary data and display the data using charts and graphs, including relative frequency tables and circle graphs;

Graphing Skills

6.1.2: make and evaluate convincing arguments, based on the analysis of data;

Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)

6.1.3: compare experimental probabilities with the theoretical probability of an outcome involving two independent events.

Compound Independent Events
Compound Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

6.2: Collection and Organization of Data

6.2.2: 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);

Describing Data Using Statistics
Graphing Skills
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

6.2.3: 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);

Graphing Skills

6.3: Data Relationships

6.3.1: 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);

Graphing Skills
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

6.3.2: identify, through investigation, graphs that present data in misleading ways (e.g., line graphs that exaggerate change by starting the vertical axis at a point greater than zero);

Box-and-Whisker Plots
Elevator Operator (Line Graphs)
Graphing Skills
Line Plots
Stem-and-Leaf Plots

6.3.3: 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
Line Plots
Mean, Median and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

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

Correlation
Graphing Skills
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Solving Using Trend Lines

6.3.5: 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.).

Graphing Skills
Histograms
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

6.4: Probability

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

Probability Simulations
Theoretical and Experimental Probability

6.4.3: 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?);

Compound Independent Events
Compound Independent and Dependent Events
Permutations and Combinations
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

6.4.4: 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.).

Compound Independent Events
Compound Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability