N7: Number

N7.2: Expand and demonstrate understanding of the addition, subtraction, multiplication, and division of decimals to greater numbers of decimal places, and the order of operations.

N7.2.d: Solve a problem involving the addition, or subtraction, of two or more decimal numbers.

Sums and Differences with Decimals

N7.2.g: Check the reasonableness of solutions using estimation.

Estimating Sums and Differences

N7.2.i: Explain by using examples why it is important to follow a specific order of operations when calculating with decimals and/or whole numbers.

Order of Operations

N7.3: Demonstrate an understanding of the relationships between positive decimals, positive fractions (including mixed numbers, proper fractions and improper fractions), and whole numbers.

N7.3.b: Match a set of fractions to their decimal representations.

Percents, Fractions, and Decimals

N7.3.k: Identify, with justification, a number that would be between two given numbers (decimal, fraction, and/or whole numbers) in an ordered sequence or shown on a number line.

Rational Numbers, Opposites, and Absolute Values

N7.3.l: Identify incorrectly placed numbers within an ordered sequence or shown on a number line.

Comparing and Ordering Decimals
Fraction Garden (Comparing Fractions)
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

N7.4: Expand and demonstrate an understanding of percent to include fractional percents between 1% and 100%.

N7.4.b: Express a percent as a decimal or fraction.

Percents, Fractions, and Decimals

N7.4.c: Solve a problem that involves finding a percent.

Percent of Change
Percents, Fractions, and Decimals
Real-Time Histogram
Time Estimation

N7.4.d: Solve a problem that involves finding percents of a value.

Percent of Change
Polling: Neighborhood

N7.5: Develop and demonstrate an understanding of adding and subtracting positive fractions and mixed numbers, with like and unlike denominators, concretely, pictorially, and symbolically (limited to positive sums and differences).

N7.5.g: Simplify a positive fraction or mixed number by identifying and dividing off the common factor between the numerator and denominator.

Multiplying Fractions

N7.5.i: Solve a problem involving the addition or subtraction of positive fractions or mixed numbers.

Adding Fractions (Fraction Tiles)
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers

N7.6: Demonstrate an understanding of addition and subtraction of integers, concretely, pictorially, and symbolically.

N7.6.b: Explain, using concrete materials such as integer tiles and diagrams, that the sum of opposite integers is zero (e.g., a move in one direction followed by an equivalent move in the opposite direction results in no net change in position).

Adding and Subtracting Integers
Adding on the Number Line

N7.6.c: Illustrate, using a number line, the results of adding or subtracting negative and positive integers.

Adding and Subtracting Integers
Adding on the Number Line

N7.6.d: Add two integers using concrete materials or pictorial representations and record the process symbolically.

Addition of Polynomials

P7: Patterns and Relations

P7.1: Demonstrate an understanding of the relationships between oral and written patterns, graphs and linear relations.

P7.1.f: Create a table of values for a linear relation by evaluating the relation for different variable values.

Function Machines 1 (Functions and Tables)

P7.2: Demonstrate an understanding of equations and expressions by: distinguishing between equations and expressions, evaluating expressions, verifying solutions to equations.

P7.2.a: Explain what a variable is and how it is used in an expression.

Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Using Algebraic Equations

P7.2.b: Provide an example of an expression and an equation, and explain how they are similar and different.

Compound Interest
Using Algebraic Equations

P7.2.c: Explain how to evaluate an expression and how that result is different from a solution to an equation.

Order of Operations

P7.3: Demonstrate an understanding of one-and two-step linear equations of the form ax/b + c = d (where a, b, c, and d are whole numbers, c less than or equal to d and b does not equal 0) by modeling the solution of the equations concretely, pictorially, physically, and symbolically and explaining the solution in terms of the preservation of equality.

P7.3.b: Generalize strategies for carrying out operations that involve the use of the preservation of equality.

Solving Two-Step Equations
Using Algebraic Equations

P7.3.c: Solve an equation by applying the preservation of equality.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Two-Step Equations

P7.3.d: Identify and provide an example of a constant term, a numerical coefficient, and a variable in an expression and an equation.

Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations I
Solving Equations on the Number Line
Using Algebraic Equations

P7.3.g: Verify the solution to a linear equation using concrete materials or diagrams.

Modeling and Solving Two-Step Equations

P7.3.i: Represent a problem situation using a linear equation.

Solving Equations by Graphing Each Side

P7.3.j: Solve a problem using a linear equation.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Equations by Graphing Each Side
Solving Two-Step Equations

P7.4: Demonstrate an understanding of linear equations of the form x + a = b (where a and b are integers) by modeling problems as a linear equation and solving the problems concretely, pictorially, and symbolically.

P7.4.b: Verify a solution to a problem involving a linear equation of the form x + a = b where a and b are integers.

Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Two-Step Equations

SS7: Shape and Space

SS7.1: Demonstrate an understanding of circles including circumference and central angles.

SS7.1.a: Identify the characteristics of a circle.

Chords and Arcs
Circles

SS7.1.b: Define and illustrate the relationship between the diameter and radius of a circle.

Chords and Arcs

SS7.1.g: Generalize, from investigations, the relationship between the circumference and the diameter of a circle.

Circumference and Area of Circles

SS7.1.i: Sort a set of angles as central angles of a circle or not.

Chords and Arcs

SS7.1.l: Solve problems involving circles.

Chords and Arcs
Circles

SS7.2: Develop and apply formulas for determining the area of: triangles, parallelograms, circles.

SS7.2.a: Illustrate and explain how the area of a rectangle can be used to determine the area of a triangle.

Area of Triangles

SS7.2.b: Generalize, using examples, a formula for determining the area of triangles.

Area of Triangles

SS7.2.c: Illustrate and explain how the area of a rectangle can be used to determine the area of a parallelogram.

Area of Parallelograms
Area of Triangles
Perimeter and Area of Rectangles

SS7.2.d: Generalize, using examples, a formula for determining the area of parallelograms.

Area of Triangles
Perimeter and Area of Rectangles

SS7.2.g: Generalize a formula for finding the area of a circle.

Circumference and Area of Circles

SS7.2.h: Solve problems involving the area of triangles, parallelograms, or circles.

Area of Parallelograms
Area of Triangles
Circumference and Area of Circles
Perimeter and Area of Rectangles

SS7.3: Demonstrate an understanding of 2-D relationships involving lines and angles.

SS7.3.a: Identify and describe examples of parallel line segments, perpendicular line segments, perpendicular bisectors, and angle bisectors in the environment.

Parallel, Intersecting, and Skew Lines

SS7.3.c: Investigate and explain how paper, pencil, compass, and rulers can be used to construct parallel lines, perpendicular lines, angle bisectors, and perpendicular bisectors.

Segment and Angle Bisectors

SS7.3.e: Use technology to construct parallel lines, perpendicular lines, angle bisectors, and perpendicular bisectors.

Parallel, Intersecting, and Skew Lines

SS7.3.h: Draw the bisector of a given angle using more than one method and verify that the resulting angles are equal.

Segment and Angle Bisectors

SS7.3.i: Draw the perpendicular bisector of a line segment using more than one method and verify the construction.

Segment and Angle Bisectors

SS7.4: Demonstrate an understanding of the Cartesian plane and ordered pairs with integral coordinates.

SS7.4.a: Label the axes of a four quadrant Cartesian plane and identify the origin.

City Tour (Coordinates)
Points in the Coordinate Plane

SS7.4.c: Identify the location of a point in any quadrant of a Cartesian plane using an ordered pair with integral coordinates.

City Tour (Coordinates)
Points in the Coordinate Plane

SS7.4.d: Plot the point corresponding to an ordered pair with integral coordinates on a Cartesian plane with a scale of 1, 2, 5, or 10 on its axes.

Points in the Coordinate Plane

SP7: Statistics and Probability

SP7.1: Demonstrate an understanding of the measures of central tendency and range for sets of data.

SP7.1.a: Concretely represent mean, median, and mode and explain the similarities and differences among them.

Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)

SP7.1.b: Determine mean, median, and mode for a set of data, and explain why these values may be the same or different.

Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

SP7.1.c: Determine the range of a set of data.

Describing Data Using Statistics
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

SP7.1.d: Provide a context in which the mean, median, or mode is the most appropriate measure of central tendency to use when reporting findings and explain the choice.

Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots

SP7.1.e: Solve a problem involving the measures of central tendency.

Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

SP7.1.f: Analyze a set of data to identify any outliers.

Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)

SP7.1.g: Explain the effect of outliers on the measures of central tendency for a data set.

Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)

SP7.1.h: Identify outliers in a set of data and justify whether or not they should be included in the reporting of the measures of central tendency.

Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)

SP7.1.i: Provide examples of situations in which outliers would and would not be used in reporting the measures of central tendency.

Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)

SP7.1.j: Explain why qualitative data, such as colour or favourite activity, cannot be analyzed for all three measures of central tendency.

Stem-and-Leaf Plots

SP7.2: Demonstrate an understanding of circle graphs.

SP7.2.a: Identify common attributes of circle graphs, such as:

SP7.2.a.3: the data is reported as a percent of the total and the sum of the percents is equal to 100%.

Graphing Skills

SP7.2.b: Create and label a circle graph, with and without technology, to display a set of data.

Graphing Skills

SP7.2.c: Find, describe, and compare circle graphs in a variety of print and electronic media such as newspapers, magazines, and the Internet.

Graphing Skills

SP7.2.e: Interpret a circle graph to answer questions.

Graphing Skills

SP7.2.f: Identify the characteristics of a set of data that make it possible to create a circle graph.

Graphing Skills

SP7.3: Demonstrate an understanding of theoretical and experimental probabilities for two independent events where the combined sample space has 36 or fewer elements.

SP7.3.a: Explain what a probability tells about the situation to which it refers.

Probability Simulations
Theoretical and Experimental Probability

SP7.3.b: Provide an example of two independent events, such as:

SP7.3.b.1: spinning a four section spinner and an eight-sided die

Independent and Dependent Events
Theoretical and Experimental Probability

SP7.3.b.2: tossing a coin and rolling a twelve-sided die

Independent and Dependent Events
Theoretical and Experimental Probability

SP7.3.b.3: tossing two coins

Independent and Dependent Events
Theoretical and Experimental Probability

SP7.3.b.4: rolling two dice and explain why they are independent.

Independent and Dependent Events
Theoretical and Experimental Probability

SP7.3.d: Determine the theoretical probability of an outcome involving two independent events.

Independent and Dependent Events
Theoretical and Experimental Probability

SP7.3.e: Conduct a probability experiment for an outcome involving two independent events, with and without technology, to compare the experimental probability to the theoretical probability.

Independent and Dependent Events
Theoretical and Experimental Probability

SP7.3.f: Solve a probability problem involving two independent events.

Independent and Dependent Events
Theoretical and Experimental Probability

SP7.3.g: Explain how theoretical and experimental probabilities are related and why they cannot be assumed to be equal.

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

SP7.3.h: Represent a probability stated as a percent as a fraction or a decimal.

Estimating Population Size
Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

SP7.3.i: Represent a probability stated as a fraction or decimal as a percent.

Estimating Population Size
Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability