1: Patterns and Relations

1.7PR: Patterns and Relations

1.7PR2: Create a table of values from a linear relation, graph the table of values, and analyze the graph to draw conclusions and solve problems.

Function Machines 1 (Functions and Tables)

1.7PR2.1: Create a table of values for a given linear relation by substituting values for the variable.

Direct and Inverse Variation
Points, Lines, and Equations

1.7PR2.2: Create a table of values, using a linear relation, and graph the table of values (limited to discrete elements).

Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Points, Lines, and Equations
Slope-Intercept Form of a Line

1.7PR2.5: Match a given set of linear relations to a given set of graphs.

Absolute Value with Linear Functions
Linear Functions
Solving Equations by Graphing Each Side
Standard Form of a Line

1.7PR2.6: Match a given set of graphs to a given set of linear relations.

Absolute Value with Linear Functions
Linear Functions
Solving Equations by Graphing Each Side
Standard Form of a Line

1.7PR4: Explain the difference between an expression and an equation.

Compound Interest
Using Algebraic Equations

1.7PR4.1: Explain what a variable is and how it is used in a given expression.

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

1.7PR4.2: Identify and provide an example of a constant term, numerical coefficient and 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

1.7PR4.3: Provide an example of an expression and an equation, and explain how they are similar and different.

Compound Interest
Solving Equations on the Number Line
Using Algebraic Equations

1.7PR4.4: Represent a given oral or written pattern using an algebraic expression.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

1.7PR4.5: Represent a given oral or written pattern using an equation.

Arithmetic Sequences
Geometric Sequences

1.7PR5: Evaluate an expression, given the value of the variable(s).

Solving Equations by Graphing Each Side
Solving Equations on the Number Line

1.7PR7: Model and solve, concretely, pictorially and symbolically, problems that can be represented by linear equations of the form:

1.7PR7.a: ax + b = c

Modeling One-Step Equations
Modeling and Solving Two-Step Equations

1.7PR7.b: ax - b = c

Modeling One-Step Equations
Modeling and Solving Two-Step Equations

1.7PR7.c: ax = b

Modeling One-Step Equations
Solving Equations on the Number Line

1.7PR7.d: x/a = b, a ≠ 0 where a, b and c are whole numbers.

Modeling One-Step Equations
Solving Equations on the Number Line

1.7PR7.1: Model a given problem with a linear equation and solve the equation, using concrete models, e.g., counters, integer tiles.

Solving Equations by Graphing Each Side

2: Integers

2.7N: Number

2.7N6: Demonstrate an understanding of addition and subtraction of integers, concretely, pictorially and symbolically.

Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials

2.7N6.1: Explain, using concrete materials such as integer tiles and diagrams, that the sum of opposite integers is zero.

Adding and Subtracting Integers

2.7N6.2: Solve a given problem involving the addition and subtraction of integers.

Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials

2.7N6.3: Add two given integers, using concrete materials or pictorial representations, and record the process symbolically.

Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials

2.7N6.4: Illustrate, using a number line, the results of adding negative and positive integers.

Adding and Subtracting Integers
Adding on the Number Line

2.7N6.5: Subtract two given integers, using concrete materials or pictorial representations, and record the process symbolically.

Adding and Subtracting Integers
Adding on the Number Line

2.7N6.6: Illustrate, using a number line, the results of subtracting negative and positive integers.

Adding and Subtracting Integers
Adding on the Number Line

3: Fractions, Decimals, and Percents

3.7N: Number

3.7N2: Demonstrate an understanding of the addition, subtraction, multiplication and division of decimals to solve problems (for more than 1-digit divisors or 2-digit multipliers, the use of technology is expected).

Multiplying with Decimals
Sums and Differences with Decimals

3.7N2.1: Solve a given problem involving the addition of two or more decimal numbers.

Sums and Differences with Decimals

3.7N2.2: Solve a given problem involving the subtraction of decimal numbers.

Sums and Differences with Decimals

3.7N2.4: Solve a given problem involving the multiplication of decimal numbers with two digit multipliers (whole numbers or decimals) without the use of technology.

Multiplying with Decimals
Square Roots

3.7N2.6: Solve a given problem involving the multiplication or division of decimal numbers with more than 2-digit multipliers or more than 1-digit divisors (whole numbers or decimals) with the use of technology.

Multiplying with Decimals
Square Roots

3.7N2.8: Check the reasonableness of solutions using estimation.

Estimating Sums and Differences

3.7N3: Solve problems involving percents from 1% to 100%.

3.7N3.1: Express a given percent as a decimal or fraction.

Percents, Fractions, and Decimals

3.7N3.2: Solve a given problem that involves finding a percent.

Percent of Change
Percents and Proportions
Polling: Neighborhood

3.7N4: Demonstrate an understanding of the relationship between positive terminating decimals and positive fractions and between positive repeating decimals and positive fractions.

3.7N4.2: Match a given set of fractions to their decimal representations.

Percents, Fractions, and Decimals

3.7N7: Compare and order positive fractions, positive decimals (to thousandths) and whole numbers by using:

3.7N7.b: place value

Comparing and Ordering Decimals

3.7N7.c: equivalent fractions and/or decimals.

Adding Fractions (Fraction Tiles)
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)

3.7N7.1: Order the numbers of a given set that includes positive fractions, positive decimals and/or whole numbers in ascending or descending order, and verify the result using a variety of strategies.

Comparing and Ordering Decimals
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

3.7N7.2: Position fractions with like and unlike denominators from a given set on a number line, and explain strategies used to determine order.

Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Rational Numbers, Opposites, and Absolute Values

3.7N7.5: Identify a number that would be between two given numbers in an ordered sequence or on a number line.

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

4: Circles and Area

4.7SS: Shape and Space (Measurement)

4.7SS1: Demonstrate an understanding of circles by:

4.7SS1.a: describing the relationships among radius, diameter and circumference

Circumference and Area of Circles

4.7SS1.b: relating circumference to pi

Circumference and Area of Circles

4.7SS1.c: determining the sum of the central angles

Chords and Arcs

4.7SS1.e: solving problems involving the radii, diameters and circumferences of circles.

Chords and Arcs
Circles
Circumference and Area of Circles

4.7SS1.4: Explain that, for all circles, pi is the ratio of the circumference to the diameter (C/d) and its value is approximately 3.14.

Circumference and Area of Circles

4.7SS1.6: Explain, using an illustration, that the sum of the central angles of a circle is 360°.

Chords and Arcs

4.7SS2: Develop and apply a formula for determining the area of:

4.7SS2.a: triangles

Area of Triangles

4.7SS2.b: parallelograms

Area of Parallelograms
Area of Triangles
Perimeter and Area of Rectangles

4.7SS2.c: circles.

Circumference and Area of Circles

4.7SS2.1: 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

4.7SS2.2: Generalize a rule to create a formula for determining the area of parallelograms.

Area of Parallelograms
Area of Triangles
Perimeter and Area of Rectangles

4.7SS2.3: Solve a given problem involving the area of triangles, parallelograms and/or circles.

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

4.7SS2.4: Illustrate and explain how the area of a rectangle or a parallelogram can be used to determine the area of a triangle.

Area of Triangles

4.7SS2.5: Generalize a rule to create a formula for determining the area of triangles.

Area of Triangles

4.7SS2.7: Apply a formula for determining the area of a given circle.

Circumference and Area of Circles

4.7SP: Statistics and Probability (Data Analysis)

4.7SP3: Construct, label and interpret circle graphs to solve problems.

Graphing Skills

4.7SP3.2: Identify common attributes of circle graphs, such as:

4.7SP3.2.a: title, label or legend

Graphing Skills

4.7SP3.4: Interpret a given circle graph to answer questions.

Graphing Skills

4.7SP3.5: Create and label a circle graph, with and without technology, to display a given set of data.

Graphing Skills

5: Operations with Fractions

5.7N: Number

5.7N5: 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).

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

5.7N5.2: Determine the sum of two given positive fractions with like denominators.

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

5.7N5.3: Simplify a given positive fraction by identifying the common factor between the numerator and denominator.

Adding Fractions (Fraction Tiles)
Multiplying Fractions
Toy Factory (Set Models of Fractions)

5.7N5.4: Determine a common denominator for a given set of positive fractions.

Adding Fractions (Fraction Tiles)
Estimating Sums and Differences
Fractions with Unlike Denominators

5.7N5.5: Determine the sum of two given positive fractions with unlike denominators.

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

5.7N5.6: Model subtraction of positive fractions, using concrete representations, and record symbolically.

Adding Fractions (Fraction Tiles)
Fractions with Unlike Denominators

5.7N5.7: Determine the difference of two given positive fractions.

Adding Fractions (Fraction Tiles)
Estimating Sums and Differences
Fractions with Unlike Denominators

5.7N5.8: Model addition and subtraction of mixed numbers, using concrete representations, and record symbolically.

Fractions Greater than One (Fraction Tiles)
Improper Fractions and Mixed Numbers

5.7N5.9: Determine the sum or difference of two mixed numbers.

Fractions Greater than One (Fraction Tiles)
Improper Fractions and Mixed Numbers

5.7N5.10: Simplify the solution to a given problem involving the sum or difference of two positive fractions or mixed numbers.

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

5.7N5.11: Solve a given problem involving the addition or subtraction of positive fractions or mixed numbers and determine if the solution is reasonable.

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

6: Equations

6.7PR: Patterns and Relations (Variables and Equations)

6.7PR3: Demonstrate an understanding of preservation of equality by:

6.7PR3.a: modelling preservation of equality, concretely, pictorially and symbolically

Solving Equations on the Number Line

6.7PR3.b: applying preservation of equality to solve equations.

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

6.7PR3.2: Write equivalent forms of a given equation by applying the preservation of equality, and verify, using concrete materials, e.g., 3b = 12 is the same as 3b + 5 = 12 + 5 or 2r = 7 is the same as 3(2r) = 3(7).

Solving Algebraic Equations II

6.7PR3.3: Solve a given problem by applying preservation of equality.

Solving Two-Step Equations
Using Algebraic Equations

6.7PR6: Model and solve, concretely, pictorially and symbolically, problems that can be represented by one-step linear equations of the form x + a = b, where a and b are integers.

Modeling One-Step Equations
Solving Equations on the Number Line

6.7PR6.2: Draw a visual representation of the steps required to solve a given linear equation.

Solving Equations on the Number Line

6.7PR6.3: Solve a given problem using a linear equation.

Modeling One-Step Equations
Solving Equations by Graphing Each Side
Standard Form of a Line

6.7PR7: Model and solve, concretely, pictorially and symbolically, problems that can be represented by linear equations of the form:

6.7PR7.a: ax + b = c

Modeling One-Step Equations
Modeling and Solving Two-Step Equations

6.7PR7.b: ax - b = c

Modeling One-Step Equations
Modeling and Solving Two-Step Equations

6.7PR7.c: ax = b

Modeling One-Step Equations
Solving Equations on the Number Line

6.7PR7.d: x/a = b, a ≠ 0 where a, b and c are whole numbers.

Modeling One-Step Equations
Solving Equations on the Number Line

6.7PR7.1: Model a given problem with a linear equation and solve the equation using concrete models, e.g., counters, integer tiles.

Absolute Value with Linear Functions
Linear Functions
Modeling and Solving Two-Step Equations

6.7PR7.4: Solve a given problem, using a linear equation, and record the process.

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

6.7PR7.5: Verify the solution to a given linear equation, using concrete materials and diagrams.

Modeling and Solving Two-Step Equations

7: Data Analysis

7.7SP: Statistics and Probability (Data Analysis)

7.7SP1: Demonstrate an understanding of central tendency and range by:

7.7SP1.a: determining the measures of central tendency (mean, median, mode) and range

Box-and-Whisker Plots
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)
Sight vs. Sound Reactions
Stem-and-Leaf Plots

7.7SP1.b: determining the most appropriate measures of central tendency to report findings.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Polling: City
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

7.7SP1.1: Determine mean, median and mode for a given set of data, and explain why these values may be the same or different.

Box-and-Whisker Plots
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)
Sight vs. Sound Reactions
Stem-and-Leaf Plots

7.7SP1.2: Determine the range for a given 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

7.7SP1.4: Solve a given 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)

7.7SP2: Determine the effect on the mean, median and mode when an outlier is included in a data set.

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

7.7SP2.1: Analyze a given 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)

7.7SP2.2: Explain the effect of outliers on the measures of central tendency for a given data set.

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

7.7SP2.3: Identify outliers in a given set of data, and justify whether or not they are to be included 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)

7.7SP2.4: 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)

7.7SP4: Express probabilities as ratios, fractions and percents.

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

7.7SP4.1: Determine the probability of a given outcome occurring for a given probability experiment, and express it as a ratio, fraction and percent.

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

7.7SP4.2: Provide an example of an event with a probability of 0 or 0% (impossible) and an example of an event with a probability of 1 or 100% (certain).

Spin the Big Wheel! (Probability)

7.7SP5: Identify the sample space (where the combined sample space has 36 or fewer elements) for a probability experiment involving two independent events.

Independent and Dependent Events

7.7SP5.1: Provide an example of two independent events, such as:

7.7SP5.1.a: spinning a four section spinner and rolling an eight-sided die

Independent and Dependent Events
Theoretical and Experimental Probability

7.7SP5.1.b: tossing a coin and rolling a twelve-sided die

Independent and Dependent Events
Theoretical and Experimental Probability

7.7SP5.1.c: tossing two coins

Independent and Dependent Events
Theoretical and Experimental Probability

7.7SP5.1.d: rolling two dice and explain why they are independent.

Independent and Dependent Events
Theoretical and Experimental Probability

7.7SP: Statistics and Probability (Chance and Uncertainty)

7.7SP6: Conduct a probability experiment to compare the theoretical probability (determined using a tree diagram, table or other graphic organizer) and experimental probability of two independent events.

7.7SP6.1: Determine the theoretical probability of a given outcome involving two independent events.

Independent and Dependent Events
Theoretical and Experimental Probability

7.7SP6.2: Conduct a probability experiment for an outcome involving two independent events, with and without technology, to compare the experimental probability with the theoretical probability.

Independent and Dependent Events
Theoretical and Experimental Probability

7.7SP6.3: Solve a given probability problem involving two independent events.

Independent and Dependent Events
Theoretical and Experimental Probability

8: Geometry

8.7SS: Shape and Space (3-D Objects and 2-D Shapes)

8.7SS3: Perform geometric constructions, including:

8.7SS3.1: Identify line segments on a given diagram that are either parallel or perpendicular.

Special Parallelograms

8.7SS3.7: Draw the perpendicular bisector of a line segment, using more than one method, and verify the construction.

Segment and Angle Bisectors

8.7SS3.9: Draw the bisector of a given angle, using more than one method, and verify that the resulting angles are equal.

Segment and Angle Bisectors

8.7SS: Shape and Space (Transformations)

8.7SS4: Identify and plot points in the four quadrants of a Cartesian plane, using integral ordered pairs.

City Tour (Coordinates)
Points in the Coordinate Plane

8.7SS4.1: Label the axes of a four quadrant coordinate plane (or Cartesian plane), and identify the origin.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Linear Functions
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

8.7SS4.2: Identify the location of a given point in any quadrant of a Cartesian plane, using an integral ordered pair.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations

8.7SS4.3: Plot the point corresponding to a given integral ordered pair on a Cartesian plane with units of 1, 2, 5 or 10 on its axes.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Points in the Coordinate Plane
Points, Lines, and Equations

8.7SS4.4: Draw shapes and designs in a Cartesian plane, using integral ordered pairs.

Points in the Coordinate Plane

8.7SS4.5: Create shapes and designs, and identify the points used to produce the shapes and designs, in any quadrant of a Cartesian plane.

Points in the Coordinate Plane

8.7SS5: Perform and describe transformations (translations, rotations or reflections) of a 2-D shape in all four quadrants of a Cartesian plane (limited to integral number vertices).

8.7SS5.1: Identify the coordinates of the vertices of a given 2-D shape on a Cartesian plane.

Points in the Coordinate Plane

8.7SS5.2: Describe the horizontal and vertical movement required to move from a given point to another point on a Cartesian plane.

Dilations
Rock Art (Transformations)
Rotations, Reflections, and Translations