N6: Number

N6.1: Demonstrate understanding of place value including:

N6.1.1: greater than one million

Number Systems

N6.1.2: less than one thousandth with and without technology.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Comparing and Ordering Decimals
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals
Treasure Hunter (Decimals on the Number Line)

N6.1.b: Change the representation of numbers larger than one million given in decimal and word form to place value form (e.g., $1.8 billion would be changed to $1 800 000 000) and vice versa.

Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)

N6.1.e: Solve situational questions involving operations on quantities larger than one million or smaller than one thousandth (with the use of technology).

Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals
Treasure Hunter (Decimals on the Number Line)

N6.1.f: Estimate the solution to a situational question, without the use of technology, involving operations on quantities larger than one million or smaller than one thousandth and explain the strategies used to determine the estimate.

Multiplying Decimals (Area Model)

N6.2: Demonstrate understanding of factors and multiples (concretely, pictorially, and symbolically) including:

N6.2.1: determining factors and multiples of numbers less than 100

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)
Finding Factors with Area Models
Operations with Radical Expressions

N6.2.2: relating factors and multiples to multiplication and division

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)

N6.2.3: determining and relating prime and composite numbers.

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)

N6.2.a: Determine the whole-numbered dimensions of all rectangular regions with a given whole-numbered area and explain how those dimensions are related to the factors of the whole number.

Chocomatic (Multiplication, Arrays, and Area)

N6.2.b: Represent a set of whole-numbered multiples for a given quantity concretely, pictorially, or symbolically and explain the strategy used to create the representation.

Factor Trees (Factoring Numbers)

N6.2.d: Explain why 0 and 1 are neither prime nor composite.

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)
Finding Factors with Area Models

N6.2.g: Explain how the composite factors of a whole number can be determined from the prime factors of the whole number and vice versa.

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)
Finding Factors with Area Models
Operations with Radical Expressions

N6.2.h: Solve situational questions involving factors, multiples, and prime factors.

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)
Finding Factors with Area Models
Operations with Radical Expressions

N6.2.i: Analyze two whole numbers for their common factors.

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)
Finding Factors with Area Models
Operations with Radical Expressions

N6.2.j: Analyze two whole numbers to determine at least one multiple (greater than both whole numbers) that is common to both.

Factor Trees (Factoring Numbers)
Finding Factors with Area Models

N6.3: Demonstrate understanding of the order of operations on whole numbers (excluding exponents) with and without technology.

N6.3.a: Explain, with the support of examples, why there is a need to have a standardized order of operations.

Order of Operations

N6.3.c: Verify, by using technology, whether or not the simplification of an expression involving the use of the order of operations is correct.

Order of Operations

N6.3.d: Solve situational questions involving multiple operations, with and without the use of technology.

Order of Operations

N6.3.e: Analyze the simplification of multiple operation expressions for errors in the application of the order of operations.

Order of Operations

N6.4: Extend understanding of multiplication and division to decimals (1-digit whole number multipliers and 1-digit natural number divisors).

N6.4.d: Estimate products and quotients involving decimals.

Multiplying Decimals (Area Model)
Multiplying with Decimals
Square Roots

N6.4.e: Develop a generalization about the impact on overall quantity when multiplied by a decimal number between 0 and 1.

Multiplying Decimals (Area Model)

N6.4.g: Solve a given situational question that involves multiplication and division of decimals, using multipliers from 0 to 9 and divisors from 1 to 9.

Multiplying Decimals (Area Model)

N6.5: Demonstrate understanding of percent (limited to whole numbers to 100) concretely, pictorially, and symbolically.

N6.5.c: Create and explain representations (concrete, visual, or both) that establish relationships between whole number percents to 100, fractions, and decimals.

Percents, Fractions, and Decimals

N6.5.f: Describe a situation in which 0% or 100% might be stated.

Percent of Change
Percents, Fractions, and Decimals

N6.6: Demonstrate understanding of integers concretely, pictorially, and symbolically.

N6.6.a: Explore and explain the representation and meaning of negative quantities in First Nations and Métis peoples, past and present.

Adding and Subtracting Integers
Adding on the Number Line
Addition of Polynomials
Integers, Opposites, and Absolute Values

N6.6.b: Observe and describe examples of integers relevant to self, family, or community and explain the meaning of those quantities within the contexts they are found.

Integers, Opposites, and Absolute Values

N6.6.c: Compare two integers and describe their relationship symbolically using <, >, or =.

Integers, Opposites, and Absolute Values

N6.6.d: Represent integers concretely, pictorially, or physically.

Adding and Subtracting Integers

N6.7: Extend understanding of fractions to improper fractions and mixed numbers.

N6.7.a: Observe and describe situations relevant to self, family, or community in which quantities greater than a whole, but which are not whole numbers, occur and describe those situations using either an improper fraction or a mixed number.

Improper Fractions and Mixed Numbers
Multiplying Mixed Numbers

N6.7.d: Explain the meaning of a given improper fraction or mixed number by setting it into a situation.

Improper Fractions and Mixed Numbers
Multiplying Mixed Numbers

N6.7.f: Respond to the question ?Can quantities less than 1 be represented by a mixed number or improper fraction??.

Fraction Artist 1 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)
Percents, Fractions, and Decimals
Toy Factory (Set Models of Fractions)

N6.8: Demonstrate an understanding of ratio concretely, pictorially, and symbolically.

N6.8.a: Observe situations relevant to self, family, or community which could be described using a ratio, write the ratio, and explain what the ratio means in that situation.

Beam to Moon (Ratios and Proportions) - Metric
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Road Trip (Problem Solving)

N6.8.d: Express a ratio in colon and word form.

Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

N6.8.e: Describe a situation in which a ratio (given in colon, word, or fractional form) might occur.

Beam to Moon (Ratios and Proportions) - Metric
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Road Trip (Problem Solving)

N6.8.f: Solve situational questions involving ratios (e.g., the ratio of students from a Grade 6 class going to a movie this weekend to those not going to a movie is 15:8. How many students are likely in the class and why?)

Beam to Moon (Ratios and Proportions) - Metric
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Road Trip (Problem Solving)

P6: Patterns and Relationships

P6.1: Extend understanding of patterns and relationships in tables of values and graphs.

P6.1.a: Create and describe a concrete or visual model of a table of values.

Function Machines 1 (Functions and Tables)

P6.1.b: Create a table of values to represent a concrete or visual pattern.

Function Machines 1 (Functions and Tables)

P6.1.c: Determine missing values and correct errors found within a table of values and describe the strategy used.

Function Machines 1 (Functions and Tables)

P6.1.d: Analyze the relationship between consecutive values within each of the columns in a table of values and describe the relationship orally and symbolically.

Function Machines 1 (Functions and Tables)
Points, Lines, and Equations

P6.1.e: Analyze the relationship between the two columns in a table of values and describe the relationship orally and symbolically.

Function Machines 1 (Functions and Tables)
Points, Lines, and Equations

P6.1.f: Create a table of values for a given equation.

Function Machines 2 (Functions, Tables, and Graphs)
Introduction to Functions
Points, Lines, and Equations

P6.1.g: Analyze patterns in a table of values to solve a given situational question.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)

P6.1.h: Translate a concrete, visual, or physical pattern into a table of values and a graph (limit graphs to linear relations with discrete elements).

Arithmetic Sequences
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Geometric Sequences

P6.1.i: Describe how a graph and a table of values are related.

Function Machines 2 (Functions, Tables, and Graphs)
Introduction to Functions
Points, Lines, and Equations

P6.1.j: Identify errors in the matching of graphs and tables of values and explain the reasoning.

Points, Lines, and Equations

P6.1.k: Describe, using everyday language (orally or in writing), the relationship shown on a graph (limited to linear relations with discrete elements).

Slope-Intercept Form of a Line

P6.1.l: Describe a situation that could be represented by a given graph (limited to linear relations with discrete elements).

Arithmetic Sequences
Slope-Intercept Form of a Line

P6.3: Extend understanding of patterns and relationships by using expressions and equations involving variables.

P6.3.b: Analyze patterns arising from the determination of area of rectangles and generalize an equation describing a formula for the area of all rectangles.

Chocomatic (Multiplication, Arrays, and Area)

P6.3.d: Develop and justify equations using letter variables that illustrate the commutative property of addition and multiplication (e.g., a + b = b + a or a × b = b × a).

Using Algebraic Equations

P6.3.e: Generalize an expression that describes the relationship between the two columns in a table of values.

Geometric Sequences

P6.3.f: Write an equation to represent a table of values.

Points, Lines, and Equations

P6.3.h: Provide examples to explain the difference between an expression and an equation, both in terms of what each looks like and what each means.

Absolute Value Equations and Inequalities
Compound Interest
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Equations on the Number Line
Using Algebraic Equations

SS6: Shape and Space

SS6.1: Demonstrate understanding of angles including:

SS6.1.2: classifying angles

Triangle Angle Sum

SS6.1.4: determining angle measures in degrees

Triangle Angle Sum

SS6.1.6: applying angle relationships in triangles and quadrilaterals.

Polygon Angle Sum
Triangle Angle Sum

SS6.1.e: Explain the relationship between 0° and 360°.

Triangle Angle Sum

SS6.1.f: Describe how measuring an angle is different from measuring a length.

Measuring Trees
Triangle Angle Sum

SS6.1.h: Describe and provide examples for different uses of angles, such as the amount of rotation or as the angle of opening between two sides of a polygon.

Rotations, Reflections, and Translations

SS6.1.i: Generalize a relationship for the sum of the measures of the angles in any triangle.

Polygon Angle Sum
Triangle Angle Sum

SS6.1.j: Generalize a relationship for the sum of the measures of the angles in any quadrilateral.

Polygon Angle Sum

SS6.1.l: Solve situational questions involving angles in triangles and quadrilaterals.

Concurrent Lines, Medians, and Altitudes
Polygon Angle Sum
Triangle Angle Sum

SS6.2: Extend and apply understanding of perimeter of polygons, area of rectangles, and volume of right rectangular prisms (concretely, pictorially, and symbolically) including:

SS6.2.4: generalizing strategies and formulae

Area of Triangles
Balancing Blocks (Volume)
Chocomatic (Multiplication, Arrays, and Area)
Perimeter and Area of Rectangles
Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders

SS6.2.6: solving situational questions.

Area of Parallelograms
Area of Triangles
Balancing Blocks (Volume)
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles
Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders

SS6.2.a: Generalize formulae and strategies for determining the perimeter of polygons, including rectangles and squares.

Perimeter and Area of Rectangles

SS6.2.b: Generalize a formula for determining the area of rectangles.

Area of Triangles
Perimeter and Area of Rectangles

SS6.2.d: Generalize a rule (formula) for determining the volume of right rectangular prisms.

Balancing Blocks (Volume)
Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders

SS6.2.f: Solve a situational question involving the perimeter of polygons, the area of rectangles, and/or the volume of right rectangular prisms.

Area of Parallelograms
Area of Triangles
Balancing Blocks (Volume)
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles
Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders

SS6.3: Demonstrate understanding of regular and irregular polygons including:

SS6.3.1: classifying types of triangles

Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Pythagorean Theorem with a Geoboard
Similarity in Right Triangles
Triangle Inequalities

SS6.3.f: Draw and classify examples of different types of triangles (scalene, isosceles, equilateral, right, obtuse, and acute) and explain the reasoning.

Classifying Triangles
Pythagorean Theorem with a Geoboard

SS6.4: Demonstrate understanding of the first quadrant of the Cartesian plane and ordered pairs with whole number coordinates.

SS6.4.b: Plot a point in the first quadrant of the Cartesian plane given its ordered pair.

Points in the Coordinate Plane

SS6.4.e: Explain how to plot points on the Cartesian plane given the scale to be used on the axes (by 1, 2, 5, or 10).

Points in the Coordinate Plane

SS6.4.f: Create a design in the first quadrant of the Cartesian plane, identify the coordinates of points on the design, and write or record orally directions for recreating the design.

City Tour (Coordinates)
Points in the Coordinate Plane

SS6.5: Demonstrate understanding of single, and combinations of, transformations of 2-D shapes (with and without the use of technology) including:

SS6.5.1: identifying

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

SS6.5.2: describing

Rotations, Reflections, and Translations

SS6.5.3: performing.

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

SS6.5.a: Observe and classify different transformations found in situations relevant to self, family, or community.

Circles
Rotations, Reflections, and Translations

SS6.5.c: Analyze 2-D shapes and their respective transformations to determine if the original shapes and their transformed images are congruent.

Rock Art (Transformations)
Rotations, Reflections, and Translations

SS6.5.d: Determine the resulting image of applying a series of transformations upon a 2-D shape.

Rock Art (Transformations)

SS6.5.e: Describe a set of transformations, that when applied to a given 2-D shape, would result in a given image.

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

SS6.5.f: Verify whether or not a given set of transformations would transform a given 2-D shape into a given image.

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

SS6.5.g: Identify designs within situations relevant to self, family, or community that could be described in terms of transformations of one or more 2-D shapes.

Circles
Rotations, Reflections, and Translations

SS6.5.h: Analyze a given design created by transforming one or more 2-D shapes, and identify the original shape(s) and the transformations used to create the design.

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

SS6.5.i: Create a design using the transformation of two or more 2-D shapes and write, or record orally, instructions that could be followed to reproduce the design.

Rotations, Reflections, and Translations

SS6.5.j: Describe the creation and use of single and multiple transformations in First Nations and Métis lifestyles (e.g., birch bark biting).

Rotations, Reflections, and Translations

SP6: Statistics and Probability

SP6.1: Extend understanding of data analysis to include:

SP6.1.1: line graphs

Elevator Operator (Line Graphs)
Graphing Skills
Prairie Ecosystem

SP6.1.3: data collection through questionnaires, experiments, databases, and electronic media

Describing Data Using Statistics
Movie Reviewer (Mean and Median)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Time Estimation

SP6.1.b: Determine whether a set of data should be represented by a line graph (continuous data) or a series of points (discrete data) and explain why.

Box-and-Whisker Plots
Graphing Skills

SP6.1.d: Construct a graph (line graph or a graph of discrete data points) to represent data given in a table for a particular situation.

Graphing Skills
Polling: City
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Stem-and-Leaf Plots

SP6.1.f: Observe and describe situations relevant to self, family, or community in which data might be collected through questionnaires, experiments, databases, or electronic media.

Estimating Population Size

SP6.1.g: Select a method for collecting data to answer a given question and justify the choice.

Estimating Population Size
Reaction Time 2 (Graphs and Statistics)

SP6.1.i: Answer a self-generated question using databases or electronic media to collect data, then graphing and interpreting the data to draw a conclusion.

Reaction Time 2 (Graphs and Statistics)

SP6.1.j: Justify the selection of a type of graph for a set of data collected through questionnaires, experiments, databases, or electronic media.

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

SP6.2: Demonstrate understanding of probability by:

SP6.2.1: determining sample space

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

SP6.2.2: differentiating between experimental and theoretical probability

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

SP6.2.3: determining the theoretical probability

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

SP6.2.4: determining the experimental probability

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

SP6.2.5: comparing experimental and theoretical probabilities.

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

SP6.2.a: Observe situations relevant to self, family, or community where probabilities are stated and/or used to make decisions.

Estimating Population Size
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

SP6.2.b: List the sample space (possible outcomes) for an event (such as the tossing of a coin, rolling of a die with 10 sides, spinning a spinner with five sections, random selection of a classmate for a special activity, or guessing a hidden quantity) and explain the reasoning.

Independent and Dependent Events

SP6.2.c: Explain what a probability of 0 for a specific outcome means by providing an example.

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

SP6.2.d: Explain what a probability of 1 for a specific outcome means by providing an example.

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

SP6.2.g: Compare the results of a probability experiment to the expected theoretical probabilities.

Independent and Dependent Events

SP6.2.h: Explain how theoretical and experimental probabilities are related.

Probability Simulations

SP6.2.i: Critique the statement: ?You can determine the sample space for an event by carrying out an experiment.?

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