N8: Number

N8.1: Demonstrate understanding of the square and principle square root of whole numbers concretely or pictorially and symbolically.

N8.1.a: Recognize, show, and explain the relationship between whole numbers and their factors using concrete or pictorial representations (e.g., using a set number of tiles, create rectangular regions and record the dimensions of those regions, and describe how those dimensions relate to the factors of the number).

Chocomatic (Multiplication, Arrays, and Area)

N8.1.d: Describe and apply the relationship between the principle square roots of numbers and benchmarks using a number line.

Square Roots

N8.1.e: Explain why the square root of a number shown on a calculator may be an approximation.

Square Roots

N8.1.f: Apply estimation strategies to determine approximate values for principle square roots.

Square Roots

N8.1.g: Determine the value or an approximate value of a principle square root with or without the use of technology.

Square Roots

N8.1.i: Share the story, in writing, orally, drama, dance, art, music, or other media, of the role and significance of square roots in a personally selected historical or modern application situation (e.g., Archimedes and the square root of 3, Pythagoras and the existence of square roots, role of square roots in Pythagoras? theorem, use of square roots in determining dimensions of a square region from the area, use of square roots to determine measurements in First Nations beading patterns, use of square roots to determine dimensions of nets).

Square Roots

N8.2: Expand and demonstrate understanding of percents greater than or equal to 0% (including fractional and decimal percents) concretely, pictorially, and symbolically.

N8.2.a: Recognize, represent, and explain situations, including for self, family, and communities, in which percents greater than 100 or fractional percents are meaningful (e.g., the percent profit made on the sale of fish).

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

N8.2.h: Analyze choices and make decisions based upon percents and personal or community concerns and issues (e.g., deciding whether or not to have surgery if given a 75% chance of survival, deciding how much to buy if you can save 25% when two items are purchased, deciding whether or not to hunt for deer when a known percent of deer have chronic wasting disease, deciding about whether or not to use condoms knowing that they are 95% effective as birth control, making decisions about diet knowing that a high percentage of Aboriginal peoples have or will get diabetes).

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

N8.2.j: Pose and solve problems involving percents stated as a percent, fraction, or decimal quantity.

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

N8.3: Demonstrate understanding of rates, ratios, and proportional reasoning concretely, pictorially, and symbolically.

N8.3.b: Identify situations (such as providing for the family or community through hunting) in which a given quantity of represents a:

N8.3.b.1: fraction

Percents, Fractions, and Decimals
Proportions and Common Multipliers

N8.3.b.4: percent

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

N8.3.b.5: probability

Estimating Population Size
Probability Simulations
Theoretical and Experimental Probability

N8.3.b.6: ratio.

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)

N8.3.e: Write the symbolic form (e.g., 3:5 or 3 to 5 as a ratio, $3/min or $3 per one minute as a rate) for a concrete, physical, or pictorial representation of a ratio or rate.

Part-to-part and Part-to-whole Ratios

N8.3.g: Create and solve problems involving rates, ratios, and/or probabilities.

Beam to Moon (Ratios and Proportions) - Metric
Estimating Population Size
Household Energy Usage
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers
Road Trip (Problem Solving)
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

N8.4: Demonstrate understanding of multiplying and dividing positive fractions and mixed numbers, concretely, pictorially, and symbolically.

N8.4.a: Identify and describe situations relevant to self, family, or community in which multiplication and division of fractions are involved.

Adding on the Number Line
Dividing Mixed Numbers
Estimating Population Size
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

N8.4.o: Create, represent (concretely, pictorially, or symbolically) and solve problems that involve one or more operations on positive fractions (including multiplication and division).

Fractions with Unlike Denominators

N8.5: Demonstrate understanding of multiplication and division of integers concretely, pictorially, and symbolically.

N8.5.a: Identify and describe situations that are relevant to self, family, or community in which multiplication or division of integers would be involved.

Dividing Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

N8.5.f: Create and solve problems involving the multiplication or division (without technology for one-digit divisors, with technology for two-digit divisors) of integers.

Adding and Subtracting Integers

N8.5.g: Explain how the order of operations can be extended to include integers and provide examples to demonstrate the use of the order of operations.

Order of Operations

N8.5.h: Create and solve problems requiring the use of the order of operations on integers.

Order of Operations

P8: Patterns and Relations

P8.1: Demonstrate understanding of linear relations concretely, pictorially (including graphs), physically, and symbolically.

P8.1.a: Analyze and describe the relationship shown on a graph for a given situation (e.g., "The graph is showing that, as the temperature rises, the number of people in the mall decreases").

Absolute Value with Linear Functions
Quadratics in Polynomial Form

P8.1.b: Explain how a given linear relation is represented by a given table of values.

Function Machines 1 (Functions and Tables)

P8.1.g: Determine if an ordered pair satisfies a linear relation given as a table of values, concrete or pictorial representation, graph, or equation and explain the reasoning.

Linear Functions

P8.2: Model and solve problems using linear equations of the form:

P8.2.1: ax = B

Absolute Value with Linear Functions
Linear Functions
Modeling and Solving Two-Step Equations
Solving Equations by Graphing Each Side
Standard Form of a Line

P8.2.2: x/a = b, a ≠ 0

Absolute Value with Linear Functions
Linear Functions
Modeling and Solving Two-Step Equations
Solving Equations by Graphing Each Side
Standard Form of a Line

P8.2.3: ax + b = c

Absolute Value with Linear Functions
Linear Functions
Modeling and Solving Two-Step Equations
Solving Equations by Graphing Each Side
Standard Form of a Line

P8.2.5: a (x + b) = c

Absolute Value with Linear Functions
Linear Functions
Modeling and Solving Two-Step Equations
Solving Equations by Graphing Each Side
Standard Form of a Line

P8.2.a: Identify and describe situations, which are relevant to self, family, or community, that can be modeled by a linear equation (e.g., the cost of purchasing x fish from a fisherman).

Absolute Value with Linear Functions

P8.2.e: Generalize and apply symbolic strategies for solving linear equations.

Solving Equations by Graphing Each Side

P8.2.g: Demonstrate the application of the distributive property in the solving of linear equations (e.g., 2(x + 3); 2x + 6= 5)

Solving Algebraic Equations II
Solving Equations by Graphing Each Side

P8.2.j: Explain the algebra behind a particular algebra puzzle such as this puzzle written for 2008:

P8.2.j.2: Multiply this number by 2 (just to be bold).

Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

P8.2.j.3: Add 5.

Adding Fractions (Fraction Tiles)
Adding on the Number Line
Sums and Differences with Decimals

P8.2.j.4: Multiply it by 50.

Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals

P8.2.j.5: If you have already had your birthday this year add 1758. If you have not, add 1757.

Adding Fractions (Fraction Tiles)
Adding on the Number Line
Sums and Differences with Decimals

P8.2.j.6: Now subtract the four digit year that you were born.

Adding Fractions (Fraction Tiles)
Adding on the Number Line
Sums and Differences with Decimals

SS8: Shape and Space Strand

SS8.1: Demonstrate understanding of the Pythagorean Theorem concretely or pictorially and symbolically and by solving problems.

SS8.1.b: Explore right and non-right triangles, using technology, and generalize the relationship between the type of triangle and the Pythagorean Theorem (i.e., if the sides of a triangle satisfy the Pythagorean equation, then the triangle is a right triangle which is known as the Converse of the Pythagorean Theorem).

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

SS8.1.d: Create and solve problems involving the Pythagorean Theorem, Pythagorean triples, or the Converse of the Pythagorean Theorem.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

SS8.2: Demonstrate understanding of the surface area of 3-D objects limited to right prisms and cylinders (concretely, pictorially, and symbolically) by:

SS8.2.1: analyzing views

Surface and Lateral Areas of Prisms and Cylinders

SS8.2.2: sketching and constructing 3-D objects, nets, and top, side, and front views

Surface and Lateral Areas of Prisms and Cylinders

SS8.2.3: generalizing strategies and formulae

Surface and Lateral Areas of Prisms and Cylinders

SS8.2.h: Demonstrate how the net of a 3-D object (including right rectangular prisms, right triangular prisms, and cylinders) can be used to determine the surface area of the 3-D object and describe strategies used to determine the surface area.

Surface and Lateral Areas of Prisms and Cylinders

SS8.2.i: Generalize and apply strategies for determining the surface area of 3-D objects.

Surface and Lateral Areas of Prisms and Cylinders

SS8.2.j: Create and solve personally relevant problems involving the surface area or nets of 3-D objects.

Surface and Lateral Areas of Pyramids and Cones

SS8.3: Demonstrate understanding of volume limited to right prisms and cylinders (concretely, pictorially, or symbolically) by:

SS8.3.1: relating area to volume

Pyramids and Cones

SS8.3.2: generalizing strategies and formulae

Prisms and Cylinders
Pyramids and Cones

SS8.3.4: solving problems.

Prisms and Cylinders
Pyramids and Cones

SS8.3.a: Identify situations from one?s home, school, or community in which the volume of right prism or right cylinder would need to be determined.

Prisms and Cylinders

SS8.3.c: Generalize and apply formulas for determining the area of a right prism and right cylinder.

Surface and Lateral Areas of Prisms and Cylinders

SS8.3.e: Create and solve personally relevant problems involving the volume of right prisms and right cylinders.

Prisms and Cylinders

SP8: Statistics and Probability

SP8.1: Analyze the modes of displaying data and the reasonableness of conclusions.

SP8.1.a: Investigate and report on the advantages and disadvantages of different types of graphs, including circle graphs, line graphs, bar graphs, double bar graphs, and pictographs (e.g., circle graphs are good for qualitative data such as favourite activities and categories such as money spent on clothes, whereas line graphs are good for quantitative data such as heights and ages

Reaction Time 1 (Graphs and Statistics)

SP8.1.b: Engage in a project that involves:

SP8.1.b.1: the collection and organization of first- or second-hand data related to a topic of interest (such as local wildlife counts or surveying of peers)

Box-and-Whisker Plots
Describing Data Using Statistics
Estimating Population Size
Stem-and-Leaf Plots

SP8.1.b.2: representation of the data using a graph

Box-and-Whisker Plots
Correlation
Distance-Time Graphs - Metric
Stem-and-Leaf Plots

SP8.1.b.4: description of the project, challenges, and conclusions

Polling: City

SP8.1.b.5: self-assessment.

Box-and-Whisker Plots

SP8.1.c: Suggest alternative ways to represent data from a given situation and explain the choices made.

Correlation
Stem-and-Leaf Plots

SP8.1.f: Provide examples of misrepresentations of data and data graphs found within different media and explain what types of misinterpretations might result from such displays.

Polling: City
Populations and Samples

SP8.2: Demonstrate understanding of the probability of independent events concretely, pictorially, orally, and symbolically.

SP8.2.a: Ask questions relevant to self, family, or community in which probabilities involving two events are known or which can be researched.

Estimating Population Size
Probability Simulations
Theoretical and Experimental Probability

SP8.2.b: Explore and explain the relationship between the probability of two independent events and the probability of each event separately.

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

SP8.2.c: Make and test predictions about the results of experiments and simulations for two independent events.

Independent and Dependent Events

SP8.2.d: Create and solve problems related to independent events, probabilities of independent events, and decision making.

Independent and Dependent Events
Theoretical and Experimental Probability