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).
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).
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).
N8.2.b Represent a fractional percent and/or a percent greater than 100 using grid paper.
N8.2.c Describe relationships between different types of representation (concrete, pictorial, and symbolic in percent, fractional, and decimal forms) for the same percent (e.g., how do 345 coloured grid squares relate to 345%, or why is 345% the same as 3.45).
N8.2.d Record the percent, fraction, and decimal forms of a quantity shown by a representation on grid paper.
N8.2.e Apply understanding of percents to solve problems, including situations involving combined percents or percents of percents (e.g., PST + GST, or 10% discount on a purchase already discounted 30%) and explain the reasoning.
N8.2.f Explain, using concrete, pictorial, or symbolic representations, why the order of consecutive percents does not impact the final value (e.g., a decrease of 15% followed by an increase of 5% results in the same quantity as an increase of 5% followed by a decrease of 15%).
N8.2.g Demonstrate, using concrete, pictorial, or symbolic representations, that two consecutive percents applied to a specific situation cannot be added or subtracted to give an overall percent change (e.g., a population increase of 10% followed by a population increase of 15% is not a 25% increase, a decrease of 10% followed by an increase of 10% will result in an overall change).
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).
N8.2.i Explain the role and significance of percents in different situations (e.g., polls during elections, medical reports, percent down on purchases).
N8.3 Demonstrate understanding of rates, ratios, and proportional reasoning concretely, pictorially, and symbolically.
N8.3.a Identify and explain ratios and rates in familiar situations (e.g., cost per music download, traditional mixtures for bleaching, time for a hand-sized piece of fungus to burn, mixing of colours, number of boys to girls at a school dance, rates of traveling such as car, skidoo, motor boat or canoe, fishing nets and expected catches, or number of animals hunted and number of people to feed).
N8.4.f Critique the statement "Multiplication always results in a larger quantity" and reword the statement to capture the points of correction or clarification raised (e.g., 1/2 x 1/2= 1/4 which is smaller than 1/2)
N8.4.g Explain, using concrete or pictorial models as well as symbolic reasoning, how the distributive property can be used to multiply mixed numbers.
N8.4.m Critique the statement "Division always results in a smaller quantity" and reword the statement to capture the points of correction or clarification raised (e.g., 1/2 ÷ 1/4= 2, but 2 is bigger than 1/2 or 1/4).
N8.4.n Identify, without calculating, the operation required to solve a problem involving fractions and justify the reasoning.
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).
P8.1.h Identify situations relevant to self, family, or community that appear to define linear relations and determine, with justification, whether the graph for the situation would be shown with a solid line or not.
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).
SS8.1.c Explore right triangles, using technology, using the Pythagorean Theorem to identify Pythagorean triples (e.g., 3, 4, 5 or 5, 12, 13), hypothesize about the nature of triangles with side lengths that are multiples of the Pythagorean triples, and verify the hypothesis.
SS8.1.e Give a presentation that explains a historical or personal use or story of the Pythagorean Theorem (e.g., Pythagoras and his denial of irrational numbers, the use of the 3:4:5 right triangle ratio in the Pyramids, squaring off the corner of a sandbox being built for a sibling, or determining the straight line distance between two towns to be travelled on a snowmobile).
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.f Create a net for a 3-D object, have a peer predict the type of 3-D object that the net represents, explain to the peer the reasoning used in designing the net, and have the peer verify the net by constructing the 3-D object from the net.
SS8.2.g Build a 3-D object made of right rectangular prisms based on the top, front, and side views (with and without the use of technology).
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.
SS8.2.i Generalize and apply strategies for determining the surface area of 3-D objects.
SS8.3.d Explain the effect of changing the orientation of a right prism or right cylinder on the volume of the 3-D object.
SS8.3.e Create and solve personally relevant problems involving the volume of right prisms and right cylinders.
SS8.4 Demonstrate an understanding of tessellation by:
SS8.4.1 explaining the properties of shapes that make tessellating possible
SS8.4.2 creating tessellations
SS8.4.3 identifying tessellations in the environment.
SS8.4.a Identify, describe (in terms of translations, reflections, rotations, and combinations of any of the three), and reproduce (concretely or pictorially) a tessellation that is relevant to self, family, or community (e.g., a Star Blanket or wall paper).
SS8.4.b Predict and verify which of a given set of 2-D shapes (regular and irregular) will tessellate and generalize strategies for determining whether a new 2-D shape will tessellate (i.e., an angle must be a factor of 360°).
SS8.4.c Identify one or more 2-D shapes that will tessellate with a given 2-D shape and explain the choice (e.g., knowing that the sum of the measures of one angle from each of the 2-D shapes must be a factor of 360°, and if the given shape has an angle of 12°, then two shapes with angles of 13° and 5° can be used to tessellate with the original shape because 12+13+5=30 which is a factor of 360 - these shapes would need to be repeated at least 12 times because 30 x 12 is 360).
SS8.4.d Design and create (concretely or pictorially) a tessellation involving one or more 2-D shapes, and document the mathematics involved within the tessellation (e.g., types of transformations, measures of angles, or types of shapes).
SS8.4.e Identify different transformations (translations, reflections, rotations, and combinations of any of the three) present within a tessellation.
SS8.4.f Make a new tessellating shape (polygonal or non-polygonal) by transforming a portion of a known tessellating shape and use the new shape to create an Escher-type design that can be used as a picture or wrapping paper.
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
SP8.1.d Find examples of graphs of data in media and personal experiences and interpret the information in the graphs for personal value.
SP8.1.e Analyze a data graph found in media for features that might bias the interpretation of the graph (such as the size of intervals, the width of bars, and the visual representation) and suggest alterations to remove or downplay the bias.
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.
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.
SP8.2.b Explore and explain the relationship between the probability of two independent events and the probability of each event separately.