N6.1.a Explain, concretely, pictorially, or orally, how numbers larger than one million found in mass media and other contexts are related to one million by referencing place value and/or extending concrete or pictorial representations.
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.
N6.1.c Explain, concretely, pictorially, or orally, how numbers smaller than one thousandth found in mass media and other contexts are related to one thousandth by referencing place value and/or extending concrete or pictorial representations.
N6.1.d Explain how the pattern of the place value system (e.g., the repetition of ones, tens, and hundreds), makes it possible to read and write numerals for numbers of any magnitude.
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.
N6.3.b Verify, by using repeated addition and repeated subtraction for multiplication and division respectively, whether or not the simplification of an expression involving the use of the order of operations is correct.
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.
N6.3.d Solve situational questions involving multiple operations, with and without the use of technology.
N6.5 Demonstrate understanding of percent (limited to whole numbers to 100) concretely, pictorially, and symbolically.
N6.5.a Observe and describe examples of percents (whole numbered to 100) relevant to self, family, or community, represent the percent concretely or pictorially (possibly physically), and explain what the percent tells about the context in which it is being used.
N6.6.h Explain the role of zero within integers and how it is different from other 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.
N6.8.b Critique the statement "Ratios and fractions are the same thing".
N6.8.c Create representations of and compare part/whole and part/ part ratios (e.g., from a group of 3 boys and 5 girls, compare the representations boys to girls, boys to entire group, and girls to entire group - 3:5, 3:8, and 5:8 respectively).
N6.8.e Describe a situation in which a ratio (given in colon, word, or fractional form) might occur.
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?)
N6.9 Research and present how First Nations and Métis peoples, past and present, envision, represent, and use quantity in their lifestyles and worldviews.
N6.9.a Gather and document information regarding the significance and use of quantity for at least one First Nation or Métis peoples from a variety of sources such as Elders and traditional knowledge keepers.
N6.9.b Compare the significance, representation, and use of quantity for different First Nations, Métis peoples, and other cultures.
N6.9.c Communicate to others concretely, pictorially, orally, visually, physically, and/or in writing, what has been learned about the envisioning, representing, and use of quantity by First Nations and Métis peoples and how these understandings parallel, differ from, and enhance one's own mathematical understandings about numbers.
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.
P6.2.b Create, and record symbolically, equivalent forms of an equation by applying the preservation of equality (of a single operation) and verify the results concretely or pictorially (e.g., 3b = 12 is the same as 3b + 5 = 12 + 5 or 2r = 7 is the same as 3(2r) = 3(7)).
P6.3 Extend understanding of patterns and relationships by using expressions and equations involving variables.
P6.3.a Analyze patterns arising from the determination of perimeter of rectangles and generalize an equation describing a formula for the perimeter of all rectangles.
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.
P6.3.c Describe and represent geometric patterns and relationships relevant to First Nations and Métis peoples and explain how those patterns or relationships could be represented mathematically.
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).
SS6.1.k Provide a visual, concrete, and/or oral informal proof for the sum of the measures of the angles in a quadrilateral being 360° (assuming that the sum of the measures of the angles in a triangle is 180°).
SS6.1.l Solve situational questions involving angles in triangles and quadrilaterals.
SS6.2 Extend and apply understanding of perimeter of polygons, area of rectangles, and volume of right rectangular prisms (concretely, pictorially, and symbolically) including:
SS6.4.c Analyze the coordinates of the ordered pairs of points that lie on the horizontal axis and generalize a strategy for identifying the ordered pairs of points on the horizontal axis without plotting them.
SS6.4.d Analyze the coordinates of the ordered pairs of points that lie on the vertical axis and generalize a strategy for identifying the ordered pairs of points on the vertical axis without plotting them.
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).
SP6.2 Demonstrate understanding of probability by:
SP6.2.1 determining sample space
SP6.2.2 differentiating between experimental and theoretical probability
SP6.2.3 determining the theoretical probability
SP6.2.4 determining the experimental probability
SP6.2.5 comparing experimental and theoretical probabilities.
SP6.2.a Observe situations relevant to self, family, or community where probabilities are stated and/or used to make decisions.
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.