representing using powers

evaluating powers

powers with an exponent of zero

solving situational questions.

]]> Demonstrate the difference between the exponent and base of a power by representing two powers with exponent and base interchanged (e.g., $2^3$ and $3^2$ or $10^3$ and $3^10$) using repeated multiplication or concrete models and describe the result.

]]> Predict which of two powers represents the greater quantity, explain the reasoning, and verify using technology.

]]> 110851 Analyze the role of brackets in powers by using repeated multiplication [e.g., $(-2)^4$, $(-2^4)$, and $–2^4$] and generalize strategies for evaluating powers involving brackets.

]]> 110852 Justify why $a^0, a \u2260 0$, must equal to 1.

]]> 110853 Predict whether the value of a given power will be positive or negative (e.g., what will the sign of $-7^15$ be?).

]]> 110854 Evaluate powers with integral bases (excluding base 0) and whole number exponents, with or without the use of technology.

]]> 110855 Generalize, using repeated multiplication to represent powers, the exponent laws of powers with integral bases (excluding base 0) and whole number exponents:

• $(a^m)(a^n)=a^{m+n}$
• $a^m/a^n =a^{m-n},m>n$
• $(a^m)^n = a^{mn}$
• $(ab)^m=a^mb^m$

]]> 110856 Apply the exponent laws to expressions involving powers, and determine the quantity represented by the expression, with or without the use of technology.

]]> 110857 Prove by contradiction that $a^m+a^n \u2260 a^{mn}$, $a^m-a^n \u2260 a^{m-n}$, and $a^m-a^n \u2260 a^{m/n}$

]]> 110858 Describe and apply strategies for evaluating sums or differences of powers.

]]> 110859 Analyze a simplification of an expression involving powers for errors.

]]> 110860

comparing and ordering

relating to other types of numbers

solving situational questions.

]]> 110850 Order a given set of rational numbers, in fraction and decimal form, by placing them on a number line and explaining the reasoning used (e.g., 3/5, - 0.666, 4,... , 0.5, -5/8).

]]> Determine a rational number between two given rational numbers and describe the strategy used.

]]> 110863 Create a representation depicting how whole numbers, fractions, decimals, integers, square roots, and rational numbers are related to each other.

]]> 110864 Provide examples to explain how knowing about how to add, subtract, multiply, and divide integers and positive rational numbers informs knowing how to add, subtract, multiply, and divide rational numbers.

]]> 110865 Provide examples to demonstrate how the order of operations can be extended to rational numbers.

]]> 110866 Solve situational questions involving operations on rational numbers, with or without the use of technology.

]]> 110867 Analyze a simplification of an expression involving rational numbers for errors.

]]> 110868 110862 Develop a generalization about what type of number results from the squaring of a rational number.

]]> Describe strategies for determining if a rational number is a perfect square.

]]> 110871 Determine the square root of a rational number that is a perfect square.

]]> 110872 Determine the rational number for which a given rational number is its square root (e.g., $4/3$ is the square root of what rational number?).

]]> 110873 Explain and apply strategies involving benchmarks for determining an estimate of the square root of a rational number that is not a perfect square.

]]> 110874 Determine, with the use of technology, an approximate value for the square root of a rational number that is not a perfect square.

]]> 110875 Explain why the value shown by technology may only be an approximation of the square root of a rational number.

]]> 110876 Describe a strategy that, if applied to writing a decimal number, would result in an irrational number (e.g., students describe a strategy in which they repeatedly write the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 but separate each group of these digits by an increasing number of repeats of the digit 7 or 0.0123456789701234567897701234567897770123...).

]]> 110877 Determine a rational number whose square root would be between two given rational numbers and explain the reasoning used (e.g., a rational number whose square root is between $1/2$ and $1/3$ would be between $1/4$ and $1/9$ because those are $1/2$ and $1/3$ squared. I need to find a number between $1/4$ and $1/9$. I can do this by making the two fractions into fractions of the same type: $9/36$ and $4/36$. One number between these is $6/36$ or $8/36$).

]]> 110878 110849

graphing

analyzing

interpolating and extrapolating

solving situational questions.

]]> Observe and describe a situation relevant to self, family, or community that a given graph might represent and explain the meaning conveyed by the graph.

]]> Sort a set of graphs into representations of linear and non-linear relations.

]]> 110882 Sketch graphs for given linear relations, including horizontal and vertical lines, with and without the use of technology.

]]> 110883 Generalize strategies for determining if a given linear relation will have a graph that is horizontal, vertical, increasing, or decreasing.

]]> 110884 Extrapolate to determine a value for either variable in a linear relation beyond the shown graph.

]]> 110885 Verify an extrapolated value from a graph by using substitution in the related linear relation.

]]> 110886 Interpolate to determine a value for either variable in a linear relation within the shown graph.

]]> 110887 Verify an interpolated value from a graph by using substitution in the related linear relation.

]]> 110888 Solve situational questions by graphing linear relations and interpreting the resulting graphs.

]]> 110889

$ax = b$

$x/a = b, a \u2260 0$

$ax + b = c$

$x/a + b = c, a \u2260 0$

$ax = b + cx$

$a(x + b) = c$

$ax + b = cx + d$

$a(bx + c) = d(ex + f)$

$a/x = b, x \u2260 0$

where a, b, c, d, e, and f are rational numbers.]]> 110881 Explain why the equation $a/x = b$, cannot have a solution of $x = 0$.

]]> Write a linear expression representing a given pictorial, oral, or written pattern.

]]> 110892 Write a linear equation to represent a particular situation.

]]> 110893 Observe and describe a situation relevant to self, family, or community which could be represented by a linear equation.

]]> 110894 Write a linear equation representing the pattern in a given table of values and verify the equation by substituting values from the table.

]]> 110895 Model the solution of a linear equation using concrete or pictorial representations, and explain how to record the process symbolically.

]]> 110896 Explain how the preservation of equality is involved in the solving of linear equations.

]]> 110897 Verify, by substitution, whether or not a given rational number is a solution to a given linear equation.

]]> 110898 Solve a linear equation symbolically.

]]> 110899 Analyze the given solution for a linear equation that has resulted in an incorrect solution, and identify and explain the error(s) made.

]]> 110900 Provide examples from the modern world in which linear equations are used and solved.

]]> 110901

solving inequalities

verifying

comparing

graphing.

]]> 110891 Observe and describe situations relevant to self, family, or community, including First Nations and Métis communities, that involve inequalities and classify the inequality as being less than, greater than, less than or equal to, or greater than or equal to.

]]> Verify whether or not a given rational number is part of the solution set for a linear inequality.

]]> 110904 Generalize and apply rules for adding or subtracting a positive or negative number to determine the solution of an inequality.

]]> 110905 Generalize and apply a rule for multiplying or dividing by a positive or negative number to determine the solution of an inequality.

]]> 110906 Solve a linear inequality algebraically and explain the strategies used.

]]> 110907 Compare and explain the process for solving a linear equation to the process for solving a linear inequality.

]]> 110908 Explain how knowing the solution to a linear equality can be used to determine the solution of a related linear inequality, and provide an example.

]]> 110909 Critique the statement: “For any linear equality, there are two related linear inequalities”.

]]> 110910 Graph the solution of a linear inequality on a number line.

]]> 110911 Explain why there is more than one solution to a linear inequality.

]]> 110912 Verify the solution of a given linear inequality using substitution for multiple elements, in the solution and outside of the solution.

]]> 110913 Solve a situational question involving a single variable linear inequality and graph the solution.

]]> 110914

modeling

generalizing strategies for addition, subtraction, multiplication, and division

analyzing

relating to context

comparing for equivalency.

]]> 110903 Model (concretely or pictorially) and describe the relationship between $x$ and $x^2$.

]]> Represent polynomials concretely or pictorially, and describe how the concrete or pictorial model reflects the symbolic form

]]> 110917 Write a polynomial for a given concrete or pictorial representation.

]]> 110918 Identify the variables, degree, number of terms, and coefficients, including the constant term, of a given simplified polynomial expression and explain the role or significance of each.

]]> 110919 Identify the type of expression that is represented by a polynomial of degree 1.

]]> 110920 Sort a set of polynomials into monomials, binomials, and trinomials.

]]> 110921 Critique the statement “A binomial can never be a degree 2 polynomial”.

]]> 110922 Write equivalent forms of a polynomial expression by interchanging terms or by decomposing terms, and justify the equivalence.

]]> 110923 Explain why terms with different variable exponents cannot be added or subtracted.

]]> 110924 Generalize, from concrete and pictorial models, and apply strategies for adding and subtracting polynomials symbolically.

]]> 110925 Verify whether or not the simplification of the addition or subtraction of two polynomials is correct and explain.

]]> 110926 Describe the relationship between multiplication of a polynomial and a monomial, and determining the area of a rectangular region.

]]> 110927 Generalize, from concrete and pictorial models, and apply strategies for multiplying a polynomial by a monomial.

]]> 110928 Generalize, from concrete and pictorial models, and apply strategies for dividing a polynomial by a monomial.

]]> 110929 Verify whether or not the simplification of the multiplication or division of a polynomial by a monomial is correct.

]]> 110930 110880

perpendicular line segments from the centre of a circle to a chord bisect the chord

inscribed angles subtended by the same arc have the same measure

the measure of a central angle is twice the measure of an inscribed angle subtending the same arc

tangents to a circle are perpendicular to the radius ending at the point of tangency.

]]> Observe and describe situations relevant to self, family, or community that involve circles, chords, central angles, inscribed angles, radii, arcs, and/or points of tangency.

]]> Construct a tangent line to a circle by applying the knowledge that a tangent line to the circle is perpendicular to a radius of the circle.

]]> 110934 Generalize, from personal explorations, the relationship between the measures of inscribed angles subtended by the same arc.

]]> 110935 Generalize, from personal explorations, the relationship between the measure of a central angle and the measure of inscribed angles subtended by the same arc.

]]> 110936 Generalize, from personal explorations, the relationship between a perpendicular line segment from the centre of a circle to a chord and the chord.

]]> 110937 Model how to find the diameter of a circle using an inscribed angle of 90° and explain why the strategy works.

]]> 110938 Describe examples of where First Nations and Métis, past and present, lifestyles and worldviews demonstrate one or more of the circle properties (e.g., tipi and medicine wheel).

]]> 110939 Solve a situational question involving the application of one or more of the circle properties.

]]> 110940 110933 Describe 3-D composite objects from the natural and constructed world, including objects relevant to First Nations and Métis people (e.g., Mesoamerican pyramids).

]]> Analyze a composite 3-D object to identify areas of overlap and explain the impact of these areas on determining the surface area of the composite 3-D object.

]]> 110943 Critique the statement “To find the surface area of a composite 3-D object, add together the surface areas of the individual 3-D objects from which the composite 3-D object is comprised”.

]]> 110944 Determine the surface area of composite 3-D objects.

]]> 110945 Solve situational questions involving the surface area of composite 3-D objects.

]]> 110946 Give dimensions for a single 3-D object that will have the same surface area as a composite 3-D object.

]]> 110947 Approximate the surface area of a 3-D object from the natural environment using composites of standard 3-D objects such as right rectangular prisms, right cylinders, and right triangular prisms.

]]> 110948 110942 Observe and describe 2-D shapes, relevant to self, family, or community, that are similar.

]]> Explain the difference between similarity and congruence of polygons.

]]> 110951 Verify whether or not two polygons are similar.

]]> 110952 Explain how ratios and proportionality are related to similarity of polygons.

]]> 110953 Draw a polygon similar to a given polygon and explain the strategies used.

]]> 110954 Solve situational questions involving the similarity of polygons.

]]> 110955 Identify and describe situations relevant to self, family, or community that involve scale diagrams and explain the meaning of the scale factor involved.

]]> 110956 Explain how scale diagrams are related to similarity, ratios, and proportionality.

]]> 110957 Draw a diagram to scale that represents an enlargement or reduction of a given 2-D shape and explain the strategies used.

]]> 110958 Explain how to determine the scale factor for a given 2-D shape and an enlargement or reduction of the shape.

]]> 110959 Verify whether or not a given diagram is a scale diagram of a 2-D shape and, if it is, identify the scale factor for the diagram.

]]> 110960 Solve situational questions involving scale diagrams and scale factors.

]]> 110961 110950 Observe and describe examples of line and rotation symmetry in situations relevant to self, family, or community.

]]> Classify different 2-D shapes or designs made of 2-D shapes, according to the number of lines of symmetry.

]]> 110964 Complete a 2-D shape or design given part of a shape or design and one or more lines of symmetry.

]]> 110965 Determine, with justification, if a given 2-D shape or design has rotation symmetry about the point at the centre of the shape or design and, if it does, state the order and angle of rotation.

]]> 110966 Identify a line of symmetry, or the order and angle of rotation symmetry, in a given tessellation.

]]> 110967 Describe examples of the use and significance of line and rotation symmetry in First Nations and Métis art.

]]> 110968 Analyze different transformations of 2-D shapes on the Cartesian plane and describe the type of symmetry, if any, that results.

]]> 110969 Determine whether or not two 2-D shapes on the Cartesian plane are related by either rotation or line symmetry and explain.

]]> 110970 Create or provide an art work (such as a painting or dance) that demonstrates line and rotation symmetry, and identify the line(s) of symmetry and the order and angle of rotation.

]]> 110971 110932

bias

use of language

ethics

cost

time and timing

privacy

cultural sensitivity and

population or sample

on data collection.]]> Analyze given case studies of data collection, including data pertaining to First Nations and Métis peoples, and identify potential problems related to bias, use of language, ethics, cost, time and timing, privacy, or cultural sensitivity.

]]> Provide examples to illustrate how bias, use of language, ethics, cost, time and timing, privacy, or cultural sensitivity may influence the data collected.

]]> 110975 Identify situations relevant to self, family, or community where a set of data was collected and classify each situation as involving a sample or the population.

]]> 110976 Provide an example of a situation in which a population may be used to answer a question, and justify the choice.

]]> 110977 Provide an example of a question where a limitation precludes the use of a population and describe the limitation (e.g., too costly, not enough time, limited resources).

]]> 110978 Identify and critique given examples in which a generalization from a sample of a population, including from First Nations and Métis data, may or may not be valid for the population.

]]> 110979 Explain different strategies for trying to minimize negative effects on data collection.

]]> 110980 Explain the importance of protocols for respectful data collection and information sharing.

]]> 110981 110974 Devise a project plan related to a situation relevant to self, family, or community, that involves:

• formulating a question for investigation
• choosing a data collection method that includes social considerations
• electing a population or a sample, and justifying the choice
• collecting the data
• displaying the collected data in an appropriate manner
• drawing conclusions to answer the question.

]]> Create and apply a rubric to assess a project that includes the assessment of all requirements for the project.

]]> 110984 Complete the project according to the plan, draw conclusions, and communicate findings to an audience.

]]> 110985 110983 Observe examples of probabilities that impact or influence aspects of one’s self, family, community, or environment and describe those impacts or influences.

]]> Analyze the meaningfulness of a probability against the limitations of assumptions associated with that probability.

]]> 110988 Provide examples of how a single probability could be used to support opposing positions.

]]> 110989 Explain, using examples, how decisions based on probability may be a combination of theoretical probability, experimental probability, and subjective judgement.

]]> 110990 110987 Gather and document information regarding the significance and use of probability and statistics for at least one First Nation or Métis peoples from a variety of sources such as Elders and traditional knowledge keepers.

]]> Compare the significance, representation, and use of probability and statistics for different First Nations and Métis peoples, and other cultures.

]]> 110993 Communicate concretely, pictorially, orally, visually, physically, and/or in writing, what has been learned about the envisioning, representing, and use of probability and statistics by First Nations and Métis peoples and how these understandings parallel, differ from, and enhance one’s own mathematical understandings about probability and statistics.

]]> 110994