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Skills available for Quebec grade 8 math curriculum

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8-9.AR Arithmetic

8-9.AR.1 Understanding real numbers
- 8-9.AR.1.2 Fractions
  - 8-9.AR.1.2.b Identifies the different meanings of fractions: part of a whole, division, ratio, operator, measurement
    - Understanding ratios (8-I.1)
- 8-9.AR.1.10 Defines the concept absolute value in context (e.g. difference between two numbers, distance between two points)
- 8-9.AR.1.11 Represents and writes
  - 8-9.AR.1.11.b squares and square roots
  - 8-9.AR.1.11.c numbers in exponential notation (integral exponent)
- 8-9.AR.1.13 Estimates the order of magnitude of a real number in different contexts
  - Write powers of ten with exponents (8-G.3)
- 8-9.AR.1.15 Compares and arranges in order
  - 8-9.AR.1.15.b numbers expressed in different ways (fractional, decimal, exponential [integral exponent], percentage, square root, scientific notation)
    - Compare positive rational numbers (8-E.5)
8-9.AR.3 Operations involving real numbers
- 8-9.AR.3.5 Approximates the result of an operation or sequence of operations
- 8-9.AR.3.6 Mentally computes the four operations, especially with numbers written in decimal notation, using equivalent ways of writing numbers and the properties of operations
- 8-9.AR.3.7 Computes, in writing, the four operations with numbers that are easy to work with (including large numbers), using equivalent ways of writing numbers and the properties of operations
  - 8-9.AR.3.7.b positive numbers written in fractional notation, with or without the use of objects or diagrams
- 8-9.AR.3.11 Switches, as needed, from one way of writing numbers to another
8-9.AR.4 Understanding and analyzing proportional situations
- 8-9.AR.4.1 Calculates
  - 8-9.AR.4.1.b the value corresponding to 100 per cent
    - Solve percent equations (8-K.9)
    - Sale prices: find the original price (8-L.6)
- 8-9.AR.4.2 Recognizes ratios and rates
  - Understanding ratios (8-I.1)
- 8-9.AR.4.3 Interprets ratios and rates
  - Ratios and rates: word problems (8-I.12)
- 8-9.AR.4.4 Describes the effect of changing a term in a ratio or rate
- 8-9.AR.4.5 Compares
  - 8-9.AR.4.5.a ratios and rates qualitatively (equivalent rates and ratios, unit rate)
  - 8-9.AR.4.5.b ratios and rates quantitatively (equivalent rates and ratios, unit rate)
- 8-9.AR.4.6 Translates a situation using a ratio or rate
  - Ratios and rates: word problems (8-I.12)
- 8-9.AR.4.7 Recognizes a proportional situation using the context, a table of values or a graph
- 8-9.AR.4.8 Represents or interprets a proportional situation using a graph, a table of values or a proportion
- 8-9.AR.4.9 Solves proportional situations (direct or inverse variation) by using different strategies (e.g. unit-rate method, factor of change, proportionality ratio, additive procedure, constant product [inverse variation])

8-9.AL Algebra

8-9.AL.1 Understanding and manipulating algebraic expressions
- 8-9.AL.1.A Algebraic expressions
  - 8-9.AL.1.A.4 Describes the role of components of algebraic expressions:
    - 8-9.AL.1.A.4.a unknown
    - 8-9.AL.1.A.4.b variable, constant
    - 8-9.AL.1.A.4.c parameter
    - 8-9.AL.1.A.4.d coefficient, degree, term, constant term, like terms
      - Identify terms and coefficients (8-W.10)
  - 8-9.AL.1.A.5 Constructs an algebraic expression using a register (type) of representation
    - Write variable expressions (8-W.1)
    - Write variable expressions from diagrams (8-W.2)
  - 8-9.AL.1.A.6 Interprets an algebraic expression in light of the context
    - Write variable expressions: word problems (8-W.3)
  - 8-9.AL.1.A.7 Recognizes or constructs equivalent algebraic expressions
  - 8-9.AL.1.A.8 Recognizes or constructs
    - 8-9.AL.1.A.8.a equalities and equations
      - Write an equation from words (8-X.2)
- 8-9.AL.1.B Manipulating algebraic expressions
  - 8-9.AL.1.B.1 Calculates the numeric value of an algebraic expression
  - 8-9.AL.1.B.2 Performs the following operations on algebraic expressions, with or without objects or diagrams: addition and subtraction, multiplication and division by a constant, multiplication of first-degree monomials
  - 8-9.AL.1.B.3 Factors out the common factor in numerical expressions (distributive property of multiplication over addition or subtraction)
- 8-9.AL.1.C Analyzing situations using equations or inequalities
  - 8-9.AL.1.C.1 Recognizes whether a situation can be translated by
    - 8-9.AL.1.C.1.a an equation
  - 8-9.AL.1.C.2 Recognizes or constructs
    - 8-9.AL.1.C.2.a relations or formulas
      - Write an equation from words (8-X.2)
  - 8-9.AL.1.C.3 Manipulates relations or formulas (e.g. isolates an element)
    - Rearrange multi-variable equations (8-X.13)
  - 8-9.AL.1.C.4 Represents a situation using
    - 8-9.AL.1.C.4.a a first-degree equation with one unknown
      - Write and solve equations that represent diagrams (8-X.4)
      - Solve equations: word problems (8-X.12)
  - 8-9.AL.1.C.5 Represents
    - 8-9.AL.1.C.5.a an equation using another register (type) of representation, if necessary
      - Model and solve equations using algebra tiles (8-X.3)
  - 8-9.AL.1.C.7 Transforms arithmetic equalities and equations to maintain equivalence (properties and rules for transforming equalities) and justifies the steps followed, if necessary
    - Properties of equality (8-X.5)
    - Solve equations: complete the solution (8-X.11)
  - 8-9.AL.1.C.9 Uses different methods to solve first-degree equations with one unknown of the form ax + b = cx + d: trial and error, drawings, arithmetic methods (inverse or equivalent operations), algebraic methods (balancing equations or hidden terms)
  - 8-9.AL.1.C.13 Validates a solution, with or without technological tools, by substitution
    - Which x satisfies an equation? (8-X.1)
  - 8-9.AL.1.C.15 Interprets solutions or makes decisions, if necessary, depending on the context
    - Solve equations: word problems (8-X.12)
8-9.AL.2 Understanding dependency relationships
- 8-9.AL.2.A Relations, functions and inverses
  - 8-9.AL.2.A.2 Analyzes situations using different registers (types) of representation
  - 8-9.AL.2.A.3 Represents a situation generally using a graph
    - Graph proportional relationships (8-J.8)
    - Graph a line from an equation (8-Z.7)

8-9.P Probability

8-9.P.1 Understanding data from random experiments
- 8-9.P.1.A Processing data from random experiments
  - 8-9.P.1.A.7 Conducts or simulates random experiments involving one or more steps (with or without replacement, with or without order)
  - 8-9.P.1.A.9 Enumerates the possible outcomes of a random experiment using
    - 8-9.P.1.A.9.b networks, tables, diagrams, Venn diagrams
  - 8-9.P.1.A.10 Defines the sample space of a random experiment
    - Compound events: find the number of outcomes (8-CC.5)
    - Counting principle (8-CC.6)
  - 8-9.P.1.A.11 Recognizes certain, probable, impossible, simple, complementary, compatible, incompatible, dependent, independents events
    - Identify independent and dependent events (8-CC.7)
- 8-9.P.1.B Analyzing probability situations
  - 8-9.P.1.B.3 Distinguishes between theoretical and experimental probability
    - Experimental probability (8-CC.3)
  - 8-9.P.1.B.4 Calculates the probability of an event
  - 8-9.P.1.B.9 Interprets probabilities and makes appropriate decisions
    - Make predictions (8-CC.4)

8-9.S Statistics

8-9.S.1 Analyzing and making decisions about one- or two-variable distributions, using statistical tools
- 8-9.S.1.A One-variable distributions
  - 8-9.S.1.A.1 Conducts a survey or a census
    - 8-9.S.1.A.1.b Chooses a sampling method:
    - 8-9.S.1.A.1.b.i simple random, systematic
    - 8-9.S.1.A.1.c Chooses a representative sample
      - Identify representative, random and biased samples (8-BB.10)
  - 8-9.S.1.A.2 Recognizes possible sources of bias
    - Identify representative, random and biased samples (8-BB.10)
  - 8-9.S.1.A.4 Distinguishes different types of statistical variables: qualitative, discrete or continuous quantitative
  - 8-9.S.1.A.6 Organizes and presents data using
    - 8-9.S.1.A.6.b a table presenting variables or frequencies, or using a circular graph
      - Create frequency charts (8-AA.12)
      - Interpret circle graphs (8-AA.16)
  - 8-9.S.1.A.7 Compares one-variable distributions
  - 8-9.S.1.A.9 Describes the concept of arithmetic mean (leveling or balance point)
  - 8-9.S.1.A.10 Calculates and interprets an arithmetic mean
  - 8-9.S.1.A.11 Determines and interprets
    - 8-9.S.1.A.11.b measures of dispersion:
    - 8-9.S.1.A.11.b.i range
    - 8-9.S.1.A.11.c measures of position:
    - 8-9.S.1.A.11.c.i minimum, maximum
  - 8-9.S.1.A.12 Chooses the appropriate statistical measures for a given situation

8-9.G Geometry

8-9.G.1 Spatial sense and analyzing situations involving geometric figures
- 8-9.G.1.A Plane figures
  - 8-9.G.1.A.6 Decomposes plane figures into circles (sectors), triangles or quadrilaterals
  - 8-9.G.1.A.7 Describes circles and sectors
    - Parts of a circle (8-P.18)
  - 8-9.G.1.A.8 Recognizes and draws main segments and lines
    - 8-9.G.1.A.8.a diagonal, altitude, median, perpendicular bisector, bisector, apothem, radius, diameter, chord
      - Parts of a circle (8-P.18)
  - 8-9.G.1.A.9 Identifies the properties of plane figures using geometric transformations and constructions
    - Find lengths and measures of bisected line segments and angles (8-P.17)
  - 8-9.G.1.A.10 Justifies statements using definitions or properties of plane figures
- 8-9.G.1.B Solids
  - 8-9.G.1.B.2 Determines the possible nets of a solid
    - Nets of three-dimensional figures (8-T.2)
  - 8-9.G.1.B.3 Names the solid corresponding to a net
    - Nets of three-dimensional figures (8-T.2)
  - 8-9.G.1.B.4 Describes solids:
    - 8-9.G.1.B.4.b altitude, apothem, lateral face
  - 8-9.G.1.B.6 Recognizes solids that can be split into
    - 8-9.G.1.B.6.a right prisms, right cylinders, right pyramids
- 8-9.G.1.C Geometric constructions and transformations in the Euclidian plane
  - 8-9.G.1.C.2 Identifies properties and invariants resulting from geometric constructions and transformations
  - 8-9.G.1.C.3 Identifies congruence (translation, rotation and reflection) between two figures
    - Congruence statements and corresponding parts (8-Q.12)
  - 8-9.G.1.C.4 Constructs the image of a figure under a translation, rotation and reflection
  - 8-9.G.1.C.5 Recognizes dilatation with a positive scale factor
    - Dilations: scale factor and classification (8-R.4)
  - 8-9.G.1.C.6 Constructs the image of a figure under a dilatation with a positive scale factor
- 8-9.G.1.D Congruent, similar or equivalent figures
  - 8-9.G.1.D.2 Recognizes congruent or similar figures
    - Similar and congruent figures (8-R.1)
    - Identify similar triangles (8-R.5)
  - 8-9.G.1.D.3 Recognizes the geometric transformation(s) linking a figure and its image
  - 8-9.G.1.D.4 Determines the properties and invariants of congruent or similar figures
  - 8-9.G.1.D.8 Justifies statements using definitions or properties of congruent, similar or equivalent figures, depending on the cycle and year
8-9.G.2 Analyzing situations involving measurements
- 8-9.G.2.B Time
  - 8-9.G.2.B.4 Distinguishes between duration and position in time
- 8-9.G.2.C Angles
  - 8-9.G.2.C.3 Describes the characteristics of different types of angles: complementary, supplementary, adjacent, vertically opposite, alternate interior, alternate exterior and corresponding
    - Identify complementary, supplementary, vertical, adjacent and congruent angles (8-P.13)
    - Transversals of parallel lines: name angle pairs (8-P.15)
  - 8-9.G.2.C.4 Determines measures of angles using the properties of the following angles: complementary, supplementary, vertically opposite, alternate interior, alternate exterior and corresponding
    - Find measures of complementary, supplementary, vertical and adjacent angles (8-P.14)
    - Transversals of parallel lines: find angle measures (8-P.16)
  - 8-9.G.2.C.5 Finds unknown measurements using the properties of figures and relations
    - 8-9.G.2.C.5.b degree measures of central angles and arcs
      - Central angles and arc measures (8-P.19)
  - 8-9.G.2.C.8 Justifies statements using definitions or properties associated with angles and their measures
- 8-9.G.2.D Length
  - 8-9.G.2.D.4 Constructs relations that can be used to calculate the perimeter or circumference of figures
  - 8-9.G.2.D.5 Finds the following unknown measurements, using properties of figures and relations
    - 8-9.G.2.D.5.b a segment in a plane figure, circumference, radius, diameter, length of an arc, a segment resulting from an isometry or a similarity transformation
  - 8-9.G.2.D.6 Justifies statements concerning measures of length
- 8-9.G.2.E Area
  - 8-9.G.2.E.3 Establishes relationships between SI units of area
    - Convert square units of length (8-M.3)
  - 8-9.G.2.E.4 Constructs relations that can be used to calculate the area of plane figures: quadrilateral, triangle, circle (sectors)
    - Area and perimeter: word problems (8-U.4)
    - Circles: word problems (8-U.8)
  - 8-9.G.2.E.6 Finds unknown measurements, using properties of figures and relations
    - 8-9.G.2.E.6.a area of circles and sectors
    - 8-9.G.2.E.6.b area of figures that can be split into circles (sectors), triangles or quadrilaterals
      - Area of compound figures with triangles, semicircles and quarter circles (8-U.9)
    - 8-9.G.2.E.6.c lateral or total area of right prisms, right cylinders and right pyramids
      - Surface area of prisms and cylinders (8-U.11)
      - Surface area of pyramids (8-U.12)
    - 8-9.G.2.E.6.d lateral or total area of solids that can be split into right prisms, right cylinders or right pyramids
    - 8-9.G.2.E.6.e area of figures resulting from an isometry
    - 8-9.G.2.E.6.f area of figures resulting from a similarity transformation
      - Perimeter and area: changes in scale (8-U.14)
  - 8-9.G.2.E.7 Justifies statements concerning measures of area

8-9.AG Analytic Geometry

8-9.AG.1 Analyzing situations using analytic geometry
- 8-9.AG.1.A Locating
  - 8-9.AG.1.A.1 Locates objects/numbers on an axis, based on the types of numbers studied
    - Integers on number lines (8-B.1)
    - Graph integers on horizontal and vertical number lines (8-B.2)
  - 8-9.AG.1.A.2 Locates points in a Cartesian plane, based on the types of numbers studied (x and y-coordinates of a point)

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8-9.AR Arithmetic

8-9.AR.1 Understanding real numbers

8-9.AR.1.2 Fractions

8-9.AR.1.2.b Identifies the different meanings of fractions: part of a whole, division, ratio, operator, measurement

8-9.AR.1.10 Defines the concept absolute value in context (e.g. difference between two numbers, distance between two points)

8-9.AR.1.11 Represents and writes

8-9.AR.1.11.b squares and square roots

8-9.AR.1.11.c numbers in exponential notation (integral exponent)

8-9.AR.1.13 Estimates the order of magnitude of a real number in different contexts

8-9.AR.1.15 Compares and arranges in order

8-9.AR.1.15.b numbers expressed in different ways (fractional, decimal, exponential [integral exponent], percentage, square root, scientific notation)

8-9.AR.3 Operations involving real numbers

8-9.AR.3.5 Approximates the result of an operation or sequence of operations

8-9.AR.3.6 Mentally computes the four operations, especially with numbers written in decimal notation, using equivalent ways of writing numbers and the properties of operations

8-9.AR.3.7 Computes, in writing, the four operations with numbers that are easy to work with (including large numbers), using equivalent ways of writing numbers and the properties of operations

8-9.AR.3.7.b positive numbers written in fractional notation, with or without the use of objects or diagrams

8-9.AR.3.11 Switches, as needed, from one way of writing numbers to another

8-9.AR.4 Understanding and analyzing proportional situations

8-9.AR.4.1 Calculates

8-9.AR.4.1.b the value corresponding to 100 per cent

8-9.AR.4.2 Recognizes ratios and rates

8-9.AR.4.3 Interprets ratios and rates

8-9.AR.4.4 Describes the effect of changing a term in a ratio or rate

8-9.AR.4.5 Compares

8-9.AR.4.5.a ratios and rates qualitatively (equivalent rates and ratios, unit rate)

8-9.AR.4.5.b ratios and rates quantitatively (equivalent rates and ratios, unit rate)

8-9.AR.4.6 Translates a situation using a ratio or rate

8-9.AR.4.7 Recognizes a proportional situation using the context, a table of values or a graph

8-9.AR.4.8 Represents or interprets a proportional situation using a graph, a table of values or a proportion

8-9.AR.4.9 Solves proportional situations (direct or inverse variation) by using different strategies (e.g. unit-rate method, factor of change, proportionality ratio, additive procedure, constant product [inverse variation])

8-9.AL Algebra

8-9.AL.1 Understanding and manipulating algebraic expressions

8-9.AL.1.A Algebraic expressions

8-9.AL.1.A.4 Describes the role of components of algebraic expressions:

8-9.AL.1.A.4.a unknown

8-9.AL.1.A.4.b variable, constant

8-9.AL.1.A.4.c parameter

8-9.AL.1.A.4.d coefficient, degree, term, constant term, like terms

8-9.AL.1.A.5 Constructs an algebraic expression using a register (type) of representation

8-9.AL.1.A.6 Interprets an algebraic expression in light of the context

8-9.AL.1.A.7 Recognizes or constructs equivalent algebraic expressions

8-9.AL.1.A.8 Recognizes or constructs

8-9.AL.1.A.8.a equalities and equations

8-9.AL.1.B Manipulating algebraic expressions

8-9.AL.1.B.1 Calculates the numeric value of an algebraic expression

8-9.AL.1.B.2 Performs the following operations on algebraic expressions, with or without objects or diagrams: addition and subtraction, multiplication and division by a constant, multiplication of first-degree monomials

8-9.AL.1.B.3 Factors out the common factor in numerical expressions (distributive property of multiplication over addition or subtraction)

8-9.AL.1.C Analyzing situations using equations or inequalities

8-9.AL.1.C.1 Recognizes whether a situation can be translated by

8-9.AL.1.C.1.a an equation

8-9.AL.1.C.2 Recognizes or constructs

8-9.AL.1.C.2.a relations or formulas

8-9.AL.1.C.3 Manipulates relations or formulas (e.g. isolates an element)

8-9.AL.1.C.4 Represents a situation using

8-9.AL.1.C.4.a a first-degree equation with one unknown

8-9.AL.1.C.5 Represents

8-9.AL.1.C.5.a an equation using another register (type) of representation, if necessary

8-9.AL.1.C.7 Transforms arithmetic equalities and equations to maintain equivalence (properties and rules for transforming equalities) and justifies the steps followed, if necessary

8-9.AL.1.C.9 Uses different methods to solve first-degree equations with one unknown of the form ax + b = cx + d: trial and error, drawings, arithmetic methods (inverse or equivalent operations), algebraic methods (balancing equations or hidden terms)

8-9.AL.1.C.13 Validates a solution, with or without technological tools, by substitution

8-9.AL.1.C.15 Interprets solutions or makes decisions, if necessary, depending on the context

8-9.AL.2 Understanding dependency relationships

8-9.AL.2.A Relations, functions and inverses

8-9.AL.2.A.2 Analyzes situations using different registers (types) of representation

8-9.AL.2.A.3 Represents a situation generally using a graph

8-9.P Probability

8-9.P.1 Understanding data from random experiments

8-9.P.1.A Processing data from random experiments

8-9.P.1.A.7 Conducts or simulates random experiments involving one or more steps (with or without replacement, with or without order)

8-9.P.1.A.9 Enumerates the possible outcomes of a random experiment using

8-9.P.1.A.9.b networks, tables, diagrams, Venn diagrams

8-9.P.1.A.10 Defines the sample space of a random experiment

8-9.P.1.A.11 Recognizes certain, probable, impossible, simple, complementary, compatible, incompatible, dependent, independents events

8-9.P.1.B Analyzing probability situations

8-9.P.1.B.3 Distinguishes between theoretical and experimental probability

8-9.P.1.B.4 Calculates the probability of an event

8-9.P.1.B.9 Interprets probabilities and makes appropriate decisions