### AR: Arithmetic

#### AR.1: Understanding real numbers

AR.1.2: Fractions

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

AR.1.2.c: Verifies whether two fractions are equivalent

AR.1.2.d: Compares a fraction to 0, ½ or 1

AR.1.2.e: Orders fractions with the same denominator or where one denominator is a multiple of the other or with the same numerator

AR.1.3: Decimals up to thousandths

AR.1.3.a: Represents decimals in a variety of ways (using objects or drawings) and identifies equivalent representations

AR.1.3.b: Reads and writes numbers written in decimal notation

AR.1.3.d: Composes and decomposes a number written in decimal notation and recognizes equivalent expressions

AR.1.3.e: Compares numbers written in decimal notation or arranges them in increasing or decreasing order

AR.1.4: Integers

AR.1.4.a: Represents integers in a variety of ways (using objects or drawings)

AR.1.4.c: Compares integers or arranges integers in increasing or decreasing order

AR.1.5: Expresses numbers in a variety of ways (fractional, decimal percentage notation)

AR.1.6: Represents, reads and writes numbers written in fractional or decimal notation

AR.1.7: Approximates, in various contexts, the numbers under study (e.g. estimates, rounds off, truncates)

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

AR.1.11: Represents and writes

AR.1.11.b: squares and square roots

AR.1.15: Compares and arranges in order

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

#### AR.2: Understanding operations involving real numbers

AR.2.5: Looks for equivalent expressions: decomposing (additive, multiplicative, etc.), equivalent fractions, simplifying and reducing, factoring, etc.

AR.2.6: Translates (mathematizes) a situation using a sequence of operations (no more than two levels of parentheses)

AR.2.7: Anticipates the results of operations

AR.2.8: Interprets the results of operations in light of the context

#### AR.3: Operations involving real numbers

AR.3.5: Approximates the result of an operation or sequence of operations

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

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

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

AR.3.9: Computes, using a calculator, operations and sequences of operations in accordance with the order of operations

AR.3.11: Switches, as needed, from one way of writing numbers to another

AR.3.13: Decomposes a natural number into prime factors

#### AR.4: Understanding and analyzing proportional situations

AR.4.1: Calculates

AR.4.1.a: a certain percentage of a number

AR.4.1.b: the value corresponding to 100 per cent

AR.4.2: Recognizes ratios and rates

AR.4.3: Interprets ratios and rates

AR.4.4: Describes the effect of changing a term in a ratio or rate

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

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

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])

### AL: Algebra

#### AL.1: Understanding and manipulating algebraic expressions

AL.1.A: Algebraic expressions

AL.1.A.1: Describes, using his/her own words and mathematical language, numerical patterns

AL.1.A.2: Describes, using his/her own words and mathematical language, series of numbers and family of operations

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

AL.1.A.4.a: unknown

AL.1.A.4.b: variable, constant

AL.1.A.4.c: parameter

AL.1.A.4.d: coefficient, degree, term, constant term, like terms

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

AL.1.A.6: Interprets an algebraic expression in light of the context

AL.1.A.7: Recognizes or constructs equivalent algebraic expressions

AL.1.A.8: Recognizes or constructs

AL.1.A.8.a: equalities and equations

AL.1.B: Manipulating algebraic expressions

AL.1.B.1: Calculates the numeric value of an algebraic expression

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

AL.1.C: Analyzing situations using equations or inequalities

AL.1.C.1: Recognizes whether a situation can be translated by

AL.1.C.1.a: an equation

AL.1.C.2: Recognizes or constructs

AL.1.C.2.a: relations or formulas

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

AL.1.C.4: Represents a situation using

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

AL.1.C.6: Determines the missing term in an equation (relations between operations): a + b = □, a + □ = c, □ + b = c, a – b = □, a – □ = c, □ – b = c, a × b = □, a × □ = c, □ × b = c, a ÷ b = □, a ÷ □ = c, □ ÷ b = c

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

#### AL.2: Understanding dependency relationships

AL.2.A: Relations, functions and inverses

AL.2.A.1: Identifies patterns in various situations and in various forms

AL.2.A.2: Analyzes situations using different registers (types) of representation

AL.2.A.3: Represents a situation generally using a graph

### P: Probability

#### P.1: Understanding data from random experiments

P.1.A: Processing data from random experiments

P.1.A.1: Simulates random experiments with or without the use of technological tools

P.1.A.2: Experiments with activities involving chance, using various objects (e.g. spinners, rectangular prisms, glasses, marbles, thumb tacks, 6-, 8- or 12-sided dice)

P.1.A.3: In activities involving chance

P.1.A.3.a: recognizes variability in possible outcomes (uncertainty)

P.1.A.3.b: recognizes equiprobability (e.g. quantity of objects, symmetry of an object such as a cube)

P.1.A.3.c: becomes aware of the independence of events (e.g. rolling dice, tossing a coin, drawing lots)

P.1.A.4: Uses tables or diagrams to collect and display the outcomes of an experiment

P.1.A.5: Compares the outcomes of a random experiment with known theoretical probabilities

P.1.A.6: Distinguishes between prediction and outcome

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

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

P.1.A.9.a: tables, tree diagram

P.1.A.10: Defines the sample space of a random experiment

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

P.1.A.13: Uses fractions, decimals or percentages to quantify a probability

P.1.A.14: Recognizes that a probability is always between 0 and 1

P.1.A.15: Predicts qualitatively an outcome or several events using a probability line, among other things

P.1.A.15.a: certain, possible or impossible outcome

P.1.A.15.b: more likely, just as likely, less likely event

P.1.B: Analyzing probability situations

P.1.B.1: Represents an event using different registers (types of representation)

P.1.B.2: Compares qualitatively the theoretical or experimental probability of an event occurring

P.1.B.3: Distinguishes between theoretical and experimental probability

P.1.B.4: Calculates the probability of an event

P.1.B.9: Interprets probabilities and makes appropriate decisions

### S: Statistics

#### S.1: Analyzing and making decisions about one- or two-variable distributions, using statistical tools

S.1.A: One-variable distributions

S.1.A.1: Conducts a survey or a census

S.1.A.1.a: Formulates questions for a survey

S.1.A.1.b: Chooses a sampling method:

S.1.A.1.b.i: simple random, systematic

S.1.A.1.c: Chooses a representative sample

S.1.A.1.d: Collects, describes and organizes data (classifies or categorizes) using tables

S.1.A.2: Recognizes possible sources of bias

S.1.A.3: Interprets data presented in a table or a bar graph, a pictograph, a broken-line graph or a circle graph

S.1.A.5: Chooses appropriate register(s) (types) of representation to organize, interpret and present data

S.1.A.6: Organizes and presents data using

S.1.A.6.a: a table, a bar graph, a pictograph and a broken-line graph

S.1.A.6.b: a table presenting variables or frequencies, or using a circular graph

S.1.A.7: Compares one-variable distributions

S.1.A.8: Understands and calculates the arithmetic mean

S.1.A.9: Describes the concept of arithmetic mean (leveling or balance point)

S.1.A.10: Calculates and interprets an arithmetic mean

S.1.A.11: Determines and interprets

S.1.A.11.b: measures of dispersion:

S.1.A.11.b.i: range

S.1.A.11.c: measures of position:

S.1.A.11.c.i: minimum, maximum

S.1.A.12: Chooses the appropriate statistical measures for a given situation

### G: Geometry

#### G.1: Spatial sense and analyzing situations involving geometric figures

G.1.A: Plane figures

G.1.A.3: Describes and classifies triangles

G.1.A.4: Describes circles: radius, diameter, circumference, central angle

G.1.A.6: Decomposes plane figures into circles (sectors), triangles or quadrilaterals

G.1.A.8: Recognizes and draws main segments and lines

G.1.A.8.a: diagonal, altitude, median, perpendicular bisector, bisector, apothem, radius, diameter, chord

G.1.A.9: Identifies the properties of plane figures using geometric transformations and constructions

G.1.A.10: Justifies statements using definitions or properties of plane figures

G.1.B: Solids

G.1.B.2: Determines the possible nets of a solid

G.1.B.3: Names the solid corresponding to a net

G.1.B.4: Describes solids:

G.1.B.4.b: altitude, apothem, lateral face

G.1.B.6: Recognizes solids that can be split into

G.1.B.6.a: right prisms, right cylinders, right pyramids

G.1.C: Geometric constructions and transformations in the Euclidian plane

G.1.C.2: Identifies properties and invariants resulting from geometric constructions and transformations

G.1.C.3: Identifies congruence (translation, rotation and reflection) between two figures

G.1.C.4: Constructs the image of a figure under a translation, rotation and reflection

G.1.C.5: Recognizes dilatation with a positive scale factor

G.1.D: Congruent, similar or equivalent figures

G.1.D.3: Recognizes the geometric transformation(s) linking a figure and its image

G.1.D.4: Determines the properties and invariants of congruent or similar figures

G.1.D.8: Justifies statements using definitions or properties of congruent, similar or equivalent figures, depending on the cycle and year

#### G.2: Analyzing situations involving measurements

G.2.C: Angles

G.2.C.3: Describes the characteristics of different types of angles: complementary, supplementary, adjacent, vertically opposite, alternate interior, alternate exterior and corresponding

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

G.2.C.5: Finds unknown measurements using the properties of figures and relations

G.2.C.5.a: measures of angles in a triangle

G.2.C.5.b: degree measures of central angles and arcs

G.2.C.8: Justifies statements using definitions or properties associated with angles and their measures

G.2.D: Length

G.2.D.4: Constructs relations that can be used to calculate the perimeter or circumference of figures

G.2.D.5: Finds the following unknown measurements, using properties of figures and relations

G.2.D.5.a: perimeter of plane figures

G.2.E: Area

G.2.E.1: Chooses the appropriate unit of area for the context

G.2.E.4: Constructs relations that can be used to calculate the area of plane figures: quadrilateral, triangle, circle (sectors)

G.2.E.6: Finds unknown measurements, using properties of figures and relations

G.2.E.6.b: area of figures that can be split into circles (sectors), triangles or quadrilaterals

G.2.E.6.c: lateral or total area of right prisms, right cylinders and right pyramids

G.2.E.6.d: lateral or total area of solids that can be split into right prisms, right cylinders or right pyramids

G.2.E.6.f: area of figures resulting from a similarity transformation

G.2.E.7: Justifies statements concerning measures of area

### AG: Analytic Geometry

#### AG.1: Analyzing situations using analytic geometry

AG.1.A: Locating

AG.1.A.1: Locates objects/numbers on an axis, based on the types of numbers studied

AG.1.A.2: Locates points in a Cartesian plane, based on the types of numbers studied (x and y-coordinates of a point)

Correlation last revised: 9/16/2020

This correlation lists the recommended Gizmos for this province's curriculum standards. Click any Gizmo title below for more information.