Math Games

Describes convex and nonconvex polygons

Justifies statements using definitions or properties of plane figures

Describes and classifies quadrilaterals

Describes and classifies triangles

Describes circles: radius, diameter, circumference, central angle

Recognizes and names regular convex polygons

Decomposes plane figures into circles (sectors), triangles or quadrilaterals

Describes circles and sectors

Recognizes and draws main segments and lines that are diagonal, altitude, median, perpendicular bisector, bisector, apothem, radius, diameter, chord

Recognizes and draws main segments and lines that are leg, hypotenuse

Identifies the properties of plane figures using geometric transformations and constructions

Matches the net of a convex polyhedron to the corresponding convex polyhedron

Determines the possible nets of a solid

Names the solid corresponding to a net

Describes solids: vertex, edge, base, face

Describes solids:altitude, apothem, lateral face

Tests Euler's relation on convex polyhedrons

Recognizes solids that can be split into right prisms, right cylinders, right pyramids

Identifies properties and invariants resulting from geometric constructions and transformations

Identifies congruence (translation, rotation and reflection) between two figures

Constructs the image of a figure under a translation, rotation and reflection

Recognizes dilatation with a positive scale factor

Constructs the image of a figure under a dilatation with a positive scale factor

Identifies congruent figures in frieze patterns and tessellations

Recognizes congruent or similar figures

Recognizes the geometric transformation(s) linking a figure and its image

Determines the properties and invariants of congruent or similar figures

Justifies statements using definitions or properties of congruent, similar or equivalent figures, depending on the cycle and year

Represents a situation generally using a graph

Identifies patterns in various situations and in various forms

Analyzes situations using different registers (types) of representation

Locates objects/numbers on an axis, based on the types of numbers studied

Locates points in a Cartesian plane, based on the types of numbers studied (x and y-coordinates of a point)

Chooses the appropriate unit of mass for the context

Estimates and measures mass using unconventional units: grams, kilograms

Establishes relationships between units of mass

Chooses the appropriate unit of time for the context

Estimates and measures time using conventional units

Establishes relationships between units of time: second, minute, hour, day, daily cycle, weekly cycle, yearly cycle

Distinguishes between duration and position in time

Compares angles: acute angle, right angle, obtuse angle

Estimates and determines the degree measure of angles

Describes the characteristics of different types of angles: complementary, supplementary, adjacent, vertically opposite, alternate interior, alternate exterior and corresponding

Determines measures of angles using the properties of the following angles: complementary, supplementary, vertically opposite, alternate interior, alternate exterior and corresponding

Finds unknown measurements using the properties of figures and relations, measures of angles in a triangle

Finds unknown measurements using the properties of figures and relations, degree measures of central angles and arcs

Justifies statements using definitions or properties associated with angles and their measures

Chooses the appropriate unit of length for the context

Estimates and measures the dimensions of an object using conventional units: millimetre, centimetre, decimetre, metre and kilometre

Establishes relationships between units of length: millimetre, centimetre, decimetre, metre and kilometre

Establishes relationships between measures of length of the international system (SI)

Constructs relations that can be used to calculate the perimeter or circumference of figures

Finds the following unknown measurements, using properties of figures and relations: perimeter of plane figures

Finds the following unknown measurements, using properties of figures and relations: a segment in a plane figure, circumference, radius, diameter, length of an arc, a segment resulting from an isometry or a similarity transformation

Justifies statements concerning measures of length

Chooses the appropriate unit of area for the context

Estimates and measures surface areas using conventional units: square centimetre, square decimetre, square metre

Establishes relationships between SI units of area

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

Finds unknown measurements, using properties of figures and relations: area of circles and sectors

Finds unknown measurements, using properties of figures and relations: area of figures that can be split into circles (sectors), triangles or quadrilaterals

Finds unknown measurements, using properties of figures and relations: lateral or total area of right prisms, right cylinders and right pyramids

Finds unknown measurements, using properties of figures and relations: lateral or total area of solids that can be split into right prisms, right cylinders or right pyramids

Finds unknown measurements, using properties of figures and relations: area of figures resulting from an isometry

Justifies statements concerning measures of area

Chooses the appropriate unit of volume for the context

Estimates and measures volume or capacity using conventional units: cubic centimetre, cubic decimetre, cubic metre, millilitre, litre

Establishes relationships between capacity units: millilitre, litre

Determines, through exploration or deduction, different metric relations associated with plane figures

Simulates random experiments with or without the use of technological tools

Recognizes certain, probable, impossible, simple, complementary, compatible, incompatible, dependent, independents events

Uses fractions, decimals or percentages to quantify a probability

Recognizes that a probability is always between 0 and 1

Predicts qualitatively an outcome or several events using a probability line, among other things as certain, possible or impossible outcome

Predicts qualitatively an outcome or several events using a probability line, among other things as more likely, just as likely, less likely event

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

In activities involving chance, recognizes variability in possible outcomes (uncertainty)

In activities involving chance, recognizes equiprobability (e.g. quantity of objects, symmetry of an object such as a cube)

In activities involving chance, becomes aware of the independence of events (e.g. rolling dice, tossing a coin, drawing lots)

Uses tables or diagrams to collect and display the outcomes of an experiment

Compares the outcomes of a random experiment with known theoretical probabilities

Distinguishes between prediction and outcome

Conducts or simulates random experiments involving one or more steps (with or without replacement, with or without order)

Enumerates the possible outcomes of a random experiment using tables, tree diagram

Enumerates the possible outcomes of a random experiment using networks, tables, diagrams, Venn diagrams

Defines the sample space of a random experiment

Represents an event using different registers (types of representation)

Compares qualitatively the theoretical or experimental probability of an event occurring

Distinguishes between theoretical and experimental probability

Calculates the probability of an event

Interprets probabilities and makes appropriate decisions

Describes, using his/her own words and mathematical language, numerical patterns

Describes, using his/her own words and mathematical language, series of numbers and family of operations

Adds new terms to a series when the first three terms or more are given

Describes the role of components of algebraic expressions: unknown

Describes the role of components of algebraic expressions: variable, constant

Describes the role of components of algebraic expressions: parameter

Describes the role of components of algebraic expressions: coefficient, degree, term, constant term, like terms

Constructs an algebraic expression using a register (type) of representation

Interprets an algebraic expression in light of the context

Recognizes or constructs equivalent algebraic expressions

Recognizes or constructs equalities and equations

Calculates the numeric value of an algebraic expression

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

Factors out the common factor in numerical expressions (distributive property of multiplication over addition or subtraction)

Recognizes whether a situation can be translated by an equation

Validates a solution, with or without technological tools, by substitution

Interprets solutions or makes decisions, if necessary, depending on the context

Recognizes or constructs relations or formulas

Manipulates relations or formulas (e.g. isolates an element)

Represents a situation using a first-degree equation with one unknown

Represents an equation using another register (type) of representation, if necessary

Determines the missing term in an equation (relations between operations): a + b = __, a + __ = c, __ + b = c, a - b = __, a - __ = c, __ - b = c

Transforms arithmetic equalities and equations to maintain equivalence (properties and rules for transforming equalities) and justifies the steps followed, if necessary

Transforms inequalities to maintain equivalence (properties and rules for transforming inequalities) and justifies the steps followed, if necessary

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)

Estimates the order of magnitude of a real number in different contexts

Compares and arranges in order numbers written in fractional or decimal notation

Compares and arranges in order numbers expressed in different ways (fractional, decimal, exponential [integral exponent], percentage, square root, scientific notation)

Reads and writes any natural number less than 1 000 000

Represents natural numbers less than 1 000 000 in different ways

Composes and decomposes a natural numbers less than 1 000 000 in a variety of ways and identifies equivalent expressions

Approximates a natural number less than 1 000 000

Compares natural numbers less than 1 000 000 or arranges natural numbers less than 1 000 000 in increasing or decreasing order

Classifies natural numbers less than 1 000 000 in various ways, based on their properties (e.g. even numbers, composite numbers)

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

Represents and writes squares and square roots

Represents and writes numbers in exponential notation (integral exponent)

Represents a fraction in a variety of ways (using objects or drawings)

Identifies the different meanings of fractions: part of a whole, division, ratio, operator, measurement

Verifies whether two fractions are equivalent

Compares a fraction to 0, ½ or 1

Orders fractions with the same denominator or where one denominator is a multiple of the other or with the same numerator

Represents decimals up to thousandths in a variety of ways (using objects or drawings) and identifies equivalent representations

Reads and writes numbers written in decimal notation up to thousandths

Composes and decomposes a number written in decimal notation up to thousandths and recognizes equivalent expressions

Compares numbers written in decimal notation up to thousandths or arranges them in increasing or decreasing order

Represents integers in a variety of ways (using objects or drawings)

Reads and writes integers

Compares integers or arranges integers in increasing or decreasing order

Expresses numbers in a variety of ways (fractional, decimal percentage notation)

Represents, reads and writes numbers written in fractional or decimal notation

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

Calculates and interprets an arithmetic mean

Determines and interprets measures of dispersion: range

Conducts a survey or a census: Formulates questions for a survey

Conducts a survey or a census: Chooses a sampling method: simple random, systematic

Conducts a survey or a census: Chooses a representative sample

Conducts a survey or a census: Collects, describes and organizes data (classifies or categorizes) using tables

Recognizes possible sources of bias

Interprets data presented in a table or a bar graph, a pictograph, a broken-line graph or a circle graph

Distinguishes different types of statistical variables: qualitative, discrete or continuous quantitative

Chooses appropriate register(s) (types) of representation to organize, interpret and present data

Organizes and presents data using a table, a bar graph, a pictograph and a broken-line graph

Organizes and presents data using a table presenting variables or frequencies, or using a circular graph

Compares one-variable distributions

Understands and calculates the arithmetic mean

Describes the concept of arithmetic mean (leveling or balance point)

measures of position: minimum, maximum

Chooses the appropriate statistical measures for a given situation

Determines the operation(s) to perform in a given situation using natural numbers up to 1000000

Uses objects, diagrams or equations to represent a situation and, conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of the four operations) for natural numbers under 1000000

Establishes equality relations between numerical expressions for natural numbers under 1000000 (e.g. 3 + 2 = 6 - 1)

Determines numerical equivalencies using relationships between operations, the commutative and associative properties of addition and multiplication, the distributive property of multiplication over addition or subtraction for natural numbers under 1000000

Translates a situation using a sequence of operations in accordance with the order of operations for natural numbers under 1000000

Uses objects, diagrams or an operation to represent fractions and, conversely, describes fractions represented by objects, diagrams or an operation (use of different meanings of addition, subtraction and multiplication by a natural number)

Uses an operation and fractions to represent a situation (use of different meanings of operations)

Uses objects, diagrams or equations to represent a situation involving decimals, conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of the four operations)

Determines numerical equivalencies of decimals using relationships between operations (inverse operations), the commutative and associative properties of addition and multiplication, the distributive property of multiplication over addition or subtraction

Translates a situation using a sequence of operations in accordance with the order of operations for decimals

Chooses an appropriate way of writing numbers for a given context

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

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

Anticipates the results of operations

Interprets the results of operations in light of the context

Calculates a certain percentage of a number

Calculates the value corresponding to 100 per cent

Recognizes ratios and rates

Interprets ratios and rates

Describes the effect of changing a term in a ratio or rate

Compares ratios and rates qualitatively (equivalent rates and ratios, unit rate)

Compares ratios and rates quantitatively (equivalent rates and ratios, unit rate)

Translates a situation using a ratio or rate

Recognizes a proportional situation using the context, a table of values or a graph

Represents or interprets a proportional situation using a graph, a table of values or a proportion

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])

Approximates the result of an operation for natural numbers less than 1 000 000

Using personal processes, mentally computes operations for natural numbers less than 1 000 000

Determines in writing
-the sum of two natural numbers of up to 4 digits
- the difference between two natural numbers of up to 4 digits whose result is greater than 0
- the product of a three-digit number by a two-digit number
- the quotient of a four-digit number and a two-digit number and expresses the remainder of a division as a decimal that does not go beyond the second decimal place
-the result of a sequence of operations in accordance with the order of operations

Switches, as needed, from one way of writing numbers to another: from fractional to percentage notation, from decimal to fractional notation, from decimal to percentage notation, and vice versa

Switches, as needed, from one way of writing numbers to another

Calculates the power of a natural number

Decomposes a natural number into prime factors

Generates a set of equivalent fractions

Reduces a fraction to its simplest form

Adds and subtracts fractions when the denominator of one fraction is a multiple of the other fraction

Multiplies a natural number by a fraction and a fraction by a natural number

Approximates the result of an operation with decimal numbers up to thousandths

Mentally computes the four operations
-(addition, subtraction, multiplication, division by a natural number)
-multiplications by 10, 100, 1000

Computes in writing
-additions and subtractions of numbers whose result does not go beyond the second decimal place
-multiplications of numbers whose product does not go beyond the second decimal place
-divisions of a decimal by a natural number less than 11

Determines the divisibility of a number by 2, 3, 4, 5, 6, 8, 9 and 10

Uses, in different contexts, the properties of divisibility: 2, 3, 4, 5 and 10

Approximates the result of an operation or sequence of operations

Mentally computes the four operations, especially with numbers written in decimal notation, using equivalent ways of writing numbers and the properties of operations

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, with numbers written in decimal notation, using rules of signs

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 with positive numbers written in fractional notation, with or without the use of objects or diagrams

Computes, in writing, sequences of operations (numbers written in decimal notation) in accordance with the order of operations, using equivalent ways of writing numbers and the properties of operations (with no more than two levels of parentheses)

Computes, using a calculator, operations and sequences of operations in accordance with the order of operations