Describes convex and nonconvex polygons
Justifies statements using definitions or properties of plane figures
Describes circles: radius, diameter, circumference, central angle
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
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 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
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)
Represents a situation generally using a graph
Identifies patterns in various situations and in various forms
Analyzes situations using different registers (types) of representation
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
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
Evaluate Variable Expressions with Whole Numbers
Evaluate Multi-Variable Expressions
Solve Two-Step Linear Equations
Solve One-Step Linear Equations
Evaluate Variable Expressions with Squares and Square Roots
Evaluate Exponents
Exponents: Solve for the Variable
Solve Two-Step Linear Equations
Solve One-Step Linear Equations
Solve Multi Step Equations
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)
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
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)
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
Mean, Median, Mode, and Range: Find the Missing Number
Mode: Find the Missing Number
Median: Find the Missing Number
Mean: Find the Missing Number
Range: Find the Missing Number
Changes in Median
Changes in Mean, Median, Mode, and Range
Changes in Mode
Changes in Range
Changes in 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
Calculate Mean
Calculate Range
Calculate Mode
Calculate Median
Calculate Mean, Median, Mode and Range
Interpret Charts to Find Mean, Median, Mode, and Range
Interpret Charts to Find Median
Interpret Charts to Find Mode
Interpret Charts to Find Mean
Interpret Charts to Find Range
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)
Add, Subtract Fractions with Like Denominators
Add Fractions
Subtract Fractions
Add and Subtract Fractions with Unlike Denominators
Multiply Fractions by Whole Numbers
Multiply Fractions by Whole Numbers
Divide by Fractions with Models
Divide Fractions and Mixed Numbers Up to 1/16, 1/32
Divide Fractions and Mixed Numbers Up to 1/32
Divide Fractions and Mixed Numbers
Divide Fractions and Mixed Numbers Up to 1/16
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)
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
Interprets ratios and rates
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
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