Formulates questions for a survey (based on age-appropriate topics, students' language level, etc.)
Collects, describes and organizes data (classifies or categorizes) using tables
Interprets data using a table, a bar graph, a pictograph, a broken-line graph and a circle graph
Displays data using a table, a bar graph, a pictograph and a broken-line graph
Understands and calculates the arithmetic mean
Calculate Mean
Calculate Mode
Calculate Median
Calculate Mean, Median, Mode and Range
Mean, Median, Mode, and Range: Find the Missing Number
Interpret Charts to Find Mean, Median, Mode, and Range
Interpret Charts to Find Median
Interpret Charts to Find Mean
Interpret Charts to Find Mode
When applicable, recognizes variability in possible outcomes (uncertainty)
Recognizes that a probability is always between 0 and 1
Uses fractions, decimals or percentages to quantify a probability
Compares the outcomes of a random experiment with known theoretical probabilities
Simulates random experiments with or without the use of technology
When applicable, recognizes equiprobability (e.g. quantity, symmetry of an object [cube])
When applicable, becomes aware of the independence of events in an experiment
Experiments with activities involving chance, using various objects (e.g. spinners, rectangular prisms, glasses, marbles, thumb tacks, 6-, 8- or 12-sided dice)
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
Distinguishes between prediction and outcome
Uses tables or diagrams to collect and display the outcomes of an experiment
Enumerates possible outcomes of a random experiment, using a table, a tree diagram
Compares qualitatively the theoretical or experimental probability of events
Determines the operation(s) to perform in a given situation
Subtraction with Numbers Up to 5000000
Numbers Up to 5000000
Estimate Differences
Estimate Sums
Add and Subtract Decimals
Add and Subtract Decimals Up to 10
Add and Subtract Decimal Up to 100
Mixed Equations with Whole Numbers
Multi-Step
Extra or Missing Information
Solve Using Guess-And-Check
Convert Graphs to Input/Output Tables
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 addition and subtraction)
Uses objects, diagrams or equations to represent and describe transformations with natural numbers up to 1000000: adding, taking away, uniting, comparing
Uses objects, diagrams or equations to represent and describe the composition of transformations (positive or negative) with natural numbers up to 1000000
Uses objects, diagrams, or equations to represent and describe the composition of mixed transformations with natural numbers up too 1000000.
Uses objects, diagrams or equations to represent and describe rectangular arrays, repeated addition, Cartesian product, area, volume, repeated subtraction, sharing, number of times x goes into y, and comparisons (using objects, diagrams or equations) with natural numbers up to 1000000
Multiplication
Multiplication with Operands Up to 100 III
Multiplication Up to 1000
Multiply Three or More Numbers Up to 1000
Division with Divisors Up to 100
Division with Dividends Up to 60
Division with Dividend Up to 1000
Divide Numbers Ending in Zeroes
Multiply Money Amounts
Use Venn Diagrams to Solve Problems
Area of Squares and Rectangles
Establishes equality relations between numerical expressions (e.g. 3 + 2 = 6 - 1)
Determines numerical equivalencies using relationships between: operations (the four operations), the commutative property of addition and multiplication, the associative property and the distributive property of multiplication over addition or subtraction
Translates a situation using a series of operations in accordance with the order of operations
Uses objects, diagrams or equations to represent and describe transformations with decimals to the thousandth place value: composition of mixed transformations
Uses objects, diagrams or equations to represent and describe transformations with decimals to the thousandth place value: adding, taking away, uniting, comparing
Uses objects, diagrams or equations to represent and describe transformations with decimals to the thousandth place value: composition of transformations: positive, negative
Uses objects, diagrams or equations to represent and describe transformations with decimals to the thousandth place value: composition of mixed transformations
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 multiplication and division: rectangular arrays, Cartesian product, area, volume, sharing, number of times x goes into y, and comparisons)
Determines numerical equivalencies using relationships between operations (the four operations), the commutative property of addition and multiplication, the associative property and the distributive property of multiplication over addition or subtraction with decimals up to the thousandth place value
Translates a situation into a series of operations in accordance with the order of operations with decimals up to the thousandth place value
Uses objects, diagrams or equations to represent a situation using fractions (use of different meanings of addition, subtraction and multiplication by a natural number)
Locates objects on an axis (based on the types of numbers studied)
Locates points in a Cartesian plane in all four quadrants
Compares objects or parts of objects in the environment with solids (e.g. spheres, cones, cubes, cylinders, prisms, pyramids)
Identifies the main solids (e.g. spheres, cones, cubes, cylinders, prisms, pyramids)
Identifies and represents the different faces of a prism or pyramid
Describes prisms and pyramids in terms of faces, vertices and edges
Classifies prisms and pyramids
Constructs a net of a prism or pyramid
Matches the net of a convex polyhedron to the corresponding convex polyhedron
Tests Euler's theorem on convex polyhedrons
Identifies plane figures (square, rectangle, triangle, rhombus and circle)
Describes plane figures (square, rectangle, triangle and rhombus)
Describes convex and nonconvex polygons
Identifies and constructs parallel lines and perpendicular lines
Describes quadrilaterals (e.g. parallel segments, perpendicular segments, right angles, acute angles, obtuse angles)
Classifies quadrilaterals
Describes triangles: scalene triangles, right triangles, isosceles triangles, equilateral triangles
Classifies triangles
Describes circles
Identifies congruent figures
Observes and produces frieze patterns and tessellations using reflections
Observes and produces frieze patterns and tessellations using translations
Estimates and measures the dimensions of an object using conventional units of metre, decimetre, centimetre, millimetre and kilometre
Establishes relationships between units of measure for length using metre, decimetre, centimetre, millimetre and kilometre
Calculates the perimeter of plane figures
Estimates and measures surface area using conventional units
Estimates and measures volume using conventional units
Compares angles
Estimates and determines the degree measurement of angles
Estimates and measures capacity using unconventional units
Estimates and measures capacity using conventional units
Establishes relationships between units of measure (e.g. : 1 L = 1000 mL, 1/2 L = 500 mL)
Estimates and measures mass using unconventional units
Estimates and measures mass using conventional units
Establishes relationships between units of measure (e.g. : 1 kg = 1000 g, 1/2 kg = 500 g)
Estimates and measures time using conventional units
Establishes relationships between units of measure
Estimates and measures temperature using conventional units
skip counts (e.g. by twos) up to 1000000
Locates natural numbers up to 1000000 using different visual aids (e.g. hundreds chart, number strip, number line)
Identifies properties of natural numbers up to 1000000 as odd or even numbers
Identifies properties of natural numbers up to 1000000 as square, prime or composite numbers
Classifies natural numbers in various ways, based on their properties (e.g. even numbers, composite numbers)
Approximates a collection, using objects or drawings (e.g. estimate, round up/down to a given value)
Represents the power of a natural number
Counts or recites counting rhymes involving natural numbers up to 1000000
counts forward or backward up to 1000000
Counts collections (using objects or drawings)
counts a collection by grouping or regrouping
counts a pre-grouped collection
Reads and writes any natural number up to 1000000
Represents natural numbers up to 1000000 in different ways or associates a number with a set of objects or drawings with emphasis on place value in non-apparent, non-accessible groupings, using materials for which groupings are symbolic (e.g. abacus, money)
Composes and decomposes a natural number up to 1000000 in a variety of ways (e.g. 123 = 100 + 23, 123 = 100 + 20 + 3, 123 = 50 + 50 + 20 + 3)
Identifies equivalent expressions (e.g. 52 = 40 + 12, 25 + 27 = 40 + 12, 52 = 104 ÷ 2)
Arranges natural numbers up to 1000000 in increasing or decreasing order
Describes number patterns, using his/her own words and appropriate mathematical vocabulary (e.g. even numbers, odd numbers, square numbers, triangular numbers, prime numbers, composite numbers)
Represents a fraction in a variety of ways, based on a whole or a collection of objects
Orders fractions where one denominator is a multiple of the other(s)
Orders fractions with the same numerator
Locates fractions on a number line
Matches a fraction to part of a whole (congruent or equivalent parts) or part of a group of objects, and vice versa
Identifies the different meanings of fractions (sharing, division, ratio)
Distinguishes a numerator from a denominator
Reads and writes a fraction
Compares a fraction to 0, 1/2 or 1
Verifies whether two fractions are equivalent
Matches a decimal or percentage to a fraction
Represents decimals up to thousandths in a variety of ways (using objects or drawings)
Matches a fraction to its decimal
Matches a fraction or percentage to its decimal
Identifies equivalent representations (using objects or drawings)
Reads and writes numbers written in decimal notation up to the thousandths place
Composes and decomposes a decimal written in decimal notation up to the thousandths place
Recognizes equivalent expressions (e.g. 12 tenths is equivalent to 1 unit and 2 tenths; 0.5 is equivalent to 0.50)
Locates decimals on a number line up to the thousandths place between two consecutive natural numbers
Locates decimals on a number line up to the thousandths place between two decimals
Compares two decimals
Approximates decimals (e.g. estimates, rounds to a given value, truncates decimal places)
Arranges decimals in increasing or decreasing order
Represents integers in a variety of ways (using objects or drawings) (e.g. tokens in two different colours, number line, thermometer, football field, elevator, hot air balloon)
Reads and writes integers
Locates integers on a number line or Cartesian plane
Arranges integers in increasing or decreasing order
Calculates the power of a number
Determines the divisibility of a number by 2, 3, 4, 5, 6, 8, 9, 10
Performs a series of operations in accordance with the order of operations
Using his/her own words and mathematical language that is at an appropriate level for the cycle, describes non-numerical patterns (e.g. series of colours, shapes, sounds, gestures)
Using his/her own words and mathematical language that is at an appropriate level for the cycle, describes numerical patterns (e.g. number rhymes, tables and charts)
Using his/her own words and mathematical language that is at an appropriate level for the cycle, describes series of numbers and family of operations
Adds new terms to a series when the first three terms or more are given
Uses a calculator and becomes familiar with its basic functions (+, -, =, 0 to 9 number keys, all clear, clear)
Uses a calculator and becomes familiar with its × and ÷ functions
Uses a calculator and becomes familiar with memory keys and change of sign keys (+/-)
Approximates the result of an addition or subtraction involving natural numbers
Approximates the result of any of the four operations involving natural numbers
Builds a repertoire of memorized addition and subtraction facts
Develops various strategies that promote mastery of number facts and relates them to the properties of addition up to 1000000
Masters all addition facts (0 + 0 to 10 + 10) and the corresponding subtraction facts up to 1000000
Develops processes for mental computation and uses their own processes to determine the sum or difference of two natural numbers up to 1000000
Develops processes for mental computation and uses their own processes to determine the product or quotient of two natural numbers up to 1000000
Develops processes for written computation (addition and subtraction) and uses conventional processes to determine the sum of two natural numbers of up to four digits
Develops processes for written computation (addition and subtraction) and uses conventional processes to determine the difference between two natural numbers of up to four digits whose result is greater than 0
Determines the missing term in an equation (relationships between operations): a + b =__, a + __ = c, __ + b = c, a - b = __, a - __= c, __ - b = c
Builds a repertoire of memorized multiplication and division facts and develops various strategies that promote mastery of number facts and relate them to the properties of multiplication
Builds a repertoire of memorized multiplication and division facts and masters all multiplication facts (0 × 0 to 10 × 10) and the corresponding division facts
Develops processes for written computation (multiplication and division) and uses conventional processes to determine the product of a three-digit natural number and a two-digit natural number
Develops processes for written computation (multiplication and division) and uses conventional processes to determine the quotient of a four-digit natural number and a two-digit natural number, expresses the remainder of a division as a decimal that does not go beyond the second decimal place
Determines the missing term in an equation (relationships between operations): a — b = __, a — __ = c, __ — b = c
Decomposes a number into prime factors
Generates a set of equivalent fractions
Reduces a fraction to its simplest form (lowest terms)
Adds and subtracts fractions when the denominator of one fraction is a multiple of the other fraction(s)
Approximates the result of an addition or a subtraction using decimals to the thousandth
Approximates the result of a multiplication or division using decimals to the thousandth
Develops processes for mental computation adds and subtracts decimals to the thousandth
Develops processes for mental computation performs operations involving decimals (multiplication, division by a natural number) to the thousandth
Develops processes for mental computation multiplies and divides by 10, 100, 1000
Develops processes for written computation adds and subtracts decimals whose result does not go beyond the second decimal place
Develops processes for written computation multiplies decimals whose product does not go beyond the second decimal place
Develops processes for written computation divides a decimal by a natural number less than 11
Expresses a decimal as a fraction, and vice versa
Expresses a decimal as a percentage, and vice versa
Expresses a fraction as a percentage, and vice versa
Chooses an appropriate number form for a given context