When applicable, recognizes variability in possible outcomes (uncertainty)
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: certain, possible or impossible outcomes
Predicts qualitatively an outcome or several events using a probability line, among other things: more likely, just as likely, less likely events
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
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 and a broken-line graph
Displays data using a table, a bar graph, a pictograph and a broken-line graph
Determines the operation(s) to perform in a given situation
Uses objects, diagrams or equations to represent and describe transformations of numbers up to 100000: adding, taking away, uniting, comparing
Uses objects, diagrams or equations to represent and describe transformations of numbers up to 100000: adding, taking away, uniting, comparing
Uses objects, diagrams or equations to represent and describe the composition of transformations (positive or negative) of numbers up to 100000
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.
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 and the associative property.
Uses objects, diagrams or equations to represent and describe transformations with decimals to the hundredth place value: adding, taking away, uniting, comparing
Uses objects, diagrams or equations to represent and describe the composition of transformations (positive or negative) with decimals to the hundreth place value.
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, with decimals to the hundreth place value.
Determines numerical equivalencies using the relationship between operations (the four operations), the commutative property of addition and multiplication and the associative property with decimals up to the hundreth place value.
Locates objects in a plane
Locates objects on an axis (based on the types of numbers studied)
Locates points in a Cartesian plane in the first quadrant
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 prism to the corresponding prism and vice versa
Matches the net of a pyramid to the corresponding pyramid and vice versa
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)
Identifies congruent figures
Observes and produces patterns using geometric figures
Observes and produces frieze patterns and tessellations using reflections
Estimates and measures the dimensions of an object using conventional units metre, decimetre, centimetre and millimetre
Establishes relationships between units of measure for length using metre, decimetre, centimetre and millimetre
Calculates the perimeter of plane figures
Estimates and measures surface area using unconventional units
Estimates and measures volume using unconventional units
Estimates and measures capacity using unconventional units
Estimates and measures capacity using conventional units
Estimates and measures mass using unconventional units
Estimates and measures mass using conventional units
Estimates and measures time using conventional units
Establishes relationships between units of measure
Estimates and measures temperature using conventional units
Counts or recites counting rhymes involving natural numbers up to 100000
Locates natural numbers using different visual aids (e.g. hundreds chart, number strip, number line) up to 100000
Identifies properties of odd or even natural numbers up to 100000
Identifies properties of natural numbers up to 100000 as square, prime or composite numbers
Classifies natural numbers up to 100000 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)
Skip counts (e.g. by twos) up to 100000
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 100000
Represents natural numbers in different ways or associates a number with a set of objects or drawings with emphasis on exchanging apparent, non-accessible groupings, using structured materials (e.g. base ten blocks, number tables) up to 100000
Represents natural numbers 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 100000 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 100000 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)
Addition Patterns Over Increasing Place Values
Increasing Addition Patterns
Increasing Subtraction Patterns
Multiplication Patterns Over Increasing Place Values
Increasing Multiplication Patterns with Numbers Up to 10,000
Increasing Division Patterns
Increasing Growth Patterns
Geometric Growth Patterns
Numeric Patterns
Represents a fraction in a variety of ways, based on a whole or a collection of objects
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 in a variety of ways (using objects or drawings) up to the hundredths place
Arranges decimals up to the hundredths place value in increasing or decreasing order
Matches a fraction to its decimal
Identifies equivalent representations (using objects or drawings)
Reads and writes numbers written in decimal notation up to the hundredths place
Understands the role of the decimal point up to hundredths place
Composes and decomposes a decimal written in decimal notation up to the hundredths 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 hundredths place between two consecutive natural numbers
Locates decimals on a number line between two decimals up to the hundredths place
Compares two decimals up to the hundredths place
Approximates (e.g. estimates, rounds to a given value, truncates decimal places)
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)
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
Approximates the result of an addition or subtraction involving natural numbers up to 100000
Approximates the result of any of the four operations involving natural numbers up to 100000
Develops various strategies that promote mastery of number facts and relates them to the properties of addition
Masters all addition facts (0 + 0 to 10 + 10) and the corresponding subtraction facts
Develops processes for mental computation that uses their own processes to determine the sum or difference of two natural numbers up to 100000
Develops processes for mental computation that uses their own processes to determine the product or quotient of two natural numbers up to 100000
Multiplication with a Specific Number Up to 12
Multiply Two Numbers Up to 500
Multiply Two Numbers Up to 100
Multiplication
Multiply Numbers Up to 1000 Ending in Zeros
Division with Divisors Up to 10
Division with Remainder with Numbers Up to 1000
Division Patterns with Zeroes
Divisibility Rules with Numbers Up to 10,000
Divisibility Rules with Dividend Up to 10,000,000
Divisibility Rules
Develops processes for written computation (addition and subtraction) up to 100000
Uses conventional processes to determine the sum of two natural numbers of up to four digits
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 memory of multiplication facts (0 × 0 to 10 × 10) and the corresponding division facts, using objects, drawings, charts or tables
Develops various strategies that promote mastery of number facts and relate them to the properties of multiplication
Masters all multiplication facts (0 × 0 to 10 × 10) and the corresponding division facts
Develops processes for written computation and uses their own processes as well as materials and drawings to determine the product or quotient of a three-digit natural number and a one-digit natural number, expresses the remainder of a division as a fraction, depending on the context
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
Approximates the result of an addition or a subtraction of decimals to the hundredth place
Develops processes for mental computation adds and subtracts decimals to the hundredth
Add and Subtract Decimal Numbers Up to 2 Places
Add and Subtract Decimals
Add and Subtract Decimals Up to 10
Add and Subtract Decimal Up to 100
Choose Decimals with a Particular Sum or Difference
Complete the Addition or Subtraction Sentence
Inequalities with Decimal Addition and Subtraction
Develops processes for written computation, and adds and subtracts decimals whose result does not go beyond the second decimal place