Mathematics, Grade 5

Counts or recites counting rhymes involving natural numbers — counts forward or backward

I can count forward and backward.

Counts collections (using objects or drawings)

I can count collections (using objects or drawings).

Counts collections (using objects or drawings) — counts a collection by grouping or regrouping

I can count a collection by grouping or regrouping.

Reads and writes any natural number

I can read and write any natural number.

Represents natural numbers in different ways or associates a number with a set of objects or drawings

I can show natural numbers in different ways and match a number to a set of objects or drawings.

Composes and decomposes a natural number in a variety of ways

I can build and break apart a natural number in a variety of ways.

Identifies equivalent expressions

I can spot equivalent expressions.

Compares natural numbers

I can compare natural numbers.

Arranges natural numbers in increasing or decreasing order

I can put natural numbers in increasing or decreasing order.

Describes number patterns, using his/her own words and appropriate mathematical vocabulary

I can describe number patterns in my own words, using math words like square, cubed, triangular and prime.

Locates natural numbers using different visual aids

I can find natural numbers using different visual aids.

Classifies natural numbers in various ways, based on their properties

I can sort natural numbers in various ways, based on their properties.

Approximates a collection, using objects or drawings

I can estimate a collection, using objects or drawings.

Represents the power of a natural number

I can show the power of a natural number.

Represents a fraction in a variety of ways, based on a whole or a collection of objects

I can show a fraction in a variety of ways, based on a whole or a collection of objects.

Identifies the different meanings of fractions (sharing, division, ratio)

I can spot the different meanings of fractions (sharing, division, ratio).

Verifies whether two fractions are equivalent

I can verify whether two fractions are equivalent.

Matches a decimal or percentage to a fraction

I can match a decimal or percentage to a fraction.

Orders fractions with the same denominator

I can order fractions with the same denominator.

Orders fractions where one denominator is a multiple of the other(s)

I can order fractions where one denominator is a multiple of the other(s).

Orders fractions with the same numerator

I can order fractions with the same numerator.

Locates fractions on a number line

I can find fractions on a number line.

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

I can represent decimals to hundredths and thousandths in different ways, using objects or drawings.

Identifies equivalent representations (using objects or drawings)

I can spot equivalent representations (using objects or drawings).

Reads and writes numbers written in decimal notation

I can read and write numbers written in decimal notation.

Composes and decomposes a decimal written in decimal notation

I can build and break apart a decimal written in decimal notation.

Recognizes equivalent expressions

I can recognize equivalent expressions.

Locates decimals on a number line

I can find decimals on a number line.

Compares two decimals

I can compare two decimals.

Approximates a decimal (estimates, rounds or truncates)

I can approximate a decimal by estimating it, rounding it to a given value, or truncating its decimal places.

Arranges decimals in increasing or decreasing order

I can put decimals in increasing or decreasing order.

Matches a fraction or percentage to its decimal

I can match a fraction or a percentage to its decimal.

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

I can show integers in a variety of ways (using objects or drawings).

Reads and writes integers

I can read and write integers.

Locates integers on a number line or Cartesian plane

I can find integers on a number line or Cartesian plane.

Compares integers

I can compare integers.

Arranges integers in increasing or decreasing order

I can put integers in increasing or decreasing order.

Determines the operation(s) to perform in a given situation

I can work out the operation(s) to perform in a given situation.

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)

I can use objects, diagrams or equations to represent a situation, and describe a situation shown that way, using the different meanings of the operations.

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, repeated addition, Cartesian product, area, volume, repeated subtraction, sharing, number of times x goes into y, and comparisons (using objects, diagrams or equations)

I can use objects, diagrams or equations to represent multiplication and division situations (arrays, repeated addition, area, sharing and comparison), and describe them.

Establishes equality relations between numerical expressions

I can show equality relations between numerical expressions.

Determines numerical equivalencies using operations and the commutative property

I can find numerical equivalencies using the relationships between the operations and the commutative, associative and distributive properties.

Translates a situation using a series of operations in accordance with the order of operations

I can translate a situation using a series of operations in accordance with the order of operations.

Represents a situation with objects, diagrams or equations (addition and subtraction of decimals)

I can use objects, diagrams or equations to represent a situation, and describe a situation shown by objects, diagrams or equations.

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)

I can use objects, diagrams or equations to represent a situation, and describe a situation shown that way, using the different meanings of the operations.

Determines numerical equivalencies using relationships between operations

I can find numerical equivalencies with decimals using the relationships between the operations and the commutative, associative and distributive properties.

Translates a situation into a series of operations in accordance with the order of operations

I can translate a situation into a series of operations in accordance with the order of operations.

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, subtraction and multiplication by a natural number)

I can use objects, diagrams or equations to represent a situation, and describe a situation shown that way, using the different meanings of the operations.

Approximates the result of any of the four operations on natural numbers

I can estimate the result of any of the four operations on natural numbers before I compute it.

Develops processes for mental computation — uses his/her own processes to determine the product or quotient of two natural numbers

I can use my own processes to find the product or quotient of two natural numbers mentally.

Builds a repertoire of memorized multiplication and division facts — develops various strategies that promote mastery of number facts and relate them to the properties of multiplication

I can develop strategies that help me master number facts and relate them to the properties of multiplication.

Develops processes for written computation (multiplication and division) — uses conventional processes to determine the product of a three-digit natural number and a two-digit natural number

I can use conventional processes to find the product of a three-digit natural number and a two-digit natural number.

Develops processes for written computation (multiplication and division) — 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

I can divide a four-digit number by a two-digit number on paper and write the remainder as a decimal.

Determines the missing term in an equation (relationships between operations) — a × b = □, a × □ = c, □ × b = c, a ÷ b = □, a ÷ □ = c, □ ÷ b = c

I can work out the missing term in an equation (relationships between operations): a × b = □, a × □ = c, □ × b = c, a ÷ b = □, a ÷ □ = c, □ ÷ b = c.

Decomposes a number into prime factors

I can break apart a number into prime factors.

Calculates the power of a number

I can work out the power of a number.

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

I can work out 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

I can perform a series of operations in accordance with the order of operations.

Describes patterns in a series of numbers and a family of operations

I can describe, in my own words and with math language, a series of numbers and a family of operations.

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

I can add new terms to a series when the first three terms or more are given.

Uses a calculator: becomes familiar with memory keys and change-of-sign keys

I can use a calculator, including its memory keys and change-of-sign keys (+/–).

Generates a set of equivalent fractions

I can generate a set of equivalent fractions.

Reduces a fraction to its simplest form (lowest terms)

I can reduce 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)

I can add and subtract fractions when the denominator of one fraction is a multiple of the other fraction(s).

Multiplies a natural number by a fraction

I can multiply a natural number by a fraction.

Approximates the result of an operation on decimals

I can estimate the result of an addition, subtraction, multiplication or division before I compute it.

Develops processes for mental computation

I can build up processes for mental computation.

Multiplies decimals whose product stays within two decimal places

I can multiply decimals in writing when the product stays within two decimal places.

Divides a decimal by a natural number less than 11

I can divide a decimal by a natural number less than 11 using a written process.

Expresses a decimal as a fraction, and vice versa

I can express a decimal as a fraction, and vice versa.

Expresses a decimal as a percentage, and vice versa

I can express a decimal as a percentage, and vice versa.

Expresses a fraction as a percentage, and vice versa

I can express a fraction as a percentage, and vice versa.

Chooses an appropriate number form for a given context

I can choose an appropriate number form for a given context.

Locates objects on an axis (based on the types of numbers studied)

I can find objects on an axis (based on the types of numbers studied).

Locates points in a Cartesian plane — in all four quadrants

I can find points in a Cartesian plane — in all four quadrants.

Matches the net of a convex polyhedron to the corresponding solid

I can match the net of a convex polyhedron to the matching solid, and back again.

Tests Euler's theorem on convex polyhedrons (vertex, edge, net of a solid)

I can test Euler's theorem on convex polyhedrons by counting vertices, edges and faces.

Describes triangles — scalene, right, isosceles and equilateral triangles

I can describe triangles as scalene, right, isosceles or equilateral.

Classifies triangles

I can sort triangles.

Describes circles

I can describe circles.

Observes and produces frieze patterns and tessellations — using translations

I can observe and make frieze patterns and tessellations using translations.

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

I can estimate and measure the dimensions of an object in metres, decimetres, centimetres, millimetres and kilometres.

Establishes relationships between units of measure for length

I can establish relationships between the units of measure for length: metre, decimetre, centimetre, millimetre and kilometre.

Estimates and measures surface area — using conventional units

I can estimate and measure surface area in square centimetres, square decimetres and square metres.

Estimates and measures volume — using conventional units

I can estimate and measure volume in cubic centimetres, cubic decimetres and cubic metres.

Estimates and determines the degree measurement of angles (right, acute, obtuse)

I can estimate and determine the degree measurement of angles.

Estimates and measures capacity using unconventional units

I can estimate and measure capacity using unconventional units.

Estimates and measures capacity using conventional units

I can estimate and measure capacity using conventional units.

Establishes relationships between units of measure for capacity

I can establish relationships between the units of measure for capacity.

Estimates and measures mass using unconventional units

I can estimate and measure mass using unconventional units.

Estimates and measures mass using conventional units

I can estimate and measure mass using conventional units.

Establishes relationships between units of measure for mass

I can establish relationships between the units of measure for mass.

Establishes relationships between units of measure for time

I can establish relationships between the units of measure for time.

Estimates and measures temperature using conventional units

I can estimate and measure temperature using conventional units.

Formulates questions for a survey (based on age-appropriate topics, students’ language level, etc.)

I can write clear, fair survey questions on a topic the people I ask can answer.

Collects, describes and organizes data (classifies or categorizes) using tables

I can collect, describe and organize data in a table, sorting it into categories or classes.

Interprets data using a table, a bar graph, a pictograph, a broken-line graph and a circle graph

I can interpret data from a table, a bar graph, a pictograph, a broken-line graph and a circle graph.

Understands and calculates the arithmetic mean

I can understand and work out the arithmetic mean.

When applicable, recognizes variability in possible outcomes (uncertainty)

I can recognize that the outcome of a chance experiment can vary and is not certain.

When applicable, recognizes equiprobability

I can recognize when every outcome of a chance experiment is equally likely.

When applicable, becomes aware of the independence of events in an experiment

I can recognize that one result does not change what is likely to happen next.

Experiments with activities involving chance, using various objects

I can experiment with activities involving chance, using various objects.

Predicts qualitatively an outcome or several events using a probability line, among other things

I can predict how likely an outcome or several events are, using a probability line and other tools.

Distinguishes between prediction and outcome

I can tell a prediction apart from an outcome.

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

I can use tables or diagrams to collect and display the outcomes of an experiment.

Enumerates the possible outcomes of a random experiment using a table or tree diagram

I can list the possible outcomes of a random experiment using a table or a tree diagram.

Compares qualitatively the theoretical or experimental probability of events

I can compare qualitatively the theoretical or experimental probability of events.

Recognizes that a probability is always between 0 and 1

I can recognize that a probability is always between 0 and 1.

Uses fractions, decimals or percentages to quantify a probability

I can use fractions, decimals or percentages to quantify a probability.

Compares the outcomes of a random experiment with known theoretical probabilities

I can compare the outcomes of a random experiment with known theoretical probabilities.

Simulates random experiments with or without the use of technology

I can simulate random experiments with or without the use of technology.