Mathematics, Grade 5

Unit 1: Arithmetic

Understanding numbers, their meanings, and the four operations — the PDA Arithmetic branch.

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

• Counts collections (using objects or drawings)

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

• Reads and writes any natural number

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

• Composes and decomposes a natural number in a variety of ways

• Identifies equivalent expressions

• Compares natural numbers

• Arranges natural numbers in increasing or decreasing order

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

• Locates natural numbers using different visual aids

• Classifies natural numbers in various ways, based on their properties

• Approximates a collection, using objects or drawings

• Represents the power of a natural number

• Represents 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)

• Verifies whether two fractions are equivalent

• Matches a decimal or percentage to a fraction

• Orders fractions with the same denominator

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

• Orders fractions with the same numerator

• Locates fractions on a number line

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

• Identifies equivalent representations (using objects or drawings)

• Reads and writes numbers written in decimal notation

• Composes and decomposes a decimal written in decimal notation

• Recognizes equivalent expressions

• Locates decimals on a number line

• Compares two decimals

• Approximates a decimal (estimates, rounds or truncates)

• Arranges decimals in increasing or decreasing order

• Matches a fraction or percentage to its decimal

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

• Reads and writes integers

• Locates integers on a number line or Cartesian plane

• Compares integers

• Arranges integers in increasing or decreasing order

• Determines 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)

• 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)

• Establishes equality relations between numerical expressions

• Determines numerical equivalencies using operations and the commutative property

• Translates 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)

• 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

• Translates 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)

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

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

• 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

• 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

• Determines 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

• 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

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

• Adds 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

• 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)

• Multiplies a natural number by a fraction

• Approximates the result of an operation on decimals

• Develops processes for mental computation

• Multiplies decimals whose product stays within two decimal places

• 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

Unit 2: Geometry

Space, plane figures and solids, and spatial sense — the PDA Geometry branch.

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

• Locates points in a Cartesian plane — in all four quadrants

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

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

• Describes triangles — scalene, right, isosceles and equilateral triangles

• Classifies triangles

• Describes circles

• Observes and produces frieze patterns and tessellations — using translations

Unit 3: Measurement

Comparing and measuring length, area, volume, time, angles and more — the PDA Measurement branch.

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

• Establishes relationships between units of measure for length

• Estimates and measures surface area — using conventional units

• Estimates and measures volume — using conventional units

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

• Estimates and measures capacity using unconventional units

• Estimates and measures capacity using conventional units

• Establishes relationships between units of measure for capacity

• Estimates and measures mass using unconventional units

• Estimates and measures mass using conventional units

• Establishes relationships between units of measure for mass

• Establishes relationships between units of measure for time

• Estimates and measures temperature using conventional units

Unit 4: Statistics

Collecting, organizing and reading data — the PDA Statistics branch.

• 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

• Understands and calculates the arithmetic mean

Unit 5: Probability

Chance, likelihood and simple experiments — the PDA Probability branch.

• When applicable, recognizes variability in possible outcomes (uncertainty)

• When applicable, recognizes equiprobability

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

• Experiments with activities involving chance, using various objects

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

• Distinguishes between prediction and outcome

• Uses 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

• Compares qualitatively the theoretical or experimental probability of events

• 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