Mathematics, Grade 3

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

• Identifies properties of natural numbers — square, prime or composite numbers

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

• Approximates a collection, using objects or drawings

• 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, ½ or 1

• Verifies whether two fractions are equivalent

• 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

• Understands the role of the decimal point

• 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 to its decimal or percentage

• 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

• 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

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

• Builds a repertoire of memorized addition and subtraction facts1 — develops various strategies that promote mastery of number facts and relates them to the properties of addition

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

• Develops processes for written computation (addition and subtraction) — uses conventional processes to determine the sum of two natural numbers of up to four digits

• Builds a repertoire of memorized multiplication and division facts

• Develops processes for written computation (multiplication and division)

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

• 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 its × and ÷ functions

• Generates a set of equivalent fractions

• Approximates the result of an operation on decimals

• Develops processes for mental computation

• Develops processes for written computation

Unit 2: Geometry

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

• Locates objects in a plane

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

• Locates points in a Cartesian plane

• 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 solid to the corresponding solid

• Describes convex and non-convex polygons

• Identifies and constructs parallel lines and perpendicular lines

• Describes quadrilaterals

• Classifies quadrilaterals

• Observes and produces patterns using geometric figures

• Observes and produces frieze patterns and tessellations

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 and millimetre

• Establishes relationships between units of measure for length

• Calculates the perimeter of plane figures

• Estimates and measures surface area

• Estimates and measures volume

• Compares angles

• 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 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 and a broken-line graph

• Displays data using a table, a bar graph, a pictograph and a broken-line graph

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

• Simulates random experiments with or without the use of technology