Elementary Mathematics Program Memory Aid

Document de travail – Équipe des programmes d’études en mathématique – Ministère de l’Éducation – 2020

Elementary Mathematics Program Memory Aid

• In mathematics, students develop three competencies concurrently:• To solve a situational problem• To reason using mathematical concepts and processes• To communicate by using mathematical language

• The development of the three competencies covered in the program is closely connected with the acquisition of knowledges related toarithmetic, geometry, measurement, statistics and probability. These branches of mathematics include the mathematical concepts andprocesses studied in this program.

• In essence, the three competencies are distinguished by the emphasis placed on different facets of mathematical thinking, which are, in fact, allintegrated.

• The activities assigned to students lead them to reflect, manipulate, explore, construct, simulate, discuss, cooperate, structure their thinking ormake connections. These activities help them take ownership of concepts and processes as well as various strategies.

• The diagram on the following page illustrates various intradisciplinary links that must be taken into account in the construction of mathematicalknowledge. These links include, for example, the different mathematical fields, concepts and processes.

• The following diagrams illustrate the concepts and processes of the elementary program, organized by mathematical field.• The circled symbols below indicate some, but not all, of the examples of connections between the various mathematical fields.

Arithmetic Geometry Measurement Statistics Probability

Understanding and writing numbers

Meaning of operations involving numbers

Operations involving numbers

G PM S

UN

MO

ON


Exploration activities

Collaborative work

Discussions or exchange of

ideas

Interdisciplinary activities

Hands-on activities

Simulation activities

ArithmeticUnderstanding and writing numbers

Meaning of operations involving numbersOperations involving numbers

GeometrySpaceSolids

Plane figuresFrieze patterns and tessellations

MeasurementLengths

Surface areasVolumesAngles

CapacitiesMasses

TimeTemperatures

StatisticsFormulating questions for a survey

Collecting, describing and organizing data

ProbabilityExperimentation with activities

involving chanceQualitative prediction

Theoretical or experimental probability

Different types of

representations

Cultural references

Interpreting anddisplaying data

Quantitative prediction

Understanding and calculating the arithmetic mean


Understanding and writing numbers

Natural numbers Fractions Decimals Integers

Reads and writes numbers

Compares numbers

Arranges numbers in increasing or decreasing order

Represents numbers in a variety of ways

Identifies equivalent expressions

Locates numbers using different visual aids (number line)

Counts collections (using objects or drawings)

Describes patterns

Classifies numbers based on their properties

Represents the power of a number

Counts or recites counting rhymes involving numbers

Composes and decomposes a number

Identifies properties of numbers

Approximates a collection, using objects or drawings

Identifies fractions related to everyday items

Identifies different meanings

Matches a decimal or percentage to a fraction

Matches a fraction to part of a whole

Distinguishes a numerator from a denominator

Understands the role of the decimal point

Approximates

Composes and decomposes a number

Arithmetic

G

P

M

G

G

G


Meaning of operations involving numbers

FractionsDecimals Integers

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

Represents and describes a situation that uses different meanings of addition and subtraction

Represents and describes a situation that uses different meanings of multiplication and division

Establishes equality relations between numerical expressions

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

Determines numerical equivalencies between operations

Natural numbers

Arithmetic

M

M


Arithmetic

Operations involving numbers

FractionsDecimals Integers

Approximates the result

Builds a memorized repertoire

Determines the missing term in an equation

Decomposes a number into prime factors

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

Describes patterns

Generates a set of equivalent fractions

Calculates the power of a number

Performs a series of operations in accordance with the order of operations

Adds new terms to a series

Reduces a fraction to its simplest form (lowest terms)

Adds and subtracts fractions

Multiplies a natural number by a fraction

Develops processes for mental computation

Develops processes for written computation for addition and subtraction

Develops processes for written computation for multiplication and division

Natural numbers

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

G

S

P

P

PP


Space Solids Plane figures Frieze patterns and tessellations

Gets his/her bearings and locates objects

Locates objects in a plane

Locates objects on an axis

Locates points in a Cartesian plane

Geometry

Compares objects or parts of objects in the environment with solids

Compares and constructs solids

Identifies the main solids

Represents the different faces of a prism or pyramid

Classifies prisms and pyramids

Describes prisms and pyramids in terms of faces, vertices and edges

Matches the net of a pyramid to the corresponding pyramid

Tests Euler’s theorem

Matches the net of a prism to the corresponding prism

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

Compares and constructs figures

Identifies plane figures

Describes plane figures

Describes convex and nonconvex polygons

Describes and classifies quadrilaterals

Identifies and constructs parallel lines and perpendicular lines

Describes circles

Describes and classifies triangles

Identifies congruent figures

Observes and produces patterns using geometric figures

Observes and produces frieze patterns and tessellations

UN

UN UN

UN

UN


Lengths Surface areas Volumes Capacities

Compares lengths

Constructs rulers

Estimates and measures using unconventional units

Estimates and measures using conventional units

Measurement

Calculates the perimeter of plane figures

Establishes relationships between units of measure


Angles Masses Time TemperaturesEstimates and measures using

unconventional units

Estimates and measures using conventional units


Compares angles

UN UN

UN

UN

MO

G


Collects, describes and organizes data using tables

Interprets data

Displays data

Understands and calculates the arithmetic mean

Statistics

Formulates questions for a survey

Probability

When applicable, recognizes equiprobability

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

Experiments with activities involving chance

Predicts qualitatively an outcome or several events

When applicable, recognizes variability in possible outcomes

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

Enumerates possible outcomes of a random experiment

Compares quantitatively the theoretical or experimental probability of events

Recognizes that a probability is always between 0 and 1

Distinguishes between prediction and outcome

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

UN

S

ON

ON

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Elementary Mathematics Program Memory Aid