elementary mathematics program memory aid
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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
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Document de travail – Équipe des programmes d’études en mathématique – Ministère de l’Éducation – 2020
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
Document de travail – Équipe des programmes d’études en mathématique – Ministère de l’Éducation – 2020
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
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Document de travail – Équipe des programmes d’études en mathématique – Ministère de l’Éducation – 2020
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
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Document de travail – Équipe des programmes d’études en mathématique – Ministère de l’Éducation – 2020
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
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Document de travail – Équipe des programmes d’études en mathématique – Ministère de l’Éducation – 2020
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
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Document de travail – Équipe des programmes d’études en mathématique – Ministère de l’Éducation – 2020
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
Establishes relationships between units of measure
Angles Masses Time TemperaturesEstimates and measures using
unconventional units
Estimates and measures using conventional units
Establishes relationships between units of measure
Compares angles
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Document de travail – Équipe des programmes d’études en mathématique – Ministère de l’Éducation – 2020
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
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