Gizmos for Quebec - Mathematics: Cycle 1: Year 1 (Progression of Learning adopted 2010)

This correlation lists the recommended Gizmos for this province's curriculum standards. Click any Gizmo title below for more information.

AR: : Arithmetic

AR.1: : Understanding real numbers

AR.1.1: : Natural numbers less thann1 000 000

AR.1.1.e: : Compares natural numbersnor arranges natural numbers in increasing or decreasing order

AR.1.1.f: : Classifies natural numbersnin various ways, based on their properties (e.g. even numbers, composite numbers)

AR.1.2: : Fractions

AR.1.2.a: : Represents a fractionnin a variety of ways (using objects or drawings)

AR.1.2.b: : Identifies the differentnmeanings of fractions: part of a whole, division, ratio, operator, measurement

AR.1.2.c: : Verifies whether two fractionsnare equivalent

AR.1.2.d: : Compares a fraction ton0, ½ or 1

AR.1.2.e: : Orders fractions withnthe same denominator or where one denominator is a multiple of the other or with thensame numerator

AR.1.3: : Decimals up to thousandths

AR.1.3.a: : Represents decimals inna variety of ways (using objects or drawings) and identifies equivalent representations

AR.1.3.b: : Reads and writes numbersnwritten in decimal notation

AR.1.3.d: : Composes and decomposesna number written in decimal notation and recognizes equivalent expressions

AR.1.3.e: : Compares numbers writtennin decimal notation or arranges them in increasing or decreasing order

AR.1.4: : Integers

AR.1.4.a: : Represents integers inna variety of ways (using objects or drawings)

AR.1.4.b: : Reads and writes integers

AR.1.4.c: : Compares integers or arrangesnintegers in increasing or decreasing order

AR.1.5: : Expresses numbers in a varietynof ways (fractional, decimal percentage notation)

AR.1.6: : Represents, reads and writesnnumbers written in fractional or decimal notation

AR.1.7: : Approximates, in various contexts,nthe numbers under study (e.g. estimates, rounds off, truncates)

AR.1.10: : Defines the concept absolutenvalue in context (e.g. difference between two numbers, distance between two points)

AR.1.11: : Represents and writes

AR.1.11.b: : squares and square roots

AR.1.15: : Compares and arranges innorder

AR.1.15.a: : numbers written in fractionalnor decimal notation

AR.1.15.b: : numbers expressed inndifferent ways (fractional, decimal, exponential [integral exponent], percentage,nsquare root, scientific notation)

AR.2: : Understanding operations involvingnreal numbers

AR.2.1: : Natural numbers less thann1 000 000

AR.2.1.b: : Uses objects, diagramsnor equations to represent a situation and, conversely, describes a situation representednby objects, diagrams or equations (use of different meanings of the four operations)

AR.2.1.d: : Determines numerical equivalenciesnusing relationships between operations, the commutative and associative propertiesnof addition and multiplication, the distributive property of multiplication over additionnor subtraction

AR.2.1.e: : Translates a situationnusing a sequence of operations in accordance with the order of operations

AR.2.2: : Fractions

AR.2.2.a: : Uses objects, diagramsnor an operation to represent a situation and, conversely, describes a situation representednby objects, diagrams or an operation (use of different meanings of addition, subtractionnand multiplication by a natural number)

AR.2.3: : Decimals

AR.2.3.a: : Uses objects, diagramsnor equations to represent a situation and, conversely, describes a situation representednby objects, diagrams or equations (use of different meanings of the four operations)

AR.2.5: : Looks for equivalent expressions:ndecomposing (additive, multiplicative, etc.), equivalent fractions, simplifying andnreducing, factoring, etc.

AR.2.6: : Translates (mathematizes)na situation using a sequence of operations (no more than two levels of parentheses)

AR.2.7: : Anticipates the results ofnoperations

AR.2.8: : Interprets the results ofnoperations in light of the context

AR.3: : Operations involving real numbers

AR.3.1: : Natural numbers less thann1 000 000

AR.3.1.a: : Approximates the resultnof an operation

AR.3.1.b: : Using personal processes,nmentally computes operations

AR.3.1.c: : Determines in writing

AR.3.1.c.1: : the sum of two naturalnnumbers of up to 4 digits

AR.3.1.c.2: : the difference betweenntwo natural numbers of up to 4 digits whose result is greater than 0

AR.3.1.c.5: : the result of a sequencenof operations in accordance with the order of operations

AR.3.2: : Fractions (using objects orndiagrams)

AR.3.2.a: : Generates a set of equivalentnfractions

AR.3.2.b: : Reduces a fraction tonits simplest form

AR.3.2.c: : Adds and subtracts fractionsnwhen the denominator of one fraction is a multiple of the other fraction

AR.3.3: : Decimal numbers up to thousandths

AR.3.3.a: : Approximates the resultnof an operation

AR.3.3.b: : Mentally computes

AR.3.3.b.1: : operations (addition,nsubtraction, multiplication, division by a natural number)

AR.3.3.c: : Computes in writing

AR.3.3.c.1: : additions and subtractionsnof numbers whose result does not go beyond the second decimal place

AR.3.3.c.2: : multiplications ofnnumbers whose product does not go beyond the second decimal place

AR.3.5: : Approximates the result ofnan operation or sequence of operations

AR.3.6: : Mentally computes the fournoperations, especially with numbers written in decimal notation, using equivalentnways of writing numbers and the properties of operations

AR.3.7: : Computes, in writing, thenfour operations with numbers that are easy to work with (including large numbers),nusing equivalent ways of writing numbers and the properties of operations

AR.3.7.b: : positive numbers writtennin fractional notation, with or without the use of objects or diagrams

AR.3.9: : Computes, using a calculator,noperations and sequences of operations in accordance with the order of operations

AR.3.10: : Switches, as needed, fromnone way of writing numbers to another: from fractional to percentage notation, fromndecimal to fractional notation, from decimal to percentage notation, and vice versa

AR.3.11: : Switches, as needed, fromnone way of writing numbers to another

AR.3.13: : Decomposes a natural numberninto prime factors

AR.4: : Understanding and analyzing proportionalnsituations

AR.4.1: : Calculates

AR.4.1.a: : a certain percentage ofna number

AR.4.1.b: : the value correspondingnto 100 per cent

AR.4.2: : Recognizes ratios and rates

AR.4.3: : Interprets ratios and rates

AR.4.4: : Describes the effect of changingna term in a ratio or rate

AR.4.7: : Recognizes a proportionalnsituation using the context, a table of values or a graph

AR.4.8: : Represents or interprets anproportional situation using a graph, a table of values or a proportion

AR.4.9: : Solves proportional situationsn(direct or inverse variation) by using different strategies (e.g. unit-rate method,nfactor of change, proportionality ratio, additive procedure, constant product [inversenvariation])

AL: : Algebra

AL.1: : Understanding and manipulatingnalgebraic expressions

AL.1.A: : Algebraic expressions

AL.1.A.1: : Describes, using his/hernown words and mathematical language, numerical patterns

AL.1.A.2: : Describes, using his/hernown words and mathematical language, series of numbers and family of operations

AL.1.A.3: : Adds new terms to a seriesnwhen the first three terms or more are given

AL.1.A.4: : Describes the role ofncomponents of algebraic expressions:

AL.1.A.4.a: : unknown

AL.1.A.4.b: : variable, constant

AL.1.A.4.c: : parameter

AL.1.A.4.d: : coefficient, degree,nterm, constant term, like terms

AL.1.A.5: : Constructs an algebraicnexpression using a register (type) of representation

AL.1.A.6: : Interprets an algebraicnexpression in light of the context

AL.1.A.7: : Recognizes or constructsnequivalent algebraic expressions

AL.1.A.8: : Recognizes or constructs

AL.1.A.8.a: : equalities and equations

AL.1.B: : Manipulating algebraic expressions

AL.1.B.1: : Calculates the numericnvalue of an algebraic expression

AL.1.B.2: : Performs the followingnoperations on algebraic expressions, with or without objects or diagrams: additionnand subtraction, multiplication and division by a constant, multiplication of first-degreenmonomials

AL.1.C: : Analyzing situations usingnequations or inequalities

AL.1.C.1: : Recognizes whether a situationncan be translated by

AL.1.C.1.a: : an equation

AL.1.C.2: : Recognizes or constructs

AL.1.C.2.a: : relations or formulas

AL.1.C.3: : Manipulates relationsnor formulas (e.g. isolates an element)

AL.1.C.4: : Represents a situationnusing

AL.1.C.4.a: : a first-degree equationnwith one unknown

AL.1.C.6: : Determines the missingnterm in an equation (relations between operations): a + b = □, a + □ = c, □ + b =nc, a – b = □, a – □ = c, □ – b = c, a × b = □, a × □ = c, □ × b = c, a ÷ b = □, an÷ □ = c, □ ÷ b = c

AL.1.C.7: : Transforms arithmeticnequalities and equations to maintain equivalence (properties and rules for transformingnequalities) and justifies the steps followed, if necessary

AL.1.C.9: : Uses different methodsnto solve first-degree equations with one unknown of the form ax + b = cx + d: trialnand error, drawings, arithmetic methods (inverse or equivalent operations), algebraicnmethods (balancing equations or hidden terms)

AL.2: : Understanding dependency relationships

AL.2.A: : Relations, functions and inverses

AL.2.A.1: : Identifies patterns innvarious situations and in various forms

AL.2.A.2: : Analyzes situations usingndifferent registers (types) of representation

AL.2.A.3: : Represents a situationngenerally using a graph

P: : Probability

P.1: : Understanding data from random experiments

P.1.A: : Processing data from randomnexperiments

P.1.A.1: : Simulates random experimentsnwith or without the use of technological tools

P.1.A.2: : Experiments with activitiesninvolving chance, using various objects (e.g. spinners, rectangular prisms, glasses,nmarbles, thumb tacks, 6-, 8- or 12-sided dice)

P.1.A.3: : In activities involvingnchance

P.1.A.3.a: : recognizes variabilitynin possible outcomes (uncertainty)

P.1.A.3.b: : recognizes equiprobabilityn(e.g. quantity of objects, symmetry of an object such as a cube)

P.1.A.3.c: : becomes aware of thenindependence of events (e.g. rolling dice, tossing a coin, drawing lots)

P.1.A.4: : Uses tables or diagramsnto collect and display the outcomes of an experiment

P.1.A.5: : Compares the outcomes ofna random experiment with known theoretical probabilities

P.1.A.6: : Distinguishes between predictionnand outcome

P.1.A.7: : Conducts or simulates randomnexperiments involving one or more steps (with or without replacement, with or withoutnorder)

P.1.A.9: : Enumerates the possiblenoutcomes of a random experiment using

P.1.A.9.a: : tables, tree diagram

P.1.A.10: : Defines the sample spacenof a random experiment

P.1.A.11: : Recognizes certain, probable,nimpossible, simple, complementary, compatible, incompatible, dependent, independentsnevents

P.1.A.13: : Uses fractions, decimalsnor percentages to quantify a probability

P.1.A.14: : Recognizes that a probabilitynis always between 0 and 1

P.1.A.15: : Predicts qualitativelynan outcome or several events using a probability line, among other things

P.1.A.15.a: : certain, possiblenor impossible outcome

P.1.A.15.b: : more likely, justnas likely, less likely event

P.1.B: : Analyzing probability situations

P.1.B.1: : Represents an event usingndifferent registers (types of representation)

P.1.B.2: : Compares qualitatively thentheoretical or experimental probability of an event occurring

P.1.B.3: : Distinguishes between theoreticalnand experimental probability

P.1.B.4: : Calculates the probabilitynof an event

P.1.B.9: : Interprets probabilitiesnand makes appropriate decisions

S: : Statistics

S.1: : Analyzing and making decisions aboutnone- or two-variable distributions, using statistical tools

S.1.A: : One-variable distributions

S.1.A.1: : Conducts a survey or a census

S.1.A.1.a: : Formulates questionsnfor a survey

S.1.A.1.b: : Chooses a sampling method:

S.1.A.1.b.i: : simple random, systematic

S.1.A.1.c: : Chooses a representativensample

S.1.A.1.d: : Collects, describesnand organizes data (classifies or categorizes) using tables

S.1.A.2: : Recognizes possible sourcesnof bias

S.1.A.3: : Interprets data presentednin a table or a bar graph, a pictograph, a broken-line graph or a circle graph

S.1.A.5: : Chooses appropriate register(s)n(types) of representation to organize, interpret and present data

S.1.A.6: : Organizes and presents datanusing

S.1.A.6.a: : a table, a bar graph,na pictograph and a broken-line graph

S.1.A.6.b: : a table presenting variablesnor frequencies, or using a circular graph

S.1.A.7: : Compares one-variable distributions

S.1.A.8: : Understands and calculatesnthe arithmetic mean

S.1.A.9: : Describes the concept ofnarithmetic mean (leveling or balance point)

S.1.A.10: : Calculates and interpretsnan arithmetic mean

S.1.A.11: : Determines and interprets

S.1.A.11.b: : measures of dispersion:

S.1.A.11.b.i: : range

S.1.A.11.c: : measures of position:

S.1.A.11.c.i: : minimum, maximum

S.1.A.12: : Chooses the appropriatenstatistical measures for a given situation

G: : Geometry

G.1: : Spatial sense and analyzing situationsninvolving geometric figures

G.1.A: : Plane figures

G.1.A.2: : Describes and classifiesnquadrilaterals

G.1.A.3: : Describes and classifiesntriangles

G.1.A.4: : Describes circles: radius,ndiameter, circumference, central angle

G.1.A.6: : Decomposes plane figuresninto circles (sectors), triangles or quadrilaterals

G.1.A.8: : Recognizes and draws mainnsegments and lines

G.1.A.8.a: : diagonal, altitude,nmedian, perpendicular bisector, bisector, apothem, radius, diameter, chord

G.1.A.9: : Identifies the propertiesnof plane figures using geometric transformations and constructions

G.1.A.10: : Justifies statements usingndefinitions or properties of plane figures

G.1.B: : Solids

G.1.B.2: : Determines the possiblennets of a solid

G.1.B.3: : Names the solid correspondingnto a net

G.1.B.4: : Describes solids:

G.1.B.4.b: : altitude, apothem, lateralnface

G.1.B.6: : Recognizes solids that cannbe split into

G.1.B.6.a: : right prisms, rightncylinders, right pyramids

G.1.C: : Geometric constructions andntransformations in the Euclidian plane

G.1.C.2: : Identifies properties andninvariants resulting from geometric constructions and transformations

G.1.C.3: : Identifies congruence (translation,nrotation and reflection) between two figures

G.1.C.4: : Constructs the image ofna figure under a translation, rotation and reflection

G.1.C.5: : Recognizes dilatation withna positive scale factor

G.1.D: : Congruent, similar or equivalentnfigures

G.1.D.3: : Recognizes the geometricntransformation(s) linking a figure and its image

G.1.D.4: : Determines the propertiesnand invariants of congruent or similar figures

G.1.D.8: : Justifies statements usingndefinitions or properties of congruent, similar or equivalent figures, depending onnthe cycle and year

G.2: : Analyzing situations involving measurements

G.2.B: : Time

G.2.B.2: : Estimates and measures timenusing conventional units

G.2.B.3: : Establishes relationshipsnbetween units of time: second, minute, hour, day, daily cycle, weekly cycle, yearlyncycle

G.2.B.4: : Distinguishes between durationnand position in time

G.2.C: : Angles

G.2.C.3: : Describes the characteristicsnof different types of angles: complementary, supplementary, adjacent, vertically opposite,nalternate interior, alternate exterior and corresponding

G.2.C.4: : Determines measures of anglesnusing the properties of the following angles: complementary, supplementary, verticallynopposite, alternate interior, alternate exterior and corresponding

G.2.C.5: : Finds unknown measurementsnusing the properties of figures and relations

G.2.C.5.a: : measures of angles inna triangle

G.2.C.5.b: : degree measures of centralnangles and arcs

G.2.C.8: : Justifies statements usingndefinitions or properties associated with angles and their measures

G.2.D: : Length

G.2.D.2: : Estimates and measures thendimensions of an object using conventional units: millimetre, centimetre, decimetre,nmetre and kilometre

G.2.D.4: : Constructs relations thatncan be used to calculate the perimeter or circumference of figures

G.2.D.5: : Finds the following unknownnmeasurements, using properties of figures and relations

G.2.D.5.a: : perimeter of plane figures

G.2.E: : Area

G.2.E.1: : Chooses the appropriatenunit of area for the context

G.2.E.4: : Constructs relations thatncan be used to calculate the area of plane figures: quadrilateral, triangle, circlen(sectors)

G.2.E.6: : Finds unknown measurements,nusing properties of figures and relations

G.2.E.6.b: : area of figures thatncan be split into circles (sectors), triangles or quadrilaterals

G.2.E.6.c: : lateral or total areanof right prisms, right cylinders and right pyramids

G.2.E.6.d: : lateral or total areanof solids that can be split into right prisms, right cylinders or right pyramids

G.2.E.7: : Justifies statements concerningnmeasures of area

G.2.G: : Metric or trigonometric relations

G.2.G.1: : Determines, through explorationnor deduction, different metric relations associated with plane figures

AG: : Analytic Geometry

AG.1: : Analyzing situations using analyticngeometry

AG.1.A: : Locating

AG.1.A.1: : Locates objects/numbersnon an axis, based on the types of numbers studied

AG.1.A.2: : Locates points in a Cartesiannplane, based on the types of numbers studied (x and y-coordinates of a point)

Correlation last revised: 9/16/2020

Quebec - Mathematics: Cycle 1: Year 1

Progression of Learning | Adopted: 2010