
8Grade 8 Standards
Top Mathematicians

Geometry: Analyzing situations involving measures

8.GAM.1.1.1
Chooses the appropriate unit of mass for the context


8.GAM.1.1.2
Estimates and measures mass using unconventional units: grams, kilograms


8.GAM.1.1.3
Establishes relationships between units of mass


8.GAM.1.2.1
Chooses the appropriate unit of time for the context


8.GAM.1.2.2
Estimates and measures time using conventional units


8.GAM.1.2.3
Establishes relationships between units of time: second, minute, hour, day, daily cycle, weekly cycle, yearly cycle


8.GAM.1.2.4
Distinguishes between duration and position in time


8.GAM.1.3.1
Compares angles: acute angle, right angle, obtuse angle

8.GAM.1.3.2
Estimates and determines the degree measure of angles

8.GAM.1.3.3
Describes the characteristics of different types of angles: complementary, supplementary, adjacent, vertically opposite, alternate interior, alternate exterior and corresponding

8.GAM.1.3.4
Determines measures of angles using the properties of the following angles: complementary, supplementary, vertically opposite, alternate interior, alternate exterior and corresponding

8.GAM.1.3.5a
Finds unknown measurements using the properties of figures and relations: measures of angles in a triangle

8.GAM.1.3.5b
Finds unknown measurements using the properties of figures and relations: degree measures of central angles and arcs


8.1905


8.GAM.1.3.6
Justifies statements using definitions or properties associated with angles and their measures

8.GAM.1.4.1
Chooses the appropriate unit of length for the context


8.GAM.1.4.2
Estimates and measures the dimensions of an object using conventional units: millimetre, centimetre, decimetre, metre and kilometre


8.GAM.1.4.3a
Establishes relationships between units of length: millimetre, centimetre, decimetre, metre and kilometre


8.GAM.1.4.3b
Establishes relationships between measures of length of the international system (SI)


8.GAM.1.4.4
Constructs relations that can be used to calculate the perimeter or circumference of figures


8.2165

8.2475

8.2485

8.2495

8.2505

8.2515


8.GAM.1.4.5a
Finds the following unknown measurements, using properties of figures and relations: perimeter of plane figures


8.25215

8.2535

8.2545


8.GAM.1.4.5b
Finds the following unknown measurements, using properties of figures and relations: a segment in a plane figure, circumference, radius, diameter, length of an arc, a segment resulting from an isometry or a similarity transformation


8.2165

8.2175

8.2185


8.GAM.1.4.6
Justifies statements concerning measures of length


8.GAM.1.5.1
Chooses the appropriate unit of area for the context


8.2535

8.2555


8.GAM.1.5.2
Estimates and measures surface areas using conventional units: square centimetre, square decimetre, square metre


8.2565


8.GAM.1.5.3
Establishes relationships between SI units of area


8.GAM.1.5.4
Constructs relations that can be used to calculate the area of plane figures: quadrilateral, triangle, circle (sectors)


8.GAM.1.5.5a
Finds unknown measurements, using properties of figures and relations: area of circles and sectors


8.2165

8.2175

8.2185


8.GAM.1.5.5b
Finds unknown measurements, using properties of figures and relations: area of figures that can be split into circles (sectors), triangles or quadrilaterals


8.21910


8.GAM.1.5.5c
Finds unknown measurements, using properties of figures and relations: lateral or total area of right prisms, right cylinders and right pyramids


8.2565

8.2575


8.GAM.1.5.5d
Finds unknown measurements, using properties of figures and relations: lateral or total area of solids that can be split into right prisms, right cylinders or right pyramids


8.GAM.1.5.5e
Finds unknown measurements, using properties of figures and relations: area of figures resulting from an isometry


8.GAM.1.5.5f
Finds unknown measurements, using properties of figures and relations: area of figures resulting from a similarity transformation


8.GAM.1.5.6
Justifies statements concerning measures of area

8.GAM.1.6.1
Chooses the appropriate unit of volume for the context


8.GAM.1.6.2
Estimates and measures volume or capacity using conventional units: cubic centimetre, cubic decimetre, cubic metre, millilitre, litre


8.GAM.1.6.3
Establishes relationships between capacity units: millilitre, litre


8.2475


8.GAM.1.7.1
Determines, through exploration or deduction, different metric relations associated with plane figures


8.GAM.1.1.1

Analytic Geometry

8.AG.1.1.1
Locates objects/numbers on an axis, based on the types of numbers studied


8.AG.1.1.2
Locates points in a Cartesian plane, based on the types of numbers studied (x and ycoordinates of a point)


8.25810

8.25915


8.AG.1.1.1

Arithmetic: Understanding Operations involving real numbers

8.AUOR.1.1.1
Chooses an appropriate way of writing numbers for a given context


8.AUOR.1.1.2
Looks for equivalent expressions: decomposing (additive, multiplicative, etc.), equivalent fractions, simplifying and reducing, factoring, etc.


8.515

8.620

8.4310

8.4415

8.4520

8.4615

8.4715

8.485

8.4920

8.5020

8.5115

8.5210

8.5315

8.5415

8.555


8.AUOR.1.1.3
Translates (mathematizes) a situation using a sequence of operations (no more than two levels of parentheses)

8.AUOR.1.1.4
Anticipates the results of operations

8.AUOR.1.1.5
Interprets the results of operations in light of the context

8.AUOR.1.1.1

Artithmetic: Operations involving real numbers

8.AOR.1.1.1
Uses, in different contexts, the properties of divisibility: 2, 3, 4, 5 and 10


8.6220

8.6320

8.6420

8.6515

8.6620

8.6720

8.4310


8.AOR.1.2.1
Approximates the result of an operation or sequence of operations


8.AOR.1.3.1
Mentally computes the four operations, especially with numbers written in decimal notation, using equivalent ways of writing numbers and the properties of operations


8.515

8.620

8.4415

8.4520

8.4615

8.4715

8.485

8.4920

8.5020

8.5115

8.5210

8.5315

8.5415

8.555


8.AOR.1.4.1a
Computes, in writing, the four operations with numbers that are easy to work with (including large numbers), using equivalent ways of writing numbers and the properties of operations: numbers written in decimal notation, using rules of signs


8.6815

8.6915

8.7015

8.715

8.7215

8.7315


8.AOR.1.4.1b
Computes, in writing, the four operations with numbers that are easy to work with (including large numbers), using equivalent ways of writing numbers and the properties of operations: positive numbers written in fractional notation, with or without the use of objects or diagrams


8.7420

8.7520

8.7620

8.7715

8.7815

8.7915

8.8015

8.8115

8.8215

8.8315


8.AOR.1.5.1
Computes, in writing, sequences of operations (numbers written in decimal notation) in accordance with the order of operations, using equivalent ways of writing numbers and the properties of operations (with no more than two levels of parentheses)

8.AOR.1.6.1
Computes, using a calculator, operations and sequences of operations in accordance with the order of operations

8.AOR.1.7.1
Switches, as needed, from one way of writing numbers to another


8.8410

8.3010

8.4115

8.4215

8.1710

8.1815


8.AOR.1.8.1
Calculates the power of a natural number


8.3010

8.3115

8.3215

8.3310

8.3415

8.3510

8.3610

8.3710

8.385

8.395


8.AOR.1.9.1
Decomposes a natural number into prime factors


8.6515

8.6620

8.6720

8.4310


8.AOR.1.1.1

Algebra: Relationships

8.AR.1.1.1
Identifies patterns in various situations and in various forms


8.15315

8.15410


8.AR.1.1.2
Analyzes situations using different registers (types) of representation


8.1555


8.AR.1.1.3
Represents a situation generally using a graph


8.11810

8.15610

8.15710


8.AR.1.1.1

Geometry: Spacial sense and analyzing situations involving geometric figures

8.GSS.1.1.1
Describes convex and nonconvex polygons


8.2125

8.2135


8.GSS.1.1.10
Justifies statements using definitions or properties of plane figures

8.GSS.1.1.2
Describes and classifies quadrilaterals


8.2145


8.GSS.1.1.3
Describes and classifies triangles


8.2155


8.GSS.1.1.4
Describes circles: radius, diameter, circumference, central angle


8.2165

8.2175

8.2185


8.GSS.1.1.5
Recognizes and names regular convex polygons


8.2125


8.GSS.1.1.6
Decomposes plane figures into circles (sectors), triangles or quadrilaterals


8.21910


8.GSS.1.1.7
Describes circles and sectors


8.2205


8.GSS.1.1.8
Recognizes and draws main segments and lines: diagonal, altitude, median, perpendicular bisector, bisector, apothem, radius, diameter, chord

8.GSS.1.1.9
Identifies the properties of plane figures using geometric transformations and constructions


8.2225

8.2235

8.22410

8.2255

8.22610

8.22710

8.22810

8.2295

8.2305

8.2315

8.2325


8.GSS.1.2.1
Matches the net of a convex polyhedron to the corresponding convex polyhedron


8.2205

8.2345


8.GSS.1.2.2
Determines the possible nets of a solid


8.2345


8.GSS.1.2.3
Names the solid corresponding to a net


8.2345


8.GSS.1.2.4a
Describes solids: vertex, edge, base, face


8.GSS.1.2.4b
Describes solids: altitude, apothem, lateral face


8.GSS.1.2.5
Tests Euler's relation on convex polyhedrons


8.GSS.1.2.6
Recognizes solids that can be split into right prisms, right cylinders, right pyramids


8.GSS.1.3.1
Identifies properties and invariants resulting from geometric constructions and transformations


8.22410

8.22610

8.22810

8.2305


8.GSS.1.3.2
Identifies congruence (translation, rotation and reflection) between two figures

8.GSS.1.3.3
Constructs the image of a figure under a translation, rotation and reflection


8.2235

8.2255

8.22710

8.2295


8.GSS.1.3.4
Recognizes dilatation with a positive scale factor


8.2295

8.2305


8.GSS.1.3.5
Constructs the image of a figure under a dilatation with a positive scale factor


8.2295


8.GSS.1.4.1
Identifies congruent figures in frieze patterns and tessellations


8.GSS.1.4.2
Recognizes congruent or similar figures


8.2365


8.GSS.1.4.3
Recognizes the geometric transformation(s) linking a figure and its image

8.GSS.1.4.4
Determines the properties and invariants of congruent or similar figures

8.GSS.1.4.5
Justifies statements using definitions or properties of congruent, similar or equivalent figures, depending on the cycle and year

8.GSS.1.1.1

Algebra: Expressions

8.AE.1.1.1
Describes, using his/her own words and mathematical language, numerical patterns


8.11515

8.11615

8.11715

8.11810


8.AE.1.1.2
Describes, using his/her own words and mathematical language, series of numbers and family of operations


8.11515

8.11615

8.1195

8.1215

8.1225

8.12310


8.AE.1.1.3
Adds new terms to a series when the first three terms or more are given


8.AE.1.1.4a
Describes the role of components of algebraic expressions:unknown


8.AE.1.1.4b
Describes the role of components of algebraic expressions:variable, constant


8.AE.1.1.4c
Describes the role of components of algebraic expressions: parameter


8.AE.1.1.4d
Describes the role of components of algebraic expressions: coefficient, degree, term, constant term, like terms


8.1245

8.12510


8.AE.1.1.5
Constructs an algebraic expression using a register (type) of representation


8.1195

8.1215

8.1225

8.12310


8.AE.1.1.6
Interprets an algebraic expression in light of the context


8.AE.1.1.7
Recognizes or constructs equivalent algebraic expressions


8.12510

8.12610

8.1275

8.12810

8.12915

8.395


8.AE.1.1.8
Recognizes or constructs equalities and equations

8.AE.1.2.1
Calculates the numeric value of an algebraic expression


8.11810

8.1315

8.1325

8.13315

8.13410

8.1355

8.13610

8.1375

8.1385

8.13910

8.3115

8.395


8.AE.1.2.2
Performs the following operations on algebraic expressions, with or without objects or diagrams: addition and subtraction, multiplication and division by a constant, multiplication of firstdegree monomials


8.12510

8.12810

8.1405

8.14110

8.14210

8.1435


8.AE.1.2.3
Factors out the common factor in numerical expressions (distributive property of multiplication over addition or subtraction)


8.12610

8.1275

8.12810


8.AE.1.3.1
Recognizes whether a situation can be translated by an equation


8.10515


8.AE.1.3.10
Interprets solutions or makes decisions, if necessary, depending on the context


8.14715

8.14810

8.1495

8.15020

8.15120

8.15210

8.11110

8.11210

8.11410


8.AE.1.3.2
Recognizes or constructs relations or formulas


8.11210

8.11410


8.AE.1.3.3
Manipulates relations or formulas (e.g. isolates an element)


8.AE.1.3.4
Represents a situation using a firstdegree equation with one unknown


8.10515


8.AE.1.3.5
Represents an equation using another register (type) of representation, if necessary

8.AE.1.3.6
Determines the missing term in an equation (relations between operations): a + b = __, a + __ = c, __ + b = c, a  b = __, a  __ = c, __  b = c


8.AE.1.3.7
Transforms arithmetic equalities and equations to maintain equivalence (properties and rules for transforming equalities) and justifies the steps followed, if necessary


8.13315


8.AE.1.3.8
Uses different methods to solve firstdegree equations with one unknown of the form ax + b = cx + d: trial and error, drawings, arithmetic methods (inverse or equivalent operations), algebraic methods (balancing equations or hidden terms)


8.13315

8.13410

8.1355

8.1385

8.14410

8.1455

8.14610


8.AE.1.3.9
Validates a solution, with or without technological tools, by substitution

8.AE.1.1.1

Probability

8.PR.1.1.1
Simulates random experiments with or without the use of technological tools


8.PR.1.1.10
Recognizes certain, probable, impossible, simple, complementary, compatible, incompatible, dependent, independents events

8.PR.1.1.11
Uses fractions, decimals or percentages to quantify a probability


8.1635

8.1645

8.1655

8.16615

8.1675


8.PR.1.1.12
Recognizes that a probability is always between 0 and 1


8.PR.1.1.13a
Predicts qualitatively an outcome or several events using a probability line, among other things: certain, possible or impossible outcome


8.1595

8.1605


8.PR.1.1.13b
Predicts qualitatively an outcome or several events using a probability line, among other things: more likely, just as likely, less likely event


8.1595

8.1605


8.PR.1.1.2
Experiments with activities involving chance, using various objects (e.g. spinners, rectangular prisms, glasses, marbles, thumb tacks, 6, 8 or 12sided dice)


8.PR.1.1.3a
In activities involving chance, recognizes variability in possible outcomes (uncertainty)


8.PR.1.1.3b
In activities involving chance, recognizes equiprobability (e.g. quantity of objects, symmetry of an object such as a cube)


8.PR.1.1.3c
In activities involving chance, becomes aware of the independence of events (e.g. rolling dice, tossing a coin, drawing lots)

8.PR.1.1.4
Uses tables or diagrams to collect and display the outcomes of an experiment


8.PR.1.1.5
Compares the outcomes of a random experiment with known theoretical probabilities


8.1595

8.1605


8.PR.1.1.6
Distinguishes between prediction and outcome


8.1595

8.1605


8.PR.1.1.7
Conducts or simulates random experiments involving one or more steps (with or without replacement, with or without order)


8.PR.1.1.8a
Enumerates the possible outcomes of a random experiment using tables, tree diagram


8.PR.1.1.8b
Enumerates the possible outcomes of a random experiment using networks, tables, diagrams, Venn diagrams

8.PR.1.1.9
Defines the sample space of a random experiment


8.1615

8.16215


8.PR.1.2.1
Represents an event using different registers (types of representation)


8.PR.1.2.2
Compares qualitatively the theoretical or experimental probability of an event occurring


8.PR.1.2.3
Distinguishes between theoretical and experimental probability


8.1655

8.16615


8.PR.1.2.4
Calculates the probability of an event


8.1635

8.1645

8.1655

8.16615

8.1675


8.PR.1.2.5
Interprets probabilities and makes appropriate decisions


8.1595

8.1605


8.PR.1.1.1

Statistics

8.ST.1.1.10
Calculates and interprets an arithmetic mean


8.1925

8.1935

8.1945

8.1955

8.1965

8.1975

8.1985

8.1995

8.2005

8.2015

8.20210

8.20310

8.20410

8.20510

8.20610

8.20710

8.20810

8.20910

8.21010

8.21110


8.ST.1.1.11a
Determines and interprets measures of dispersion: range


8.ST.1.1.11b
Determines and interprets measures of position: maximum, minimum


8.ST.1.1.12
Chooses the appropriate statistical measures for a given situation


8.ST.1.1.1a
Conducts a survey or a census: Formulates questions for a survey


8.ST.1.1.1b
Conducts a survey or a census: Chooses a sampling method: simple random, systematic


8.ST.1.1.1c
Conducts a survey or a census: Chooses a representative sample


8.ST.1.1.1d
Conducts a survey or a census: Collects, describes and organizes data (classifies or categorizes) using tables


8.1685


8.ST.1.1.2
Recognizes possible sources of bias


8.1695

8.1705

8.1715

8.1725


8.ST.1.1.3
Interprets data presented in a table or a bar graph, a pictograph, a brokenline graph or a circle graph


8.9310

8.1735

8.1745

8.1755

8.1765

8.1775

8.1785

8.17910

8.1805

8.1815

8.1825


8.ST.1.1.4
Distinguishes different types of statistical variables: qualitative, discrete or continuous quantitative


8.ST.1.1.5
Chooses appropriate register(s) (types) of representation to organize, interpret and present data


8.1835


8.ST.1.1.6a
Organizes and presents data using a table, a bar graph, a pictograph and a brokenline graph


8.1845

8.1855

8.1865

8.1875

8.1885

8.1895


8.ST.1.1.6b
Organizes and presents data using a table presenting variables or frequencies, or using a circular graph


8.1685

8.1825

8.1905

8.1915


8.ST.1.1.7
Compares onevariable distributions


8.1925

8.1935

8.1945

8.1955

8.1965

8.1975

8.1985

8.1995

8.2005

8.2015


8.ST.1.1.8
Understands and calculates the arithmetic mean


8.20210

8.20310

8.20410

8.20510

8.20610


8.ST.1.1.9
Describes the concept of arithmetic mean (leveling or balance point)


8.1925

8.1935

8.1945

8.1955

8.1965

8.20710

8.20810

8.20910

8.21010

8.21110


8.ST.1.1.10

Arithmetic: Understanding Real Numbers

8.AUN.1.1.1a
Identifies the different meanings of fractions: part of a whole, division, ratio, operator, measurement


8.110

8.25


8.AUN.1.1.1b
Verifies whether two fractions are equivalent


8.320

8.415

8.515

8.620

8.75

8.815

8.95


8.AUN.1.1.1c
Compares a fraction to 0, 1/2 or 1


8.AUN.1.1.1d
Orders fractions with the same denominator or where one denominator is a multiple of the other or with the same numerator


8.1015

8.1115

8.1220

8.1315

8.145


8.AUN.1.10.1.b
Compares and arranges in order numbers expressed in different ways (fractional, decimal, exponential [integral exponent], percentage, square root, scientific notation)

8.AUN.1.10.1a
Compares and arranges in order numbers written in fractional or decimal notation


8.1015

8.1920


8.AUN.1.2.1a
Represents decimals up to thousandths in a variety of ways (using objects or drawings) and identifies equivalent representations

8.AUN.1.2.1b
Reads and writes numbers up to thousandths written in decimal notation

8.AUN.1.2.1c
Composes and decomposes a number written in decimal notation up to thousandths and recognizes equivalent expressions

8.AUN.1.2.1d
Compares numbers written in decimal notation up to thousandths or arranges them in increasing or decreasing order

8.AUN.1.3.1a
Represents integers in a variety of ways (using objects or drawings)


8.AUN.1.3.1b
Reads and writes integers


8.AUN.1.3.1c
Compares integers or arranges integers in increasing or decreasing order

8.AUN.1.4.1
Expresses numbers in a variety of ways (fractional, decimal percentage notation)

8.AUN.1.5.1
Represents, reads and writes numbers written in fractional or decimal notation

8.AUN.1.6.1
Approximates, in various contexts, the numbers under study (e.g. estimates, rounds off, truncates)


8.2315


8.AUN.1.7.1
Defines the concept absolute value in context (e.g. difference between two numbers, distance between two points)

8.AUN.1.8.1a
Represents and writes squares and square roots

8.AUN.1.8.1b
Represents and writes numbers in exponential notation (integral exponent)


8.3010

8.3115

8.3215

8.3310

8.3415

8.3510

8.3610

8.3710

8.385

8.395


8.AUN.1.9.1
Estimates the order of magnitude of a real number in


8.AUN.1.1.1a

Arithmetic: Understanding and analyzing proportional situations

8.AUP.1.1.1a
Calculates a certain percentage of a number


8.855

8.8615

8.8715

8.885

8.8915


8.AUP.1.1.1b
Calculates the value corresponding to 100 per cent


8.AUP.1.2.1
Recognizes ratios and rates


8.9015

8.9120

8.9215

8.9310

8.25


8.AUP.1.3.1
Interprets ratios and rates


8.9015

8.9120

8.9215

8.9310

8.25


8.AUP.1.4.1
Describes the effect of changing a term in a ratio or rate


8.8615

8.9310

8.9415


8.AUP.1.5.1a
Compares ratios and rates qualitatively (equivalent rates and ratios, unit rate)


8.9015

8.75

8.95


8.AUP.1.5.1b
Compares ratios and rates quantitatively (equivalent rates and ratios, unit rate)


8.9015

8.75

8.815

8.95

8.145


8.AUP.1.6.1
Translates a situation using a ratio or rate


8.9015

8.9120

8.9215

8.9310

8.815

8.145

8.9520

8.9615

8.9720

8.9815

8.9915

8.1005

8.1015


8.AUP.1.7.1
Recognizes a proportional situation using the context, a table of values or a graph


8.10215

8.10315

8.1045


8.AUP.1.8.1
Represents or interprets a proportional situation using a graph, a table of values or a proportion


8.1045

8.10515

8.1065


8.AUP.1.9.1
Solves proportional situations (direct or inverse variation) by using different strategies (e.g. unitrate method, factor of change, proportionality ratio, additive procedure, constant product [inverse variation])


8.8615

8.1045

8.1065

8.10715

8.10815

8.10915

8.11015

8.11110

8.11210

8.11315

8.11410


8.AUP.1.1.1a