
5Grade 5 Standards
Top Mathematicians

Statistics

5.ST.1.1.1
Formulates questions for a survey (based on ageappropriate topics, students' language level, etc.)


5.ST.1.1.2
Collects, describes and organizes data (classifies or categorizes) using tables


5.ST.1.1.3
Interprets data using a table, a bar graph, a pictograph, a brokenline graph and a circle graph

5.ST.1.1.4
Displays data using a table, a bar graph, a pictograph and a brokenline graph


5.ST.1.1.5
Understands and calculates the arithmetic mean


5.ST.1.1.1

Probability

5.PR.1.1.1
When applicable, recognizes variability in possible outcomes (uncertainty)


5.PR.1.1.10
Recognizes that a probability is always between 0 and 1


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


5.PR.1.1.12
Compares the outcomes of a random experiment with known theoretical probabilities


5.PR.1.1.13
Simulates random experiments with or without the use of technology


5.PR.1.1.2
When applicable, recognizes equiprobability (e.g. quantity, symmetry of an object [cube])


5.1655

5.1665


5.PR.1.1.3
When applicable, becomes aware of the independence of events in an experiment


5.PR.1.1.4
Experiments with activities involving chance, using various objects (e.g. spinners, rectangular prisms, glasses, marbles, thumb tacks, 6, 8 or 12sided dice)


5.1655

5.1665


5.PR.1.1.5a
Predicts qualitatively an outcome or several events using a probability line, among other things as certain, possible or impossible outcome


5.1655

5.1665


5.PR.1.1.5b
Predicts qualitatively an outcome or several events using a probability line, among other things as more likely, just as likely, less likely event


5.1655

5.1665


5.PR.1.1.6
Distinguishes between prediction and outcome


5.PR.1.1.7
Uses tables or diagrams to collect and display the outcomes of an experiment


5.PR.1.1.8
Enumerates possible outcomes of a random experiment, using a table, a tree diagram


5.PR.1.1.9
Compares qualitatively the theoretical or experimental probability of events


5.PR.1.1.1

Arithmetic: Meaning of operations involving numbers

5.ARTM.1.1.1
Determines the operation(s) to perform in a given situation


5.ARTM.1.1.2a
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)


5.ARTM.1.1.2b
Uses objects, diagrams or equations to represent and describe transformations with natural numbers up to 1000000: adding, taking away, uniting, comparing


5.395

5.4020


5.ARTM.1.1.2c
Uses objects, diagrams or equations to represent and describe the composition of transformations (positive or negative) with natural numbers up to 1000000


5.ARTM.1.1.2d
Uses objects, diagrams, or equations to represent and describe the composition of mixed transformations with natural numbers up too 1000000.


5.ARTM.1.1.3
Uses objects, diagrams or equations to represent and describe 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) with natural numbers up to 1000000


5.ARTM.1.1.4
Establishes equality relations between numerical expressions (e.g. 3 + 2 = 6  1)


5.ARTM.1.1.5
Determines numerical equivalencies using relationships between: operations (the four operations), the commutative property of addition and multiplication, the associative property and the distributive property of multiplication over addition or subtraction


5.ARTM.1.1.6
Translates a situation using a series of operations in accordance with the order of operations


5.4720


5.ARTM.1.2.1a
Uses objects, diagrams or equations to represent and describe transformations with decimals to the thousandth place value: composition of mixed transformations


5.ARTM.1.2.1b
Uses objects, diagrams or equations to represent and describe transformations with decimals to the thousandth place value: adding, taking away, uniting, comparing


5.4315

5.4420

5.4515


5.ARTM.1.2.1c
Uses objects, diagrams or equations to represent and describe transformations with decimals to the thousandth place value: composition of transformations: positive, negative


5.ARTM.1.2.1d
Uses objects, diagrams or equations to represent and describe transformations with decimals to the thousandth place value: composition of mixed transformations


5.ARTM.1.2.2
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) 

5.5910


5.ARTM.1.2.3
Determines numerical equivalencies using relationships between operations (the four operations), the commutative property of addition and multiplication, the associative property and the distributive property of multiplication over addition or subtraction with decimals up to the thousandth place value


5.ARTM.1.2.4
Translates a situation into a series of operations in accordance with the order of operations with decimals up to the thousandth place value


5.4720


5.ARTM.1.3.1
Uses objects, diagrams or equations to represent a situation using fractions (use of different meanings of addition, subtraction and multiplication by a natural number)


5.ARTM.1.1.1

Geometry

5.G.1.1.1
Locates objects on an axis (based on the types of numbers studied)


5.G.1.1.2
Locates points in a Cartesian plane in all four quadrants

5.G.1.2.1
Compares objects or parts of objects in the environment with solids (e.g. spheres, cones, cubes, cylinders, prisms, pyramids)


5.G.1.2.2
Identifies the main solids (e.g. spheres, cones, cubes, cylinders, prisms, pyramids)


5.G.1.2.3
Identifies and represents the different faces of a prism or pyramid


5.G.1.2.4
Describes prisms and pyramids in terms of faces, vertices and edges


5.G.1.2.5
Classifies prisms and pyramids


5.G.1.2.6
Constructs a net of a prism or pyramid


5.G.1.2.7
Matches the net of a convex polyhedron to the corresponding convex polyhedron


5.G.1.2.8
Tests Euler's theorem on convex polyhedrons


5.G.1.3.1
Identifies plane figures (square, rectangle, triangle, rhombus and circle)


5.G.1.3.2
Describes plane figures (square, rectangle, triangle and rhombus)


5.G.1.3.3
Describes convex and nonconvex polygons


5.G.1.3.4
Identifies and constructs parallel lines and perpendicular lines


5.G.1.3.5
Describes quadrilaterals (e.g. parallel segments, perpendicular segments, right angles, acute angles, obtuse angles)


5.G.1.3.6
Classifies quadrilaterals


5.1235


5.G.1.3.7
Describes triangles: scalene triangles, right triangles, isosceles triangles, equilateral triangles


5.G.1.3.8
Classifies triangles


5.1225


5.G.1.3.9
Describes circles


5.G.1.4.1
Identifies congruent figures


5.G.1.4.2a
Observes and produces frieze patterns and tessellations using reflections


5.G.1.4.2b
Observes and produces frieze patterns and tessellations using translations

5.G.1.1.1

Measurement

5.MT.1.1.1
Estimates and measures the dimensions of an object using conventional units of metre, decimetre, centimetre, millimetre and kilometre


5.MT.1.1.2
Establishes relationships between units of measure for length using metre, decimetre, centimetre, millimetre and kilometre


5.MT.1.1.3
Calculates the perimeter of plane figures


5.MT.1.2.1
Estimates and measures surface area using conventional units


5.MT.1.3.1
Estimates and measures volume using conventional units

5.MT.1.4.1
Compares angles


5.MT.1.4.2
Estimates and determines the degree measurement of angles


5.14010


5.MT.1.5.1
Estimates and measures capacity using unconventional units


5.MT.1.5.2
Estimates and measures capacity using conventional units

5.MT.1.5.3
Establishes relationships between units of measure (e.g. : 1 L = 1000 mL, 1/2 L = 500 mL)


5.1305


5.MT.1.6.1
Estimates and measures mass using unconventional units


5.MT.1.6.2
Estimates and measures mass using conventional units

5.MT.1.6.3
Establishes relationships between units of measure (e.g. : 1 kg = 1000 g, 1/2 kg = 500 g)


5.1305


5.MT.1.7.1
Estimates and measures time using conventional units


5.10015


5.MT.1.7.2
Establishes relationships between units of measure


5.MT.1.8.1
Estimates and measures temperature using conventional units


5.MT.1.1.1

Arithmetic: Understanding and writing numbers

5.ARTU.1.1.1.c
skip counts (e.g. by twos) up to 1000000


5.ARTU.1.1.10
Locates natural numbers up to 1000000 using different visual aids (e.g. hundreds chart, number strip, number line)


5.ARTU.1.1.11a
Identifies properties of natural numbers up to 1000000 as odd or even numbers


5.710

5.810


5.ARTU.1.1.11b
Identifies properties of natural numbers up to 1000000 as square, prime or composite numbers


5.910


5.ARTU.1.1.12
Classifies natural numbers in various ways, based on their properties (e.g. even numbers, composite numbers)


5.710

5.810

5.910


5.ARTU.1.1.13
Approximates a collection, using objects or drawings (e.g. estimate, round up/down to a given value)


5.ARTU.1.1.14
Represents the power of a natural number


5.ARTU.1.1.1a
Counts or recites counting rhymes involving natural numbers up to 1000000


5.ARTU.1.1.1b
counts forward or backward up to 1000000


5.ARTU.1.1.2a
Counts collections (using objects or drawings)


5.ARTU.1.1.2b
counts a collection by grouping or regrouping


5.ARTU.1.1.2c
counts a pregrouped collection


5.ARTU.1.1.3
Reads and writes any natural number up to 1000000


5.ARTU.1.1.4
Represents natural numbers up to 1000000 in different ways or associates a number with a set of objects or drawings with emphasis on place value in nonapparent, nonaccessible groupings, using materials for which groupings are symbolic (e.g. abacus, money)


5.ARTU.1.1.5
Composes and decomposes a natural number up to 1000000 in a variety of ways (e.g. 123 = 100 + 23, 123 = 100 + 20 + 3, 123 = 50 + 50 + 20 + 3)


5.ARTU.1.1.6
Identifies equivalent expressions (e.g. 52 = 40 + 12, 25 + 27 = 40 + 12, 52 = 104 ÷ 2)


5.ARTU.1.1.7
Compares natural numbers up to 1000000


5.ARTU.1.1.8
Arranges natural numbers up to 1000000 in increasing or decreasing order


5.ARTU.1.1.9
Describes number patterns, using his/her own words and appropriate mathematical vocabulary (e.g. even numbers, odd numbers, square numbers, triangular numbers, prime numbers, composite numbers)


5.ARTU.1.2.1
Represents a fraction in a variety of ways, based on a whole or a collection of objects


5.ARTU.1.2.10
Orders fractions where one denominator is a multiple of the other(s)


5.ARTU.1.2.11
Orders fractions with the same numerator

5.ARTU.1.2.12
Locates fractions on a number line


5.ARTU.1.2.2
Matches a fraction to part of a whole (congruent or equivalent parts) or part of a group of objects, and vice versa


5.115


5.ARTU.1.2.3
Identifies the different meanings of fractions (sharing, division, ratio)


5.1220


5.ARTU.1.2.4
Distinguishes a numerator from a denominator


5.ARTU.1.2.5
Reads and writes a fraction


5.ARTU.1.2.6
Compares a fraction to 0, 1/2 or 1


5.ARTU.1.2.7
Verifies whether two fractions are equivalent


5.ARTU.1.2.8
Matches a decimal or percentage to a fraction


5.ARTU.1.2.9
Orders fractions with the same denominator


5.ARTU.1.3.1
Represents decimals up to thousandths in a variety of ways (using objects or drawings)


5.ARTU.1.3.10a
Matches a fraction to its decimal

5.ARTU.1.3.10b
Matches a fraction or percentage to its decimal

5.ARTU.1.3.2
Identifies equivalent representations (using objects or drawings)


5.ARTU.1.3.3
Reads and writes numbers written in decimal notation up to the thousandths place


5.ARTU.1.3.4
Composes and decomposes a decimal written in decimal notation up to the thousandths place


5.ARTU.1.3.5
Recognizes equivalent expressions (e.g. 12 tenths is equivalent to 1 unit and 2 tenths; 0.5 is equivalent to 0.50)


5.ARTU.1.3.6a
Locates decimals on a number line up to the thousandths place between two consecutive natural numbers


5.ARTU.1.3.6b
Locates decimals on a number line up to the thousandths place between two decimals


5.ARTU.1.3.7
Compares two decimals


5.ARTU.1.3.8
Approximates decimals (e.g. estimates, rounds to a given value, truncates decimal places)


5.ARTU.1.3.9
Arranges decimals in increasing or decreasing order


5.ARTU.1.4.1
Represents integers in a variety of ways (using objects or drawings) (e.g. tokens in two different colours, number line, thermometer, football field, elevator, hot air balloon)


5.ARTU.1.4.2
Reads and writes integers

5.ARTU.1.4.3
Locates integers on a number line or Cartesian plane


5.ARTU.1.4.4
Compares integers


5.ARTU.1.4.5
Arranges integers in increasing or decreasing order


5.3815


5.ARTU.1.1.1.c

Arithmetic: Operations involving numbers

5.ARTO.1.1.10
Calculates the power of a number


5.ARTO.1.1.11
Determines the divisibility of a number by 2, 3, 4, 5, 6, 8, 9, 10


5.ARTO.1.1.12
Performs a series of operations in accordance with the order of operations


5.ARTO.1.1.13a
Using his/her own words and mathematical language that is at an appropriate level for the cycle, describes nonnumerical patterns (e.g. series of colours, shapes, sounds, gestures)


5.ARTO.1.1.13b
Using his/her own words and mathematical language that is at an appropriate level for the cycle, describes numerical patterns (e.g. number rhymes, tables and charts)

5.ARTO.1.1.13c
Using his/her own words and mathematical language that is at an appropriate level for the cycle, describes series of numbers and family of operations


5.9615

5.9715

5.9820

5.9915

5.1520


5.ARTO.1.1.14
Adds new terms to a series when the first three terms or more are given


5.9615

5.9715

5.9820

5.9915

5.1520


5.ARTO.1.1.15a
Uses a calculator and becomes familiar with its basic functions (+, , =, 0 to 9 number keys, all clear, clear)


5.ARTO.1.1.15b
Uses a calculator and becomes familiar with its × and ÷ functions


5.ARTO.1.1.15c
Uses a calculator and becomes familiar with memory keys and change of sign keys (+/)


5.ARTO.1.1.1a
Approximates the result of an addition or subtraction involving natural numbers


5.4120

5.4220


5.ARTO.1.1.1b
Approximates the result of any of the four operations involving natural numbers


5.4120

5.4220

5.6920

5.7020


5.ARTO.1.1.2a
Builds a repertoire of memorized addition and subtraction facts


5.ARTO.1.1.2b
Develops various strategies that promote mastery of number facts and relates them to the properties of addition up to 1000000


5.395

5.4020

5.220

5.320

5.6215


5.ARTO.1.1.2c
Masters all addition facts (0 + 0 to 10 + 10) and the corresponding subtraction facts up to 1000000


5.ARTO.1.1.3a
Develops processes for mental computation and uses their own processes to determine the sum or difference of two natural numbers up to 1000000


5.6920

5.7020

5.7525

5.765


5.ARTO.1.1.3b
Develops processes for mental computation and uses their own processes to determine the product or quotient of two natural numbers up to 1000000


5.7120

5.7220

5.7320

5.7420

5.5220

5.5315

5.5815


5.ARTO.1.1.4a
Develops processes for written computation (addition and subtraction) and uses conventional processes to determine the sum of two natural numbers of up to four digits


5.ARTO.1.1.4b
Develops processes for written computation (addition and subtraction) and uses conventional processes to determine the difference between two natural numbers of up to four digits whose result is greater than 0


5.ARTO.1.1.5
Determines the missing term in an equation (relationships between operations): a + b =__, a + __ = c, __ + b = c, a  b = __, a  __= c, __  b = c


5.ARTO.1.1.6a
Builds a repertoire of memorized multiplication and division facts and develops various strategies that promote mastery of number facts and relate them to the properties of multiplication


5.7120

5.7220

5.7320

5.7420

5.795

5.8020

5.8115

5.8220

5.8320

5.8415

5.420

5.515

5.6315

5.6415

5.6515


5.ARTO.1.1.6b
Builds a repertoire of memorized multiplication and division facts and masters all multiplication facts (0 × 0 to 10 × 10) and the corresponding division facts


5.ARTO.1.1.7a
Develops processes for written computation (multiplication and division) and uses conventional processes to determine the product of a threedigit natural number and a twodigit natural number


5.5315


5.ARTO.1.1.7b
Develops processes for written computation (multiplication and division) and uses conventional processes to determine the quotient of a fourdigit natural number and a twodigit natural number, expresses the remainder of a division as a decimal that does not go beyond the second decimal place


5.ARTO.1.1.8
Determines the missing term in an equation (relationships between operations): a — b = __, a — __ = c, __ — b = c


5.ARTO.1.1.9
Decomposes a number into prime factors


5.910


5.ARTO.1.2.1
Generates a set of equivalent fractions


5.1315

5.1415

5.1520

5.1620

5.1720


5.ARTO.1.2.2
Reduces a fraction to its simplest form (lowest terms)


5.1620

5.1720


5.ARTO.1.2.3
Adds and subtracts fractions when the denominator of one fraction is a multiple of the other fraction(s)


5.ARTO.1.2.4
Multiplies a natural number by a fraction

5.ARTO.1.3.1a
Approximates the result of an addition or a subtraction using decimals to the thousandth


5.ARTO.1.3.1b
Approximates the result of a multiplication or division using decimals to the thousandth


5.ARTO.1.3.2a
Develops processes for mental computation adds and subtracts decimals to the thousandth

5.ARTO.1.3.2b
Develops processes for mental computation performs operations involving decimals (multiplication, division by a natural number) to the thousandth


5.955

5.5910

5.6720


5.ARTO.1.3.2c
Develops processes for mental computation multiplies and divides by 10, 100, 1000

5.ARTO.1.3.3a
Develops processes for written computation adds and subtracts decimals whose result does not go beyond the second decimal place


5.4315

5.4420

5.4515

5.10720


5.ARTO.1.3.3b
Develops processes for written computation multiplies decimals whose product does not go beyond the second decimal place

5.ARTO.1.3.3c
Develops processes for written computation divides a decimal by a natural number less than 11


5.ARTO.1.4.1
Expresses a decimal as a fraction, and vice versa

5.ARTO.1.4.2
Expresses a decimal as a percentage, and vice versa

5.ARTO.1.4.3
Expresses a fraction as a percentage, and vice versa

5.ARTO.1.4.4
Chooses an appropriate number form for a given context


5.ARTO.1.1.10