
4Grade 4 Standards
Top Mathematicians

Probability

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


4.PR.1.1.10
Simulates random experiments with or without the use of technology


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


4.1745

4.1755


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


4.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)


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


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


4.PR.1.1.6
Distinguishes between prediction and outcome


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


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

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


4.PR.1.1.1

Statistics

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


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


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


4.16120

4.1625

4.1635

4.16415

4.1655

4.1665

4.1675


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


4.1685

4.1695

4.1705

4.1715

4.1725

4.1735


4.ST.1.1.1

Arithmetic: Meaning of operations involving numbers

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


4.5320

4.5420

4.5520

4.5620

4.5720


4.ARTM.1.1.2
Uses objects, diagrams or equations to represent and describe transformations of numbers up to 100000: adding, taking away, uniting, comparing


4.ARTM.1.1.2a
Uses objects, diagrams or equations to represent and describe transformations of numbers up to 100000: adding, taking away, uniting, comparing


4.5820

4.595


4.ARTM.1.1.2b
Uses objects, diagrams or equations to represent and describe the composition of transformations (positive or negative) of numbers up to 100000


4.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.


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


4.ARTM.1.1.5
Determines numerical equivalencies using relationships between operations (the four operations), the commutative property of addition and multiplication and the associative property.


4.7115

4.7215

4.7315

4.7415


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


4.ARTM.1.2.1b
Uses objects, diagrams or equations to represent and describe the composition of transformations (positive or negative) with decimals to the hundreth place value.


4.ARTM.1.2.2
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, with decimals to the hundreth place value.


4.ARTM.1.2.3
Determines numerical equivalencies using the relationship between operations (the four operations), the commutative property of addition and multiplication and the associative property with decimals up to the hundreth place value.


4.ARTM.1.1.1

Geometry

4.G.1.1.1
Locates objects in a plane


4.12810

4.12915

4.13010

4.1315


4.G.1.1.2
Locates objects on an axis (based on the types of numbers studied)


4.G.1.1.3
Locates points in a Cartesian plane in the first quadrant


4.12810

4.12915

4.13010

4.1315

4.13210

4.13310


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


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

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


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


4.1365

4.1375

4.1385

4.1395


4.G.1.2.5
Classifies prisms and pyramids


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


4.G.1.2.7a
Matches the net of a prism to the corresponding prism and vice versa


4.1405


4.G.1.2.7b
Matches the net of a pyramid to the corresponding pyramid and vice versa


4.1405


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

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


4.1415

4.1425

4.1435


4.G.1.3.3
Describes convex and nonconvex polygons


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

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


4.G.1.3.6
Classifies quadrilaterals


4.1455


4.G.1.4.1
Identifies congruent figures


4.1465

4.1475


4.G.1.4.2
Observes and produces patterns using geometric figures


4.G.1.4.3
Observes and produces frieze patterns and tessellations using reflections


4.1485

4.1495


4.G.1.1.1

Measurement

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

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


4.1515


4.MT.1.1.3
Calculates the perimeter of plane figures


4.705

4.15215

4.1535


4.MT.1.2.1
Estimates and measures surface area using unconventional units


4.MT.1.3.1
Estimates and measures volume using unconventional units


4.MT.1.4.1
Compares angles

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


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


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


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

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


4.15520

4.15620

4.1575


4.MT.1.7.2
Establishes relationships between units of measure


4.1585

4.1595

4.1605


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


4.MT.1.1.1

Arithmetic: Understanding and writing numbers

4.ARTU.1.1.1
Counts or recites counting rhymes involving natural numbers up to 100000


4.ARTU.1.1.10
Locates natural numbers using different visual aids (e.g. hundreds chart, number strip, number line) up to 100000


4.ARTU.1.1.11a
Identifies properties of odd or even natural numbers up to 100000


4.2410

4.2510


4.ARTU.1.1.11b
Identifies properties of natural numbers up to 100000 as square, prime or composite numbers


4.2610


4.ARTU.1.1.12
Classifies natural numbers up to 100000 in various ways, based on their properties (e.g. even numbers, composite numbers)


4.2410

4.2510

4.2610


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


4.2715


4.ARTU.1.1.1a
counts forward or backward up to 100000


4.220


4.ARTU.1.1.1b
Skip counts (e.g. by twos) up to 100000


4.ARTU.1.1.2
Counts collections (using objects or drawings)


4.ARTU.1.1.2a
counts a collection by grouping or regrouping


4.ARTU.1.1.2b
counts a pregrouped collection


4.ARTU.1.1.3
Reads and writes any natural number up to 100000

4.ARTU.1.1.4a
Represents natural numbers in different ways or associates a number with a set of objects or drawings with emphasis on exchanging apparent, nonaccessible groupings, using structured materials (e.g. base ten blocks, number tables) up to 100000

4.ARTU.1.1.4b
Represents natural numbers 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)


4.ARTU.1.1.5
Composes and decomposes a natural number up to 100000 in a variety of ways (e.g. 123 = 100 + 23, 123 = 100 + 20 + 3, 123 = 50 + 50 + 20 + 3)

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

4.ARTU.1.1.7
Compares natural numbers up to 100000


4.1425


4.ARTU.1.1.8
Arranges natural numbers up to 100000 in increasing or decreasing order


4.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)


4.1515

4.1620

4.1715

4.185

4.1920

4.2020

4.2115

4.2215

4.2315


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

4.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


4.285

4.2920


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


4.285

4.2920


4.ARTU.1.2.4
Distinguishes a numerator from a denominator


4.ARTU.1.2.5
Reads and writes a fraction


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


4.ARTU.1.2.7
Verifies whether two fractions are equivalent


4.3010

4.3120

4.3315

4.3415

4.3520

4.3620

4.3720


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

4.ARTU.1.2.9
Orders fractions with the same denominator

4.ARTU.1.3.1
Represents decimals in a variety of ways (using objects or drawings) up to the hundredths place


4.3810


4.ARTU.1.3.10
Arranges decimals up to the hundredths place value in increasing or decreasing order

4.ARTU.1.3.11
Matches a fraction to its decimal

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


4.3810


4.ARTU.1.3.3
Reads and writes numbers written in decimal notation up to the hundredths place

4.ARTU.1.3.4
Understands the role of the decimal point up to hundredths place


4.3810

4.4310

4.4410


4.ARTU.1.3.5
Composes and decomposes a decimal written in decimal notation up to the hundredths place


4.ARTU.1.3.6
Recognizes equivalent expressions (e.g. 12 tenths is equivalent to 1 unit and 2 tenths; 0.5 is equivalent to 0.50)


4.4515


4.ARTU.1.3.7a
Locates decimals on a number line up to the hundredths place between two consecutive natural numbers


4.ARTU.1.3.7b
Locates decimals on a number line between two decimals up to the hundredths place


4.ARTU.1.3.8
Compares two decimals up to the hundredths place

4.ARTU.1.3.9
Approximates (e.g. estimates, rounds to a given value, truncates decimal places)


4.4815


4.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)


4.505

4.515


4.ARTU.1.1.1

Arithmetic: Operations involving numbers

4.ARTO.1.1.10a
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)


4.1175


4.ARTO.1.1.10b
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)


4.2115

4.2215

4.2315


4.ARTO.1.1.10c
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


4.2115

4.2215

4.2315


4.ARTO.1.1.11
Adds new terms to a series when the first three terms or more are given


4.2115

4.2215

4.2315


4.ARTO.1.1.12
Uses a calculator and becomes familiar with its basic functions (+, , =, 0 to 9 number keys, all clear, clear)


4.ARTO.1.1.13
Uses a calculator and becomes familiar with its × and ÷ functions


4.ARTO.1.1.1a
Approximates the result of an addition or subtraction involving natural numbers up to 100000


4.7620

4.7720

4.7820

4.7920


4.ARTO.1.1.1b
Approximates the result of any of the four operations involving natural numbers up to 100000


4.8020

4.8120

4.8220

4.8320

4.8420

4.8520


4.ARTO.1.1.2a
Develops various strategies that promote mastery of number facts and relates them to the properties of addition


4.8620

4.8720

4.1515

4.1620

4.1715


4.ARTO.1.1.2b
Masters all addition facts (0 + 0 to 10 + 10) and the corresponding subtraction facts

4.ARTO.1.1.3a
Develops processes for mental computation that uses their own processes to determine the sum or difference of two natural numbers up to 100000


4.8620

4.8720

4.1515

4.1620

4.1715


4.ARTO.1.1.3b
Develops processes for mental computation that uses their own processes to determine the product or quotient of two natural numbers up to 100000


4.9165

4.9220

4.9320

4.9420

4.9515

4.9620

4.9720

4.9815

4.9920

4.10020

4.10120

4.185

4.1920

4.2020


4.ARTO.1.1.4
Develops processes for written computation (addition and subtraction) up to 100000


4.ARTO.1.1.4a
Uses conventional processes to determine the sum of two natural numbers of up to four digits


4.8620

4.10225


4.ARTO.1.1.4b
Uses conventional processes to determine the difference between two natural numbers of up to four digits whose result is greater than 0


4.10320

4.1045


4.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

4.ARTO.1.1.6a
Builds a memory of multiplication facts (0 × 0 to 10 × 10) and the corresponding division facts, using objects, drawings, charts or tables


4.9165

4.9620

4.11020

4.11115


4.ARTO.1.1.6b
Develops various strategies that promote mastery of number facts and relate them to the properties of multiplication


4.6015

4.6120

4.6220

4.6320

4.9515

4.6520

4.9720

4.9815

4.9920

4.10020

4.10120

4.820

4.915

4.7215

4.7315

4.7415

4.11115

4.11220

4.11320

4.11415

4.185

4.1920

4.2020


4.ARTO.1.1.6c
Masters all multiplication facts (0 × 0 to 10 × 10) and the corresponding division facts

4.ARTO.1.1.7
Develops processes for written computation and uses their own processes as well as materials and drawings to determine the product or quotient of a threedigit natural number and a onedigit natural number, expresses the remainder of a division as a fraction, depending on the context


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


4.10920

4.11515

4.11615


4.ARTO.1.1.9
Decomposes a number into prime factors


4.2610


4.ARTO.1.2.1
Generates a set of equivalent fractions


4.11810

4.3010

4.3120


4.ARTO.1.3.1
Approximates the result of an addition or a subtraction of decimals to the hundredth place

4.ARTO.1.3.2
Develops processes for mental computation adds and subtracts decimals to the hundredth


4.11915

4.12015

4.12110

4.12215

4.12320

4.12415

4.12520

4.12620

4.12710


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


4.12110

4.12215

4.12320

4.12415

4.12620


4.ARTO.1.1.10a