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Skills available for Quebec grade 4 math curriculum

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4.A Arithmetic

4.A.U Understanding and writing numbers
- 4.A.U.A Natural numbers less than 100 000
  - 4.A.U.A.1 Counts or recites counting rhymes involving natural numbers
    - 4.A.U.A.1.b counts forward or backward
    - 4.A.U.A.1.c skip counts (e.g. by twos)
      - Skip-counting sequences (4-A.15)
  - 4.A.U.A.2 Counts collections (using objects or drawings)
    - 4.A.U.A.2.c counts a collection by grouping or regrouping
    - 4.A.U.A.2.d counts a pre-grouped collection
  - 4.A.U.A.3 Reads and writes any natural number
    - Word names for numbers (4-A.8)
  - 4.A.U.A.4 Represents natural numbers in different ways or associates a number with a set of objects or drawings emphasis on apparent, accessible groupings using objects, drawings or unstructured materials (e.g. tokens, nesting cubes, groups of ten objects placed inside a bag and ten of these bags placed inside another container)
    - 4.A.U.A.4.b emphasis on exchanging apparent, non-accessible groupings, using structured materials (e.g. base ten blocks, number tables)
      - Place value models (4-A.1)
      - Place values review (4-A.7)
    - 4.A.U.A.4.c emphasis on place value in non-apparent, non-accessible groupings, using materials for which groupings are symbolic (e.g. abacus, money)
  - 4.A.U.A.5 Composes and decomposes a natural number in a variety of ways (e.g. 123 = 100 + 23, 123 = 100 + 20 + 3, 123 = 50 + 50 + 20 + 3, 123 = 2 × 50 + 30 - 7, 123 = 2 × 60 + 3)
    - Convert between standard and expanded form (4-A.2)
  - 4.A.U.A.6 Identifies equivalent expressions (e.g. 52 = 40 + 12, 25 + 27 = 40 + 12, 52 = 104 ÷ 2)
  - 4.A.U.A.7 Compares natural numbers
    - Compare numbers (4-A.19)
  - 4.A.U.A.8 Arranges natural numbers in increasing or decreasing order
    - Put numbers in order (4-A.20)
  - 4.A.U.A.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.A.U.A.10 Locates natural numbers using different visual aids (e.g. hundreds chart, number strip, number line)
  - 4.A.U.A.11 Identifies properties of natural numbers
    - 4.A.U.A.11.b square, prime or composite numbers
      - Prime and composite numbers (4-A.17)
  - 4.A.U.A.12 Classifies natural numbers in various ways, based on their properties (e.g. even numbers, composite numbers)
    - Even or odd (4-A.12)
    - Prime and composite numbers (4-A.17)
  - 4.A.U.A.13 Approximates a collection, using objects or drawings (e.g. estimate, round up/down to a given value)
- 4.A.U.B Fractions (using objects or drawings)
  - 4.A.U.B.2 Represents a fraction in a variety of ways, based on a whole or a collection of objects
  - 4.A.U.B.3 Matches a fraction to part of a whole (congruent or equivalent parts) or part of a group of objects, and vice versa
  - 4.A.U.B.4 Identifies the different meanings of fractions (sharing, division, ratio)
  - 4.A.U.B.5 Distinguishes a numerator from a denominator
  - 4.A.U.B.6 Reads and writes a fraction
    - Understand fractions: fraction bars (4-T.5)
    - Understand fractions: area models (4-T.6)
  - 4.A.U.B.7 Compares a fraction to 0, 1/2 or 1
    - Compare fractions using ½ as a benchmark (4-V.6)
  - 4.A.U.B.8 Verifies whether two fractions are equivalent
    - Identify equivalent fractions on number lines (4-U.2)
    - Graph equivalent fractions on number lines (4-U.4)
  - 4.A.U.B.9 Matches a decimal or percentage to a fraction
  - 4.A.U.B.10 Orders fractions with the same denominator
    - Order fractions with like denominators (4-V.12)
- 4.A.U.C Decimals up to hundreths
  - 4.A.U.C.1 Represents decimals in a variety of ways (using objects or drawings)
  - 4.A.U.C.2 Identifies equivalent representations (using objects or drawings)
  - 4.A.U.C.3 Reads and writes numbers written in decimal notation
    - Understanding decimals expressed in words: up to tenths (4-W.2)
    - Understanding decimals expressed in words: up to hundredths (4-X.3)
  - 4.A.U.C.4 Understands the role of the decimal point
  - 4.A.U.C.5 Composes and decomposes a decimal written in decimal notation
    - Convert decimals between standard and expanded form using fractions: up to tenths (4-W.9)
    - Convert decimals between standard and expanded form using fractions: up to hundredths (4-X.13)
  - 4.A.U.C.6 Recognizes equivalent expressions (e.g. 12 tenths is equivalent to 1 unit and 2 tenths; 0.5 is equivalent to 0.50)
    - Equivalent decimals: up to hundredths (4-X.6)
  - 4.A.U.C.7 Locates decimals on a number line
    - 4.A.U.C.7.a between two consecutive natural numbers
      - Decimal number lines: up to tenths (4-W.5)
      - Decimal number lines: up to hundredths (4-X.8)
    - 4.A.U.C.7.b between two decimals
      - Graph decimals on number lines: up to tenths (4-W.4)
      - Graph decimals on number lines: up to hundredths (4-X.7)
  - 4.A.U.C.8 Compares two decimals
  - 4.A.U.C.9 Approximates (e.g. estimates, rounds to a given value, truncates decimal places)
    - Put decimal numbers in order: up to tenths (4-W.12)
    - Round decimals: up to hundredths (4-X.14)
  - 4.A.U.C.10 Arranges decimals in increasing or decreasing order
  - 4.A.U.C.11 Matches
    - 4.A.U.C.11.a a fraction to its decimal
- 4.A.U.D Integers
  - 4.A.U.D.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)
    - Understanding integers (4-A.14)
4.A.M Meaning of operations involving numbers
- 4.A.M.A Natural numbers less than 100 000
  - 4.A.M.A.1 Determines the operation(s) to perform in a given situation
  - 4.A.M.A.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 addition and subtraction)
    - 4.A.M.A.2.a transformation (adding, taking away), uniting, comparing
    - 4.A.M.A.2.b composition of transformations: positive, negative
  - 4.A.M.A.3 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)
    - 4.A.M.A.3.b 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)
  - 4.A.M.A.4 Establishes equality relations between numerical expressions (e.g. 3 + 2 = 6 - 1)
  - 4.A.M.A.5 Determines numerical equivalencies using relationships between
    - 4.A.M.A.5.b operations (the four operations), the commutative property of addition and multiplication and the associative property
- 4.A.M.B Decimals up to hundreths
  - 4.A.M.B.1 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)
    - 4.A.M.B.1.a transformation (adding, taking away), uniting, comparing
    - 4.A.M.B.1.b composition of transformations: positive, negative
  - 4.A.M.B.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)
  - 4.A.M.B.3 Determines numerical equivalencies
    - 4.A.M.B.3.a using the relationship between operations (addition and subtraction), the commutative property of addition and the associative property
      - Choose decimals with a particular sum or difference: up to tenths (4-Y.4)
      - Choose decimals with a particular sum or difference: up to hundredths (4-Z.4)
4.A.O Operations involving numbers
- 4.A.O.A Natural numbers
  - 4.A.O.A.1 Approximates the result of
    - 4.A.O.A.1.b any of the four operations involving natural numbers
  - 4.A.O.A.2 Builds a repertoire of memorized addition and subtraction facts
  - 4.A.O.A.3 Develops processes for mental computation
    - 4.A.O.A.3.b Uses his/her own processes to determine the product or quotient of two natural numbers
  - 4.A.O.A.4 Develops processes for written computation (addition and subtraction)
    - 4.A.O.A.4.b Uses conventional processes to determine the sum of two natural numbers of up to four digits
    - 4.A.O.A.4.c Uses conventional processes to determine the difference between two natural numbers of up to four digits whose result is greater than 0
  - 4.A.O.A.6 Builds a repertoire of memorized multiplication and division facts
    - 4.A.O.A.6.a Builds a memory of multiplication facts (0 × 0 to 10 × 10) and the corresponding division facts, using objects, drawings, charts or tables
    - 4.A.O.A.6.b Develops various strategies that promote mastery of number facts and relate them to the properties of multiplication
      - Properties of multiplication (4-E.21)
    - 4.A.O.A.6.c Masters all multiplication facts (0 × 0 to 10 × 10) and the corresponding division facts
      - Multiplication facts up to 10 (4-E.1)
      - Division facts up to 10 (4-H.1)
  - 4.A.O.A.7 Develops processes for written computation (multiplication and division)
    - 4.A.O.A.7.a Uses his/her own processes as well as materials and drawings to determine the product or quotient of a three-digit natural number and a one-digit natural number, expresses the remainder of a division as a fraction, depending on the context
  - 4.A.O.A.8 Determines the missing term in an equation (relationships between operations): a × b = __, a × __ = c, __ × b = c, a ÷ b = __, a ÷ __ = c,__ ÷ b = c
  - 4.A.O.A.9 Decomposes a number into prime factors
    - Prime factorization (4-E.7)
  - 4.A.O.A.13 Using his/her own words and mathematical language that is at an appropriate level for the cycle, describes
    - 4.A.O.A.13.c series of numbers and family of operations
  - 4.A.O.A.14 Adds new terms to a series when the first three terms or more are given
  - 4.A.O.A.15 Uses a calculator and
    - 4.A.O.A.15.b becomes familiar with its × and ÷ functions
- 4.A.O.B Fractions (using objects or diagrams)
  - 4.A.O.B.1 Generates a set of equivalent fractions
- 4.A.O.C Decimals
  - 4.A.O.C.1 Approximates the result of
    - 4.A.O.C.1.a an addition or a subtraction
      - Estimate sums and differences of decimals: up to tenths (4-Y.9)
      - Estimate sums and differences of decimals: up to hundredths (4-Z.9)
  - 4.A.O.C.2 Develops processes for mental computation
    - 4.A.O.C.2.a adds and subtracts decimals
      - Choose decimals with a particular sum or difference: up to tenths (4-Y.4)
      - Choose decimals with a particular sum or difference: up to hundredths (4-Z.4)
  - 4.A.O.C.3 Develops processes for written computation
    - 4.A.O.C.3a adds and subtracts decimals whose result does not go beyond the second decimal place
- 4.A.O.D Using Numbers

4.G Geometry

4.G.A Space
- 4.G.A.2 Locates objects in a plane
  - Objects on a coordinate plane (4-M.1)
- 4.G.A.3 Locates objects on an axis (based on the types of numbers studied)
- 4.G.A.4 Locates points in a Cartesian plane
  - 4.G.A.4.a in the first quadrant
4.G.B Solids
- 4.G.B.5 Describes prisms and pyramids in terms of faces, vertices and edges
  - Identify three-dimensional figures (4-R.2)
  - Count vertices, edges and faces (4-R.3)
- 4.G.B.6 Classifies prisms and pyramids
  - Which three-dimensional figure is being described? (4-R.5)
- 4.G.B.7 Constructs a net of a prism or pyramid
- 4.G.B.8 Matches the net of
  - 4.G.B.8.a a prism to the corresponding prism and vice versa
    - Nets of three-dimensional figures (4-R.6)
  - 4.G.B.8.b a pyramid to the corresponding pyramid and vice versa
    - Nets of three-dimensional figures (4-R.6)
4.G.C Plane figures
- 4.G.C.4 Describes convex and nonconvex polygons
  - Is it a polygon? (4-R.7)
- 4.G.C.5 Identifies and constructs parallel lines and perpendicular lines
  - Parallel, perpendicular and intersecting lines (4-R.11)
- 4.G.C.6 Describes quadrilaterals (e.g. parallel segments, perpendicular segments, right angles, acute angles, obtuse angles)
  - Parallel sides in quadrilaterals (4-R.16)
- 4.G.C.7 Classifies quadrilaterals
4.G.D Frieze patterns and tessellations
- 4.G.D.2 Observes and produces patterns using geometric figures
- 4.G.D.3 Observes and produces frieze patterns and tessellations
  - 4.G.D.3.a using reflections
    - Reflection, rotation and translation (4-R.25)

4.M Measurement

4.M.A Lengths
- 4.M.A.4 Estimates and measures the dimensions of an object using conventional units
  - 4.M.A.4.b metre, decimetre, centimetre and millimetre
    - Measure using a centimetre ruler (4-P.3)
    - Which unit of length is appropriate? (4-P.4)
- 4.M.A.5 Establishes relationships between units of measure for length
  - 4.M.A.5.a metre, decimetre, centimetre and millimetre
    - Compare units of length (4-P.5)
    - Convert units of length (4-P.6)
- 4.M.A.6 Calculates the perimeter of plane figures
4.M.B Surface areas
- 4.M.B.1 Estimates and measures surface area
  - 4.M.B.1.a using unconventional units
4.M.C Volumes
- 4.M.C.1 Estimates and measures volume
  - 4.M.C.1.a using unconventional units
    - Volume (4-S.16)
4.M.D Angles
- 4.M.D.1 Compares angles
  - Acute, right, obtuse and straight angles (4-R.12)
4.M.E Capacities
- 4.M.E.1 Estimates and measures capacity using unconventional units
- 4.M.E.2 Estimates and measures capacity using conventional units
  - Which unit of volume is appropriate? (4-P.10)
4.M.F Masses
- 4.M.F.1 Estimates and measures mass using unconventional units
- 4.M.F.2 Estimates and measures mass using conventional units
  - Which unit of mass is appropriate? (4-P.7)
4.M.G Time
- 4.M.G.1 Estimates and measures time using conventional units
- 4.M.G.2 Establishes relationships between units of measure
4.M.H Temperatures
- 4.M.H.1 Estimates and measures temperature using conventional units
  - Read a thermometer (4-P.1)
  - Reasonable temperature (4-P.2)

4.S Statistics

4.S.1 Formulates questions for a survey (based on age-appropriate topics, students' language level, etc.)
4.S.2 Collects, describes and organizes data (classifies or categorizes) using tables
- Read a table (4-N.1)
4.S.3 Interprets data using
- 4.S.3.b a table, a bar graph, a pictograph and a broken-line graph
4.S.4 Displays data using
- 4.S.4.b a table, a bar graph, a pictograph and a broken-line graph

4.P Probability

4.P.1 When applicable, recognizes variability in possible outcomes (uncertainty)
4.P.2 When applicable, recognizes equiprobability (e.g. quantity, symmetry of an object [cube])
- Make predictions (4-AA.4)
4.P.3 When applicable, becomes aware of the independence of events in an experiment
4.P.4 Experiments with activities involving chance, using various objects (e.g. spinners, rectangular prisms, glasses, marbles, thumb tacks, 6-, 8- or 12-sided dice)
- Understanding probability (4-AA.2)
4.P.5 Predicts qualitatively an outcome or several events using a probability line, among other things
- 4.P.5.a certain, possible or impossible outcome
  - Certain, probable, unlikely and impossible (4-AA.1)
- 4.P.5.b more likely, just as likely, less likely event
  - Certain, probable, unlikely and impossible (4-AA.1)
4.P.6 Distinguishes between prediction and outcome
- Make predictions (4-AA.4)
4.P.7 Uses tables or diagrams to collect and display the outcomes of an experiment
4.P.8 Enumerates possible outcomes of
- 4.P.8.b a random experiment, using a table, a tree diagram
  - Make predictions (4-AA.4)
4.P.9 Compares qualitatively the theoretical or experimental probability of events
4.P.13 Simulates random experiments with or without the use of technology

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4.A Arithmetic

4.A.U Understanding and writing numbers

4.A.U.A Natural numbers less than 100 000

4.A.U.A.1 Counts or recites counting rhymes involving natural numbers

4.A.U.A.1.b counts forward or backward

4.A.U.A.1.c skip counts (e.g. by twos)

4.A.U.A.2 Counts collections (using objects or drawings)

4.A.U.A.2.c counts a collection by grouping or regrouping

4.A.U.A.2.d counts a pre-grouped collection

4.A.U.A.3 Reads and writes any natural number

4.A.U.A.4.b emphasis on exchanging apparent, non-accessible groupings, using structured materials (e.g. base ten blocks, number tables)

4.A.U.A.4.c emphasis on place value in non-apparent, non-accessible groupings, using materials for which groupings are symbolic (e.g. abacus, money)

4.A.U.A.5 Composes and decomposes a natural number in a variety of ways (e.g. 123 = 100 + 23, 123 = 100 + 20 + 3, 123 = 50 + 50 + 20 + 3, 123 = 2 × 50 + 30 - 7, 123 = 2 × 60 + 3)

4.A.U.A.6 Identifies equivalent expressions (e.g. 52 = 40 + 12, 25 + 27 = 40 + 12, 52 = 104 ÷ 2)

4.A.U.A.7 Compares natural numbers

4.A.U.A.8 Arranges natural numbers in increasing or decreasing order

4.A.U.A.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.A.U.A.10 Locates natural numbers using different visual aids (e.g. hundreds chart, number strip, number line)

4.A.U.A.11 Identifies properties of natural numbers

4.A.U.A.11.b square, prime or composite numbers

4.A.U.A.12 Classifies natural numbers in various ways, based on their properties (e.g. even numbers, composite numbers)

4.A.U.A.13 Approximates a collection, using objects or drawings (e.g. estimate, round up/down to a given value)

4.A.U.B Fractions (using objects or drawings)

4.A.U.B.2 Represents a fraction in a variety of ways, based on a whole or a collection of objects

4.A.U.B.3 Matches a fraction to part of a whole (congruent or equivalent parts) or part of a group of objects, and vice versa

4.A.U.B.4 Identifies the different meanings of fractions (sharing, division, ratio)

4.A.U.B.5 Distinguishes a numerator from a denominator

4.A.U.B.6 Reads and writes a fraction

4.A.U.B.7 Compares a fraction to 0, 1/2 or 1

4.A.U.B.8 Verifies whether two fractions are equivalent

4.A.U.B.9 Matches a decimal or percentage to a fraction

4.A.U.B.10 Orders fractions with the same denominator

4.A.U.C Decimals up to hundreths

4.A.U.C.1 Represents decimals in a variety of ways (using objects or drawings)

4.A.U.C.2 Identifies equivalent representations (using objects or drawings)

4.A.U.C.3 Reads and writes numbers written in decimal notation

4.A.U.C.4 Understands the role of the decimal point

4.A.U.C.5 Composes and decomposes a decimal written in decimal notation

4.A.U.C.6 Recognizes equivalent expressions (e.g. 12 tenths is equivalent to 1 unit and 2 tenths; 0.5 is equivalent to 0.50)

4.A.U.C.7 Locates decimals on a number line

4.A.U.C.7.a between two consecutive natural numbers

4.A.U.C.7.b between two decimals

4.A.U.C.8 Compares two decimals

4.A.U.C.9 Approximates (e.g. estimates, rounds to a given value, truncates decimal places)

4.A.U.C.10 Arranges decimals in increasing or decreasing order

4.A.U.C.11 Matches

4.A.U.C.11.a a fraction to its decimal

4.A.U.D Integers

4.A.U.D.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.A.M Meaning of operations involving numbers

4.A.M.A Natural numbers less than 100 000

4.A.M.A.1 Determines the operation(s) to perform in a given situation

4.A.M.A.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 addition and subtraction)

4.A.M.A.2.a transformation (adding, taking away), uniting, comparing

4.A.M.A.2.b composition of transformations: positive, negative

4.A.M.A.3 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)

4.A.M.A.3.b 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)

4.A.M.A.4 Establishes equality relations between numerical expressions (e.g. 3 + 2 = 6 - 1)

4.A.M.A.5 Determines numerical equivalencies using relationships between

4.A.M.A.5.b operations (the four operations), the commutative property of addition and multiplication and the associative property

4.A.M.B Decimals up to hundreths

4.A.M.B.1 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)

4.A.M.B.1.a transformation (adding, taking away), uniting, comparing

4.A.M.B.1.b composition of transformations: positive, negative

4.A.M.B.3 Determines numerical equivalencies

4.A.M.B.3.a using the relationship between operations (addition and subtraction), the commutative property of addition and the associative property

4.A.O Operations involving numbers

4.A.O.A Natural numbers

4.A.O.A.1 Approximates the result of

4.A.O.A.1.b any of the four operations involving natural numbers

4.A.O.A.2 Builds a repertoire of memorized addition and subtraction facts

4.A.O.A.3 Develops processes for mental computation

4.A.O.A.3.b Uses his/her own processes to determine the product or quotient of two natural numbers

4.A.O.A.4 Develops processes for written computation (addition and subtraction)

4.A.O.A.4.b Uses conventional processes to determine the sum of two natural numbers of up to four digits

4.A.O.A.4.c Uses conventional processes to determine the difference between two natural numbers of up to four digits whose result is greater than 0

4.A.O.A.6 Builds a repertoire of memorized multiplication and division facts

4.A.O.A.8 Determines the missing term in an equation (relationships between operations): a × b = , a × = c, × b = c, a ÷ b = , a ÷ = c, ÷ b = c