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Skills available for Louisiana fifth-grade math standards

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Louisiana Student Standards (adopted in 2025): Grade 5 Louisiana Student Standards (adopted in 2025): Grade 5
Louisiana Student Standards: Grade 5 Louisiana Student Standards: Grade 5
Louisiana Student Standards: Mathematical Practices Louisiana Student Standards: Mathematical Practices

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5.NOF Numeracy & Operational Fluency

5.NOF.A Use equivalent fractions as a strategy to add and subtract fractions.
- 5.NOF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers and fractions greater than 1) by replacing given fractions with equivalent fractions to produce an equivalent equation with fractions that have like denominators.
- 5.NOF.A.2 Solve real-world mathematical tasks involving addition and subtraction of fractions.
  - 5.NOF.A.2a Add and subtract fractions referring to the same whole, including cases of unlike denominators.
  - 5.NOF.A.2b Use benchmark fractions and number sense of fractions to estimate mentally and justify the reasonableness of answers.
    - Estimate sums and differences of fractions using benchmarks (5-L.1)
    - Estimate sums and differences of mixed numbers (5-M.1)
5.NOF.B Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
- 5.NOF.B.3 Interpret a fraction as division of the numerator by the denominator (^a/_b = a ÷ b). Solve real-world mathematical tasks involving division of whole numbers in the form of fractions to include fractions greater than one or mixed numbers.
  - Relate division and fractions (5-T.1)
  - Understand fractions as division: word problems (5-T.2)
- 5.NOF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
  - 5.NOF.B.4a Interpret the product (^m/_n) × q as m parts of a partition of q into n equal parts; equivalently, as the result of a sequence of operations, m × q ÷ n.
  - 5.NOF.B.4b Construct or critique a precise model to develop understanding of the concept of multiplying two fractions and create a story context for the equation. In general, (^m/_n) × (^c/_d) = ^(mc)/_(nd).
- 5.NOF.B.5 Interpret multiplication as scaling (resizing) by:
  - 5.NOF.B.5a Comparing the size of a product to the size of one factor based on the size of the other factor, without performing the indicated multiplication.
  - 5.NOF.B.5b Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case).
    - Scaling whole numbers by fractions: justify your answer (5-S.1)
  - 5.NOF.B.5c Explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number.
    - Scaling whole numbers by fractions: justify your answer (5-S.1)
  - 5.NOF.B.5d Relating the principle of fraction equivalence.
- 5.NOF.B.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions in the context of real-world mathematical tasks.
  - 5.NOF.B.7a Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.
  - 5.NOF.B.7b Interpret division of a whole number by a unit fraction, and compute such quotients.
5.NOF.C Understand the place value system.
- 5.NOF.C.8 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and ¹/₁₀ of what it represents in the place to its left.
- 5.NOF.C.9 Use place value understanding to:
  - 5.NOF.C.9a Round multi-digit numbers with decimals to any place; and
    - Round decimals (5-W.9)
  - 5.NOF.C.9b Use compatible numbers to estimate solutions to real-world mathematical tasks.
5.NOF.D Multiply multi-digit numbers.
- 5.NOF.D.10 Fluently multiply multi-digit whole numbers using a standard algorithm.

5.AR Algebraic Reasoning

5.AR.A Write and interpret numerical expressions.
- 5.AR.A.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols, attending to the order of operations and the properties of operations.
  - Evaluate numerical expressions (5-H.3)
  - Evaluate numerical expressions with parentheses (5-H.4)
  - Identify mistakes involving the order of operations (5-H.6)
  - Evaluate numerical expressions with parentheses in different places (5-H.7)
  - Evaluate numerical expressions with fractions (5-H.8)
  - Use numerical expressions to solve multi-step word problems (5-I.2)
  - 5.AR.A.1a Compare two simple expressions using >, =, or < to record the comparison of expressions limited to three operations and one grouping symbol.
    - Comparison statements with numerical expressions (5-H.10)
- 5.AR.A.2 Write simple expressions that record calculations with whole numbers, fractions, and decimals, and interpret numerical expressions without evaluating them.
5.AR.B Compare whole numbers.
- 5.AR.B.3 Generate and extend two numerical patterns using two given rules. Identify apparent relationships between corresponding terms.
  - Compare patterns (5-KK.2)
  - Complete a table for a two-variable relationship (5-MM.6)
  - Complete a table from a graph (5-MM.7)
  - 5.AR.B.3a Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.
    - Use a rule to complete a table and a graph (5-LL.6)
    - Graph a two-variable relationship (5-MM.9)
  - 5.AR.B.3b Explain these relationships informally.
5.AR.C Use place value understanding to apply patterns beyond whole numbers.
- 5.AR.C.4 Construct a written explanation and apply patterns in the number of zeros of the product when multiplying a number by powers of 10.
  - Multiply a whole number by a power of ten (5-D.4)
  - Divide by a power of ten with decimals: find the missing number (5-EE.5)
  - 5.AR.C.4a Explain and apply patterns in the values of the digits in the product or the quotient when a decimal is multiplied or divided by a power of 10.
  - 5.AR.C.4b Use whole-number exponents to denote powers of 10.
- 5.AR.C.5 Using understanding of the base-ten system:
  - 5.AR.C.5a Read and write decimals to thousandths using base-ten numerals/standard form, written form (number names), unit form, and expanded form.
  - 5.AR.C.5b Compare and order multi-digit whole numbers and decimals to thousandths based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons.
5.AR.D Perform operations with multi-digit whole numbers with decimals to hundredths.
- 5.AR.D.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value understanding, the properties of operations, subtracting multiples of the divisor, and/or the relationship between multiplication and division.
  - Divide numbers ending in zeros (5-E.2)
  - Divide numbers ending in zeros: word problems (5-E.3)
  - Divide by 2-digit numbers using partial quotients (5-E.11)
  - Divide 2-digit and 3-digit numbers by 2-digit numbers (5-E.12)
  - Divide 2-digit and 3-digit numbers by 2-digit numbers: word problems (5-E.13)
  - Divide 4-digit numbers by 2-digit numbers (5-E.14)
  - Divide 4-digit numbers by 2-digit numbers: word problems (5-E.15)
  - Adjust quotients (5-E.16)
  - Relate multiplication and division (5-E.17)
  - Choose numbers with a particular quotient (5-E.19)
  - Multi-step word problems: multiplicative comparison (5-I.8)
  - 5.AR.D.6a Illustrate and/or explain the calculation by using equations, rectangular arrays, area models, or other strategies based on place value understanding.
    - Divide by 2-digit numbers using models (5-E.10)
- 5.AR.D.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value understanding, properties of operations, and/or the part-whole relationship between addition and subtraction or multiplication and division.

5.GL Geometric Reasoning & Logic

5.GL.A Generate and analyze patterns.
- 5.GL.A.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates: Understand that in an ordered pair, the first number shows how far to move along the x-axis, and the second number shows how far to move along the y-axis from the origin.
  - Describe the coordinate plane (5-LL.1)
  - Objects on a coordinate plane (5-LL.2)
- 5.GL.A.2 Represent real-world mathematical tasks by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
5.GL.B Classify two-dimensional figures into categories based on their properties.
- 5.GL.B.3 Analyze and relate attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.
  - Identify the relationships between quadrilaterals (5-QQ.9)
  - Describe relationships among quadrilaterals (5-QQ.10)
- 5.GL.B.4 Classify quadrilaterals in a hierarchy based on properties.
  - Classify triangles (5-PP.3)
  - Classify quadrilaterals (5-QQ.6)
  - Pick all the names for a quadrilateral (5-QQ.7)
  - Sort polygons into Venn diagrams (5-RR.4)
  - 5.GL.B.4a Justify the reasoning for classification with a written response.

5.DM Data Analysis & Measurement

5.DM.A Convert like measurement units within a given measurement system.
- 5.DM.A.1 Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step, real-world mathematical tasks involving: distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving whole numbers, decimals, and fractions.
5.DM.B Compare whole numbers.
- 5.DM.B.2 Make a line plot to display a data set of measurements in fractions of a unit (¹/₂, ¹/₄, ¹/₈): Use operations on fractions, excluding dividing fractions by fractions, to solve real-world mathematical tasks involving information presented in line plots.
  - Create and interpret line plots with fractions (5-NN.4)
  - Interpret line plots with fractions: multi-step problems (5-NN.5)
5.DM.C Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
- 5.DM.C.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
  - 5.DM.C.3a A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.
    - Volume of rectangular prisms made of unit cubes (5-UU.3)
  - 5.DM.C.3b A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
    - Volume of rectangular prisms made of unit cubes (5-UU.3)
- 5.DM.C.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
  - Volume of rectangular prisms made of unit cubes (5-UU.3)
- 5.DM.C.5 Relate volume to the operations of multiplication and addition and solve real-world mathematical tasks involving volume.
  - 5.DM.C.5a Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and connect that the volume is the same as multiplying the edge lengths, also by multiplying the height by the area of the base: Represent threefold whole-number products as volumes.
    - Volume of rectangular prisms made of unit cubes: expressions (5-UU.2)
    - Volume of rectangular prisms made of unit cubes: word problems (5-UU.4)
  - 5.DM.C.5b Apply the formulas V = l × w × h and V = B × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world mathematical tasks.
  - 5.DM.C.5c Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world mathematical tasks.
    - Volume of compound figures (5-UU.9)
5.DM.D Geometric measurement: extend previous understandings of area and multiplication to multiply fractions.
- 5.DM.D.6 Apply and extend previous understandings of area and multiplication to multiply a fraction or whole number by a fraction.
  - 5.DM.D.6a Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths.
    - Understand fraction multiplication and area (5-P.6)
  - 5.DM.D.6b Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
  - 5.DM.D.6c Compose and decompose rectangular regions to calculate area.
    - Area of compound figures (5-TT.4)
    - Area of figures on grids (5-TT.6)

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5.NOF Numeracy & Operational Fluency

5.NOF.A Use equivalent fractions as a strategy to add and subtract fractions.

5.NOF.A.1 Add and subtract fractions with unlike denominators (including mixed numbers and fractions greater than 1) by replacing given fractions with equivalent fractions to produce an equivalent equation with fractions that have like denominators.

5.NOF.A.2 Solve real-world mathematical tasks involving addition and subtraction of fractions.

5.NOF.A.2a Add and subtract fractions referring to the same whole, including cases of unlike denominators.

5.NOF.A.2b Use benchmark fractions and number sense of fractions to estimate mentally and justify the reasonableness of answers.

5.NOF.B Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

5.NOF.B.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve real-world mathematical tasks involving division of whole numbers in the form of fractions to include fractions greater than one or mixed numbers.

5.NOF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

5.NOF.B.4a Interpret the product (m/n) × q as m parts of a partition of q into n equal parts; equivalently, as the result of a sequence of operations, m × q ÷ n.

5.NOF.B.4b Construct or critique a precise model to develop understanding of the concept of multiplying two fractions and create a story context for the equation. In general, (m/n) × (c/d) = (mc)/(nd).

5.NOF.B.5 Interpret multiplication as scaling (resizing) by:

5.NOF.B.5a Comparing the size of a product to the size of one factor based on the size of the other factor, without performing the indicated multiplication.

5.NOF.B.5b Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case).

5.NOF.B.5c Explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number.

5.NOF.B.5d Relating the principle of fraction equivalence.

5.NOF.B.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions in the context of real-world mathematical tasks.

5.NOF.B.7a Interpret division of a unit fraction by a non-zero whole number, and compute such quotients.

5.NOF.B.7b Interpret division of a whole number by a unit fraction, and compute such quotients.

5.NOF.C Understand the place value system.

5.NOF.C.8 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

5.NOF.C.9 Use place value understanding to:

5.NOF.C.9a Round multi-digit numbers with decimals to any place; and

5.NOF.C.9b Use compatible numbers to estimate solutions to real-world mathematical tasks.

5.NOF.D Multiply multi-digit numbers.

5.NOF.D.10 Fluently multiply multi-digit whole numbers using a standard algorithm.

5.AR Algebraic Reasoning

5.AR.A Write and interpret numerical expressions.

5.AR.A.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols, attending to the order of operations and the properties of operations.

5.AR.A.1a Compare two simple expressions using >, =, or < to record the comparison of expressions limited to three operations and one grouping symbol.

5.AR.A.2 Write simple expressions that record calculations with whole numbers, fractions, and decimals, and interpret numerical expressions without evaluating them.

5.AR.B Compare whole numbers.

5.AR.B.3 Generate and extend two numerical patterns using two given rules. Identify apparent relationships between corresponding terms.

5.AR.B.3a Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.

5.AR.B.3b Explain these relationships informally.

5.AR.C Use place value understanding to apply patterns beyond whole numbers.

5.AR.C.4 Construct a written explanation and apply patterns in the number of zeros of the product when multiplying a number by powers of 10.

5.AR.C.4a Explain and apply patterns in the values of the digits in the product or the quotient when a decimal is multiplied or divided by a power of 10.

5.AR.C.4b Use whole-number exponents to denote powers of 10.

5.AR.C.5 Using understanding of the base-ten system:

5.AR.C.5a Read and write decimals to thousandths using base-ten numerals/standard form, written form (number names), unit form, and expanded form.

5.AR.C.5b Compare and order multi-digit whole numbers and decimals to thousandths based on the values of the digits in each place, using >, =, and < symbols to record the results of comparisons.

5.AR.D Perform operations with multi-digit whole numbers with decimals to hundredths.

5.AR.D.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value understanding, the properties of operations, subtracting multiples of the divisor, and/or the relationship between multiplication and division.

5.AR.D.6a Illustrate and/or explain the calculation by using equations, rectangular arrays, area models, or other strategies based on place value understanding.

5.AR.D.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value understanding, properties of operations, and/or the part-whole relationship between addition and subtraction or multiplication and division.

5.AR.D.7a Justify the reasoning of methods used for calculation with a written explanation.

5.GL Geometric Reasoning & Logic

5.GL.A Generate and analyze patterns.

5.GL.A.2 Represent real-world mathematical tasks by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

5.GL.B Classify two-dimensional figures into categories based on their properties.

5.GL.B.3 Analyze and relate attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

5.GL.B.4 Classify quadrilaterals in a hierarchy based on properties.

5.GL.B.4a Justify the reasoning for classification with a written response.

5.DM Data Analysis & Measurement

5.DM.A Convert like measurement units within a given measurement system.

5.DM.B Compare whole numbers.

5.DM.B.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8): Use operations on fractions, excluding dividing fractions by fractions, to solve real-world mathematical tasks involving information presented in line plots.

5.DM.C Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

5.DM.C.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

5.DM.C.3a A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.

5.DM.C.3b A solid figure that can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

5.DM.C.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

5.DM.C.5 Relate volume to the operations of multiplication and addition and solve real-world mathematical tasks involving volume.

5.DM.C.5a Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and connect that the volume is the same as multiplying the edge lengths, also by multiplying the height by the area of the base: Represent threefold whole-number products as volumes.

5.DM.C.5b Apply the formulas V = l × w × h and V = B × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world mathematical tasks.

5.DM.C.5c Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real-world mathematical tasks.

5.DM.D Geometric measurement: extend previous understandings of area and multiplication to multiply fractions.

5.DM.D.6 Apply and extend previous understandings of area and multiplication to multiply a fraction or whole number by a fraction.

5.DM.D.6a Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths.

5.DM.D.6b Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

5.DM.D.6c Compose and decompose rectangular regions to calculate area.

5.NOF.B.3 Interpret a fraction as division of the numerator by the denominator (^a/_b = a ÷ b). Solve real-world mathematical tasks involving division of whole numbers in the form of fractions to include fractions greater than one or mixed numbers.

5.NOF.B.4a Interpret the product (^m/_n) × q as m parts of a partition of q into n equal parts; equivalently, as the result of a sequence of operations, m × q ÷ n.

5.NOF.B.4b Construct or critique a precise model to develop understanding of the concept of multiplying two fractions and create a story context for the equation. In general, (^m/_n) × (^c/_d) = ^(mc)/_(nd).

5.NOF.C.8 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and ¹/₁₀ of what it represents in the place to its left.

5.DM.B.2 Make a line plot to display a data set of measurements in fractions of a unit (¹/₂, ¹/₄, ¹/₈): Use operations on fractions, excluding dividing fractions by fractions, to solve real-world mathematical tasks involving information presented in line plots.