The Common Core in Maryland

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Skills available for Maryland fifth-grade math standards

Standards are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practice that skill.

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Maryland College and Career Ready Standards (adopted in 2025): Grade 5 Maryland College and Career Ready Standards (adopted in 2025): Grade 5
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Maryland College and Career-Ready Standards: Grade 5 Maryland College and Career-Ready Standards: Grade 5
Maryland College and Career-Ready Standards: Mathematical Practices Maryland College and Career-Ready Standards: Mathematical Practices

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5.NOS Number and Operation Sense

5.NOS.A Understand the place value system.
- 5.NOS.A.1 Explain 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.NOS.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10.
- 5.NOS.A.3 Read, write, and compare decimals to thousandths.
  - 5.NOS.A.3.a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.
  - 5.NOS.A.3.b Estimate decimal quantities by reasoning about their location on a number line, their relationship to benchmark numbers, and rounding to any place.
    - Round decimals (5-W.9)
    - Decimal number lines (5-W.10)
  - 5.NOS.A.3.c Compare two decimals to thousandths by reasoning about the values of the digits and the location on the number line. Record the results of comparisons with the symbols >, =, <.
5.NOS.B Perform operations on multi-digit whole numbers and with decimals to hundredths.
- 5.NOS.B.4 Fluently multiply multi-digit whole numbers.
  - 5.NOS.B.4.a Apply estimation strategies to estimate products.
    - Estimate products (5-D.5)
    - Estimate products: word problems (5-D.6)
  - 5.NOS.B.4.b Use computational strategies efficiently to multiply.
  - 5.NOS.B.4.c Use a standard algorithm to multiply.
  - 5.NOS.B.4.d Determine and explain when a strategy or algorithm is most efficient.
- 5.NOS.B.5 Divide multi-digit whole numbers with up to four-digit dividends and two-digit divisors.
  - 5.NOS.B.5.a Apply estimation strategies to estimate quotients.
    - Estimate quotients: 2-digit divisors (5-E.4)
    - Estimate quotients (5-E.5)
  - 5.NOS.B.5.b Use partial quotients efficiently to divide.
    - Divide by 2-digit numbers using partial quotients (5-E.11)
  - 5.NOS.B.5.c Use properties of operations and/or the inverse relationship between multiplication and division to divide.
  - 5.NOS.B.5.d Represent and explain the computation by connecting rectangular arrays, area models, and/or equations to the meaning of division.
- 5.NOS.B.6 Apply and extend previous understanding of addition and subtraction of whole numbers to add and subtract decimals to hundredths.
  - 5.NOS.B.6.a Apply estimation strategies to estimate sums and differences of decimals.
    - Estimate sums and differences of decimals using rounding (5-AA.13)
  - 5.NOS.B.6.b Use concrete models, drawings, strategies based on place value, properties of operations, and/or the inverse relationship between addition and subtraction to add and subtract decimals in context.
  - 5.NOS.B.6.c Use an algorithm to add and subtract decimals.
  - 5.NOS.B.6.d Determine and explain when a strategy or algorithm is or is not needed.
- 5.NOS.B.7 Apply and extend previous understanding of multiplication and division of whole numbers to multiply and divide decimals to hundredths in context.
  - Multiply a decimal by a one-digit whole number (5-CC.5)
  - Multiply a decimal by a multi-digit whole number (5-CC.7)
  - Multiply decimals and whole numbers: word problems (5-CC.8)
  - Multiply three or more numbers, one of which is a decimal (5-CC.9)
  - Multiply two decimals: where does the decimal point go? (5-DD.4)
  - Multiply two decimals: products up to hundredths (5-DD.6)
  - Multiply two decimals: products up to thousandths (5-DD.7)
  - Division with decimal quotients (5-FF.6)
  - Division with decimal quotients and rounding (5-FF.7)
  - Division with decimal quotients: word problems (5-FF.8)
  - Divide by decimals (5-FF.11)
  - Multiply money amounts: word problems (5-HH.5)
  - Divide money amounts: word problems (5-HH.8)
  - 5.NOS.B.7.a Apply estimation strategies to estimate products and quotients.
    - Estimate products of decimals (5-DD.1)
    - Estimate decimal quotients (5-FF.1)
  - 5.NOS.B.7.b Use concrete models, drawings, and arrays to multiply and divide.
  - 5.NOS.B.7.c Use strategies based on place value to multiply and divide.
  - 5.NOS.B.7.d Use properties of operations and/or the inverse relationship between multiplication and division to multiply and divide.
    - Multiply a decimal by a one-digit whole number using the distributive property (5-CC.4)
  - 5.NOS.B.7.e Represent and explain the computation by connecting concrete models, drawings, and/or equations to the meaning of multiplication and division.
5.NOS.C Use equivalent fractions as a strategy to add and subtract fractions.
- 5.NOS.C.8 Add and subtract fractions with unlike denominators.
  - 5.NOS.C.8.a Estimate sums and differences by reasoning about benchmark numbers and assess 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.NOS.C.8.b Apply and extend whole number addition and subtraction strategies to add and subtract fractions.
    - Complete addition and subtraction sentences with fractions (5-L.10)
    - Complete addition and subtraction sentences with mixed numbers (5-M.9)
  - 5.NOS.C.8.c Use equivalent fractions to produce an equivalent sum or difference of fractions with like denominators.
- 5.NOS.C.9 Solve problems in context involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators using visual fraction models and/or equations to represent the problem.
5.NOS.D Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
- 5.NOS.D.10 Interpret a fraction as division of the numerator by the denominator (^a/_b = a ÷ b) in context using visual fraction models and equations to represent the problem.
- 5.NOS.D.11 Apply and extend previous understandings of multiplication to multiply a whole number by a fraction (^c/_d × b).
  - 5.NOS.D.11.a Estimate products by reasoning about benchmark numbers and assess reasonableness of answers.
    - Estimate products of fractions and whole numbers (5)
    - Estimate products of mixed numbers and whole numbers (5)
  - 5.NOS.D.11.b Multiply a whole number by a fraction.
- 5.NOS.D.12 Apply and extend previous understandings of multiplication to multiply a fraction by a fraction.
  - 5.NOS.D.12.a Estimate products by reasoning about benchmark numbers and assess reasonableness of answers.
  - 5.NOS.D.12.b Apply and extend whole number multiplication strategies.
  - 5.NOS.D.12.c 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.NOS.D.13 Apply and extend previous understandings of multiplication to multiply a fraction by a fraction, with one or both factors greater than 1.
  - 5.NOS.D.13.a Estimate products by reasoning about benchmark numbers and assess reasonableness of answers.
    - Estimate products of mixed numbers (5-R.1)
  - 5.NOS.D.13.b Apply and extend whole number multiplication strategies.
- 5.NOS.D.14 Interpret multiplication as scaling (sizing) in context.
  - 5.NOS.D.14.a Compare 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.NOS.D.14.b Explain why multiplying a given number by a fraction greater than a 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relate the principle of fraction equivalence ^a/_b = ^{n × a}/_{n × b} to the Identity Property of Multiplication.
    - Scaling whole numbers by fractions: justify your answer (5-S.1)
- 5.NOS.D.15 Solve problems in contexts involving multiplication of fractions and mixed numbers.
- 5.NOS.D.16 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions in context.
  - Divide unit fractions and whole numbers using area models (5-T.7)
  - Divide unit fractions and whole numbers using number lines (5-T.8)
  - Divide unit fractions and whole numbers (5-U.3)
  - Divide unit fractions and whole numbers: word problems (5-U.4)
  - Multi-step word problems with fractions and mixed numbers (5-V.3)
  - 5.NOS.D.16.a Apply estimation strategies to estimate quotients and assess reasonableness of answers.
  - 5.NOS.D.16.b Use visual fraction models and equations to interpret division of a unit fraction by a non-zero whole number and compute quotients.
  - 5.NOS.D.16.c Use visual fraction models and equations to interpret division of a whole number by a unit fraction and compute quotients.
  - 5.NOS.D.16.d Represent and explain the computation by connecting visual fraction models and/or equations to the meaning of division with unit fractions.

5.AT Algebraic Thinking

5.AT.A Write and interpret numerical expressions.
- 5.AT.A.1 Interpret and evaluate numerical expressions with grouping symbols.
- 5.AT.A.2 Write expressions that record calculations with numbers and interpret numerical expressions without evaluating them.
5.AT.B Analyze patterns and relationships.
- 5.AT.B.3 Generate and analyze number patterns.
  - 5.AT.B.3.a Generate a number pattern that follows a given rule and identify relationships between the numbers within the pattern.
  - 5.AT.B.3.b Generate two numerical patterns using two given rules and identify relationships between corresponding terms.
    - Compare patterns (5-KK.2)
  - 5.AT.B.3.c Use tables, ordered pairs, and graphs to represent the relationship between quantities.

5.GR Geometric Reasoning and Measurement

5.GR.A Understand relationships between measurement units.
- 5.GR.A.1 Apply the relationship between measurement units within a given measurement system to convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step problems.
5.GR.B Classify two-dimensional figures based on properties.
- 5.GR.B.2 Explain that 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.GR.B.3 Classify two-dimensional figures based on properties.
  - 5.GR.B.3.a Classify triangles based on properties.
  - 5.GR.B.3.b Classify quadrilaterals in a hierarchy based on properties.
5.GR.C Understand concepts of volume and relate volume to multiplication.
- 5.GR.C.4 Identify volume as an attribute of three-dimensional figures and measure volume by counting cubic units that fill a figure without gaps or overlaps.
  - Volume of rectangular prisms made of unit cubes (5-UU.3)
- 5.GR.C.5 Relate volume to the operations of multiplication and addition and solve problems in context.
  - 5.GR.C.5.a Find the volume of a right rectangular prism with whole-number side lengths by filling it with unit cubes in layers and show that the volume is the same as would be found by multiplying the edge lengths, or by multiplying the height by the area of the base. Represent products of three whole numbers 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.GR.C.5.b 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 to solve problems in the context.
  - 5.GR.C.5.c Determine the volumes of composite figures by decomposing them into non-overlapping right rectangular prisms and adding their volumes together to solve problems in context.
    - Volume of compound figures (5-UU.9)
5.GR.D Graph points on a coordinate plane to solve contextual and mathematical problems.
- 5.GR.D.6 Define the coordinate system as a pair of perpendicular lines called axes that intersect at the origin. Use understanding that the coordinate values represent the distance from the origin on the x-axis and y-axis to graph and name coordinate points in the first quadrant using ordered pairs.
  - Describe the coordinate plane (5-LL.1)
  - Objects on a coordinate plane (5-LL.2)
- 5.GR.D.7 Represent problems by graphing points in the first quadrant of the coordinate plane and interpreting coordinate values of points in the context of the situation.

5.DS Reasoning with Data and Statistics

5.DS.A Represent and interpret data.
- 5.DS.A.1 Ask and answer questions by collecting, organizing, and summarizing data, recognizing the importance of context when analyzing data.
  - 5.DS.A.1.a Create scaled data visualization to display data and communicate relationships or support a claim.
  - 5.DS.A.1.b Summarize data presented in scaled visualizations by identifying the mode, the range, and any gaps in data and draw conclusions.
  - 5.DS.A.1.c Evaluate whether a data visualization accurately represents the data and allows for accurate interpretation given the context.

The Common Core in Maryland

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5.NOS Number and Operation Sense

5.NOS.A Understand the place value system.

5.NOS.A.1 Explain 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.NOS.A.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10.

5.NOS.A.3 Read, write, and compare decimals to thousandths.

5.NOS.A.3.a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form.

5.NOS.A.3.b Estimate decimal quantities by reasoning about their location on a number line, their relationship to benchmark numbers, and rounding to any place.

5.NOS.A.3.c Compare two decimals to thousandths by reasoning about the values of the digits and the location on the number line. Record the results of comparisons with the symbols >, =, <.

5.NOS.B Perform operations on multi-digit whole numbers and with decimals to hundredths.

5.NOS.B.4 Fluently multiply multi-digit whole numbers.

5.NOS.B.4.a Apply estimation strategies to estimate products.

5.NOS.B.4.b Use computational strategies efficiently to multiply.

5.NOS.B.4.c Use a standard algorithm to multiply.

5.NOS.B.4.d Determine and explain when a strategy or algorithm is most efficient.

5.NOS.B.5 Divide multi-digit whole numbers with up to four-digit dividends and two-digit divisors.

5.NOS.B.5.a Apply estimation strategies to estimate quotients.

5.NOS.B.5.b Use partial quotients efficiently to divide.

5.NOS.B.5.c Use properties of operations and/or the inverse relationship between multiplication and division to divide.

5.NOS.B.5.d Represent and explain the computation by connecting rectangular arrays, area models, and/or equations to the meaning of division.

5.NOS.B.6 Apply and extend previous understanding of addition and subtraction of whole numbers to add and subtract decimals to hundredths.

5.NOS.B.6.a Apply estimation strategies to estimate sums and differences of decimals.

5.NOS.B.6.b Use concrete models, drawings, strategies based on place value, properties of operations, and/or the inverse relationship between addition and subtraction to add and subtract decimals in context.

5.NOS.B.6.c Use an algorithm to add and subtract decimals.

5.NOS.B.6.d Determine and explain when a strategy or algorithm is or is not needed.

5.NOS.B.7 Apply and extend previous understanding of multiplication and division of whole numbers to multiply and divide decimals to hundredths in context.

5.NOS.B.7.a Apply estimation strategies to estimate products and quotients.

5.NOS.B.7.b Use concrete models, drawings, and arrays to multiply and divide.

5.NOS.B.7.c Use strategies based on place value to multiply and divide.

5.NOS.B.7.d Use properties of operations and/or the inverse relationship between multiplication and division to multiply and divide.

5.NOS.B.7.e Represent and explain the computation by connecting concrete models, drawings, and/or equations to the meaning of multiplication and division.

5.NOS.C Use equivalent fractions as a strategy to add and subtract fractions.

5.NOS.C.8 Add and subtract fractions with unlike denominators.

5.NOS.C.8.a Estimate sums and differences by reasoning about benchmark numbers and assess reasonableness of answers.

5.NOS.C.8.b Apply and extend whole number addition and subtraction strategies to add and subtract fractions.

5.NOS.C.8.c Use equivalent fractions to produce an equivalent sum or difference of fractions with like denominators.

5.NOS.C.9 Solve problems in context involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators using visual fraction models and/or equations to represent the problem.

5.NOS.D Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

5.NOS.D.10 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b) in context using visual fraction models and equations to represent the problem.

5.NOS.D.11 Apply and extend previous understandings of multiplication to multiply a whole number by a fraction (c/d × b).

5.NOS.D.11.a Estimate products by reasoning about benchmark numbers and assess reasonableness of answers.

5.NOS.D.11.b Multiply a whole number by a fraction.

5.NOS.D.12 Apply and extend previous understandings of multiplication to multiply a fraction by a fraction.

5.NOS.D.12.a Estimate products by reasoning about benchmark numbers and assess reasonableness of answers.

5.NOS.D.12.b Apply and extend whole number multiplication strategies.

5.NOS.D.12.c 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.NOS.D.13 Apply and extend previous understandings of multiplication to multiply a fraction by a fraction, with one or both factors greater than 1.

5.NOS.D.13.a Estimate products by reasoning about benchmark numbers and assess reasonableness of answers.

5.NOS.D.13.b Apply and extend whole number multiplication strategies.

5.NOS.D.14 Interpret multiplication as scaling (sizing) in context.

5.NOS.D.14.a Compare 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.NOS.D.15 Solve problems in contexts involving multiplication of fractions and mixed numbers.

5.NOS.D.16 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions in context.

5.NOS.D.16.a Apply estimation strategies to estimate quotients and assess reasonableness of answers.

5.NOS.D.16.b Use visual fraction models and equations to interpret division of a unit fraction by a non-zero whole number and compute quotients.

5.NOS.D.16.c Use visual fraction models and equations to interpret division of a whole number by a unit fraction and compute quotients.

5.NOS.D.16.d Represent and explain the computation by connecting visual fraction models and/or equations to the meaning of division with unit fractions.

5.AT Algebraic Thinking

5.AT.A Write and interpret numerical expressions.

5.AT.A.1 Interpret and evaluate numerical expressions with grouping symbols.

5.AT.A.2 Write expressions that record calculations with numbers and interpret numerical expressions without evaluating them.

5.AT.B Analyze patterns and relationships.

5.AT.B.3 Generate and analyze number patterns.

5.AT.B.3.a Generate a number pattern that follows a given rule and identify relationships between the numbers within the pattern.

5.AT.B.3.b Generate two numerical patterns using two given rules and identify relationships between corresponding terms.

5.AT.B.3.c Use tables, ordered pairs, and graphs to represent the relationship between quantities.

5.GR Geometric Reasoning and Measurement

5.GR.A Understand relationships between measurement units.

5.GR.A.1 Apply the relationship between measurement units within a given measurement system to convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step problems.

5.GR.B Classify two-dimensional figures based on properties.

5.GR.B.2 Explain that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.

5.GR.B.3 Classify two-dimensional figures based on properties.

5.GR.B.3.a Classify triangles based on properties.

5.GR.B.3.b Classify quadrilaterals in a hierarchy based on properties.

5.GR.C Understand concepts of volume and relate volume to multiplication.

5.GR.C.4 Identify volume as an attribute of three-dimensional figures and measure volume by counting cubic units that fill a figure without gaps or overlaps.

5.GR.C.5 Relate volume to the operations of multiplication and addition and solve problems in context.

5.GR.C.5.b 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 to solve problems in the context.

5.NOS.A.1 Explain 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.NOS.D.10 Interpret a fraction as division of the numerator by the denominator (^a/_b = a ÷ b) in context using visual fraction models and equations to represent the problem.

5.NOS.D.11 Apply and extend previous understandings of multiplication to multiply a whole number by a fraction (^c/_d × b).