Common Core State Standards
5th Grade Math Standards
All 26 Common Core math standards for 5th grade, grouped into domains and written in plain English. The official wording is one click away. 4 have free practice you can print today.
26 standards
Operations & Algebraic Thinking OA
3 standardsWrite and interpret numerical expressions.
5.OA.1
Evaluate expressions with parentheses and other grouping symbols, like 3 × (4 + 2), working inside the symbols first.
Official wording
Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
5.OA.2
Write an expression for a described calculation, like 2 × (8 + 7) for add 8 and 7 then double it, and compare expressions without working them out.
Official wording
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
Analyze patterns and relationships.
5.OA.3
Build two number patterns from two rules, compare their matching terms, and graph the pairs as points on a coordinate grid.
Official wording
Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
Number & Operations in Base Ten NBT
7 standardsUnderstand the place value system.
5.NBT.1
Know that each place is worth ten times the place to its right and one tenth of the place to its left.
Official wording
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.NBT.2
Explain how the zeros and the decimal point move when a number is multiplied or divided by a power of 10, and write powers of 10 with exponents.
Official wording
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.NBT.3
Read and write decimals to thousandths, like 347.392, in words and expanded form, and compare two decimals digit by digit.
Official wording
Read, write, and compare decimals to thousandths.aRead and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).bCompare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
5.NBT.4
Round decimals to any place, like 3.467 to the nearest hundredth.
Official wording
Use place value understanding to round decimals to any place.
Perform operations with multi-digit whole numbers and with decimals to hundredths.
5.NBT.5
Multiply multi-digit whole numbers, like 346 × 27, fluently with the standard algorithm.
Official wording
Fluently multiply multi-digit whole numbers using the standard algorithm.
5.NBT.6
Divide up to four-digit numbers by two-digit numbers with place-value strategies, and show the thinking with equations, arrays or area models.
Official wording
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
5.NBT.7
Add, subtract, multiply and divide decimals to hundredths with models and place-value strategies, and explain the reasoning.
Official wording
Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
Number & Operations—Fractions NF
7 standardsUse equivalent fractions as a strategy to add and subtract fractions.
5.NF.1
Add and subtract fractions and mixed numbers with unlike denominators by rewriting them with a common denominator, like 2/3 + 1/4 using twelfths.
Official wording
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
5.NF.2
Solve word problems that add or subtract fractions with unlike denominators, and use benchmark fractions like 1/2 to check whether an answer makes sense.
Official wording
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
Apply and extend previous understandings of multiplication and division.
5.NF.3
Read a fraction as a division, like 3/4 means 3 divided by 4, and solve sharing problems whose answers are fractions or mixed numbers.
Official wording
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
5.NF.4
Multiply a fraction by a whole number or by another fraction, like 2/3 × 4/5 = 8/15, and find the area of a rectangle with fractional sides.
Official wording
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.aInterpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = (ac)/(bd).bFind 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. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
5.NF.5
Tell, without multiplying, whether a product will be bigger or smaller than one factor, since multiplying by a fraction less than 1 shrinks a number.
Official wording
Interpret multiplication as scaling (resizing), by:aComparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.bExplaining 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); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.
5.NF.6
Solve real-world problems that multiply fractions and mixed numbers, like how much flour is in half of a recipe that calls for 2 1/2 cups.
Official wording
Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
5.NF.7
Divide a unit fraction by a whole number and a whole number by a unit fraction, like 1/3 ÷ 4 = 1/12 and 4 ÷ 1/5 = 20, and use this in real-world problems.
Official wording
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.aInterpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.bInterpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.cSolve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
Measurement & Data MD
5 standardsConvert like measurement units within a given measurement system.
5.MD.1
Convert between units in the same measurement system, like 5 cm to 0.05 m, and use the conversions in multi-step problems.
Official wording
Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
Represent and interpret data.
5.MD.2
Make a line plot with measurements in halves, quarters and eighths, and use fraction operations to answer questions about it.
Official wording
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 for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
Geometric measurement: understand concepts of volume.
5.MD.3
Understand volume as the space inside a solid, measured by how many unit cubes fill it without gaps or overlaps.
Official wording
Recognize volume as an attribute of solid figures and understand concepts of volume measurement.aA 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.bA solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
5.MD.4
Measure volume by counting unit cubes, in cubic centimeters, cubic inches, cubic feet or made-up units.
Official wording
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
5.MD.5
Find the volume of a box-shaped prism with the formulas V = l × w × h and V = b × h, and add up the volumes of two prisms joined together.
Official wording
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.aFind the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.bApply 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 and mathematical problems.cRecognize 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 problems.
Geometry G
4 standardsGraph points on the coordinate plane to solve real-world and mathematical problems.
5.G.1
Plot and locate points on a coordinate grid with an ordered pair like (3, 5), going across on the x-axis first and then up on the y-axis.
Official wording
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 the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
5.G.2
Graph real-world data as points in the first quadrant of a coordinate grid and explain what each point’s coordinates mean.
Official wording
Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
Classify two-dimensional figures into categories based on their properties.
5.G.3
Know that a property of a category of shapes holds for all its subcategories, like every square has four right angles because a square is a rectangle.
Official wording
Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
5.G.4
Sort two-dimensional shapes into a hierarchy by their properties, like quadrilaterals, then parallelograms, then rectangles, then squares.
Official wording
Classify two-dimensional figures in a hierarchy based on properties.
5th Grade Practice
Worksheet generators and printables already set up for this grade’s standards, free to use.
5th Grade Math Standards: Questions
Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The plain-English lines on this page are EMStudio’s own explanations, shown beside the official wording. They are not part of the standard.