Common Core Math Standards, Grades 1–8
The 151 Common Core State Standards for Mathematics in the computational domains — Operations & Algebraic Thinking, Number & Operations in Base Ten, Fractions, Measurement & Data, The Number System, Ratios & Proportional Relationships and Expressions & Equations — listed by grade, each with the MathDrillSheets worksheets aligned to it.
88 of the 151 standards currently have at least one worksheet tagged to them. Geometry, Statistics and Functions are omitted: they need figures and data sets that a print-and-solve drill page cannot carry. A worksheet's alignment appears on its own page as a green badge, and the badge links back here.
Grade 1
Operations & Algebraic Thinking
- 1.OA.1Use addition and subtraction within 20 to solve word problems involving adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.
- 1.OA.2Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20.
- 1.OA.3Apply properties of operations as strategies to add and subtract (commutative and associative properties).
- 1.OA.4Understand subtraction as an unknown-addend problem (e.g., subtract 10 − 8 by finding the number that makes 10 when added to 8).
- 1.OA.5Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
- 1.OA.6Add and subtract within 20, demonstrating fluency for addition and subtraction within 10 using strategies such as making ten and decomposing.
- Grade 1 Addition Practice
- Grade 1 Addition Timed Drill
- Grade 1 Addition Missing Number
- Grade 1 Subtraction Timed Drill
- Grade 1 Subtraction Missing Number
- Grade 1 Subtraction Mixed Review
- Grade 1 Subtraction Vertical Format
- Grade 1 Mixed Addition and Subtraction to 20
- Grade 1 Mixed Operations Timed Drill
- Grade 1 Mixed Operations Missing Number
- Grade 1 Equal Groups: Repeated Addition to 20
- 1.OA.7Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.
- 1.OA.8Determine the unknown whole number in an addition or subtraction equation relating three whole numbers (e.g., 8 + ? = 11).
Number & Operations in Base Ten
- 1.NBT.1Count to 120, starting at any number less than 120; read and write numerals and represent a number of objects with a written numeral.
- 1.NBT.2Understand that the two digits of a two-digit number represent amounts of tens and ones (place value).
- 1.NBT.3Compare two two-digit numbers based on the meanings of the tens and ones digits, using the symbols >, =, and <.
- 1.NBT.4Add within 100, including a two-digit number and a one-digit number, and a two-digit number and a multiple of 10, using place-value strategies.
- 1.NBT.5Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count.
- 1.NBT.6Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences).
Measurement & Data
- 1.MD.1Order three objects by length; compare the lengths of two objects indirectly by using a third object.
- 1.MD.2Express the length of an object as a whole number of length units, laying multiple copies of a shorter object end to end.
- 1.MD.3Tell and write time in hours and half-hours using analog and digital clocks.
- 1.MD.4Organize, represent, and interpret data with up to three categories; ask and answer questions about the data.
Grade 2
Operations & Algebraic Thinking
- 2.OA.1Use addition and subtraction within 100 to solve one- and two-step word problems involving all situations, with unknowns in all positions.
- 2.OA.2Fluently add and subtract within 20 using mental strategies; know from memory all sums of two one-digit numbers.
- 2.OA.3Determine whether a group of objects (up to 20) has an odd or even number of members; write an even number as a sum of two equal addends.
- 2.OA.4Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and 5 columns; write an equation as a sum of equal addends.
Number & Operations in Base Ten
- 2.NBT.1Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones (place value).
- 2.NBT.2Count within 1000; skip-count by 5s, 10s, and 100s.
- 2.NBT.3Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
- 2.NBT.4Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and <.
- 2.NBT.5Fluently add and subtract within 100 using strategies based on place value, properties of operations, and the relationship between addition and subtraction.
- Grade 2 Addition Practice
- Grade 2 Addition Missing Number
- Grade 2 Addition Mixed Review
- Grade 2 Subtraction Practice
- Grade 2 Subtraction Missing Number
- Grade 2 Subtraction Vertical Format
- Grade 2 Mixed Addition and Subtraction Within 100
- Grade 2 Mixed Operations Missing Number
- Grade 2 Mixed Operations Mixed Review
- 2.NBT.6Add up to four two-digit numbers using strategies based on place value and properties of operations.
- 2.NBT.7Add and subtract within 1000 using concrete models or drawings and strategies based on place value, with composing/decomposing tens and hundreds.
- 2.NBT.8Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
- 2.NBT.9Explain why addition and subtraction strategies work, using place value and the properties of operations.
Measurement & Data
- 2.MD.1Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
- 2.MD.2Measure the length of an object twice, using length units of different lengths; describe how the measurements relate to the unit size.
- 2.MD.3Estimate lengths using units of inches, feet, centimeters, and meters.
- 2.MD.4Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.
- 2.MD.5Use addition and subtraction within 100 to solve word problems involving lengths given in the same units.
- 2.MD.6Represent whole numbers as lengths on a number line, and represent sums and differences within 100 on a number line diagram.
- 2.MD.7Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.
- 2.MD.8Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.
- 2.MD.9Generate measurement data by measuring lengths; show the measurements on a line plot with a horizontal scale marked in whole-number units.
- 2.MD.10Draw a picture graph and a bar graph to represent a data set with up to four categories; solve put-together, take-apart, and compare problems using the data.
Grade 3
Operations & Algebraic Thinking
- 3.OA.1Interpret products of whole numbers (e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each).
- 3.OA.2Interpret whole-number quotients of whole numbers (e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned into 8 equal shares).
- 3.OA.3Use multiplication and division within 100 to solve word problems involving equal groups, arrays, and measurement quantities.
- 3.OA.4Determine the unknown whole number in a multiplication or division equation relating three whole numbers (e.g., 8 × ? = 48).
- 3.OA.5Apply properties of operations as strategies to multiply and divide (commutative, associative, and distributive properties).
- 3.OA.6Understand division as an unknown-factor problem (e.g., find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8).
- 3.OA.7Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division; know from memory all products of two one-digit numbers.
- Grade 3 Multiplication Practice
- Grade 3 Multiplication Vertical Format
- Grade 4 Multiplication Timed Drill
- Grade 6 Multiplication Timed Drill
- Grade 3 Division Timed Drill
- Grade 3 Division Missing Number
- Grade 3 Division Vertical Format
- Grade 4 Division Timed Drill
- Grade 5 Division Timed Drill
- Grade 6 Division Timed Drill
- Grade 3 Mixed Operations Practice
- Grade 3 Mixed Operations Timed Drill
- Grade 3 Mixed Operations Missing Number
- Grade 3 Mixed Operations Mixed Review
- Grade 4 Mixed Operations Timed Drill
- Grade 5 Mixed Operations Timed Drill
- Grade 6 Mixed Operations Timed Drill
- 3.OA.8Solve two-step word problems using the four operations; represent these with equations using a letter for the unknown and assess reasonableness of answers.
- 3.OA.9Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations.
Number & Operations in Base Ten
- 3.NBT.1Use place-value understanding to round whole numbers to the nearest 10 or 100.
- 3.NBT.2Fluently add and subtract within 1000 using strategies and algorithms based on place value and the relationship between addition and subtraction.
- 3.NBT.3Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80) using strategies based on place value.
Number & Operations—Fractions
- 3.NF.1Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as a parts of size 1/b.
- 3.NF.2Understand a fraction as a number on the number line; represent fractions on a number line diagram.
- 3.NF.3Explain equivalence of fractions, recognize and generate simple equivalent fractions, compare fractions with the same numerator or denominator, and express whole numbers as fractions.
Measurement & Data
- 3.MD.1Tell and write time to the nearest minute and measure time intervals in minutes; solve word problems involving addition and subtraction of time intervals.
- 3.MD.2Measure and estimate liquid volumes and masses using standard units; solve one-step word problems involving masses or volumes.
- 3.MD.3Draw a scaled picture graph and a scaled bar graph; solve one- and two-step "how many more" and "how many less" problems using scaled bar graphs.
- 3.MD.4Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch; show the data on a line plot.
- 3.MD.5Recognize area as an attribute of plane figures and understand concepts of area measurement using unit squares.
- 3.MD.6Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
- 3.MD.7Relate area to the operations of multiplication and addition; find the area of rectangles and use the distributive property in area problems.
- 3.MD.8Solve real-world and mathematical problems involving perimeters of polygons, including finding an unknown side length.
Grade 4
Operations & Algebraic Thinking
- 4.OA.1Interpret a multiplication equation as a comparison (e.g., 35 = 5 × 7 as 35 is 5 times as many as 7); represent verbal statements of multiplicative comparisons.
- 4.OA.2Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison.
- 4.OA.3Solve multistep word problems with whole numbers using the four operations, including problems with remainders; assess reasonableness using estimation and mental computation.
- 4.OA.4Find all factor pairs for a whole number 1–100; recognize a number as a multiple of each of its factors; determine whether a number is prime or composite.
- 4.OA.5Generate a number or shape pattern that follows a given rule; identify apparent features of the pattern not explicit in the rule itself.
Number & Operations in Base Ten
- 4.NBT.1Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
- 4.NBT.2Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form; compare using >, =, and <.
- 4.NBT.3Use place-value understanding to round multi-digit whole numbers to any place.
- 4.NBT.4Fluently add and subtract multi-digit whole numbers using the standard algorithm.
- Grade 4 Addition Drill
- Grade 4 Addition Missing Number
- Grade 4 Addition Mixed Review
- Grade 4 Multi-Digit Addition (Standard Algorithm)
- Grade 4 Subtraction Drill
- Grade 4 Subtraction Missing Number
- Grade 4 Subtraction Mixed Review
- Grade 4 Multi-Digit Subtraction (Standard Algorithm)
- Grade 4 Mixed Operations Missing Number
- 4.NBT.5Multiply a whole number of up to four digits by a one-digit number, and multiply two two-digit numbers, using place-value strategies.
- 4.NBT.6Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using place-value strategies.
Number & Operations—Fractions
- 4.NF.1Explain why a fraction a/b is equivalent to (n×a)/(n×b); use this principle to recognize and generate equivalent fractions.
- 4.NF.2Compare two fractions with different numerators and different denominators by creating common denominators or numerators, or comparing to a benchmark such as 1/2.
- 4.NF.3Understand addition and subtraction of fractions as joining and separating parts referring to the same whole; add and subtract fractions and mixed numbers with like denominators.
- 4.NF.4Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
- 4.NF.5Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and add two fractions with respective denominators 10 and 100.
- 4.NF.6Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100).
- 4.NF.7Compare two decimals to hundredths by reasoning about their size, recording comparisons with the symbols >, =, and <.
Measurement & Data
- 4.MD.1Know relative sizes of measurement units within one system; express measurements in a larger unit in terms of a smaller unit.
- 4.MD.2Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses, and money, including fractions and decimals.
- 4.MD.3Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.
- 4.MD.4Make a line plot to display a data set of measurements in fractions of a unit; solve problems involving addition and subtraction of fractions using the line plot.
- 4.MD.5Recognize angles as geometric shapes formed by two rays and understand concepts of angle measurement in degrees.
- 4.MD.6Measure angles in whole-number degrees using a protractor; sketch angles of specified measure.
- 4.MD.7Recognize angle measure as additive; solve addition and subtraction problems to find unknown angles on a diagram.
Grade 5
Operations & Algebraic Thinking
- 5.OA.1Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols (order of operations).
- 5.OA.2Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.
- 5.OA.3Generate two numerical patterns using two given rules; identify relationships between corresponding terms and form ordered pairs.
Number & Operations in Base Ten
- 5.NBT.1Recognize that in a multi-digit number, a digit in one place represents 10 times what it represents in the place to its right and 1/10 of what it represents to its left.
- 5.NBT.2Explain patterns in the number of zeros of a product when multiplying by powers of 10, and in the placement of the decimal point; use whole-number exponents to denote powers of 10.
- 5.NBT.3Read, write, and compare decimals to thousandths using base-ten numerals, number names, and expanded form.
- 5.NBT.4Use place-value understanding to round decimals to any place.
- 5.NBT.5Fluently multiply multi-digit whole numbers using the standard algorithm.
- 5.NBT.6Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using place-value strategies.
- 5.NBT.7Add, subtract, multiply, and divide decimals to hundredths using concrete models, drawings, and strategies based on place value.
Number & Operations—Fractions
- 5.NF.1Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions with a common denominator.
- 5.NF.2Solve word problems involving addition and subtraction of fractions referring to the same whole, including unlike denominators; use benchmark fractions to estimate.
- 5.NF.3Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b); solve word problems involving division of whole numbers with fraction or mixed-number answers.
- 5.NF.4Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
- 5.NF.5Interpret multiplication as scaling (resizing); explain why multiplying a number by a fraction greater than or less than 1 changes its size.
- 5.NF.6Solve real-world problems involving multiplication of fractions and mixed numbers.
- 5.NF.7Divide unit fractions by whole numbers and whole numbers by unit fractions, and solve related real-world problems.
Measurement & Data
- 5.MD.1Convert among different-sized standard measurement units within a given system, and use these conversions in solving multistep, real-world problems.
- 5.MD.2Make a line plot to display a data set of measurements in fractions of a unit; use operations on fractions to solve problems using the data.
- 5.MD.3Recognize volume as an attribute of solid figures and understand concepts of volume measurement using unit cubes.
- 5.MD.4Measure volumes by counting unit cubes (cubic cm, cubic in, cubic ft, and improvised units).
- 5.MD.5Relate volume to multiplication and addition; find volumes of right rectangular prisms using V = l × w × h and V = b × h to solve real-world problems.
Grade 6
Ratios & Proportional Relationships
- 6.RP.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
- 6.RP.2Understand the concept of a unit rate a/b associated with a ratio a:b (b ≠ 0), and use rate language in the context of a ratio relationship.
- 6.RP.3Use ratio and rate reasoning to solve real-world problems, including tables of equivalent ratios, unit-rate problems, percent problems, and unit conversions.
- Grade 5 Percents Drill
- Grade 5 Percents Timed Drill
- Grade 5 Percents Missing Number
- Grade 5 Percents Mixed Review
- Grade 6 Percents Drill
- Grade 6 Percents Timed Drill
- Grade 6 Percents Missing Number
- Grade 6 Percents Mixed Review
- Grade 6 Ratios & Proportions Drill
- Grade 6 Ratios & Proportions Timed Drill
- Grade 6 Ratios & Proportions Missing Number
- Grade 6 Ratios & Proportions Mixed Review
- 6.RP.3 — Ratios & Rates in the Real World
The Number System
- 6.NS.1Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.
- 6.NS.2Fluently divide multi-digit numbers using the standard algorithm.
- 6.NS.3Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
- 6.NS.4Find the greatest common factor of two whole numbers ≤ 100 and the least common multiple of two whole numbers ≤ 12; use the distributive property to express a sum of two whole numbers.
- 6.NS.5Understand that positive and negative numbers describe quantities having opposite directions or values; use positive and negative numbers to represent quantities in real-world contexts.
- 6.NS.6Understand a rational number as a point on the number line; extend number-line diagrams and coordinate axes to represent points with negative coordinates.
- 6.NS.7Understand ordering and absolute value of rational numbers.
- 6.NS.8Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane; find distances between points with the same first or second coordinate.
Expressions & Equations
- 6.EE.1Write and evaluate numerical expressions involving whole-number exponents.
- 6.EE.2Write, read, and evaluate expressions in which letters stand for numbers.
- 6.EE.3Apply the properties of operations to generate equivalent expressions.
- 6.EE.4Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted).
- 6.EE.5Understand solving an equation or inequality as a process of answering which values make the equation or inequality true; use substitution to determine whether a given number makes it true.
- 6.EE.6Use variables to represent numbers and write expressions when solving a real-world or mathematical problem.
- 6.EE.7Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for nonnegative rational numbers.
- 6.EE.8Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem.
- 6.EE.9Use variables to represent two quantities that change in relationship to one another; analyze the relationship using equations, tables, and graphs.
Grade 7
Ratios & Proportional Relationships
- 7.RP.1Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.
- 7.RP.2Recognize and represent proportional relationships between quantities, identifying the constant of proportionality in tables, graphs, equations, diagrams, and verbal descriptions.
- 7.RP.3Use proportional relationships to solve multistep ratio and percent problems, including simple interest, tax, markups and markdowns, gratuities, commissions, fees, and percent increase and decrease.
The Number System
- 7.NS.1Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers, including representing subtraction of a rational number as adding its additive inverse.
- 7.NS.2Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers, including converting a rational number to a decimal using long division.
- 7.NS.3Solve real-world and mathematical problems involving the four operations with rational numbers.
Expressions & Equations
- 7.EE.1Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
- 7.EE.2Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.
- 7.EE.3Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form, applying properties of operations and assessing the reasonableness of answers.
- 7.EE.4Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities of the form px + q = r and p(x + q) = r to solve problems.
Grade 8
The Number System
- 8.NS.1Know that numbers that are not rational are called irrational; understand informally that every number has a decimal expansion, and convert a decimal expansion which repeats eventually into a rational number.
- 8.NS.2Use rational approximations of irrational numbers to compare their size, locate them approximately on a number line diagram, and estimate the value of expressions such as π².
Expressions & Equations
- 8.EE.1Know and apply the properties of integer exponents to generate equivalent numerical expressions.
- 8.EE.2Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p; evaluate square roots of small perfect squares and cube roots of small perfect cubes.
- 8.EE.3Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.
- 8.EE.4Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used; interpret scientific notation generated by technology.
- 8.EE.5Graph proportional relationships, interpreting the unit rate as the slope of the graph, and compare two different proportional relationships represented in different ways.
- 8.EE.6Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line; derive the equations y = mx and y = mx + b.
- 8.EE.7Solve linear equations in one variable, including equations with one solution, infinitely many solutions, or no solutions, and equations requiring the distributive property and collecting like terms.
- 8.EE.8Analyze and solve pairs of simultaneous linear equations algebraically, and solve real-world and mathematical problems leading to two linear equations in two variables.