Common Core Math Standards

Use 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.

Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20.

Apply properties of operations as strategies to add and subtract (commutative and associative properties).

Understand subtraction as an unknown-addend problem (e.g., subtract 10 − 8 by finding the number that makes 10 when added to 8).

Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

Add and subtract within 20, demonstrating fluency for addition and subtraction within 10 using strategies such as making ten and decomposing.

Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.

Determine the unknown whole number in an addition or subtraction equation relating three whole numbers (e.g., 8 + ? = 11).

Count to 120, starting at any number less than 120; read and write numerals and represent a number of objects with a written numeral.

Understand that the two digits of a two-digit number represent amounts of tens and ones (place value).

Compare two two-digit numbers based on the meanings of the tens and ones digits, using the symbols >, =, and <.

Add 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.

Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count.

Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range 10–90 (positive or zero differences).

Order three objects by length; compare the lengths of two objects indirectly by using a third object.

Express the length of an object as a whole number of length units, laying multiple copies of a shorter object end to end.

Tell and write time in hours and half-hours using analog and digital clocks.

Organize, represent, and interpret data with up to three categories; ask and answer questions about the data.

Use addition and subtraction within 100 to solve one- and two-step word problems involving all situations, with unknowns in all positions.

Fluently add and subtract within 20 using mental strategies; know from memory all sums of two one-digit numbers.

Determine 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.

Use 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.

Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones (place value).

Count within 1000; skip-count by 5s, 10s, and 100s.

Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and <.

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and the relationship between addition and subtraction.

Add up to four two-digit numbers using strategies based on place value and properties of operations.

Add and subtract within 1000 using concrete models or drawings and strategies based on place value, with composing/decomposing tens and hundreds.

Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.

Explain why addition and subtraction strategies work, using place value and the properties of operations.

Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

Measure the length of an object twice, using length units of different lengths; describe how the measurements relate to the unit size.

Estimate lengths using units of inches, feet, centimeters, and meters.

Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

Use addition and subtraction within 100 to solve word problems involving lengths given in the same units.

Represent whole numbers as lengths on a number line, and represent sums and differences within 100 on a number line diagram.

Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.

Generate measurement data by measuring lengths; show the measurements on a line plot with a horizontal scale marked in whole-number units.

Draw 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.

Interpret products of whole numbers (e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each).

Interpret 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).

Use multiplication and division within 100 to solve word problems involving equal groups, arrays, and measurement quantities.

Determine the unknown whole number in a multiplication or division equation relating three whole numbers (e.g., 8 × ? = 48).

Apply properties of operations as strategies to multiply and divide (commutative, associative, and distributive properties).

Understand division as an unknown-factor problem (e.g., find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8).

Fluently 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.

Solve two-step word problems using the four operations; represent these with equations using a letter for the unknown and assess reasonableness of answers.

Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations.

Use place-value understanding to round whole numbers to the nearest 10 or 100.

Fluently add and subtract within 1000 using strategies and algorithms based on place value and the relationship between addition and subtraction.

Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80) using strategies based on place value.

Understand 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.

Understand a fraction as a number on the number line; represent fractions on a number line diagram.

Explain equivalence of fractions, recognize and generate simple equivalent fractions, compare fractions with the same numerator or denominator, and express whole numbers as fractions.

Tell and write time to the nearest minute and measure time intervals in minutes; solve word problems involving addition and subtraction of time intervals.

Measure and estimate liquid volumes and masses using standard units; solve one-step word problems involving masses or volumes.

Draw 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.

Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch; show the data on a line plot.

Recognize area as an attribute of plane figures and understand concepts of area measurement using unit squares.

Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

Relate area to the operations of multiplication and addition; find the area of rectangles and use the distributive property in area problems.

Solve real-world and mathematical problems involving perimeters of polygons, including finding an unknown side length.

Interpret 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.

Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison.

Solve multistep word problems with whole numbers using the four operations, including problems with remainders; assess reasonableness using estimation and mental computation.

Find 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.

Generate a number or shape pattern that follows a given rule; identify apparent features of the pattern not explicit in the rule itself.

Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.

Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form; compare using >, =, and <.

Use place-value understanding to round multi-digit whole numbers to any place.

Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Multiply a whole number of up to four digits by a one-digit number, and multiply two two-digit numbers, using place-value strategies.

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using place-value strategies.

Explain why a fraction a/b is equivalent to (n×a)/(n×b); use this principle to recognize and generate equivalent fractions.

Compare two fractions with different numerators and different denominators by creating common denominators or numerators, or comparing to a benchmark such as 1/2.

Understand 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.

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and add two fractions with respective denominators 10 and 100.

Use decimal notation for fractions with denominators 10 or 100 (e.g., rewrite 0.62 as 62/100).

Compare two decimals to hundredths by reasoning about their size, recording comparisons with the symbols >, =, and <.

Know relative sizes of measurement units within one system; express measurements in a larger unit in terms of a smaller unit.

Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses, and money, including fractions and decimals.

Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.

Make 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.

Recognize angles as geometric shapes formed by two rays and understand concepts of angle measurement in degrees.

Measure angles in whole-number degrees using a protractor; sketch angles of specified measure.

Recognize angle measure as additive; solve addition and subtraction problems to find unknown angles on a diagram.

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols (order of operations).

Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

Generate two numerical patterns using two given rules; identify relationships between corresponding terms and form ordered pairs.

Recognize 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.

Explain 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.

Read, write, and compare decimals to thousandths using base-ten numerals, number names, and expanded form.

Use place-value understanding to round decimals to any place.

Fluently multiply multi-digit whole numbers using the standard algorithm.

Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using place-value strategies.

Add, subtract, multiply, and divide decimals to hundredths using concrete models, drawings, and strategies based on place value.

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions with a common denominator.

Solve word problems involving addition and subtraction of fractions referring to the same whole, including unlike denominators; use benchmark fractions to estimate.

Interpret 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.

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

Interpret multiplication as scaling (resizing); explain why multiplying a number by a fraction greater than or less than 1 changes its size.

Solve real-world problems involving multiplication of fractions and mixed numbers.

Divide unit fractions by whole numbers and whole numbers by unit fractions, and solve related real-world problems.

Convert among different-sized standard measurement units within a given system, and use these conversions in solving multistep, real-world problems.

Make 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.

Recognize volume as an attribute of solid figures and understand concepts of volume measurement using unit cubes.

Measure volumes by counting unit cubes (cubic cm, cubic in, cubic ft, and improvised units).

Relate 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.

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.

Understand 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.

Use ratio and rate reasoning to solve real-world problems, including tables of equivalent ratios, unit-rate problems, percent problems, and unit conversions.

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.

Fluently divide multi-digit numbers using the standard algorithm.

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Find 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.

Understand that positive and negative numbers describe quantities having opposite directions or values; use positive and negative numbers to represent quantities in real-world contexts.

Understand a rational number as a point on the number line; extend number-line diagrams and coordinate axes to represent points with negative coordinates.

Understand ordering and absolute value of rational numbers.

Solve 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.

Write and evaluate numerical expressions involving whole-number exponents.

Write, read, and evaluate expressions in which letters stand for numbers.

Apply the properties of operations to generate equivalent expressions.

Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted).

Understand 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.

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem.

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for nonnegative rational numbers.

Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem.

Use variables to represent two quantities that change in relationship to one another; analyze the relationship using equations, tables, and graphs.