Grades
Standard
Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is [...]
Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for [...]
Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which [...]
Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of [...]
Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple [...]
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an [...]
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not [...]
Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that [...]
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the [...]
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. [...]
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on [...]
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; [...]
Understand a fraction as a number on the number line; represent fractions on a number line diagram. (Grade 3 expectations [...]
Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole [...]
Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the [...]
Develop understanding of fractions as numbers. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their [...]
A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, [...]
A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an [...]
Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then [...]
Understand division as an unknown-factor problem. For example, divide 32 ÷ 8 by finding the number that makes 32 when [...]
Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the [...]
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 [...]
Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and [...]
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown [...]
Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and [...]
Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For [...]
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, properties of operations, and/or the relationship [...]
Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using [...]
Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and [...]
Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). [...]
Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- [...]
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by [...]
Recognize area as an attribute of plane figures and understand concepts of area measurement.
Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number [...]
Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when [...]
Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by [...]
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., [...]
Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring [...]
Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown [...]
Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the [...]
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 [...]
Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., [...]
Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers [...]
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 $ (dollars) and ¢ (cents) symbols appropriately. Example: [...]
Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four [...]
Grades
Standard
Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is [...]
Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for [...]
Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which [...]
Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of [...]
Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple [...]
Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an [...]
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not [...]
Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that [...]
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the [...]
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. [...]
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on [...]
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; [...]
Understand a fraction as a number on the number line; represent fractions on a number line diagram. (Grade 3 expectations [...]
Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole [...]
Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the [...]
Develop understanding of fractions as numbers. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their [...]
A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, [...]
A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an [...]
Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then [...]
Understand division as an unknown-factor problem. For example, divide 32 ÷ 8 by finding the number that makes 32 when [...]
Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the [...]
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 [...]
Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and [...]
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown [...]
Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and [...]
Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For [...]
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, properties of operations, and/or the relationship [...]
Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using [...]
Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and [...]
Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). [...]
Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- [...]
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by [...]
Recognize area as an attribute of plane figures and understand concepts of area measurement.
Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number [...]
Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when [...]
Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by [...]
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., [...]
Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring [...]
Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown [...]
Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the [...]
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 [...]
Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., [...]
Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers [...]
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 $ (dollars) and ¢ (cents) symbols appropriately. Example: [...]
Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four [...]