Grades
Standard
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 [...]
Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. [...]
Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3), Explain why the fractions are equivalent, e.g., [...]
Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form [...]
Compare two fractions with the same numerator or the same denominator, by reasoning about their size, Recognize that valid comparisons [...]
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 [...]
Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple [...]
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not [...]
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the [...]
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on [...]
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 [...]
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 [...]
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown [...]
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.
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).
Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the [...]
Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and [...]
Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and [...]
Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or [...]
Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number [...]
Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by [...]
Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring [...]
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 [...]
Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of [...]
Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal [...]
Grades
Standard
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 [...]
Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. [...]
Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3), Explain why the fractions are equivalent, e.g., [...]
Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form [...]
Compare two fractions with the same numerator or the same denominator, by reasoning about their size, Recognize that valid comparisons [...]
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 [...]
Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple [...]
Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not [...]
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the [...]
Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on [...]
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 [...]
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 [...]
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown [...]
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.
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).
Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the [...]
Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and [...]
Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and [...]
Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or [...]
Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number [...]
Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by [...]
Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring [...]
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 [...]
Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of [...]
Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal [...]
