Grades
Standard
Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs [...]
Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, [...]
Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3°C > –7°C to [...]
Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value [...]
Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars [...]
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates [...]
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Write and evaluate numerical expressions involving whole-number exponents.
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual [...]
Write, read, and evaluate expressions in which letters stand for numbers.
Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y [...]
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of [...]
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple [...]
Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, [...]
Find area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and [...]
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the [...]
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side [...]
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area [...]
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, [...]
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0 (b not equal [...]
Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as [...]
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape [...]
Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit [...]
Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs [...]
Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Interpret multiplication as scaling (resizing) by:
Solve unit rate problems including those involving unit pricing and constant speed. For example, If it took 7 hours to [...]
Comparing the size of a product to the size of one factor on the basis of the size of the [...]
Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the [...]
Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given [...]
Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve real world problems involving multiplication [...]
Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Apply and extend previous understandings of [...]
Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story [...]
Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context [...]
Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate [...]
Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, [...]
Classify two-dimensional figures into categories based on their properties. Classify two-dimensional figures in a hierarchy based on properties.
Perform operations with multi-digit whole numbers and with decimals to hundredths. Find whole-number quotients of whole numbers with up to [...]
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a [...]
Perform operations with multi-digit whole numbers and with decimals to hundredths. Add, subtract, multiply, and divide decimals to hundredths, using [...]
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., [...]
Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use [...]
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving [...]
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use [...]
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
A cube with side length 1 unit, called a "unit cube" is said to have "one cubic unit" of volume, [...]
A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a [...]
Grades
Standard
Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs [...]
Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, [...]
Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3°C > –7°C to [...]
Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value [...]
Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars [...]
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates [...]
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Write and evaluate numerical expressions involving whole-number exponents.
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual [...]
Write, read, and evaluate expressions in which letters stand for numbers.
Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y [...]
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of [...]
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple [...]
Solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, [...]
Find area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and [...]
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the [...]
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side [...]
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area [...]
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, [...]
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0 (b not equal [...]
Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as [...]
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape [...]
Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit [...]
Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs [...]
Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Interpret multiplication as scaling (resizing) by:
Solve unit rate problems including those involving unit pricing and constant speed. For example, If it took 7 hours to [...]
Comparing the size of a product to the size of one factor on the basis of the size of the [...]
Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the [...]
Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given [...]
Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve real world problems involving multiplication [...]
Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Apply and extend previous understandings of [...]
Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story [...]
Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context [...]
Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate [...]
Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, [...]
Classify two-dimensional figures into categories based on their properties. Classify two-dimensional figures in a hierarchy based on properties.
Perform operations with multi-digit whole numbers and with decimals to hundredths. Find whole-number quotients of whole numbers with up to [...]
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a [...]
Perform operations with multi-digit whole numbers and with decimals to hundredths. Add, subtract, multiply, and divide decimals to hundredths, using [...]
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., [...]
Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use [...]
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving [...]
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use [...]
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
A cube with side length 1 unit, called a "unit cube" is said to have "one cubic unit" of volume, [...]
A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a [...]