Grades
Standard
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple [...]
Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below [...]
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from [...]
Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the [...]
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two [...]
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 [...]
Write and evaluate numerical expressions involving whole-number exponents.
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 [...]
Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of [...]
Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as [...]
Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit [...]
Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Interpret multiplication as scaling (resizing) by:
Comparing the size of a product to the size of one factor on the basis of the size of 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 [...]
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 [...]
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape [...]
Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs [...]
Solve unit rate problems including those involving unit pricing and constant speed. For example, If it took 7 hours to [...]
Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the [...]
Perform operations with multi-digit whole numbers and with decimals to hundredths. Find whole-number quotients of whole numbers with up to [...]
Perform operations with multi-digit whole numbers and with decimals to hundredths. Add, subtract, multiply, and divide decimals to hundredths, using [...]
Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use [...]
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use [...]
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 [...]
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show [...]
Apply the formulas V =(l)(w)(h) and V = (b)(h) for rectangular prisms to find volumes of right rectangular prisms with [...]
Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes [...]
Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines [...]
Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate [...]
Grades
Standard
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple [...]
Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below [...]
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from [...]
Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the [...]
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two [...]
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 [...]
Write and evaluate numerical expressions involving whole-number exponents.
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 [...]
Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of [...]
Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as [...]
Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit [...]
Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Interpret multiplication as scaling (resizing) by:
Comparing the size of a product to the size of one factor on the basis of the size of 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 [...]
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 [...]
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape [...]
Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs [...]
Solve unit rate problems including those involving unit pricing and constant speed. For example, If it took 7 hours to [...]
Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the [...]
Perform operations with multi-digit whole numbers and with decimals to hundredths. Find whole-number quotients of whole numbers with up to [...]
Perform operations with multi-digit whole numbers and with decimals to hundredths. Add, subtract, multiply, and divide decimals to hundredths, using [...]
Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use [...]
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use [...]
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 [...]
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show [...]
Apply the formulas V =(l)(w)(h) and V = (b)(h) for rectangular prisms to find volumes of right rectangular prisms with [...]
Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes [...]
Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines [...]
Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate [...]
