Minnesota Academic Standards: Grade 5
Skills available for Minnesota fifth-grade math standards
Standard
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5.1
Number & Operation
5.1.1 Divide multi-digit numbers; solve real-world and mathematical problems using arithmetic.
5.1.1.1 Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal.
Place value strategies
Division models
Standard algorithm
Properties of operations
Division and fractions
5.1.1.1 Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal.
Place value strategies
Division models
Standard algorithm
Properties of operations
Division and fractions
5.1.1.2 Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately.
5.1.1.2 Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately.
5.1.1.3 Estimate solutions to arithmetic problems in order to assess the reasonableness of results.
Estimate sums and differences
Estimate products
Estimate quotients
5.1.1.3 Estimate solutions to arithmetic problems in order to assess the reasonableness of results.
Estimate sums and differences
Estimate products
Estimate quotients
5.1.1.4 Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results.
Addition and subtraction
Multiplication
Division
Mixed operations
Multi-step problems
5.1.1.4 Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the inverse relationships between operations, the use of technology, and the context of the problem to assess the reasonableness of results.
Addition and subtraction
Multiplication
Division
Mixed operations
Multi-step problems
5.1.2 Read, write, represent and compare fractions and decimals; recognize and write equivalent fractions; convert between fractions and decimals; use fractions and decimals in real-world and mathematical situations.
5.1.2.1 Read and write decimals using place value to describe decimals in terms of groups from millionths to millions.
Models
Words
Expanded form
Decimal place values
5.1.2.1 Read and write decimals using place value to describe decimals in terms of groups from millionths to millions.
Models
Words
Expanded form
Decimal place values
5.1.2.2 Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number.
5.1.2.2 Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number.
5.1.2.3 Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
Decimals
Fractions
Decimals and fractions
5.1.2.3 Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
Decimals
Fractions
Decimals and fractions
5.1.2.4 Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various contexts.
Equivalent decimals
Equivalent fractions
Decimals and fractions
5.1.2.4 Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various contexts.
Equivalent decimals
Equivalent fractions
Decimals and fractions
5.1.2.5 Round numbers to the nearest 0.1, 0.01 and 0.001.
5.1.2.5 Round numbers to the nearest 0.1, 0.01 and 0.001.
5.1.3 Add and subtract fractions, mixed numbers and decimals to solve real-world and mathematical problems.
5.1.3.1 Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms.
Decimals
Fractions with like denominators
Fractions with unlike denominators
5.1.3.1 Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms.
Decimals
Fractions with like denominators
Fractions with unlike denominators
5.1.3.2 Model addition and subtraction of fractions and decimals using a variety of representations.
Decimals
Fractions
5.1.3.2 Model addition and subtraction of fractions and decimals using a variety of representations.
Decimals
Fractions
5.1.3.3 Estimate sums and differences of decimals and fractions to assess the reasonableness of results.
Decimals
Fractions
5.1.3.3 Estimate sums and differences of decimals and fractions to assess the reasonableness of results.
Decimals
Fractions
5.1.3.4 Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data.
Decimals
Fractions
Mixed numbers
5.1.3.4 Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data.
Decimals
Fractions
Mixed numbers
5.2
Algebra
5.2.1 Recognize and represent patterns of change; use patterns, tables, graphs and rules to solve real-world and mathematical problems.
5.2.1.1 Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems.
Input/output tables
Number sequences
Two-variable relationships
5.2.1.1 Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems.
Input/output tables
Number sequences
Two-variable relationships
5.2.1.2 Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system.
Coordinate plane
Graph relationships
5.2.1.2 Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system.
Coordinate plane
Graph relationships
5.2.2 Use properties of arithmetic to generate equivalent numerical expressions and evaluate expressions involving whole numbers.
5.2.2.1 Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers.
Properties of addition
Properties of multiplication
Order of operations
5.2.2.1 Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers.
Properties of addition
Properties of multiplication
Order of operations
5.2.3 Understand and interpret equations and inequalities involving variables and whole numbers, and use them to represent and solve real-world and mathematical problems.
5.2.3.1 Determine whether an equation or inequality involving a variable is true or false for a given value of the variable.
Equations
Inequalities
5.2.3.1 Determine whether an equation or inequality involving a variable is true or false for a given value of the variable.
Equations
Inequalities
5.2.3.2 Represent real-world situations using equations and inequalities involving variables. Create real-world situations corresponding to equations and inequalities.
5.2.3.2 Represent real-world situations using equations and inequalities involving variables. Create real-world situations corresponding to equations and inequalities.
5.2.3.3 Evaluate expressions and solve equations involving variables when values for the variables are given.
5.2.3.3 Evaluate expressions and solve equations involving variables when values for the variables are given.
5.3
Geometry & Measurement
5.3.1 Describe, classify, and draw representations of three-dimensional figures.
5.3.1.1 Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces.
5.3.1.1 Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces.
5.3.1.2 Recognize and draw a net for a three-dimensional figure.
5.3.1.2 Recognize and draw a net for a three-dimensional figure.
5.3.2 Determine the area of triangles and quadrilaterals; determine the surface area and volume of rectangular prisms in various contexts.
5.3.2.1 Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles.
Triangles
Parallelograms
Trapezoids
5.3.2.1 Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles.
Triangles
Parallelograms
Trapezoids
5.3.2.2 Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms.
5.3.2.2 Use various tools and strategies to measure the volume and surface area of objects that are shaped like rectangular prisms.
5.3.2.3 Understand that the volume of a three-dimensional figure can be found by counting the total number of same-size cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements.
5.3.2.3 Understand that the volume of a three-dimensional figure can be found by counting the total number of same-size cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements.
5.3.2.4 Develop and use the formulas V = lwh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a rectangular prism by breaking the prism into layers of unit cubes.
5.3.2.4 Develop and use the formulas V = lwh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a rectangular prism by breaking the prism into layers of unit cubes.
5.4
Data Analysis
5.4.1 Display and interpret data; determine mean, median and range.
5.4.1.1 Know and use the definitions of the mean, median and range of a set of data. Know how to use a spreadsheet to find the mean, median and range of a data set. Understand that the mean is a "leveling out" of data.
Mean
Median
Range
5.4.1.1 Know and use the definitions of the mean, median and range of a set of data. Know how to use a spreadsheet to find the mean, median and range of a data set. Understand that the mean is a "leveling out" of data.
Mean
Median
Range
5.4.1.2 Create and analyze double-bar graphs and line graphs by applying understanding of whole numbers, fractions and decimals. Know how to create spreadsheet tables and graphs to display data.
Line graphs
Double bar graphs
5.4.1.2 Create and analyze double-bar graphs and line graphs by applying understanding of whole numbers, fractions and decimals. Know how to create spreadsheet tables and graphs to display data.
Line graphs
Double bar graphs