# Minnesota Mathematics Learning Standards — Grade 5

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#### 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.

#### 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.

#### 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.

#### 5.1.2.1

Read and write decimals using place value to describe decimals in terms of groups from millionths to millions.

#### 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.

#### 5.1.2.4

Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various contexts.

#### 5.1.2.5

Round numbers to the nearest 0.1, 0.01 and 0.001.

#### 5.1.3.1

Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms.

#### 5.1.3.2

Model addition and subtraction of fractions and decimals using a variety of representations.

#### 5.1.3.3

Estimate sums and differences of decimals and fractions to assess the reasonableness of results.

#### 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.

#### 5.2.1.1

Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems.

#### 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.

#### 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.

#### 5.2.3.1

Determine whether an equation or inequality involving a variable is true or false for a given value of the variable.

#### 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.

#### 5.3.1.1

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.

#### 5.3.2.1

Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles.

#### 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-sized 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 = ?wh 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.

#### 5.4.1.1

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.

#### 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.