# Minnesota Mathematics Learning Standards — Grade 7

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#### 7.1.1.1

Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. Recognize that ? is not rational, but that it can be approximated by rational numbers such as and 3.14.

#### 7.1.1.2

Understand that division of two integers will always result in a rational number. Use this information to interpret the decimal result of a division problem when using a calculator.

#### 7.1.1.3

Locate positive and negative rational numbers on a number line, understand the concept of opposites, and plot pairs of positive and negative rational numbers on a coordinate grid.

#### 7.1.1.4

Compare positive and negative rational numbers expressed in various forms using the symbols < , >, = , ? , ? .

#### 7.1.1.5

Recognize and generate equivalent representations of positive and negative rational numbers, including equivalent fractions.

#### 7.1.2.1

Add, subtract, multiply and divide positive and negative rational numbers that are integers, fractions and terminating decimals; use efficient and generalizable procedures, including standard algorithms; raise positive rational numbers to whole-number exponents.

#### 7.1.2.2

Use real-world contexts and the inverse relationship between addition and subtraction to explain why the procedures of arithmetic with negative rational numbers make sense.

#### 7.1.2.3

Understand that calculators and other computing technologies often truncate or round numbers.

#### 7.1.2.4

Solve problems in various contexts involving calculations with positive and negative rational numbers and positive integer exponents, including computing simple and compound interest.

#### 7.1.2.5

Use proportional reasoning to solve problems involving ratios in various contexts.

#### 7.1.2.6

Demonstrate an understanding of the relationship between the absolute value of a rational number and distance on a number line. Use the symbol for absolute value.

#### 7.2.1.1

Understand that a relationship between two variables, x and y, is proportional if it can be expressed in the form or . Distinguish proportional relationships from other relationships, including inversely proportional relationships ( ).

#### 7.2.1.2

Understand that the graph of a proportional relationship is a line through the origin whose slope is the unit rate (constant of proportionality). Know how to use graphing technology to examine what happens to a line when the unit rate is changed.

#### 7.2.2.1

Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations.

#### 7.2.2.2

Solve multi-step problems involving proportional relationships in numerous contexts.

#### 7.2.2.3

Use knowledge of proportions to assess the reasonableness of solutions.

#### 7.2.2.4

Represent real-world or mathematical situations using equations and inequalities involving variables and positive and negative rational numbers.

#### 7.2.3.1

Use properties of algebra to generate equivalent numerical and algebraic expressions containing rational numbers, grouping symbols and whole number exponents. Properties of algebra include associative, commutative and distributive laws.

#### 7.2.3.2

Evaluate algebraic expressions containing rational numbers and whole number exponents at specified values of their variables.

#### 7.2.3.3

Apply understanding of order of operations and grouping symbols when using calculators and other technologies.

#### 7.2.4.1

Represent relationships in various contexts with equations involving variables and positive and negative rational numbers. Use the properties of equality to solve for the value of a variable. Interpret the solution in the original context.

#### 7.2.4.2

Solve equations resulting from proportional relationships in various contexts.

#### 7.3.1.1

Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is ?. Calculate the circumference and area of circles and sectors of circles to solve problems in various contexts.

#### 7.3.1.2

Calculate the volume and surface area of cylinders and justify the formulas used.

#### 7.3.2.1

Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors.

#### 7.3.2.2

Apply scale factors, length ratios and area ratios to determine side lengths and areas of similar geometric figures.

#### 7.3.2.3

Use proportions and ratios to solve problems involving scale drawings and conversions of measurement units.

#### 7.3.2.4

Graph and describe translations and reflections of figures on a coordinate grid and determine the coordinates of the vertices of the figure after the transformation.

#### 7.4.1.1

Design simple experiments and collect data. Determine mean, median and range for quantitative data and from data represented in a display. Use these quantities to draw conclusions about the data, compare different data sets, and make predictions.

#### 7.4.1.2

Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Know how to create data displays using a spreadsheet to examine this impact.

#### 7.4.2.1

Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology.

#### 7.4.3.1

Use random numbers generated by a calculator or a spreadsheet or taken from a table to simulate situations involving randomness; make a histogram to display the results, and compare the results to known probabilities.

#### 7.4.3.2

Calculate probability as a fraction of sample space or as a fraction of area. Express probabilities as percents, decimals and fractions.

#### 7.4.3.3

Use proportional reasoning to draw conclusions about and predict relative frequencies of outcomes based on probabilities.