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Skills available for Minnesota seventh-grade math standards

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7.1 Number & Operation

7.1.1 Read, write, represent and compare positive and negative rational numbers, expressed as integers, fractions and decimals.
- 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 pi is not rational, but that it can be approximated by rational numbers such as 22/7 and 3.14.
  - Convert decimals to fractions or mixed numbers (7-H.2)
  - Identify rational numbers (7-H.4)
- 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 the 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 <, >, =, "less than or equal to", "greater than or equal to".
- 7.1.1.5 Recognize and generate equivalent representations of positive and negative rational numbers, including equivalent fractions.
7.1.2 Calculate with positive and negative rational numbers, and rational numbers with whole number exponents, to solve real-world and mathematical problems.
- 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 Algebra

7.2.1 Understand the concept of proportionality in real-world and mathematical situations, and distinguish between proportional and other relationships.
- 7.2.1.1 Understand that a relationship between two variables, x and y, is proportional if it can be expressed in the form y/x = k or y = kx. Distinguish proportional relationships from other relationships, including inversely proportional relationships (xy=k or y= k/x).
- 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.
  - Identify proportional relationships by graphing (7-K.3)
  - Identify proportional relationships from graphs and equations (7-K.6)
7.2.2 Recognize proportional relationships in real-world and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols and graphs; solve problems involving proportional relationships and explain results in the original context.
- 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 Apply understanding of order of operations and algebraic properties to generate equivalent numerical and algebraic expressions containing positive and negative rational numbers and grouping symbols; evaluate such expressions.
- 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 Represent real-world and mathematical situations using equations with variables. Solve equations symbolically, using the properties of equality. Also solve equations graphically and numerically. Interpret solutions in the original context.
- 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.
  - Solve proportions: word problems (7-J.12)
  - Scale drawings: word problems (7-Z.2)

7.3 Geometry & Measurement

7.3.1 Use reasoning with proportions and ratios to determine measurements, justify formulas and solve real-world and mathematical problems involving circles and related geometric figures.
- 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 pi. 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.
  - Surface area of cylinders (7-Y.17)
  - Volume of cylinders (7-Y.22)
7.3.2 Analyze the effect of change of scale, translations and reflections on the attributes of two-dimensional figures.
- 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 Data Analysis & Probability

7.4.1 Use mean, median and range to draw conclusions about data and make predictions.
- 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.
  - Calculate mean, median, mode, and range (7-DD.1)
  - Interpret charts and graphs to find mean, median, mode, and range (7-DD.2)
- 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.
  - Mean, median, mode, and range: find the missing number (7-DD.3)
  - Changes in mean, median, mode, and range (7-DD.4)
7.4.2 Display and interpret data in a variety of ways, including circle graphs and histograms.
- 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 Calculate probabilities and reason about probabilities using proportions to solve real-world and mathematical problems.
- 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.

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7.1 Number & Operation

7.1.1 Read, write, represent and compare positive and negative rational numbers, expressed as integers, fractions and decimals.

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 pi is not rational, but that it can be approximated by rational numbers such as 22/7 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 the 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 <, >, =, "less than or equal to", "greater than or equal to".

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

7.1.2 Calculate with positive and negative rational numbers, and rational numbers with whole number exponents, to solve real-world and mathematical problems.

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 Algebra

7.2.1 Understand the concept of proportionality in real-world and mathematical situations, and distinguish between proportional and other relationships.

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

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 Recognize proportional relationships in real-world and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols and graphs; solve problems involving proportional relationships and explain results in the original context.

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 Apply understanding of order of operations and algebraic properties to generate equivalent numerical and algebraic expressions containing positive and negative rational numbers and grouping symbols; evaluate such expressions.

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 Represent real-world and mathematical situations using equations with variables. Solve equations symbolically, using the properties of equality. Also solve equations graphically and numerically. Interpret solutions in the original context.

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 Geometry & Measurement

7.3.1 Use reasoning with proportions and ratios to determine measurements, justify formulas and solve real-world and mathematical problems involving circles and related geometric figures.

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 pi. 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 Analyze the effect of change of scale, translations and reflections on the attributes of two-dimensional figures.

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 Data Analysis & Probability

7.4.1 Use mean, median and range to draw conclusions about data and make predictions.

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 Display and interpret data in a variety of ways, including circle graphs and histograms.

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 Calculate probabilities and reason about probabilities using proportions to solve real-world and mathematical problems.

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.