North Carolina Standard Course of Study: Grade 7
Skills available for North Carolina seventh-grade math standards
Section
Print skill plan
NC.7.RP
Ratio and Proportional Relationships
Analyze proportional relationships and use them to solve real-world and mathematical problems.
NC.7.RP.1 Compute unit rates associated with ratios of fractions to solve real-world and mathematical problems.
NC.7.RP.1 Compute unit rates associated with ratios of fractions to solve real-world and mathematical problems.
NC.7.RP.2 Recognize and represent proportional relationships between quantities.
NC.7.RP.2 Recognize and represent proportional relationships between quantities.
NC.7.RP.2.a: Understand that a proportion is a relationship of equality between ratios.
NC.7.RP.2.a: Understand that a proportion is a relationship of equality between ratios.
NC.7.RP.2.a.1: Represent proportional relationships using tables and graphs.
NC.7.RP.2.a.1: Represent proportional relationships using tables and graphs.
NC.7.RP.2.a.2: Recognize whether ratios are in a proportional relationship using tables and graphs.
Ratios and proportions
Proportional relationships
NC.7.RP.2.a.2: Recognize whether ratios are in a proportional relationship using tables and graphs.
Ratios and proportions
Proportional relationships
NC.7.RP.2.a.3: Compare two different proportional relationships using tables, graphs, equations, and verbal descriptions.
NC.7.RP.2.a.3: Compare two different proportional relationships using tables, graphs, equations, and verbal descriptions.
NC.7.RP.2.b: Identify the unit rate (constant of proportionality) within two quantities in a proportional relationship using tables, graphs, equations, and verbal descriptions.
NC.7.RP.2.b: Identify the unit rate (constant of proportionality) within two quantities in a proportional relationship using tables, graphs, equations, and verbal descriptions.
NC.7.RP.2.c: Create equations and graphs to represent proportional relationships.
Represent relationships
Solve proportional problems
NC.7.RP.2.c: Create equations and graphs to represent proportional relationships.
Represent relationships
Solve proportional problems
NC.7.RP.2.d: Use a graphical representation of a proportional relationship in context to:
NC.7.RP.2.d: Use a graphical representation of a proportional relationship in context to:
NC.7.RP.2.d.1: Explain the meaning of any point (x, y).
NC.7.RP.2.d.1: Explain the meaning of any point (x, y).
NC.7.RP.2.d.2: Explain the meaning of (0, 0) and why it is included.
NC.7.RP.2.d.2: Explain the meaning of (0, 0) and why it is included.
NC.7.RP.2.d.3: Understand that the y-coordinate of the ordered pair (1, r) corresponds to the unit rate and explain its meaning.
NC.7.RP.2.d.3: Understand that the y-coordinate of the ordered pair (1, r) corresponds to the unit rate and explain its meaning.
NC.7.RP.3 Use scale factors and unit rates in proportional relationships to solve ratio and percent problems.
Unit prices
Percent of change
Percent problems
Circle graphs
NC.7.RP.3 Use scale factors and unit rates in proportional relationships to solve ratio and percent problems.
Unit prices
Percent of change
Percent problems
Circle graphs
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity
NC.7.NS
The Number System
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
NC.7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers, using the properties of operations, and describing real-world contexts using sums and differences.
Integers
Decimals
Fractions and mixed numbers
Rational numbers
NC.7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers, using the properties of operations, and describing real-world contexts using sums and differences.
Integers
Decimals
Fractions and mixed numbers
Rational numbers
NC.7.NS.2 Apply and extend previous understandings of multiplication and division.
NC.7.NS.2 Apply and extend previous understandings of multiplication and division.
NC.7.NS.2.a: Understand that a rational number is any number that can be written as a quotient of integers with a non-zero divisor.
NC.7.NS.2.a: Understand that a rational number is any number that can be written as a quotient of integers with a non-zero divisor.
NC.7.NS.2.b: Apply properties of operations as strategies, including the standard algorithms, to multiply and divide rational numbers and describe the product and quotient in real-world contexts.
Integers
Decimals
Fractions
Rational numbers
NC.7.NS.2.b: Apply properties of operations as strategies, including the standard algorithms, to multiply and divide rational numbers and describe the product and quotient in real-world contexts.
Integers
Decimals
Fractions
Rational numbers
NC.7.NS.2.c: Use division and previous understandings of fractions and decimals.
NC.7.NS.2.c: Use division and previous understandings of fractions and decimals.
NC.7.NS.2.c.1: Convert a fraction to a decimal using long division.
NC.7.NS.2.c.1: Convert a fraction to a decimal using long division.
NC.7.NS.2.c.2: Understand that the decimal form of a rational number terminates in 0s or eventually repeats.
NC.7.NS.2.c.2: Understand that the decimal form of a rational number terminates in 0s or eventually repeats.
NC.7.NS.3 Solve real-world and mathematical problems involving numerical expressions with rational numbers using the four operations.
Addition and subtraction
Multiplication and division
Mixed operations
NC.7.NS.3 Solve real-world and mathematical problems involving numerical expressions with rational numbers using the four operations.
Addition and subtraction
Multiplication and division
Mixed operations
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity
NC.7.EE
Expressions and Equations
Use properties of operations to generate equivalent expressions.
NC.7.EE.1 Apply properties of operations as strategies to:
NC.7.EE.1 Apply properties of operations as strategies to:
NC.7.EE.1.a: Add, subtract, and expand linear expressions with rational coefficients.
Properties of operations
Add and subtract
Identify linear expressions
NC.7.EE.1.a: Add, subtract, and expand linear expressions with rational coefficients.
Properties of operations
Add and subtract
Identify linear expressions
NC.7.EE.1.b: Factor linear expression with an integer GCF.
NC.7.EE.1.b: Factor linear expression with an integer GCF.
NC.7.EE.2 Understand that equivalent expressions can reveal real-world and mathematical relationships. Interpret the meaning of the parts of each expression in context.
NC.7.EE.2 Understand that equivalent expressions can reveal real-world and mathematical relationships. Interpret the meaning of the parts of each expression in context.
Checkpoint skill Checkpoint opportunity
  • •
    Coming soon: Checkpoint: Linear expressions
Checkpoint skill Checkpoint opportunity
  • •
    Coming soon: Checkpoint: Linear expressions
Solve real-world and mathematical problems using numerical and algebraic expressions, equations, and inequalities.
NC.7.EE.3 Solve multi-step real-world and mathematical problems posed with rational numbers in algebraic expressions.
NC.7.EE.3 Solve multi-step real-world and mathematical problems posed with rational numbers in algebraic expressions.
NC.7.EE.3.a: Apply properties of operations to calculate with positive and negative numbers in any form.
Order of operations
Evaluate variable expressions
Real-world problems
NC.7.EE.3.a: Apply properties of operations to calculate with positive and negative numbers in any form.
Order of operations
Evaluate variable expressions
Real-world problems
NC.7.EE.3.b: Convert between different forms of a number and equivalent forms of the expression as appropriate.
Fractions
Convert rational numbers
NC.7.EE.3.b: Convert between different forms of a number and equivalent forms of the expression as appropriate.
Fractions
Convert rational numbers
NC.7.EE.4 Use variables to represent quantities to solve real-world or mathematical problems.
NC.7.EE.4 Use variables to represent quantities to solve real-world or mathematical problems.
NC.7.EE.4.a: Construct equations to solve problems by reasoning about the quantities.
NC.7.EE.4.a: Construct equations to solve problems by reasoning about the quantities.
NC.7.EE.4.a.1: Fluently solve multistep equations with the variable on one side, including those generated by word problems.
Solve equations
Word problems
NC.7.EE.4.a.1: Fluently solve multistep equations with the variable on one side, including those generated by word problems.
Solve equations
Word problems
NC.7.EE.4.a.2: Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.
NC.7.EE.4.a.2: Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.
NC.7.EE.4.a.3: Interpret the solution in context.
NC.7.EE.4.a.3: Interpret the solution in context.
NC.7.EE.4.b: Construct inequalities to solve problems by reasoning about the quantities.
NC.7.EE.4.b: Construct inequalities to solve problems by reasoning about the quantities.
NC.7.EE.4.b.1: Fluently solve multi-step inequalities with the variable on one side, including those generated by word problems.
NC.7.EE.4.b.1: Fluently solve multi-step inequalities with the variable on one side, including those generated by word problems.
NC.7.EE.4.b.2: Compare an algebraic solution process for equations and an algebraic solution process for inequalities.
NC.7.EE.4.b.2: Compare an algebraic solution process for equations and an algebraic solution process for inequalities.
NC.7.EE.4.b.3: Graph the solution set of the inequality and interpret in context.
NC.7.EE.4.b.3: Graph the solution set of the inequality and interpret in context.
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity
NC.7.G
Geometry
Draw, construct, and describe geometrical figures and describe the relationships between them.
NC.7.G.1 Solve problems involving scale drawings of geometric figures by:
NC.7.G.1 Solve problems involving scale drawings of geometric figures by:
NC.7.G.1.a: Building an understanding that angle measures remain the same and side lengths are proportional.
NC.7.G.1.a: Building an understanding that angle measures remain the same and side lengths are proportional.
NC.7.G.1.b: Using a scale factor to compute actual lengths and areas from a scale drawing.
NC.7.G.1.b: Using a scale factor to compute actual lengths and areas from a scale drawing.
NC.7.G.1.c: Creating a scale drawing.
NC.7.G.1.c: Creating a scale drawing.
NC.7.G.2 Understand the characteristics of angles and side lengths that create a unique triangle, more than one triangle or no triangle. Build triangles from three measures of angles and/or sides.
NC.7.G.2 Understand the characteristics of angles and side lengths that create a unique triangle, more than one triangle or no triangle. Build triangles from three measures of angles and/or sides.
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity
Solve real-world and mathematical problems involving angle measure, area, surface area, and volume.
NC.7.G.4 Understand area and circumference of a circle.
NC.7.G.4 Understand area and circumference of a circle.
NC.7.G.4.a: Understand the relationships between the radius, diameter, circumference, and area.
NC.7.G.4.a: Understand the relationships between the radius, diameter, circumference, and area.
NC.7.G.4.b: Apply the formulas for area and circumference of a circle to solve problems.
NC.7.G.4.b: Apply the formulas for area and circumference of a circle to solve problems.
NC.7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve equations for an unknown angle in a figure.
NC.7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve equations for an unknown angle in a figure.
NC.7.G.6 Solve real-world and mathematical problems involving:
NC.7.G.6 Solve real-world and mathematical problems involving:
NC.7.G.6.a: Area and perimeter of two-dimensional objects composed of triangles, quadrilaterals, and polygons.
Area
Perimeter
Area and perimeter
NC.7.G.6.a: Area and perimeter of two-dimensional objects composed of triangles, quadrilaterals, and polygons.
Area
Perimeter
Area and perimeter
NC.7.G.6.b: Volume and surface area of pyramids, prisms, or three-dimensional objects composed of cubes, pyramids, and right prisms.
Volume
Surface area
NC.7.G.6.b: Volume and surface area of pyramids, prisms, or three-dimensional objects composed of cubes, pyramids, and right prisms.
Volume
Surface area
Checkpoint skill Checkpoint opportunity
Checkpoint skill Checkpoint opportunity
NC.7.SP
Statistics and Probability
Use random sampling to draw inferences about a population.
NC.7.SP.1 Understand that statistics can be used to gain information about a population by:
NC.7.SP.1 Understand that statistics can be used to gain information about a population by:
NC.7.SP.1.a: Recognizing that generalizations about a population from a sample are valid only if the sample is representative of that population.
NC.7.SP.1.a: Recognizing that generalizations about a population from a sample are valid only if the sample is representative of that population.
NC.7.SP.1.b: Using random sampling to produce representative samples to support valid inferences.
NC.7.SP.1.b: Using random sampling to produce representative samples to support valid inferences.
NC.7.SP.2 Generate multiple random samples (or simulated samples) of the same size to gauge the variation in estimates or predictions, and use this data to draw inferences about a population with an unknown characteristic of interest.
NC.7.SP.2 Generate multiple random samples (or simulated samples) of the same size to gauge the variation in estimates or predictions, and use this data to draw inferences about a population with an unknown characteristic of interest.
Checkpoint skill Checkpoint opportunity
  • •
    Coming soon: Checkpoint: Samples of a population
Checkpoint skill Checkpoint opportunity
  • •
    Coming soon: Checkpoint: Samples of a population
Make informal inferences to compare two populations.
NC.7.SP.3 Recognize the role of variability when comparing two populations.
NC.7.SP.3 Recognize the role of variability when comparing two populations.
NC.7.SP.3.a: Calculate the measure of variability of a data set and understand that it describes how the values of the data set vary with a single number.
NC.7.SP.3.a: Calculate the measure of variability of a data set and understand that it describes how the values of the data set vary with a single number.
NC.7.SP.3.a.1: Understand the mean absolute deviation of a data set is a measure of variability that describes the average distance that points within a data set are from the mean of the data set.
NC.7.SP.3.a.1: Understand the mean absolute deviation of a data set is a measure of variability that describes the average distance that points within a data set are from the mean of the data set.
NC.7.SP.3.a.2: Understand that the range describes the spread of the entire data set.
NC.7.SP.3.a.2: Understand that the range describes the spread of the entire data set.
NC.7.SP.3.a.3: Understand that the interquartile range describes the spread of the middle 50% of the data.
NC.7.SP.3.a.3: Understand that the interquartile range describes the spread of the middle 50% of the data.
NC.7.SP.3.b: Informally assess the difference between two data sets by examining the overlap and separation between the graphical representations of two data sets.
NC.7.SP.3.b: Informally assess the difference between two data sets by examining the overlap and separation between the graphical representations of two data sets.
NC.7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw comparative inferences about two populations.
NC.7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw comparative inferences about two populations.
Checkpoint skill Checkpoint opportunity
  • •
    Coming soon: Checkpoint: Compare two populations
Checkpoint skill Checkpoint opportunity
  • •
    Coming soon: Checkpoint: Compare two populations
Investigate chance processes and develop, use, and evaluate probability models.
NC.7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.
NC.7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring.
NC.7.SP.6 Collect data to calculate the experimental probability of a chance event, observing its long-run relative frequency. Use this experimental probability to predict the approximate relative frequency.
NC.7.SP.6 Collect data to calculate the experimental probability of a chance event, observing its long-run relative frequency. Use this experimental probability to predict the approximate relative frequency.
NC.7.SP.7 Develop a probability model and use it to find probabilities of simple events.
NC.7.SP.7 Develop a probability model and use it to find probabilities of simple events.
NC.7.SP.7.a: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
NC.7.SP.7.a: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
NC.7.SP.7.b: Develop a probability model (which may not be uniform) by repeatedly performing a chance process and observing frequencies in the data generated.
NC.7.SP.7.b: Develop a probability model (which may not be uniform) by repeatedly performing a chance process and observing frequencies in the data generated.
NC.7.SP.7.c: Compare theoretical and experimental probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
NC.7.SP.7.c: Compare theoretical and experimental probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
NC.7.SP.8 Determine probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
NC.7.SP.8 Determine probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
NC.7.SP.8.a: Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
NC.7.SP.8.a: Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
NC.7.SP.8.b: For an event described in everyday language, identify the outcomes in the sample space which compose the event, when the sample space is represented using organized lists, tables, and tree diagrams.
NC.7.SP.8.b: For an event described in everyday language, identify the outcomes in the sample space which compose the event, when the sample space is represented using organized lists, tables, and tree diagrams.
NC.7.SP.8.c: Design and use a simulation to generate frequencies for compound events.
NC.7.SP.8.c: Design and use a simulation to generate frequencies for compound events.
Checkpoint skill Checkpoint opportunity
  • •
    Coming soon: Checkpoint: Theoretical and experimental probability
  • •
    Coming soon: Checkpoint: Probability of compound events
Checkpoint skill Checkpoint opportunity
  • •
    Coming soon: Checkpoint: Theoretical and experimental probability
  • •
    Coming soon: Checkpoint: Probability of compound events