North Carolina Standard Course of Study for Eighth Grade Math

Applications of percent
Worksheets: 4Study Guides: 1
Collecting and describing data
Worksheets: 3Study Guides: 1
Experimental Probability
FreeExperimental probability is the probability that a certain outcome will occur based on an experiment being performed multiple times. Probability word problems worksheets. Read more...iWorksheets: 3Study Guides: 1
Numbers and percents
Worksheets: 3Study Guides: 1
Ratios, proportions and percents
Worksheets: 4Study Guides: 1
Sequences
Worksheets: 4Study Guides: 1
Theoretical probability and counting
Probability word problems worksheets. Theoretical probability is the probability that a certain outcome will occur based on all the possible outcomes. Sometimes, the number of ways that an event can happen depends on the order. A permutation is an arrangement of objects in which order matters. A combination is a set of objects in which order does not matter. Probability is also based on whether events are dependent or independent of each other. Read more...iWorksheets: 3Study Guides: 1

NC.MP. Standards for Mathematical Practice

MP.1. Make sense of problems and persevere in solving them.

Mathematical processes
Worksheets :3Study Guides :1

MP.2. Reason abstractly and quantitatively.

Mathematical processes
Worksheets :3Study Guides :1

NC.8.NS. The Number System

Know that there are numbers that are not rational, and approximate them by rational numbers.

NC.8.NS.1. Understand that every number has a decimal expansion. Building upon the definition of a rational number, know that an irrational number is defined as a non-repeating, non-terminating decimal.
Rational and Irrational Numbers
A rational number is a number that can be made into a fraction. Decimals that repeat or terminate are rational because they can be changed into fractions. An irrational number is a number that cannot be made into a fraction. Decimals that do not repeat or end are irrational numbers. Pi is an irrational number. Read more...iWorksheets :3Study Guides :1
NC.8.NS.2. Use rational approximations of irrational numbers to compare the size of irrational numbers and locate them approximately on a number line. Estimate the value of expressions involving:
NC.8.NS.2.a. Square roots and cube roots to the tenths.
Rational and Irrational Numbers
A rational number is a number that can be made into a fraction. Decimals that repeat or terminate are rational because they can be changed into fractions. An irrational number is a number that cannot be made into a fraction. Decimals that do not repeat or end are irrational numbers. Pi is an irrational number. Read more...iWorksheets :3Study Guides :1
The Pythagorean Theorem
Pythagorean Theorem is a fundamental relation in Euclidean geometry. It states the sum of the squares of the legs of a right triangle equals the square of the length of the hypotenuse. Determine the distance between two points using the Pythagorean Theorem. Read more...iWorksheets :4Study Guides :1
Real numbers
Worksheets :4Study Guides :1
NC.8.NS.2.b. ݜ to the hundredths.
Measurement, Perimeter, and Circumference
Worksheets :3Study Guides :1
Exploring Area and Surface Area
Worksheets :4Study Guides :1
Perimeter and area
Worksheets :4Study Guides :1

NC.8.EE. Expressions and Equations

Work with radicals and integer exponents.

NC.8.EE.1. Develop and apply the properties of integer exponents to generate equivalent numerical expressions.
Exponents, Factors and Fractions
In a mathematical expression where the same number is multiplied many times, it is often useful to write the number as a base with an exponent. Exponents are also used to evaluate numbers. Any number to a zero exponent is 1 and any number to a negative exponent is a number less than 1. Exponents are used in scientific notation to make very large or very small numbers easier to write. Read more...iWorksheets :4Study Guides :1
Polynomials and Exponents
Worksheets :4Study Guides :1
NC.8.EE.2. Use square root and cube root symbols to:
NC.8.EE.2.a. Represent solutions to equations of the form ݑ^2 = Űݑ and ݰݑ^3 = Űݑ, where ݰݑ is a positive rational number.
Rational and Irrational Numbers
A rational number is a number that can be made into a fraction. Decimals that repeat or terminate are rational because they can be changed into fractions. An irrational number is a number that cannot be made into a fraction. Decimals that do not repeat or end are irrational numbers. Pi is an irrational number. Read more...iWorksheets :3Study Guides :1
The Pythagorean Theorem
Pythagorean Theorem is a fundamental relation in Euclidean geometry. It states the sum of the squares of the legs of a right triangle equals the square of the length of the hypotenuse. Determine the distance between two points using the Pythagorean Theorem. Read more...iWorksheets :4Study Guides :1
Real numbers
Worksheets :4Study Guides :1
NC.8.EE.2.b. Evaluate square roots of perfect squares and cube roots of perfect cubes for positive numbers less than or equal to 400.
The Pythagorean Theorem
Pythagorean Theorem is a fundamental relation in Euclidean geometry. It states the sum of the squares of the legs of a right triangle equals the square of the length of the hypotenuse. Determine the distance between two points using the Pythagorean Theorem. Read more...iWorksheets :4Study Guides :1
Real numbers
Worksheets :4Study Guides :1
NC.8.EE.3. Use numbers expressed in scientific notation to estimate very large or very small quantities and to express how many times as much one is than the other.
Exponents, Factors and Fractions
In a mathematical expression where the same number is multiplied many times, it is often useful to write the number as a base with an exponent. Exponents are also used to evaluate numbers. Any number to a zero exponent is 1 and any number to a negative exponent is a number less than 1. Exponents are used in scientific notation to make very large or very small numbers easier to write. Read more...iWorksheets :4Study Guides :1
Polynomials and Exponents
Worksheets :4Study Guides :1

Analyze and solve linear equations and inequalities.

NC.8.EE.7. Solve real-world and mathematical problems by writing and solving equations and inequalities in one variable.
NC.8.EE.7.a. Recognize linear equations in one variable as having one solution, infinitely many solutions, or no solutions.
Introduction to Algebra
Algebra is the practice of using expressions with letters or variables that represent numbers. Words can be changed into a mathematical expression by using the words, plus, exceeds, diminished, less, times, the product, divided, the quotient and many more. Algebra uses variables to represent a value that is not yet known. Read more...iWorksheets :3Study Guides :1
Equations and Inequalities
Algebraic equations are mathematical equations that contain a letter or variable, which represents a number. To solve an algebraic equation, inverse operations are used. The inverse operation of addition is subtraction and the inverse operation of subtraction is addition. Inequalities are mathematical equations that compare two quantities using greater than, >; greater than or equal to ≥; less than, <; and less than or equal to, ≤. Read more...iWorksheets :5Study Guides :1
Using Integers
Integers are negative numbers, zero and positive numbers. To compare integers, a number line can be used. On a number line, negative integers are on the left side of zero with the larger a negative number, the farther to the left it is. Positive integers are on the right side of zero on the number line. If a number is to the left of another number it is said to be less than that number. In the coordinate plane, the x-axis is a horizontal line with negative numbers, zero and positive numbers. Read more...iWorksheets :4Study Guides :1
Decimal Operations
Decimal operations refer to the mathematical operations that can be performed with decimals: addition, subtraction, multiplication and division. The process for adding, subtracting, multiplying and dividing decimals must be followed in order to achieve the correct answer. Read more...iWorksheets :3Study Guides :1
Fraction Operations
Fraction operations are the processes of adding, subtracting, multiplying and dividing fractions and mixed numbers. A mixed number is a fraction with a whole number. Adding fractions is common in many everyday events, such as making a recipe and measuring wood. In order to add and subtract fractions, the fractions must have the same denominator. Read more...iWorksheets :3Study Guides :1
Introduction to Percent
What Is Percent? A percent is a term that describes a decimal in terms of one hundred. Percent means per hundred. Percents, fractions and decimals all can equal each other, as in the case of 10%, 0.1 and 1/10. Percents can be greater than 100% or smaller than 1%. A markup from the cost of making an item to the actual sales price is usually greater than 100%. A salesperson's commission might be 1/2% depending on the item sold. Read more...iWorksheets :4Study Guides :1
Algebraic Equations
What are algebraic equations? Algebraic equations are mathematical quations that contain a letter or variable, which represents a number. When algebraic equations are written in words, the words must be changed into the appropriate numbers and variable in order to solve. Read more...iWorksheets :4Study Guides :1
Equations and inequalities
Worksheets :3Study Guides :1
Integer operations
Worksheets :4Study Guides :1
Rational numbers and operations
Worksheets :3Study Guides :1
Solving linear equations
Worksheets :5Study Guides :1
Solving equations and inequalities
Worksheets :3Study Guides :1
NC.8.EE.7.b. Solve linear equations and inequalities including multi-step equations and inequalities with the same variable on both sides.
Introduction to Algebra
Algebra is the practice of using expressions with letters or variables that represent numbers. Words can be changed into a mathematical expression by using the words, plus, exceeds, diminished, less, times, the product, divided, the quotient and many more. Algebra uses variables to represent a value that is not yet known. Read more...iWorksheets :3Study Guides :1
Equations and Inequalities
Algebraic equations are mathematical equations that contain a letter or variable, which represents a number. To solve an algebraic equation, inverse operations are used. The inverse operation of addition is subtraction and the inverse operation of subtraction is addition. Inequalities are mathematical equations that compare two quantities using greater than, >; greater than or equal to ≥; less than, <; and less than or equal to, ≤. Read more...iWorksheets :5Study Guides :1
Using Integers
Integers are negative numbers, zero and positive numbers. To compare integers, a number line can be used. On a number line, negative integers are on the left side of zero with the larger a negative number, the farther to the left it is. Positive integers are on the right side of zero on the number line. If a number is to the left of another number it is said to be less than that number. In the coordinate plane, the x-axis is a horizontal line with negative numbers, zero and positive numbers. Read more...iWorksheets :4Study Guides :1
Decimal Operations
Decimal operations refer to the mathematical operations that can be performed with decimals: addition, subtraction, multiplication and division. The process for adding, subtracting, multiplying and dividing decimals must be followed in order to achieve the correct answer. Read more...iWorksheets :3Study Guides :1
Fraction Operations
Fraction operations are the processes of adding, subtracting, multiplying and dividing fractions and mixed numbers. A mixed number is a fraction with a whole number. Adding fractions is common in many everyday events, such as making a recipe and measuring wood. In order to add and subtract fractions, the fractions must have the same denominator. Read more...iWorksheets :3Study Guides :1
Introduction to Percent
What Is Percent? A percent is a term that describes a decimal in terms of one hundred. Percent means per hundred. Percents, fractions and decimals all can equal each other, as in the case of 10%, 0.1 and 1/10. Percents can be greater than 100% or smaller than 1%. A markup from the cost of making an item to the actual sales price is usually greater than 100%. A salesperson's commission might be 1/2% depending on the item sold. Read more...iWorksheets :4Study Guides :1
Algebraic Equations
What are algebraic equations? Algebraic equations are mathematical quations that contain a letter or variable, which represents a number. When algebraic equations are written in words, the words must be changed into the appropriate numbers and variable in order to solve. Read more...iWorksheets :4Study Guides :1
Equations and inequalities
Worksheets :3Study Guides :1
Integer operations
Worksheets :4Study Guides :1
Rational numbers and operations
Worksheets :3Study Guides :1
Solving linear equations
Worksheets :5Study Guides :1
Solving equations and inequalities
Worksheets :3Study Guides :1

NC.8.F. Functions

Define, evaluate, and compare functions.

NC.8.F.1. Understand that a function is a rule that assigns to each input exactly one output.
NC.8.F.1.a. Recognize functions when graphed as the set of ordered pairs consisting of an input and exactly one corresponding output.
Introduction to Functions
Worksheets :5Study Guides :1
Functions
Worksheets :3Study Guides :1
NC.8.F.1.b. Recognize functions given a table of values or a set of ordered pairs.
Introduction to Functions
Worksheets :5Study Guides :1
Functions
Worksheets :3Study Guides :1

Use functions to model relationships between quantities.

NC.8.F.4. Analyze functions that model linear relationships.
NC.8.F.4.a. Understand that a linear relationship can be generalized by ݑ = ưݑڰݑ + Űݑ.
Linear equations
Worksheets :3Study Guides :1
NC.8.F.4.b. Write an equation in slope-intercept form to model a linear relationship by determining the rate of change and the initial value, given at least two (ݑ, Űݑ) values or a graph.
Introduction to Functions
Worksheets :5Study Guides :1
Linear equations
Worksheets :3Study Guides :1
NC.8.F.4.c. Construct a graph of a linear relationship given an equation in slope-intercept form.
Introduction to Functions
Worksheets :5Study Guides :1
Linear equations
Worksheets :3Study Guides :1
NC.8.F.4.d. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of the slope and ݑ-intercept of its graph or a table of values.
Introduction to Functions
Worksheets :5Study Guides :1
Nonlinear Functions and Set Theory
Worksheets :4Study Guides :1
Linear equations
Worksheets :3Study Guides :1

NC.8.G. Geometry

Understand congruence and similarity using physical models, transparencies, or geometry software.

NC.8.G.2. Use transformations to define congruence.
NC.8.G.2.a. Verify experimentally the properties of rotations, reflections, and translations that create congruent figures.
Patterns in geometry
Worksheets :3Study Guides :1
NC.8.G.2.b. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations.
Plane Figures: Lines and Angles
Plane figures in regards to lines and angles refer to the coordinate plane and the various lines and angles within the coordinate plane. Lines in a coordinate plane can be parallel or perpendicular. Angles in a coordinate plane can be acute, obtuse, right or straight. Read more...iWorksheets :3Study Guides :1
Plane Figures: Closed Figure Relationships
Worksheets :3Study Guides :1
Patterns in geometry
Worksheets :3Study Guides :1
NC.8.G.4. Use transformations to define similarity.
NC.8.G.4.a. Verify experimentally the properties of dilations that create similar figures.
Similarity and scale
Worksheets :3Study Guides :1

Analyze angle relationships.

NC.8.G.5. Use informal arguments to analyze angle relationships.
NC.8.G.5.d. Solve real-world and mathematical problems involving angles.
Plane Figures: Lines and Angles
Plane figures in regards to lines and angles refer to the coordinate plane and the various lines and angles within the coordinate plane. Lines in a coordinate plane can be parallel or perpendicular. Angles in a coordinate plane can be acute, obtuse, right or straight. Read more...iWorksheets :3Study Guides :1
Plane figures
Worksheets :4Study Guides :1

Understand and apply the Pythagorean Theorem.

NC.8.G.6. Explain the Pythagorean Theorem and its converse.
The Pythagorean Theorem
Pythagorean Theorem is a fundamental relation in Euclidean geometry. It states the sum of the squares of the legs of a right triangle equals the square of the length of the hypotenuse. Determine the distance between two points using the Pythagorean Theorem. Read more...iWorksheets :4Study Guides :1
NC.8.G.7. Apply the Pythagorean Theorem and its converse to solve real-world and mathematical problems.
The Pythagorean Theorem
Pythagorean Theorem is a fundamental relation in Euclidean geometry. It states the sum of the squares of the legs of a right triangle equals the square of the length of the hypotenuse. Determine the distance between two points using the Pythagorean Theorem. Read more...iWorksheets :4Study Guides :1
NC.8.G.8. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
The Pythagorean Theorem
Pythagorean Theorem is a fundamental relation in Euclidean geometry. It states the sum of the squares of the legs of a right triangle equals the square of the length of the hypotenuse. Determine the distance between two points using the Pythagorean Theorem. Read more...iWorksheets :4Study Guides :1

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

NC.8.G.9. Understand how the formulas for the volumes of cones, cylinders, and spheres are related and use the relationship to solve real-world and mathematical problems.
Finding Volume
Volume measures the amount a solid figure can hold. Volume is measured in terms of cubed units and can be measured in inches, feet, meters, centimeters, and millimeters. The formula for the volume of a rectangular prism is V = l · w · h, where l is the length, w is the width, and h is the height. Read more...iWorksheets :4Study Guides :1
Three dimensional geometry/Measurement
Worksheets :3Study Guides :1

NC.8.SP. Statistics and Probability

Investigate patterns of association in bivariate data.

NC.8.SP.1. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Investigate and describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
Analyzing, Graphing and Displaying Data
There are many types of graphs such as, bar graphs, histograms and line graphs. A bar graph compares data in categories and uses bars, either vertical or horizontal. A histogram is similar to a bar graph, but with histograms the bars touch each other where with bar graphs the bars do not touch each other. A line graph is useful for graphing how data changes over time. With a line graph, data is plotted as points and lines are drawn to connect the points to show how the data changes. Read more...iWorksheets :3Study Guides :1
Using graphs to analyze data
Worksheets :3Study Guides :1
Displaying data
Worksheets :4Study Guides :1
NC.8.SP.2. Model the relationship between bivariate quantitative data to:
NC.8.SP.2.a. Informally fit a straight line for a scatter plot that suggests a linear association.
Linear relationships
Worksheets :3Study Guides :1
NC.8.SP.2.b. Informally assess the model fit by judging the closeness of the data points to the line.
Linear relationships
Worksheets :3Study Guides :1
NC.8.SP.4. Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.
NC.8.SP.4.a. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.
Organizing Data
The data can be organized into groups, and evaluated. Mean, mode, median and range are different ways to evaluate data. The mean is the average of the data. The mode refers to the number that occurs the most often in the data. The median is the middle number when the data is arranged in order from lowest to highest. The range is the difference in numbers when the lowest number is subtracted from the highest number. Data can be organized into a table, such as a frequency table. Read more...iWorksheets :3Study Guides :1
Analyzing, Graphing and Displaying Data
There are many types of graphs such as, bar graphs, histograms and line graphs. A bar graph compares data in categories and uses bars, either vertical or horizontal. A histogram is similar to a bar graph, but with histograms the bars touch each other where with bar graphs the bars do not touch each other. A line graph is useful for graphing how data changes over time. With a line graph, data is plotted as points and lines are drawn to connect the points to show how the data changes. Read more...iWorksheets :3Study Guides :1
Using graphs to analyze data
Worksheets :3Study Guides :1
Standards

NewPath Learning resources are fully aligned to US Education Standards. Select a standard below to view correlations to your selected resource:

Alabama Courses of StudyAlaska Content and Performance StandardsArizona's College and Career Ready StandardsArkansas Curriculum FrameworksCalifornia Content StandardsColorado Academic Standards (CAS)Common Core State StandardsConnecticut Core StandardsDelaware Standards and InstructionFlorida StandardsGeorgia Standards of ExcellenceHawaii Content and Performance StandardsIdaho Content StandardsIllinois Learning StandardsIndiana Academic StandardsIowa CoreKansas Academic StandardsKentucky Academic StandardsLouisiana Academic StandardsMaine Learning ResultsMaryland College and Career-Ready StandardsMaryland StandardsMassachusetts Curriculum FrameworksMichigan Academic StandardsMinnesota Academic StandardsMississippi College & Career Readiness StandardsMissouri Learning StandardsMontana Content StandardsNational STEM StandardsNebraska Core Academic Content StandardsNevada Academic Content StandardsNew Hampshire College and Career Ready StandardsNew Jersey Common Core StandardsNew Jersey Student Learning StandardsNew Mexico Content StandardsNew York State Learning Standards and Core CurriculumNorth Carolina Standard Course of StudyNorth Dakota Academic Content StandardsOhio Learning StandardsOklahoma Academic StandardsOregon Academic Content StandardsPennsylvania Core and Academic StandardsRhode Island World-Class StandardsSouth Carolina Standards & LearningSouth Dakota Content StandardsTennessee Academic StandardsTexas Assessments of Academic Readiness (STAAR)Texas Essential Knowledge and Skills (TEKS)U.S. National StandardsUtah Core StandardsVermont Framework of Standards and LearningVirgin Islands Common Core StandardsVirginia Standards of LearningWashington DC Academic StandardsWashington State K–12 Learning Standards and GuidelinesWest Virginia College and Career Readiness StandardsWisconsin Academic StandardsWyoming Content and Performance Standards