## Massachusetts Curriculum Frameworks for Eighth Grade Math

##### Applications of percent
Worksheets: 4Study 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
##### Perimeter and area
Worksheets: 4Study Guides: 1
##### Plane figures
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

### MA.MP. 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

### MA.8.NS. The Number System

#### 8.NS.A. Know that there are numbers that are not rational, and approximate them by rational numbers.

##### 8.NS.A.1. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion. For rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a 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

### MA.8.EE. Expressions and Equations

#### 8.EE.A. Work with radicals and integer exponents.

##### 8.EE.A.1. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 x 3^−5 = 3^−3 = (1∕3)^3 = 1∕27.
###### 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
##### 8.EE.A.2. Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
###### 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
##### 8.EE.A.3. Use numbers expressed in the form of a single digit multiplied by an integer power of 10 to estimate very large or very small quantities, and express how many times as much one is than the other. For example, estimate the population of the United States as 3 x 10^8 and the population of the world as 7 x 10^9, and determine that the world population is more than 20 times larger.
###### 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
##### 8.EE.A.4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
###### 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

#### 8.EE.B. Understand the connections between proportional relationships, lines, and linear equations.

##### 8.EE.B.5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
###### Introduction to Functions
Worksheets :5Study Guides :1
###### Linear equations
Worksheets :3Study Guides :1
##### 8.EE.B.6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane. Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
###### Introduction to Functions
Worksheets :5Study Guides :1
###### Linear equations
Worksheets :3Study Guides :1

#### 8.EE.C. Analyze and solve linear equations and pairs of simultaneous linear equations.

##### 8.EE.C.7. Solve linear equations in one variable.
###### 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
###### 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

### MA.8.F. Functions

#### 8.F.A. Define, evaluate, and compare functions.

##### 8.F.A.1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
###### Introduction to Functions
Worksheets :5Study Guides :1
###### Functions
Worksheets :3Study Guides :1
##### 8.F.A.3. Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1, 1), (2, 4) and (3, 9), which are not on a straight line.
###### Linear equations
Worksheets :3Study Guides :1

#### 8.F.B. Use functions to model relationships between quantities.

##### 8.F.B.4. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
###### Introduction to Functions
Worksheets :5Study Guides :1
###### Linear equations
Worksheets :3Study Guides :1

### MA.8.G. Geometry

#### 8.G.A. Understand congruence and similarity using physical models, transparencies, or geometry software.

##### 8.G.A.1. Verify experimentally the properties of rotations, reflections, and translations:
###### Geometric Proportions
Geometric proportions compare two similar polygons. Similar polygons have equal corresponding angles and corresponding sides that are in proportion. A proportion equation can be used to prove two figures to be similar. If two figures are similar, the proportion equation can be used to find a missing side of one of the figures. Read more...iWorksheets :4Study Guides :1
###### Plane Figures: Closed Figure Relationships
Worksheets :3Study Guides :1
###### Patterns in geometry
Worksheets :3Study Guides :1
###### Ratios, proportions and percents
Worksheets :4Study Guides :1
###### Similarity and scale
Worksheets :3Study Guides :1
###### Geometric Proportions
Geometric proportions compare two similar polygons. Similar polygons have equal corresponding angles and corresponding sides that are in proportion. A proportion equation can be used to prove two figures to be similar. If two figures are similar, the proportion equation can be used to find a missing side of one of the figures. Read more...iWorksheets :4Study Guides :1
###### Plane Figures: Closed Figure Relationships
Worksheets :3Study Guides :1
###### Patterns in geometry
Worksheets :3Study Guides :1
###### Ratios, proportions and percents
Worksheets :4Study Guides :1
###### Similarity and scale
Worksheets :3Study Guides :1
###### Geometric Proportions
Geometric proportions compare two similar polygons. Similar polygons have equal corresponding angles and corresponding sides that are in proportion. A proportion equation can be used to prove two figures to be similar. If two figures are similar, the proportion equation can be used to find a missing side of one of the figures. Read more...iWorksheets :4Study Guides :1
###### Plane Figures: Closed Figure Relationships
Worksheets :3Study Guides :1
###### Patterns in geometry
Worksheets :3Study Guides :1
###### Ratios, proportions and percents
Worksheets :4Study Guides :1
###### Similarity and scale
Worksheets :3Study Guides :1
##### 8.G.A.2. 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. Given two congruent figures, describe a sequence that exhibits the congruence between them.
###### 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

#### 8.G.B. Understand and apply the Pythagorean Theorem.

##### 8.G.B.6a. Understand the relationship among the sides of a right triangle.
###### 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
##### 8.G.B.7. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
###### 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

#### 8.G.C. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

##### 8.G.C.9. Know the formulas for the volumes of cones, cylinders, and spheres, and use them 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

### MA.8.SP. Statistics and Probability

#### 8.SP.A. Investigate patterns of association in bivariate data.

##### 8.SP.A.1. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. 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
###### Collecting and describing data
Worksheets :3Study Guides :1
###### Displaying data
Worksheets :4Study Guides :1
##### 8.SP.A.2. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line and informally assess the model fit by judging the closeness of the data points to the line.
###### Linear relationships
Worksheets :3Study Guides :1