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# Minnesota Standards Eighth Grade Mathematics resources

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Number & Operation

8.1.1. Read, write, compare, classify and represent real numbers, and use them to solve problems in various contexts.

8.1.1.1. Classify real numbers as rational or irrational. Know that when a square root of a positive integer is not an integer, then it is irrational. Know that the sum of a rational number and an irrational number is irrational, and the product of a non-zero rational number and an irrational number is irrational.

Flip Charts Math Grade 8

Flip Charts The Real Numbers

Quiz, Flash Cards, Worksheet, Game & Study Guide Rational and Irrational Numbers

8.1.1.2. Compare real numbers; locate real numbers on a number line. Identify the square root of a positive integer as an integer, or if it is not an integer, locate it as a real number between two consecutive positive integers.

Flip Charts Math Grade 8

Flip Charts The Real Numbers

Quiz, Flash Cards, Worksheet, Game & Study Guide Rational and Irrational Numbers

Quiz, Flash Cards, Worksheet, Game & Study Guide Real numbers

Quiz, Flash Cards, Worksheet, Game & Study Guide The Pythagorean Theorem

8.1.1.4. Know and apply the properties of positive and negative integer exponents to generate equivalent numerical expressions.

Flip Charts Exponents, Factors & Multiples

Flip Charts Math: Grade 7

Quiz, Flash Cards, Worksheet, Game & Study Guide Exponents, Factors and Fractions

Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

8.1.1.5. Express approximations of very large and very small numbers using scientific notation; understand how calculators display numbers in scientific notation. Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation, using the correct number of significant digits when physical measurements are involved.

Flip Charts Exponents, Factors & Multiples

Flip Charts Integers & Exponents

Flip Charts Math Grade 8

Flip Charts Math: Grade 7

Quiz, Flash Cards, Worksheet, Game & Study Guide Exponents, Factors and Fractions

Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

Algebra

8.2.1. Understand the concept of function in real world and mathematical situations, and distinguish between linear and nonlinear functions.

8.2.1.1. Understand that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable. Use functional notation, such as f(x), to represent such relationships.

Flip Charts Math: Grade 7

Flip Charts Slope

Quiz, Flash Cards, Worksheet, Game & Study Guide Functions

Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions

8.2.1.4. Understand that an arithmetic sequence is a linear function that can be expressed in the form f (x)= mx+b , where x = 0, 1, 2, 3,....

Flip Charts Arithmetic & Sequences

Flip Charts Circle Around

Flip Charts Math Grade 8

Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences

8.2.1.5. Understand that a geometric sequence is a non-linear function that can be expressed in the form f (x)= ab^x , where x = 0, 1, 2, 3,....

Flip Charts Arithmetic & Sequences

Flip Charts Circle Around

Flip Charts Math Grade 8

Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences

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

8.2.2.1. Represent linear functions with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another.

Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

8.2.2.2. Identify graphical properties of linear functions including slopes and intercepts. Know that the slope equals the rate of change, and that the y-intercept is zero when the function represents a proportional relationship.

Flip Charts Math: Grade 7

Flip Charts Slope

Vocabulary Terms Nonlinear Functions and Set Theory

Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships

Quiz, Flash Cards, Worksheet, Game & Study Guide Nonlinear Functions and Set Theory

8.2.2.4. Represent arithmetic sequences using equations, tables, graphs and verbal descriptions, and use them to solve problems.

Flip Charts Arithmetic & Sequences

Flip Charts Circle Around

Flip Charts Math Grade 8

Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences

8.2.2.5. Represent geometric sequences using equations, tables, graphs and verbal descriptions, and use them to solve problems.

Flip Charts Arithmetic & Sequences

Flip Charts Circle Around

Flip Charts Math Grade 8

Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences

8.2.4. Represent real world and mathematical situations using equations and inequalities involving linear expressions. Solve equations and inequalities symbolically and graphically. Interpret solutions in the original context.

8.2.4.2. Solve multi-step equations in one variable. Solve for one variable in a multi-variable equation in terms of the other variables. Justify the steps by identifying the properties of equalities used.

Flip Charts Math Grade 8

Flip Charts Math: Grade 7

Flip Charts Multistep Equations

Flip Charts Multistep Equations

Flip Charts Numerical & Geometric Proportions

Flip Charts Ratios, Rates & Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Algebraic Equations

Quiz, Flash Cards, Worksheet, Game & Study Guide Decimal Operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and Inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Fraction Operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Algebra

Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Percent

Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations

Quiz, Flash Cards, Worksheet, Game & Study Guide Using Integers

8.2.4.3. Express linear equations in slope-intercept, point-slope and standard forms, and convert between these forms. Given sufficient information, find an equation of a line.

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

8.2.4.5. Solve linear inequalities using properties of inequalities. Graph the solutions on a number line.

Flip Charts Inequalities

Flip Charts Inequalities

Flip Charts Math: Grade 7

Quiz, Flash Cards, Worksheet, Game & Study Guide Algebraic Inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and Inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities

Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations

Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

8.2.4.7. Represent relationships in various contexts using systems of linear equations. Solve systems of linear equations in two variables symbolically, graphically and numerically.

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

8.2.4.8. Understand that a system of linear equations may have no solution, one solution, or an infinite number of solutions. Relate the number of solutions to pairs of lines that are intersecting, parallel or identical. Check whether a pair of numbers satisfies a system of two linear equations in two unknowns by substituting the numbers into both equations.

Flip Charts Introduction to Functions

Flip Charts Math Grade 8

Flip Charts Systems of Equations

Flip Charts Systems of Equations

Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities

Geometry & Measurement

8.3.1. Solve problems involving right triangles using the Pythagorean Theorem and its converse.

8.3.1.1. Use the Pythagorean Theorem to solve problems involving right triangles.

Flip Charts Math: Grade 7

Flip Charts The Pythagorean Theorem

Quiz, Flash Cards, Worksheet, Game & Study Guide The Pythagorean Theorem

8.3.2. Solve problems involving parallel and perpendicular lines on a coordinate system.

8.3.2.1. Understand and apply the relationships between the slopes of parallel lines and between the slopes of perpendicular lines. Dynamic graphing software may be used to examine these relationships.

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures

8.3.2.2. Analyze polygons on a coordinate system by determining the slopes of their sides.

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures

Data Analysis & Probability

8.4.1. Interpret data using scatterplots and approximate lines of best fit. Use lines of best fit to draw conclusions about data.

8.4.1.1. Collect, display and interpret data using scatterplots. Use the shape of the scatterplot to informally estimate a line of best fit and determine an equation for the line. Use appropriate titles, labels and units. Know how to use graphing technology to display scatterplots and corresponding lines of best fit.

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Analyzing, Graphing and Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Displaying data

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships

Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

8.4.1.2. Use a line of best fit to make statements about approximate rate of change and to make predictions about values not in the original data set.

Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships

8.4.1.3. Assess the reasonableness of predictions using scatterplots by interpreting them in the original context.

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Analyzing, Graphing and Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Displaying data

Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data