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# Vermont Standards Eighth Grade Mathematics resources

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Mathematical Problem Solving: Applications: Students use concrete, formal, and informal strategies to solve mathematical problems, apply the process of mathematical modeling, and extend and generalize mathematical concepts. Students apply mathematics as they solve scientific and technological problems or work with technological systems.

M8:30. Demonstrate understanding of mathematical problem solving and communication through approach and reasoning - the reasoning, strategies, and skills used to solve the problem.

Quiz, Flash Cards, Worksheet, Game & Study Guide Applying Percents

M8:32. Demonstrate understanding of mathematical problem solving and communication through solution - all of the work that was done to solve the problem, including the answer.

Quiz, Flash Cards, Worksheet, Game & Study Guide Applying Percents

M8:33. Demonstrate understanding of mathematical problem solving and communication through mathematical language - the use of mathematical language in communicating the solution.

Flip Charts Dot to Dot

Flip Charts Finding Volume

Flip Charts Math Grade 8

Flip Charts Math: Grade 7

Flip Charts Numerical & Geometric Proportions

Flip Charts Perimeter & Area

Flip Charts Plane Geometry

Flip Charts Ratios, Rates & Proportions

Flip Charts The Pythagorean Theorem

Quiz, Flash Cards, Worksheet, Game & Study Guide Exploring Area and Surface Area

Quiz, Flash Cards, Worksheet, Game & Study Guide Finding Volume

Quiz, Flash Cards, Worksheet, Game & Study Guide Geometric Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Measurement, Perimeter, and Circumference

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry

Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter and area

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

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane Figures: Closed Figure Relationships

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane Figures: Lines and Angles

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

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

Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement

M8:35. Demonstrate understanding of mathematical problem solving and communication through documentation - presentation of the solution.

Quiz, Flash Cards, Worksheet, Game & Study Guide Applying Percents

Mathematical Understanding: Arithmetic, Number, and Operation Concepts: Students understand arithmetic in computation, and they select and use, in appropriate situations, mental arithmetic, pencil and paper, calculator, and computer.

M8:1. Demonstrates conceptual understanding of rational numbers with respect to percents as a way of describing change (percent increase and decrease) using explanations, models, or other representations.

Flip Charts Applying Percents

Flip Charts Math Grade 8

Quiz, Flash Cards, Worksheet, Game & Study Guide Applications of percent

Quiz, Flash Cards, Worksheet, Game & Study Guide Applying Percents

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

M8:2. Demonstrates understanding of the relative magnitude of numbers by ordering or comparing rational numbers, common irrational numbers, numbers with whole-number or fractional bases and whole-number exponents, square roots, absolute values, integers, or numbers represented in scientific notation using number lines or equality and inequality symbols.

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

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

M8:4. Accurately solves problems involving proportional reasoning (percent increase or decrease, interest rates, markups, or rates); and squares, cubes and taking square or cube roots.

Flip Charts Applying Percents

Flip Charts Integers & Exponents

Flip Charts Math Grade 8

Flip Charts Math: Grade 7

Flip Charts Numerical & Geometric Proportions

Flip Charts Ratios, Rates & Proportions

Flip Charts The Real Numbers

Quiz, Flash Cards, Worksheet, Game & Study Guide Applications of percent

Quiz, Flash Cards, Worksheet, Game & Study Guide Applying Percents

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

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

Quiz, Flash Cards, Worksheet, Game & Study Guide Numerical Proportions

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

Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents

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

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

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

M8:8. Applies properties of numbers (greatest common factor [GCF], least common multiple [LCM], prime factorization, divisibility, inverses, and identities), and commutative, distributive, and associative properties of operations to solve problems and to simplify computations.

Flip Charts Exponents, Factors & Multiples

Flip Charts Math Grade 8

Flip Charts Math: Grade 7

Flip Charts The Real Numbers

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

Mathematical Understanding: Geometric and Measurement Concepts: Students use geometric and measurement concepts.

M8:10. Applies the Pythagorean Theorem to find a missing side of a right triangle, or in problem-solving situations and solves problems by applying the Triangle Inequality Theorem to determine if three line segments with given lengths form a triangle, and the sum of the angles in a convex polygon of any number of sides.

Flip Charts Math: Grade 7

Flip Charts The Pythagorean Theorem

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

M8:13. Applies concepts of similarity to determine the impact of scaling on the volume or surface area of three-dimensional figures when linear dimensions are multiplied by a constant factor; to determine the length of sides of similar triangles, or to solve problems involving growth and rate and makes scale drawings.

Flip Charts Math Grade 8

Flip Charts Math: Grade 7

Flip Charts Numerical & Geometric Proportions

Flip Charts Ratios, Rates & Proportions

Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents

Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale

M8:14. Demonstrates conceptual understanding of surface area or volume by solving problems involving surface area and volume of rectangular prisms, cylinders, or pyramids. Expresses all measures using appropriate units.

Flip Charts Finding Volume

Flip Charts Math: Grade 7

Quiz, Flash Cards, Worksheet, Game & Study Guide Exploring Area and Surface Area

Quiz, Flash Cards, Worksheet, Game & Study Guide Finding Volume

Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement

M8:9. Models situations geometrically. Uses properties and attributes of lines, angles, and two- and three-dimensional shapes) to formulate and solve problems.

Flip Charts Dot to Dot

Flip Charts Finding Volume

Flip Charts Math Grade 8

Flip Charts Math: Grade 7

Flip Charts Numerical & Geometric Proportions

Flip Charts Perimeter & Area

Flip Charts Ratios, Rates & Proportions

Flip Charts The Pythagorean Theorem

Quiz, Flash Cards, Worksheet, Game & Study Guide Exploring Area and Surface Area

Quiz, Flash Cards, Worksheet, Game & Study Guide Perimeter and area

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

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane Figures: Closed Figure Relationships

Quiz, Flash Cards, Worksheet, Game & Study Guide Plane Figures: Lines and Angles

Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement

Mathematical Understanding: Function and Algebra Concepts: Students use function and algebra concepts.

M8:19. Identifies and extends to specific cases a variety of patterns (linear and nonlinear) represented in models, tables, sequences, graphs, or in problem situations; and generalizes a linear relationship (nonrecursive explicit equation); generalizes a linear relationship to find a specific case; generalizes a nonlinear relationship using words or symbols; or generalizes a common nonlinear relationship to find a specific case.

Flip Charts Arithmetic & Sequences

Flip Charts Circle Around

Flip Charts Math Grade 8

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

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

M8:20. Demonstrates conceptual understanding of linear relationships (y = kx; y = mx + b) as a constant rate of change by solving problems involving the relationship between slope and rate of change; informally and formally determining slopes and intercepts represented in graphs, tables, or problem situations; or describing the meaning of slope and intercept in context; and distinguishes between linear relationships (constant rates of change) and nonlinear relationships (varying rates of change) represented in tables, graphs, equations, or problem situations; or describes how change in the value of one variable relates to change in the value of a second variable in problem situations with constant and varying rates of change.

Flip Charts Math: Grade 7

Flip Charts Nonlinear Functions & Set Theory

Flip Charts Slope

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

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

M8:21. Demonstrates conceptual understanding of algebraic expressions by evaluating and simplifying (including those with square roots, whole-number exponents, or rational numbers); or by evaluating an expression within an equation.

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

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

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

M8:22. Demonstrates conceptual understanding of equality by showing equivalence between two expressions (expressions consistent with the parameters of the left- and right-hand sides of the equations being solved at this grade level) using models or different representations of the expressions, solving formulas for a variable requiring one transformation (e.g., d = rt; d/r = t); by solving multistep linear equations with integer coefficients; by showing that two expressions are or are not equivalent by applying commutative, associative, or distributive properties, order of operations, or substitution; and by informally solving problems involving systems of linear equations in a context.

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

Mathematical Understanding: Statistics and Probability Concepts: Students use statistics and probability concepts.

M8:23. Interprets a given representation (line graphs, scatter plots, histograms, or box-and-whisker plots) to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems.

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

M8:24. Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using measures of central tendency (mean, median, or mode), dispersion (range or variation), outliers, quartile values, or estimated line of best fit to analyze situations, or to solve problems; and evaluates the sample from which the statistics were developed (bias, random, or nonrandom).

Flip Charts Math Grade 8

Flip Charts Organizing & Displaying Data

Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data

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

Quiz, Flash Cards, Worksheet, Game & Study Guide Organizing Data

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

M8:25. Organizes and displays data using scatter plots to answer questions related to the data, to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems; or Identifies representations or elements of representations that best display a given set of data or situation, consistent with the representations required in M8:23.

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

M8:26. Uses counting techniques to solve problems in context involving combinations or permutations using a variety of strategies (e.g., organized lists, tables, tree diagrams, models, Fundamental Counting Principle, or others).

Flip Charts Introduction to Probability

Flip Charts Math: Grade 7

Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting

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

M8:27. For a probability event in which the sample space may or may not contain equally likely outcomes, determines the possible outcomes by either sample space (organized list, table, tree model, area model) or Fundamental Counting Principle and determines the theoretical probability of that event as a ratio of favorable outcomes to possible outcomes. Expresses the ratio as a fraction, decimal, or percent.

Flip Charts Introduction to Probability

Flip Charts Math: Grade 7

Quiz, Flash Cards, Worksheet, Game & Study Guide Experimental Probability

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

Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents

Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting

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

M8:29. Compares and contrasts theoretical and experimental probabilities of compound events using fractions, decimals, or percents; and uses theoretical or experimental probabilities to determine the fairness of a game.

Flip Charts Introduction to Probability

Flip Charts Math: Grade 7

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