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WV.M.1HS8.8th Grade High School Mathematics I

8th Grade High School Mathematics I
Congruence, Proof, and Constructions
Understand and apply the Pythagorean theorem.
M.1HS8.60. Apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Flip Charts Math: Grade 7
Quiz, Flash Cards, Worksheet, Game & Study Guide The Pythagorean Theorem
 
M.1HS8.61. Apply the Pythagorean theorem to find the distance between two points in a coordinate system.
Flip Charts Math: Grade 7
Quiz, Flash Cards, Worksheet, Game & Study Guide The Pythagorean Theorem
 
Experiment with transformations in the plane.
M.1HS8.49. Know precise definitions of angle, circle, perpendicular line, parallel line and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
Flip Charts Finding Volume
Flip Charts Math Grade 8
Flip Charts Math: Grade 7
Flip Charts Perimeter & Area
Flip Charts Plane Geometry
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
 
M.1HS8.50. Represent transformations in the plane using, example, transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale
 
M.1HS8.51. Given a rectangle, parallelogram, trapezoid or regular polygon, describe the rotations and reflections that carry it onto itself.
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
 
M.1HS8.52. Develop definitions of rotations, reflections and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments.
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
 
M.1HS8.53. Given a geometric figure and a rotation, reflection or translation draw the transformed figure using, e.g., graph paper, tracing paper or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
 
Understand congruence in terms of rigid motions.
M.1HS8.54. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
 
Reasoning with Equations
Analyze and solve linear equations and pairs of simultaneous linear equations.
M.1HS8.34. Analyze and solve pairs of simultaneous linear equations.
M.1HS8.34.a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
Flip Charts Math Grade 8
 
M.1HS8.34.b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5
Flip Charts Math Grade 8
 
Understand solving equations as a process of reasoning and explain the reasoning.
M.1HS8.32. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Flip Charts Math Grade 8
Flip Charts Math: Grade 7
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
 
Solve systems of equations.
M.1HS8.35. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
Flip Charts Math Grade 8
 
M.1HS8.36. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Flip Charts Math Grade 8
 
Solve equations and inequalities in one variable.
M.1HS8.33. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Flip Charts Inequalities
Flip Charts Inequalities
Flip Charts Math Grade 8
Flip Charts Math: Grade 7
Quiz, Flash Cards, Worksheet, Game & Study Guide Algebraic Equations
Quiz, Flash Cards, Worksheet, Game & Study Guide Algebraic Inequalities
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
 
Relationships between Quantities
Reason quantitatively and use units to solve problems.
M.1HS8.3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Quiz, Flash Cards, Worksheet, Game & Study Guide Measurement, Perimeter, and Circumference
 
Create equations that describe numbers or relationships.
M.1HS8.5. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational and exponential functions.
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 Introduction to Algebra
 
M.1HS8.6. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Algebra
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 Solving linear equations
 
M.1HS8.7. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. (e.g., Represent inequalities describing nutritional and cost constraints o
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 Introduction to Algebra
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
 
M.1HS8.8. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (e.g., Rearrange Ohm’s law V = IR to highlight resistance R.)
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities
 
Connecting Algebra and Geometry through Coordinates
Use coordinates to prove simple geometric theorems algebraically.
M.1HS8.63. Prove the slope criteria for parallel and perpendicular lines; use them to solve geometric problems. (e.g., Find the equation of a line parallel or perpendicular to a given line that passes through a given point.)
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures
 
M.1HS8.64. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, (e.g., using the distance formula).
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane figures
 
Descriptive Statistics
Summarize, represent, and interpret data on a single count or measurement variable.
M.1HS8.37. Represent data with plots on the real number line (dot plots, histograms, and box plots).
Flip Charts Math Grade 8
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data
 
M.1HS8.40. 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 associat
Flip Charts Math Grade 8
Quiz, Flash Cards, Worksheet, Game & Study Guide Analyzing, Graphing and Displaying Data
Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data
Quiz, Flash Cards, Worksheet, Game & Study Guide Displaying data
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data
 
M.1HS8.41. 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 dat
Flip Charts Math Grade 8
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships
 
Summarize, represent, and interpret data on two categorical and quantitative variables.
M.1HS8.44. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal and conditional relative frequencies). Recognize possible associations and trends in the data.
Quiz, Flash Cards, Worksheet, Game & Study Guide Analyzing, Graphing and Displaying Data
Quiz, Flash Cards, Worksheet, Game & Study Guide Organizing Data
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data
 
M.1HS8.45. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
M.1HS8.45.b. Informally assess the fit of a function by plotting and analyzing residuals. (Focus should be on situations for which linear models are appropriate.)
Flip Charts Math Grade 8
 
M.1HS8.45.c. Fit a linear function for scatter plots that suggest a linear association.
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships
 
Linear and Exponential Relationships
Construct and compare linear, quadratic, and exponential models and solve problems.
M.1HS8.28. Distinguish between situations that can be modeled with linear functions and with exponential functions.
M.1HS8.28.a. Prove that linear functions grow by equal differences over equal intervals; exponential functions grow by equal factors over equal intervals.
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
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
 
Analyze functions using different representations.
M.1HS8.23. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
M.1HS8.23.a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
 
Understand the concept of a function and use function notation.
M.1HS8.15. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f c
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
 
M.1HS8.16. Use function notation, evaluate functions for inputs in their domains and interpret statements that use function notation in terms of a context.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions
 
M.1HS8.17. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. (e.g., The Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n)+ f(n-1) for n ≥ 1.)
Flip Charts Math Grade 8
Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
 
M.1HS8.18. 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
Flip Charts Math: Grade 7
Flip Charts Slope
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
 
Represent and solve equations and inequalities graphically.
M.1HS8.10. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, (e.g., using technology to graph the functions, make tables of v
Flip Charts Math Grade 8
 
M.1HS8.11. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality) and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships
 
Interpret expressions for functions in terms of the situation they model.
M.1HS8.31. Interpret the parameters in a linear or exponential function in terms of a context.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions
 
Build a function that models a relationship between two quantities.
M.1HS8.25. Write a function that describes a relationship between two quantities.
M.1HS8.25.a. Determine an explicit expression, a recursive process or steps for calculation from a context.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Algebra
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
 
Interpret functions that arise in applications in terms of a context.
M.1HS8.20. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercept
Flip Charts Math: Grade 7
Flip Charts Slope
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
 
M.1HS8.22. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
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 Nonlinear Functions and Set Theory
 
Define, evaluate, and compare functions.
M.1HS8.12. 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.
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
 
M.1HS8.14. 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. (e.g., The function A = s^2 giving the area of a square as a function of its side length is not linear because
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
 

WV.M.8.EE.Expressions and Equations

Expressions and Equations
Analyze and solve linear equations and pairs of simultaneous linear equations.
M.8.10. Analyze and solve pairs of simultaneous linear equations.
M.8.10.a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
Flip Charts Math Grade 8
 
M.8.10.b. Solve systems of two linear equations in two variables algebraically and estimate solutions by graphing the equations. Solve simple cases by inspection. (e.g., 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.)
Flip Charts Math Grade 8
 
M.8.9. Solve linear equations in one variable.
M.8.9.a. Give examples of linear equations in one variable with one solution, infinitely many solutions or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation
Flip Charts Math Grade 8
Flip Charts Math: Grade 7
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
 
M.8.9.b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
Flip Charts Math Grade 8
Flip Charts Math: Grade 7
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
 
Work with radicals and integer exponents.
M.8.3. Know and apply the properties of integer exponents to generate equivalent numerical expressions. (e.g., 3^2 × 3^–5 = 3^–3 = 1/3^3 = 1/27.)
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
 
M.8.4. 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 irratio
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
 
M.8.5. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. (e.g., Estimate the population of the United States as 3 × 10^8
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
 
M.8.6. 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.
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
 
Understand the connections between proportional relationships, lines, and linear equations.
M.8.7. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. (e.g., Compare a distance-time graph to a distance-time equation to determine which of
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
 
M.8.8. 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 v
Flip Charts Math: Grade 7
Flip Charts Slope
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
 

WV.M.8.F.Functions

Functions
Define, evaluate, and compare functions.
M.8.11. 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.
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
 
M.8.13. 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. (e.g., The function A = s^2 giving the area of a square as a function of its side length is not linear becaus
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
 
Use functions to model relationships between quantities.
M.8.14. 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
Flip Charts Math: Grade 7
Flip Charts Slope
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
 

WV.M.8.G.Geometry

Geometry
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
M.8.24. Know the formulas for the volumes of cones, cylinders and spheres and use them to solve real-world and mathematical problems.
Flip Charts Finding Volume
Flip Charts Math: Grade 7
Quiz, Flash Cards, Worksheet, Game & Study Guide Finding Volume
Quiz, Flash Cards, Worksheet, Game & Study Guide Three dimensional geometry/Measurement
 
Understand congruence and similarity using physical models, transparencies, or geometry software.
M.8.16. Verify experimentally the properties of rotations, reflections and translations:
M.8.16.a. Lines are taken to lines, and line segments to line segments of the same length.
Flip Charts Math Grade 8
Flip Charts Math: Grade 7
Quiz, Flash Cards, Worksheet, Game & Study Guide Geometric Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane Figures: Closed Figure Relationships
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale
 
M.8.16.b. Angles are taken to angles of the same measure.
Flip Charts Math Grade 8
Flip Charts Math: Grade 7
Quiz, Flash Cards, Worksheet, Game & Study Guide Geometric Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane Figures: Closed Figure Relationships
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale
 
M.8.16.c. Parallel lines are taken to parallel lines.
Flip Charts Math Grade 8
Flip Charts Math: Grade 7
Quiz, Flash Cards, Worksheet, Game & Study Guide Geometric Proportions
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane Figures: Closed Figure Relationships
Quiz, Flash Cards, Worksheet, Game & Study Guide Ratios, proportions and percents
Quiz, Flash Cards, Worksheet, Game & Study Guide Similarity and scale
 
M.8.17. 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 t
Flip Charts Math Grade 8
Flip Charts Plane Geometry
Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns in geometry
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane Figures: Closed Figure Relationships
Quiz, Flash Cards, Worksheet, Game & Study Guide Plane Figures: Lines and Angles
 
M.8.20. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. (e.g., Arrange three copies of
Flip Charts Math Grade 8
Flip Charts Plane Geometry
 
Understand and apply the Pythagorean Theorem.
M.8.22. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Flip Charts Math: Grade 7
Quiz, Flash Cards, Worksheet, Game & Study Guide The Pythagorean Theorem
 
M.8.23. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Flip Charts Math: Grade 7
Quiz, Flash Cards, Worksheet, Game & Study Guide The Pythagorean Theorem
 

WV.M.8.NS.The Number System

The Number System
Know that there are numbers that are not rational, and approximate them by rational numbers.
M.8.1. 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 eventuall
Flip Charts Math Grade 8
Flip Charts The Real Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational and Irrational Numbers
 

WV.M.8.SP.Statistics and Probability

Statistics and Probability
Investigate patterns of association in bivariate data.
M.8.25. 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 associat
Flip Charts Math Grade 8
Quiz, Flash Cards, Worksheet, Game & Study Guide Analyzing, Graphing and Displaying Data
Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data
Quiz, Flash Cards, Worksheet, Game & Study Guide Displaying data
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data
 
M.8.26. 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 dat
Flip Charts Math Grade 8
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships
 

WV.M.A18.High School Algebra I for 8th Grade

High School Algebra I for 8th Grade
Quadratic Functions and Modeling
Analyze functions using different representations.
M.A18.67. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
M.A18.67.a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
 
M.A18.68. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
M.A18.68.b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^12t, y = (1.2)^t/10, and classify them as representing exponential
Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents
 
Understand and apply the Pythagorean theorem.
M.A18.62. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
Flip Charts Math: Grade 7
Quiz, Flash Cards, Worksheet, Game & Study Guide The Pythagorean Theorem
 
M.A18.63. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Flip Charts Math: Grade 7
Quiz, Flash Cards, Worksheet, Game & Study Guide The Pythagorean Theorem
 
Build a function that models a relationship between two quantities.
M.A18.70. Write a function that describes a relationship between two quantities.
M.A18.70.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Algebra
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
 
Interpret functions that arise in applications in terms of a context.
M.A18.64. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercep
Flip Charts Math: Grade 7
Flip Charts Slope
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
 
M.A18.66. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
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 Nonlinear Functions and Set Theory
 
Descriptive Statistics
Summarize, represent, and interpret data on two categorical and quantitative variables.
M.A18.46. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal and conditional relative frequencies). Recognize possible associations and trends in the data.
Quiz, Flash Cards, Worksheet, Game & Study Guide Analyzing, Graphing and Displaying Data
Quiz, Flash Cards, Worksheet, Game & Study Guide Organizing Data
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data
 
M.A18.47. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
M.A18.47.b. Informally assess the fit of a function by plotting and analyzing residuals.
Flip Charts Math Grade 8
 
M.A18.47.c. Fit a linear function for scatter plots that suggest a linear association.
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships
 
Summarize, represent, and interpret data on a single count or measurement variable.
M.A18.39. Represent data with plots on the real number line (dot plots, histograms, and box plots).
Flip Charts Math Grade 8
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data
 
Investigate patterns of association in bivariate data.
M.A18.42. 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 associa
Flip Charts Math Grade 8
Quiz, Flash Cards, Worksheet, Game & Study Guide Analyzing, Graphing and Displaying Data
Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data
Quiz, Flash Cards, Worksheet, Game & Study Guide Displaying data
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data
 
M.A18.43. 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 da
Flip Charts Math Grade 8
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships
 
Relationships between Quantities and Reasoning with Equations
Understand solving equations as a process of reasoning and explain the reasoning.
M.A18.9. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Flip Charts Math Grade 8
Flip Charts Math: Grade 7
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
 
Reason quantitatively and use units to solve problems.
M.A18.3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Quiz, Flash Cards, Worksheet, Game & Study Guide Measurement, Perimeter, and Circumference
 
Solve equations and inequalities in one variable.
M.A18.10. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Flip Charts Inequalities
Flip Charts Inequalities
Flip Charts Math Grade 8
Flip Charts Math: Grade 7
Quiz, Flash Cards, Worksheet, Game & Study Guide Algebraic Equations
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 Introduction to Algebra
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
 
Create equations that describe numbers or relationships.
M.A18.5. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
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 Introduction to Algebra
 
M.A18.6. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Algebra
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 Solving linear equations
 
M.A18.7. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. (e.g., Represent inequalities describing nutritional and cost constraints o
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 Introduction to Algebra
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
 
M.A18.8. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (e.g., Rearrange Ohm’s law V = IR to highlight resistance R.)
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities
 
Expressions and Equations
Create equations that describe numbers or relationships.
M.A18.55. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
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 Introduction to Algebra
 
M.A18.56. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Algebra
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 Solving linear equations
 
M.A18.57. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (e.g., Rearrange Ohm’s law V = IR to highlight resistance R.)
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving equations and inequalities
 
Write expressions in equivalent forms to solve problems.
M.A18.53. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
M.A18.53.c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15^t can be rewritten as (1.15^1/12)^12t ≈ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents
 
Perform arithmetic operations on polynomials.
M.A18.54. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents
 
Linear and Exponential Relationships
Interpret functions that arise in applications in terms of a context.
M.A18.27. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercep
Flip Charts Math: Grade 7
Flip Charts Slope
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
 
M.A18.29. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
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 Nonlinear Functions and Set Theory
 
Understand the concept of a function and use function notation.
M.A18.22. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f c
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
 
M.A18.23. Use function notation, evaluate functions for inputs in their domains and interpret statements that use function notation in terms of a context.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions
 
M.A18.24. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n)+ f(n-1) for n ≥ 1.
Flip Charts Math Grade 8
Quiz, Flash Cards, Worksheet, Game & Study Guide Sequences
 
Represent and solve equations and inequalities graphically.
M.A18.17. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately (e.g., using technology to graph the functions, make tables of va
Flip Charts Math Grade 8
 
M.A18.18. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the correspondin
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear relationships
 
Construct and compare linear, quadratic, and exponential models and solve problems.
M.A18.35. Distinguish between situations that can be modeled with linear functions and with exponential functions.
M.A18.35.a. Prove that linear functions grow by equal differences over equal intervals; exponential functions grow by equal factors over equal intervals.
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
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
 
Analyze and solve linear equations and pairs of simultaneous linear equations.
M.A18.13. Analyze and solve pairs of simultaneous linear equations.
M.A18.13.a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
Flip Charts Math Grade 8
 
M.A18.13.b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5
Flip Charts Math Grade 8
 
Analyze functions using different representations.
M.A18.30. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
M.A18.30.a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
 
Use functions to model relationships between quantities.
M.A18.25. 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
Flip Charts Math: Grade 7
Flip Charts Slope
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
 
Define, evaluate and compare functions.
M.A18.19. 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.
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
 
M.A18.21. 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. (e.g., The function A = s^2 giving the area of a square as a function of its side length is not linear because
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations
 
Interpret expressions for functions in terms of the situation they model.
M.A18.38. Interpret the parameters in a linear or exponential function in terms of a context.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions
 
Solve systems of equations.
M.A18.14. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
Flip Charts Math Grade 8
 
M.A18.15. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Flip Charts Math Grade 8
 
Build a function that models a relationship between two quantities.
M.A18.32. Write a function that describes a relationship between two quantities.
M.A18.32.a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Algebra
Quiz, Flash Cards, Worksheet, Game & Study Guide Solving linear equations
 

WV.M.MHM.Mathematical Habits of Mind

Mathematical Habits of Mind
MHM1. Make sense of problems and persevere in solving them.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes
 
MHM2. Reason abstractly and quantitatively.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes