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- Mathematics: 8th Grade
Virginia - Mathematics: 8th Grade
VA--Standards of Learning | Adopted: 2016
NS: : Number and Number Sense
NS.8.1: : The student will compare and order real numbers.
Comparing and Ordering Decimals
Use grids to model decimal numbers and compare them graphically. Then compare the numbers on a number line. 5 Minute Preview
Integers, Opposites, and Absolute Values
Compare and order integers using draggable points on a number line. Also explore opposites and absolute values on the number line. 5 Minute Preview
Rational Numbers, Opposites, and Absolute Values
Use a number line to compare rational numbers. Change values by dragging points on the number line. Compare the opposites and absolute values of the numbers. 5 Minute Preview
NS.8.3: : The student will
NS.8.3.a: : estimate and determine the two consecutive integers between which a square root lies; and
Square Roots
Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview
NS.8.3.b: : determine both the positive and negative square roots of a given perfect square.
Square Roots
Explore the meaning of square roots using an area model. Use the side length of a square to find the square root of a decimal number or a whole number. 5 Minute Preview
CE: : Computation and Estimation
CE.8.4: : The student will solve practical problems involving consumer applications.
Household Energy Usage
Explore the energy used by many household appliances, such as television sets, hair dryers, lights, computers, etc. Make estimates for how long each item is used on a daily basis to get an estimate for the total power consumed during a day, a week, a month, and a year, and how that relates to consumer costs and environmental impact. 5 Minute Preview
Percent of Change
Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations. 5 Minute Preview
MG: : Measurement and Geometry
MG.8.5: : The student will use the relationships among pairs of angles that are vertical angles, adjacent angles, supplementary angles, and complementary angles to determine the measure of unknown angles.
Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview
MG.8.6: : The student will
MG.8.6.a: : solve problems, including practical problems, involving volume and surface area of cones and square-based pyramids; and
Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
Surface and Lateral Areas of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
MG.8.6.b: : describe how changing one measured attribute of a rectangular prism affects the volume and surface area.
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
MG.8.7: : The student will
MG.8.7.a: : given a polygon, apply transformations, to include translations, reflections, and dilations, in the coordinate plane; and
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
MG.8.7.b: : identify practical applications of transformations.
Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
MG.8.8: : The student will construct a three-dimensional model, given the top or bottom, side, and front views.
3D and Orthographic Views
Arrange blocks in a three-dimensional space so that the top view, front view, and side view match the target top view, front view, and side view. 5 Minute Preview
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
MG.8.9: : The student will
MG.8.9.a: : verify the Pythagorean Theorem; and
Pythagorean Theorem
Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle. 5 Minute Preview
Pythagorean Theorem with a Geoboard
Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem. 5 Minute Preview
MG.8.9.b: : apply the Pythagorean Theorem.
Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
Distance Formula
Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation. 5 Minute Preview
Pythagorean Theorem
Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle. 5 Minute Preview
Pythagorean Theorem with a Geoboard
Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem. 5 Minute Preview
Surface and Lateral Areas of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
PS: : Probability and Statistics
PS.8.11: : The student will
PS.8.11.a: : compare and contrast the probability of independent and dependent events; and
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
PS.8.11.b: : determine probabilities for independent and dependent events.
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events. 5 Minute Preview
Theoretical and Experimental Probability
Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes. 5 Minute Preview
PS.8.12: : The student will
PS.8.12.a: : represent numerical data in boxplots;
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview
PS.8.12.b: : make observations and inferences about data represented in boxplots; and
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview
PS.8.12.c: : compare and analyze two data sets using boxplots.
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes. 5 Minute Preview
PS.8.13: : The student will
PS.8.13.a: : represent data in scatterplots;
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
PS.8.13.b: : make observations about data represented in scatterplots; and
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line. 5 Minute Preview
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
Trends in Scatter Plots
Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line. 5 Minute Preview
PS.8.13.c: : use a drawing to estimate the line of best fit for data represented in a scatterplot.
Least-Squares Best Fit Lines
Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview
Solving Using Trend Lines
Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line. 5 Minute Preview
PFA: : Patterns, Functions, and Algebra
PFA.8.14: : The student will
PFA.8.14.a: : evaluate an algebraic expression for given replacement values of the variables; and
Equivalent Algebraic Expressions I
Grumpy’s Restaurant is now hiring! As a new chef at this underwater bistro, you’ll learn the basics of manipulating algebraic expressions. Learn how to make equivalent expressions using the Commutative and Associative properties, how to handle pesky subtraction and division, and how to identify equivalent and non-equivalent expressions. 5 Minute Preview
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
PFA.8.14.b: : simplify algebraic expressions in one variable.
Dividing Exponential Expressions
Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
Equivalent Algebraic Expressions I
Grumpy’s Restaurant is now hiring! As a new chef at this underwater bistro, you’ll learn the basics of manipulating algebraic expressions. Learn how to make equivalent expressions using the Commutative and Associative properties, how to handle pesky subtraction and division, and how to identify equivalent and non-equivalent expressions. 5 Minute Preview
Equivalent Algebraic Expressions II
Continue your meteoric rise in the undersea culinary world in this follow-up to Equivalent Algebraic Expressions I. Make equivalent expressions by using the distributive property forwards and backwards, sort expressions by equivalence, and personally assist Chef Grumpy himself with a project that will bring him (and maybe you) fame and fortune. 5 Minute Preview
Multiplying Exponential Expressions
Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps. 5 Minute Preview
Operations with Radical Expressions
Identify the correct steps to complete operations with a radical expression. Use step-by-step feedback to diagnose incorrect steps. 5 Minute Preview
Order of Operations
Select and evaluate the operations in an expression following the correct order of operations. 5 Minute Preview
Simplifying Algebraic Expressions I
Meet Spidro, a quirky critter with an appetite for algebraic expressions! As Spidro's adopted owner, it's your responsibility to feed him so that he grows into… whatever it is that a Spidro grows into. But be careful - Spidro is a picky eater who prefers his food to be as simple as possible. Use the commutative property, distributive property, and the other properties of addition and multiplication to put expressions in simplest (and tastiest) form. 5 Minute Preview
Simplifying Algebraic Expressions II
Will you adopt Spidro, Centeon, or Ping Bee? They're three very different critters with one thing in common: a hunger for simplified algebraic expressions! Learn how the distributive property can be used to combine variable terms, producing expressions that will help your pet grow up healthy and strong. You'll become a pro at identifying terms that can be combined – even terms with exponents and multiple variables. With enough practice, you and your pet will be ready for the competitive expression eating circuit. Good luck! 5 Minute Preview
Solving Algebraic Equations I
Are there times when you wish you could escape from everyone and just be alone? Meet our variable friend, a real loner who doesn't like coefficients and neighboring terms. Learn how to use inverses to isolate a variable – a foundational skill for solving algebraic equations. 5 Minute Preview
Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview
PFA.8.15: : The student will
PFA.8.15.a: : determine whether a given relation is a function; and
Introduction to Functions
Determine if a relation is a function using the mapping diagram, ordered pairs, or the graph of the relation. Drag arrows from the domain to the range, type in ordered pairs, or drag points to the graph to add inputs and outputs to the relation. 5 Minute Preview
Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview
Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
PFA.8.15.b: : determine the domain and range of a function.
Introduction to Functions
Determine if a relation is a function using the mapping diagram, ordered pairs, or the graph of the relation. Drag arrows from the domain to the range, type in ordered pairs, or drag points to the graph to add inputs and outputs to the relation. 5 Minute Preview
Radical Functions
Compare the graph of a radical function to its equation. Vary the terms of the equation. Explore how the graph is translated and stretched by the changes to the equation. 5 Minute Preview
PFA.8.16: : The student will
PFA.8.16.a: : recognize and describe the graph of a linear function with a slope that is positive, negative, or zero;
Slope
Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes. 5 Minute Preview
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
PFA.8.16.b: : identify the slope and y-intercept of a linear function, given a table of values, a graph, or an equation in y = mx + b form;
Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview
Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
Slope
Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes. 5 Minute Preview
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
PFA.8.16.c: : determine the independent and dependent variable, given a practical situation modeled by a linear function;
Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview
PFA.8.16.d: : graph a linear function given the equation in y = mx + b form; and
Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
PFA.8.16.e: : make connections between and among representations of a linear function using verbal descriptions, tables, equations, and graphs.
Function Machines 1 (Functions and Tables)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview
Function Machines 2 (Functions, Tables, and Graphs)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview
Function Machines 3 (Functions and Problem Solving)
Drop a number into a function machine, and see what number comes out! You can use one of the six pre-set function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph. 5 Minute Preview
Linear Functions
Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear. 5 Minute Preview
Points, Lines, and Equations
Compare the graph of a linear function to its rule and to a table of its values. Change the function by dragging two points on the line. Examine how the rule and table change. 5 Minute Preview
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
PFA.8.17: : The student will solve multistep linear equations in one variable with the variable on one or both sides of the equation, including practical problems that require the solution of a multistep linear equation in one variable.
Modeling and Solving Two-Step Equations
Solve a two-step equation using a cup-and-counter model. Use step-by-step feedback to diagnose and correct incorrect steps. 5 Minute Preview
Solving Algebraic Equations I
Are there times when you wish you could escape from everyone and just be alone? Meet our variable friend, a real loner who doesn't like coefficients and neighboring terms. Learn how to use inverses to isolate a variable – a foundational skill for solving algebraic equations. 5 Minute Preview
Solving Algebraic Equations II
Is solving equations tricky? If you know how to isolate a variable, you're halfway there. The other half? Don't do anything to upset the balance of an equation. Join our plucky variable friend as he encounters algebraic equations and a (sometimes grumpy) equal sign. With a little practice, you'll find that solving equations isn't tricky at all. 5 Minute Preview
Solving Equations by Graphing Each Side
Solve an equation by graphing each side and finding the intersection of the lines. Vary the coefficients in the equation and explore how the graph changes in response. 5 Minute Preview
Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
PFA.8.18: : The student will solve multistep linear inequalities in one variable with the variable on one or both sides of the inequality symbol, including practical problems, and graph the solution on a number line.
Compound Inequalities
Explore the graphs of two inequalities and find their union or intersection. Determine the relationship between the endpoints of the inequalities and the endpoints of the compound inequality. 5 Minute Preview
Correlation last revised: 9/16/2020
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Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
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