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- Mathematics: 8th Grade
Virginia - Mathematics: 8th Grade
Standards of Learning | Adopted: 2023
8.NS: : Number and Number Sense
8.NS.1: : The student will compare and order real numbers and determine the relationships between real numbers.
8.NS.1.a: : Estimate and identify the two consecutive natural numbers between which the positive square root of a given number lies and justify which natural number is the better approximation. Numbers are limited to natural numbers from 1 to 400.
![Screenshot of Ordering and Approximating Square Roots](/Assets/img/blank.gif)
Ordering and Approximating Square Roots
Order square roots on a number line. Approximate the square roots using the side lengths of square regions in a grid. 5 Minute Preview
![Screenshot of Square Roots](/Assets/img/blank.gif)
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
8.NS.1.b: : Use rational approximations (to the nearest hundredth) of irrational numbers to compare, order, and locate values on a number line. Radicals may include both positive and negative square roots of values from 0 to 400 yielding an irrational number.
![Screenshot of Ordering and Approximating Square Roots](/Assets/img/blank.gif)
Ordering and Approximating Square Roots
Order square roots on a number line. Approximate the square roots using the side lengths of square regions in a grid. 5 Minute Preview
8.NS.1.c: : Use multiple strategies (e.g., benchmarks, number line, equivalency) to compare and order no more than five real numbers expressed as integers, fractions (proper or improper), decimals, mixed numbers, percents, numbers written in scientific notation, radicals, and pi. Radicals may include both positive and negative square roots of values from 0 to 400. Ordering may be in ascending or descending order. Justify solutions orally, in writing or with a model.
![Screenshot of Comparing and Ordering Decimals](/Assets/img/blank.gif)
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
![Screenshot of Integers, Opposites, and Absolute Values](/Assets/img/blank.gif)
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
![Screenshot of Ordering Percents, Fractions, and Decimals Greater Than 1](/Assets/img/blank.gif)
Ordering Percents, Fractions, and Decimals Greater Than 1
Compare and order numbers greater than 1 using area grids and a number line. Examine the numbers represented as percents, improper fractions, and decimals. 5 Minute Preview
![Screenshot of Ordering and Approximating Square Roots](/Assets/img/blank.gif)
Ordering and Approximating Square Roots
Order square roots on a number line. Approximate the square roots using the side lengths of square regions in a grid. 5 Minute Preview
![Screenshot of Rational Numbers, Opposites, and Absolute Values](/Assets/img/blank.gif)
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
8.CE: : Computation and Estimation
8.CE.1: : The student will estimate and apply proportional reasoning and computational procedures to solve contextual problems.
8.CE.1.a: : Estimate and solve contextual problems that require the computation of one discount or markup and the resulting sale price.
![Screenshot of Percent of Change](/Assets/img/blank.gif)
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
8.CE.1.c: : Estimate and solve contextual problems that require the computation of the percent increase or decrease.
![Screenshot of Percent of Change](/Assets/img/blank.gif)
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
8.MG: : Measurement and Geometry
8.MG.1: : 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.
8.MG.1.a: : Identify and describe the relationship between pairs of angles that are vertical, adjacent, supplementary, and complementary.
![Screenshot of Investigating Angle Theorems](/Assets/img/blank.gif)
Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview
8.MG.1.b: : Use the relationships among supplementary, complementary, vertical, and adjacent angles to solve problems, including those in context, involving the measure of unknown angles.
![Screenshot of Investigating Angle Theorems](/Assets/img/blank.gif)
Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview
8.MG.2: : The student will investigate and determine the surface area of square-based pyramids and the volume of cones and square-based pyramids.
8.MG.2.a: : Determine the surface area of square-based pyramids by using concrete objects, nets, diagrams, and formulas.
![Screenshot of Surface and Lateral Areas of Pyramids and Cones](/Assets/img/blank.gif)
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
8.MG.2.b: : Determine the volume of cones and square-based pyramids, using concrete objects, diagrams, and formulas.
![Screenshot of Pyramids and Cones](/Assets/img/blank.gif)
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
8.MG.2.c: : Examine and explain the relationship between the volume of cones and cylinders, and the volume of rectangular prisms and square based pyramids.
![Screenshot of Pyramids and Cones](/Assets/img/blank.gif)
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
8.MG.3: : The student will apply translations and reflections to polygons in the coordinate plane.
8.MG.3.a: : Given a preimage in the coordinate plane, identify the coordinates of the image of a polygon that has been translated vertically, horizontally, or a combination of both.
![Screenshot of Translations](/Assets/img/blank.gif)
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
8.MG.3.b: : Given a preimage in the coordinate plane, identify the coordinates of the image of a polygon that has been reflected over the x- or y-axis.
![Screenshot of Rotations, Reflections, and Translations](/Assets/img/blank.gif)
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
8.MG.3.c: : Given a preimage in the coordinate plane, identify the coordinates of the image of a polygon that has been translated and reflected over the x- or y-axis or reflected over the x- or y-axis and then translated.
![Screenshot of Rotations, Reflections, and Translations](/Assets/img/blank.gif)
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
8.MG.3.d: : Sketch the image of a polygon that has been translated vertically, horizontally, or a combination of both.
![Screenshot of Translations](/Assets/img/blank.gif)
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
8.MG.4: : The student will apply the Pythagorean Theorem to solve problems involving right triangles, including those in context.
8.MG.4.a: : Verify the Pythagorean Theorem using diagrams, concrete materials, and measurement.
![Screenshot of Pythagorean Theorem](/Assets/img/blank.gif)
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
![Screenshot of Pythagorean Theorem with a Geoboard](/Assets/img/blank.gif)
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
8.MG.4.b: : Determine whether a triangle is a right triangle given the measures of its three sides.
![Screenshot of Pythagorean Theorem](/Assets/img/blank.gif)
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
![Screenshot of Pythagorean Theorem with a Geoboard](/Assets/img/blank.gif)
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
8.MG.4.c: : Identify the parts of a right triangle (the hypotenuse and the legs) given figures in various orientations.
![Screenshot of Pythagorean Theorem](/Assets/img/blank.gif)
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
![Screenshot of Pythagorean Theorem with a Geoboard](/Assets/img/blank.gif)
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
8.MG.4.d: : Determine the measure of a side of a right triangle, given the measures of the other two sides.
![Screenshot of Pythagorean Theorem](/Assets/img/blank.gif)
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
![Screenshot of Pythagorean Theorem with a Geoboard](/Assets/img/blank.gif)
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
8.MG.4.e: : Apply the Pythagorean Theorem, and its converse, to solve problems involving right triangles in context.
![Screenshot of Pythagorean Theorem](/Assets/img/blank.gif)
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
![Screenshot of Pythagorean Theorem with a Geoboard](/Assets/img/blank.gif)
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
8.MG.5: : The student will solve area and perimeter problems involving composite plane figures, including those in context.
8.MG.5.a: : Subdivide a plane figure into triangles, rectangles, squares, trapezoids, parallelograms, circles, and semicircles. Determine the area of subdivisions and combine to determine the area of the composite plane figure.
![Screenshot of Area of Triangles](/Assets/img/blank.gif)
Area of Triangles
Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview
8.PS: : Probability and Statistics
8.PS.1: : The student will use statistical investigation to determine the probability of independent and dependent events, including those in context.
8.PS.1.a: : Determine whether two events are independent or dependent and explain how replacement impacts the probability.
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
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
8.PS.1.b: : Compare and contrast the probability of independent and dependent events.
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
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
8.PS.1.c: : Determine the probability of two independent events.
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
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
8.PS.1.d: : Determine the probability of two dependent events.
![Screenshot of Independent and Dependent Events](/Assets/img/blank.gif)
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
8.PS.2: : The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on boxplots.
8.PS.2.a: : Formulate questions that require the collection or acquisition of data with a focus on boxplots.
![Screenshot of Box-and-Whisker Plots](/Assets/img/blank.gif)
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
8.PS.2.b: : Determine the data needed to answer a formulated question and collect the data (or acquire existing data) using various methods (e.g., observations, measurement, surveys, experiments).
![Screenshot of Box-and-Whisker Plots](/Assets/img/blank.gif)
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
8.PS.2.d: : Organize and represent a numeric data set of no more than 20 items, using boxplots, with and without the use of technology.
![Screenshot of Box-and-Whisker Plots](/Assets/img/blank.gif)
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
8.PS.2.e: : Identify and describe the lower extreme (minimum), upper extreme (maximum), median, upper quartile, lower quartile, range, and interquartile range given a data set, represented by a boxplot.
![Screenshot of Box-and-Whisker Plots](/Assets/img/blank.gif)
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
8.PS.2.g: : Analyze data represented in a boxplot by making observations and drawing conclusions.
![Screenshot of Box-and-Whisker Plots](/Assets/img/blank.gif)
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
8.PS.2.h: : Compare and analyze two data sets represented in boxplots.
![Screenshot of Box-and-Whisker Plots](/Assets/img/blank.gif)
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
8.PS.3: : The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on scatterplots.
8.PS.3.a: : Formulate questions that require the collection or acquisition of data with a focus on scatterplots.
![Screenshot of Correlation](/Assets/img/blank.gif)
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
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
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
8.PS.3.b: : Determine the data needed to answer a formulated question and collect the data (or acquire existing data) of no more than 20 items using various methods (e.g., observations, measurement, surveys, experiments).
![Screenshot of Correlation](/Assets/img/blank.gif)
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
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
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
8.PS.3.c: : Organize and represent numeric bivariate data using scatterplots with and without the use of technology.
![Screenshot of Correlation](/Assets/img/blank.gif)
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
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
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
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
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
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
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
8.PS.3.d: : Make observations about a set of data points in a scatterplot as having a positive linear relationship, a negative linear relationship, or no relationship.
![Screenshot of Correlation](/Assets/img/blank.gif)
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
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
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
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
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
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
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
8.PS.3.e: : Analyze and justify the relationship of the quantitative bivariate data represented in scatterplots.
![Screenshot of Correlation](/Assets/img/blank.gif)
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
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
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
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
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
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
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
8.PS.3.f: : Sketch the line of best fit for data represented in a scatterplot.
![Screenshot of Correlation](/Assets/img/blank.gif)
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
![Screenshot of Least-Squares Best Fit Lines](/Assets/img/blank.gif)
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
![Screenshot of Solving Using Trend Lines](/Assets/img/blank.gif)
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
![Screenshot of Trends in Scatter Plots](/Assets/img/blank.gif)
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
8.PFA: : Patterns, Functions, and Algebra
8.PFA.1: : The student will represent, simplify, and generate equivalent algebraic expressions in one variable.
8.PFA.1.b: : Simplify and generate equivalent algebraic expressions in one variable by applying the order of operations and properties of real numbers. Expressions may need to be expanded (using the distributive property) or require combining like terms to simplify. Expressions will include only linear and numeric terms. Coefficients and numeric terms may be rational.
![Screenshot of Equivalent Algebraic Expressions I](/Assets/img/blank.gif)
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
![Screenshot of Equivalent Algebraic Expressions II](/Assets/img/blank.gif)
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
![Screenshot of Simplifying Algebraic Expressions I](/Assets/img/blank.gif)
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
![Screenshot of Simplifying Algebraic Expressions II](/Assets/img/blank.gif)
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
8.PFA.2: : The student will determine whether a given relation is a function and determine the domain and range of a function.
8.PFA.2.a: : Determine whether a relation, represented by a set of ordered pairs, a table, or a graph of discrete points is a function. Sets are limited to no more than 10 ordered pairs.
![Screenshot of Introduction to Functions](/Assets/img/blank.gif)
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
![Screenshot of Linear Functions](/Assets/img/blank.gif)
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
8.PFA.2.b: : Identify the domain and range of a function represented as a set of ordered pairs, a table, or a graph of discrete points.
![Screenshot of Introduction to Functions](/Assets/img/blank.gif)
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
![Screenshot of Linear Functions](/Assets/img/blank.gif)
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
8.PFA.3: : The student will represent and solve problems, including those in context, by using linear functions and analyzing their key characteristics (the value of the y-intercept (b) and the coordinates of the ordered pairs in graphs will be limited to integers).
8.PFA.3.a: : Determine how adding a constant (b) to the equation of a proportional relationship y = mx will translate the line on a graph.
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
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
8.PFA.3.b: : Describe key characteristics of linear functions including slope (m), y-intercept (b), and independent and dependent variables.
![Screenshot of Point-Slope Form of a Line](/Assets/img/blank.gif)
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
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
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
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
8.PFA.3.c: : Graph a linear function given a table, equation, or a situation in context.
![Screenshot of Point-Slope Form of a Line](/Assets/img/blank.gif)
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
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
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
![Screenshot of Standard Form of a Line](/Assets/img/blank.gif)
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
8.PFA.3.d: : Create a table of values for a linear function given a graph, equation in the form of y = mx + b, or context.
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
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
8.PFA.3.e: : Write an equation of a linear function in the form y = mx + b, given a graph, table, or a situation in context.
![Screenshot of Slope-Intercept Form of a Line](/Assets/img/blank.gif)
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
8.PFA.4: : The student will write and solve multistep linear equations in one variable, including problems in context that require the solution of a multistep linear equation in one variable.
8.PFA.4.a: : Represent and solve multistep linear equations in one variable with the variable on one or both sides of the equation (up to four steps) using a variety of concrete materials and pictorial representations.
![Screenshot of Modeling and Solving Two-Step Equations](/Assets/img/blank.gif)
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
![Screenshot of Solving Equations by Graphing Each Side](/Assets/img/blank.gif)
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
8.PFA.4.b: : Apply properties of real numbers and properties of equality to solve multistep linear equations in one variable (up to four steps). Coefficients and numeric terms will be rational. Equations may contain expressions that need to be expanded (using the distributive property) or require combining like terms to solve.
![Screenshot of Modeling and Solving Two-Step Equations](/Assets/img/blank.gif)
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
![Screenshot of Solving Algebraic Equations II](/Assets/img/blank.gif)
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
![Screenshot of Solving Equations by Graphing Each Side](/Assets/img/blank.gif)
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
![Screenshot of Solving Two-Step Equations](/Assets/img/blank.gif)
Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
8.PFA.4.c: : Write a multistep linear equation in one variable to represent a verbal situation, including those in context.
![Screenshot of Modeling and Solving Two-Step Equations](/Assets/img/blank.gif)
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
![Screenshot of Solving Equations by Graphing Each Side](/Assets/img/blank.gif)
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
![Screenshot of Solving Two-Step Equations](/Assets/img/blank.gif)
Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
8.PFA.4.e: : Solve problems in context that require the solution of a multistep linear equation.
![Screenshot of Modeling and Solving Two-Step Equations](/Assets/img/blank.gif)
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
![Screenshot of Solving Equations by Graphing Each Side](/Assets/img/blank.gif)
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
![Screenshot of Solving Two-Step Equations](/Assets/img/blank.gif)
Solving Two-Step Equations
Choose the correct steps to solve a two-step equation. Use the feedback to diagnose incorrect steps. 5 Minute Preview
8.PFA.4.g: : Confirm algebraic solutions to linear equations in one variable.
![Screenshot of Modeling and Solving Two-Step Equations](/Assets/img/blank.gif)
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
![Screenshot of Solving Equations by Graphing Each Side](/Assets/img/blank.gif)
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
8.PFA.5: : The student will write and solve multistep linear inequalities in one variable, including problems in context that require the solution of a multistep linear inequality in one variable.
8.PFA.5.a: : Apply properties of real numbers and properties of inequality to solve multistep linear inequalities (up to four steps) in one variable with the variable on one or both sides of the inequality. Coefficients and numeric terms will be rational. Inequalities may contain expressions that need to be expanded (using the distributive property) or require combining like terms to solve.
![Screenshot of Exploring Linear Inequalities in One Variable](/Assets/img/blank.gif)
Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
8.PFA.5.b: : Represent solutions to inequalities algebraically and graphically using a number line.
![Screenshot of Exploring Linear Inequalities in One Variable](/Assets/img/blank.gif)
Exploring Linear Inequalities in One Variable
Solve inequalities in one variable. Examine the inequality on a number line and determine which points are solutions to the inequality. 5 Minute Preview
Correlation last revised: 4/9/2024
About STEM Cases
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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Each STEM Case uses realtime reporting to show live student results.
Introduction to the Heatmap
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STEM Cases take between 30-90 minutes for students to complete, depending on the case.
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Student progress is automatically saved so that STEM Cases can be completed over multiple sessions.
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Multiple grade-appropriate versions, or levels, exist for each STEM Case.
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Each STEM Case level has an associated Handbook. These are interactive guides that focus on the science concepts underlying the case.
How Free Gizmos Work
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Start teaching with 20-40 Free Gizmos. See the full list.
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Access lesson materials for Free Gizmos including teacher guides, lesson plans, and more.
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All other Gizmos are limited to a 5 Minute Preview and can only be used for 5 minutes a day.
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Free Gizmos change each semester. The new collection will be available January 1 and July 1.
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