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Product Name: enVisionmath2.0 Custom Grades 6-8 Grade 8 West Virginia
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Curriculum Standards:


Solve equations of the form x² = p and x³ = p, where p is a positive rational number. - 8.EEI.A.2a
Use the Converse of the Pythagorean Theorem to identify right triangles. - 8.G.7.2
Use the Pythagorean Theorem to solve problems. - 8.G.7.3
Use the Pythagorean Theorem to find unknown sides of triangles. - 8.G.7.1
Assess the reasonableness of predictions using scatterplots by interpreting them in the original context. - 8.4.1.3
Recognize that square roots of non-perfect squares are irrational. - 8.EEI.A.2c
Collect, display and interpret data using scatterplots. Use the shape of the scatterplot to informally estimate a line of best fit and determine an equation for the line. Use appropriate titles, labels and units. Know how to use graphing technology to display scatterplots and corresponding lines of best fit. - 8.4.1.1
Evaluate square roots of perfect squares less than or equal to 625 and cube roots of perfect cubes less than or equal to 1000. - 8.EEI.A.2b
Use a line of best fit to make statements about approximate rate of change and to make predictions about values not in the original data set. - 8.4.1.2
The student will estimate and determine the two consecutive integers between which a square root lies. - 8.3a
The student will determine both the positive and negative square roots of a given perfect square. - 8.3b
Investigate if orientation is preserved under rigid transformations. - 8.GM.A.1b
Find the relative frequencies of two-way tables and interpret what they mean. - 8.DP.4.5
Display and interpret relationships between paired categorical data. - 8.DP.4.4
Make a prediction by using the equation of a line that closely fits a set of data. - 8.DP.4.3
Use a line to represent the relationship between paired data. - 8.DP.4.2
Compare characteristics of two functions each represented in a different way. - 8.F.A.2
Construct a scatter plot and use it to understand the relationship between paired data. - 8.DP.4.1
Understand that all rational numbers have a decimal expansion that terminates or repeats. - 8.NS.A.1b
Know the differences between rational and irrational numbers. - 8.NS.A.1a
Generate equivalent representations of rational numbers. - 8.NS.A.1d
Convert decimals which repeat into fractions and fractions into repeating decimals. - 8.NS.A.1c
Use the Pythagorean Theorem to find the distance between two points in the coordinate plane. - 8.G.7.4
Verify that angle measure, betweeness, collinearity and distance are preserved under rigid transformations. - 8.GM.A.1a
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. - MAFS.8.G.3.9
Determine the parameters of a linear function. - 8.F.B.4b
Determine the x-intercept of a linear function. - 8.F.B.4c
Find the surface areas of cylinders, cones, and spheres. - 8.G.8.1
Recognize functions given a table of values or a set of ordered pairs. - NC.8.F.1.b
Use what I know about finding volumes of rectangular prisms to find the volume of a cylinder. - 8.G.8.2
Recognize functions when graphed as the set of ordered pairs consisting of an input and exactly one corresponding output. - NC.8.F.1.a
Lines are taken to lines, and line segments to line segments of the same length. - MAFS.8.G.1.1a
Angles are taken to angles of the same measure. - MAFS.8.G.1.1b
Parallel lines are taken to parallel lines. - MAFS.8.G.1.1c
Explain the parameters of a linear function based on the context of a problem. - 8.F.B.4a
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. - M.8.10a
Solve real-world and mathematical problems leading to two linear equations in two variables. (e.g., Given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.) - M.8.10c
Develop and apply the properties of integer exponents, including a⁰ = 1 (with a ≠ 0), to generate equivalent numerical and algebraic expressions. - PA.N.1.1
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.) - M.8.10b
Describe the functional relationship between two quantities from a graph or a verbal description. - 8.F.B.5
Classify real numbers as rational or irrational. Explain why the rational number system is closed under addition and multiplication and why the irrational system is not. Explain why the sum of a rational number and an irrational number is irrational; and the product of a non-zero rational number and an irrational number is irrational. - PA.N.1.4
Compare real numbers; locate real numbers on a number line. Identify the square root of a perfect square to 400 or, if it is not a perfect square root, locate it as an irrational number between two consecutive positive integers. - PA.N.1.5
Express and compare approximations of very large and very small numbers using scientific notation. - PA.N.1.2
Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation. - PA.N.1.3
Understand the concept of surface area and find surface area of pyramids. - 8.GM.C.9a
Understand the concepts of volume and find the volume of pyramids, cones and spheres. - 8.GM.C.9b
Find the volumes of cones. - 8.G.8.3
Find the volume of a sphere and use it to solve problems. - 8.G.8.4
The student will solve problems, including practical problems, involving volume and surface area of cones and square-based pyramids. - 8.6a
Understand that a function assigns to each input exactly one output. - 8.F.A.1a
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. - MAFS.8.G.2.7
Explain a proof of the Pythagorean Theorem and its converse. - MAFS.8.G.2.6
Determine if a relation is a function. - 8.F.A.1b
Graph a function. - 8.F.A.1c
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. - MAFS.8.G.2.8
Given two congruent figures, describe a sequence that exhibits the congruence between them. - NC.8.G.2.c
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 eventually into a rational number. Instructional Note: A decimal expansion that repeats the digit 0 is often referred to as a “terminating decimal.” - M.8.1
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. - NC.8.G.2.b
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram and estimate the value of expressions such as π2. (e.g., By truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.) - M.8.2
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 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger.) - M.8.5
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. (e.g., Use millimeters per year for seafloor spreading.) Interpret scientific notation that has been generated by technology. - M.8.6
Know and apply the properties of integer exponents to generate equivalent numerical expressions. (e.g., 32 × 3–5 = 3–3 = 1/33 = 1/27.) - M.8.3
Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = 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 irrational. - M.8.4
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. Instructional Note: Function notation is not required in grade 8. - M.8.11
Solve systems of equations using elimination. - 8.AF.5.4
Evaluate square roots of perfect squares and cube roots of perfect cubes for positive numbers less than or equal to 400. - NC.8.EE.2.b
Represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. - NC.8.EE.2.a
Verify experimentally the properties of rotations, reflections, and translations that create congruent figures. - NC.8.G.2.a
Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of the slope and y-intercept of its graph or a table of values. - NC.8.F.4.d
Describe a possible sequence of transformations between two similar figures. - 8.GM.A.4a
Use informal arguments to analyze angle relationships. - NC.8.G.5
Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations and dilations; given two similar two dimensional figures, describe a sequence that exhibits the similarity between them. - M.8.19
Construct a graph of a linear relationship given an equation in slope-intercept form. - NC.8.F.4.c
Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. - M.8.18
Use transformations to define similarity. - NC.8.G.4
Write an equation in slope-intercept form to model a linear relationship by determining the rate of change and the initial value, given at least two (x, y) values or a graph. - NC.8.F.4.b
Perform operations with numbers in scientific notation. - 8.AF.1.10
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 them. - M.8.17
Describe the effect of dilations about the origin, translations, rotations about the origin in 90 degree increments, and reflections across the x-axis and y-axis on two-dimensional figures using coordinates. - NC.8.G.3
The student will given a polygon, apply transformations, to include translations, reflections, and dilations, in the coordinate plane. - 8.7a
Use transformations to define congruence. - NC.8.G.2
The student will identify practical applications of transformations. - 8.7b
Understand that a linear relationship can be generalized by 𝑦 =mx + b. - NC.8.F.4.a
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. - M.8.15
Solve systems of equations using substitution. - 8.AF.5.3
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. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. - M.8.14
Find the solution to a system of equations using graphs. - 8.AF.5.2
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 = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.) - M.8.13
Find the number of solutions of a system of equations by inspecting the equations. - 8.AF.5.1
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (e.g., Given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.) - M.8.12
The student will verify the Pythagorean Theorem. - 8.9a
Understand how the formulas for the volumes of cones, cylinders, and spheres are related and use the relationship to solve real-world and mathematical problems. - NC.8.G.9
The student will apply the Pythagorean Theorem. - 8.9b
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. - NC.8.G.8
Apply the Pythagorean Theorem and its converse to solve real-world and mathematical problems. - NC.8.G.7
Explain the Pythagorean Theorem and its converse. - NC.8.G.6
Use linear functions to represent and explain real-world and mathematical situations. - PA.A.1.2
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. - M.8.22
Recognize that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable. - PA.A.1.1
Explain a proof of the Pythagorean Theorem and its converse. - M.8.21
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 the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.) - M.8.20
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 two moving objects has greater speed.) - M.8.7
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 vertical axis at b. - M.8.8
Identify a function as linear if it can be expressed in the form y = mx + b or if its graph is a straight line. - PA.A.1.3
Explore the relationship between the interior and exterior angles of a triangle. - 8.GM.A.5b
Construct and explore the angles created when parallel lines are cut by a transversal. - 8.GM.A.5c
Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. (e.g., Collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?) - M.8.28
Use the properties of similar figures to solve problems. - 8.GM.A.5d
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. (e.g., In a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.) - M.8.27
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 data points to the line. - M.8.26
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 association. - M.8.25
Know the formulas for the volumes of cones, cylinders and spheres and use them to solve real-world and mathematical problems. - M.8.24
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. - M.8.23
Derive the sum of the interior angles of a triangle. - 8.GM.A.5a
Recognize that the graph of a linear function has a constant rate of change - 8.F.A.3b
Give examples of nonlinear functions. - 8.F.A.3c
Interpret the equation y = mx + b as defining a linear function, whose parameters are the slope (m) and the yintercept (b). - 8.F.A.3a
Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. - 8.EEI.A.4b
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. - 8.EEI.A.4a
Informally fit a straight line for a scatter plot that suggests a linear association. - NC.8.SP.2.a
Informally assess the model fit by judging the closeness of the data points to the line. - NC.8.SP.2.b
Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. - MAFS.8.G.1.4
Qualitatively analyze the functional relationship between two quantities. - NC.8.F.5
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. - MAFS.8.G.1.3
Analyze functions that model linear relationships. - NC.8.F.4
Describe a possible sequence of rigid transformations between two congruent figures. - 8.GM.A.2a
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. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. - MAFS.8.G.1.5
Identify linear functions from tables, equations, and graphs. - NC.8.F.3
Compare properties of two linear functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). - NC.8.F.2
Understand that a function is a rule that assigns to each input exactly one output. - NC.8.F.1
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 them. - MAFS.8.G.1.2
Verify experimentally the properties of rotations, reflections, and translations: - MAFS.8.G.1.1
Know and apply the properties of positive and negative integer exponents to generate equivalent numerical expressions. - 8.1.1.4
The student will make observations about data represented in scatterplots. - 8.13b
Express approximations of very large and very small numbers using scientific notation; understand how calculators display numbers in scientific notation. Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation, using the correct number of significant digits when physical measurements are involved. - 8.1.1.5
Use the Pythagorean Theorem to find the distance between points in a Cartesian coordinate system. - 8.GM.B.8
The student will use a drawing to estimate the line of best fit for data represented in a scatterplot. - 8.13c
Use the Pythagorean Theorem to determine unknown side lengths in right triangles in problems in two- and three-dimensional contexts. - 8.GM.B.7
Use models to demonstrate a proof of the Pythagorean Theorem and its converse. - 8.GM.B.6
The student will represent data in scatterplots. - 8.13a
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 eventually into a rational number. - MAFS.8.NS.1.1
Classify real numbers as rational or irrational. Know that when a square root of a positive integer is not an integer, then it is irrational. Know that the sum of a rational number and an irrational number is irrational, and the product of a non-zero rational number and an irrational number is irrational. - 8.1.1.1
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. - MAFS.8.NS.1.2
Compare real numbers; locate real numbers on a number line. Identify the square root of a positive integer as an integer, or if it is not an integer, locate it as a real number between two consecutive positive integers. - 8.1.1.2
Determine rational approximations for solutions to problems involving real numbers. - 8.1.1.3
Perform multiplication and division with numbers expressed in scientific notation to solve real-world problems, including problems where both decimal and scientific notation are used. - NC.8.EE.4
Use numbers expressed in scientific notation to estimate very large or very small quantities and to express how many times as much one is than the other. - NC.8.EE.3
Develop and apply the properties of integer exponents to generate equivalent numerical expressions. - NC.8.EE.1
Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. - PA.A.2.1
Estimate the value and compare the size of irrational numbers and approximate their locations on a number line. - 8.NS.A.2
Solve problems involving linear functions and interpret results in the original context. - PA.A.2.5
Construct and interpret scatter plots of bivariate measurement data to investigate patterns of association between two quantities - 8.DSP.A.1
Understand that every number has a decimal expansion. Building upon the definition of a rational number, know that an irrational number is defined as a non-repeating, non-terminating decimal. - NC.8.NS.1
Predict the effect on the graph of a linear function when the slope or y-intercept changes. Use appropriate tools to examine these effects. - PA.A.2.4
Identify graphical properties of linear functions including slope and intercepts. Know that the slope equals the rate of change, and that the yintercept is zero when the function represents a proportional relationship. - PA.A.2.3
Interpret the parameters of a linear model of bivariate measurement data to solve problems. - 8.DSP.A.3
Identify, describe, and analyze linear relationships between two variables. - PA.A.2.2
Generate and use a trend line for bivariate data, and informally assess the fit of the line. - 8.DSP.A.2
Use rational approximations of irrational numbers to compare the size of irrational numbers and locate them approximately on a number line. Estimate the value of expressions involving: - NC.8.NS.2
Use angle measures to determine whether two triangles are similar. - 8.G.6.10
The student will make connections between and among representations of a linear function using verbal descriptions, tables, equations, and graphs. - 8.16e
The student will determine the independent and dependent variable, given a practical situation modeled by a linear function. - 8.16c
The student will graph a linear function given the equation in y = mx + b form. - 8.16d
Verify experimentally the properties of dilations that create similar figures. - NC.8.G.4.a
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. - MAFS.8.F.2.5
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. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. - MAFS.8.F.2.4
Given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. - NC.8.G.4.c
Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations. - NC.8.G.4.b
The student will recognize and describe the graph of a linear function with a slope that is positive, negative, or zero. - 8.16a
The student will 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. - 8.16b
Sketch the graph of a function that has been described verbally. - 8.AF.3.6
Tell whether a relation is a function. - 8.AF.3.1
π to the hundredths. - NC.8.NS.2.b
Describe the behavior of a function and write a description to go with its graph. - 8.AF.3.5
Know and apply the properties of integer exponents to generate equivalent expressions. - 8.EEI.A.1
Write an equation in the form y = mx + b to describe a linear function. - 8.AF.3.4
Solve real-world and mathematical problems leading to systems of linear equations by graphing the equations. Solve simple cases by inspection. - NC.8.EE.8.b
Express very large and very small quantities in scientific notation and approximate how many times larger one is than the other. - 8.EEI.A.3
Compare linear and nonlinear functions. - 8.AF.3.3
Identify functions by their equations, tables, and graphs. - 8.AF.3.2
Square roots and cube roots to the tenths. - NC.8.NS.2.a
Understand that solutions to a system of two linear equations correspond to the points of intersection of their graphs because the point of intersection satisfies both equations simultaneously. - NC.8.EE.8.a
Informally justify the Pythagorean Theorem using measurements, diagrams, or dynamic software and use the Pythagorean Theorem to solve problems in two and three dimensions involving right triangles. - PA.GM.1.1
Use the Pythagorean Theorem to find the distance between any two points in a coordinate plane. - PA.GM.1.2
Understand that two-dimensional figures are congruent if a series of rigid transformations can be performed to map the preimage to the image. - 8.GM.A.2
The student will determine whether a given relation is a function. - 8.15a
Understand that two-dimensional figures are similar if a series of transformations (rotations, reflections, translations and dilations) can be performed to map the pre-image to the image. - 8.GM.A.4
Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. - 8.GM.A.3
Represent linear functions with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. - 8.2.2.1
Identify graphical properties of linear functions including slopes and intercepts. Know that the slope equals the rate of change, and that the 𝑦𝑦-intercept is zero when the function represents a proportional relationship. - 8.2.2.2
Identify how coefficient changes in the equation f(x) = mx + b affect the graphs of linear functions. Know how to use graphing technology to examine these effects. - 8.2.2.3
Compare two different proportional relationships. - 8.EEI.B.5b
Interpret the unit rate as the slope of the graph. - 8.EEI.B.5a
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Investigate and describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. - NC.8.SP.1
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. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. - MAFS.8.F.1.3
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. - MAFS.8.F.1.2
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. - MAFS.8.F.1.1
Use relative frequencies calculated for rows or columns to describe possible association between the two variables. - NC.8.SP.4.b
Use the equation of a linear model to solve problems in the context of bivariate quantitative data, interpreting the slope and y-intercept. - NC.8.SP.3
Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. - NC.8.SP.4
Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. - NC.8.SP.4.a
Sketch a graph that exhibits the qualitative features of a real-world function. - NC.8.F.5.b
Analyze a graph determining where the function is increasing or decreasing; linear or non-linear. - NC.8.F.5.a
Calculate the surface area of a cylinder, in terms of π and using approximations for π, using decomposition or nets. Use appropriate measurements such as cm². - PA.GM.2.2
Use relative frequencies calculated for rows or columns to describe possible association between the two variables. - 8.DSP.A.4b
Develop and use the formulas V = πr2ℎ and V = Bℎ to determine the volume of right cylinders, in terms of π and using approximations for π. Justify why base area (B) and height (h) are multiplied to find the volume of a right cylinder. Use appropriate measurements such as cm³. - PA.GM.2.4
Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. - 8.DSP.A.4a
Explain why the slope (m) is the same between any two distinct points on a non-vertical line in the Cartesian coordinate plane. - 8.EEI.B.6a
Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. - 8.EEI.B.6b
Understand that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable. Use functional notation, such as f(x), to represent such relationships. - 8.2.1.1
Use linear functions to represent relationships in which changing the input variable by some amount leads to a change in the output variable that is a constant times that amount. - 8.2.1.2
Represent real-world situations using equations and inequalities involving one variable. - PA.A.4.3
Understand that a function is linear if it can be expressed in the form f(x) = mx + b or if its graph is a straight line. - 8.2.1.3
Illustrate, write, and solve mathematical and real-world problems using linear equations with one variable with one solution, infinitely many solutions, or no solutions. Interpret solutions in the original context. - PA.A.4.1
Use the Pythagorean Theorem to solve problems involving right triangles. - 8.3.1.1
Explain why solution(s) to a system of two linear equations in two variables correspond to point(s) of intersection of the graphs. - 8.EEI.C.8b
Determine the distance between two points on a horizontal or vertical line in a coordinate system. Use the Pythagorean Theorem to find the distance between any two points in a coordinate system. - 8.3.1.2
Informally justify the Pythagorean Theorem by using measurements, diagrams and computer software. - 8.3.1.3
Explain why systems of linear equations can have one solution, no solution or infinitely many solutions. - 8.EEI.C.8c
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. - 8.17
Solve systems of two linear equations. - 8.EEI.C.8d
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. - MAFS.8.EE.3.8a
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 and 6. - MAFS.8.EE.3.8b
Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. - MAFS.8.EE.3.8c
Use scientific notation to write very large or very small quantities. - 8.AF.1.9
Estimate large and small quantities using a power of 10. - 8.AF.1.8
Compare and order rational and irrational numbers. - 8.AF.1.3
Identify a number that is irrational. - 8.AF.1.2
Write repeating decimals as fractions. - 8.AF.1.1
Graph systems of linear equations and recognize the intersection as the solution to the system. - 8.EEI.C.8a
Write a number with a negative or zero exponent a different way. - 8.AF.1.7
Use the properties of exponents to write equivalent expressions. - 8.AF.1.6
Solve equations involving squares or cubes. - 8.AF.1.5
Find square roots and cube roots of rational numbers. - 8.AF.1.4
Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² ×3-5=1/3³=1/27 - MAFS.8.EE.1.1
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. For example, estimate the population of the United States as 3 × 10⁸ and the population of the world as 7 × 10⁹ , and determine that the world population is more than 20 times larger. - MAFS.8.EE.1.3
Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = 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 irrational. - MAFS.8.EE.1.2
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 (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. - MAFS.8.EE.1.4
Lines are taken to lines, and line segments to line segments of the same length. - M.8.16a
Parallel lines are taken to parallel lines. - M.8.16c
Angles are taken to angles of the same measure. - M.8.16b
Solve multi-step equations in one variable. Solve for one variable in a multi-variable equation in terms of the other variables. Justify the steps by identifying the properties of equalities used. - 8.2.4.2
Express linear equations in slope-intercept, point-slope and standard forms, and convert between these forms. Given sufficient information, find an equation of a line. - 8.2.4.3
Use linear equations to represent situations involving a constant rate of change, including proportional and non-proportional relationships. - 8.2.4.1
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 of the form x = a, a = a, or a = b results (where a and b are different numbers). - M.8.9a
Represent relationships in various contexts using systems of linear equations. Solve systems of linear equations in two variables symbolically, graphically and numerically. - 8.2.4.7
Understand that a system of linear equations may have no solution, one solution, or an infinite number of solutions. Relate the number of solutions to pairs of lines that are intersecting, parallel or identical. Check whether a pair of numbers satisfies a system of two linear equations in two unknowns by substituting the numbers into both equations. - 8.2.4.8
Use the relationship between square roots and squares of a number to solve problems. - 8.2.4.9
Rotate a two-dimensional figure. - 8.G.6.3
Describe and perform a sequence of transformations. - 8.G.6.4
Translate two-dimensional figures. - 8.G.6.1
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. - M.8.9b
Reflect two-dimensional figures. - 8.G.6.2
Recognize the relationships between the angles created when parallel lines are cut by a transversal. - NC.8.G.5.b
Recognize relationships between interior and exterior angles of a triangle. - NC.8.G.5.a
Solve real-world and mathematical problems involving angles. - NC.8.G.5.d
Recognize the angle-angle criterion for similarity of triangles. - NC.8.G.5.c
Derive the equation y = mx + b. - 8.AF.2.9
Find the y-intercept of a graph and explain what it means. - 8.AF.2.8
Write equations to describe linear relationships. - 8.AF.2.7
Solve equations with variables on both sides of the equal sign. - 8.AF.2.2
Recognize linear equations in one variable as having one solution, infinitely many solutions, or no solutions. - NC.8.EE.7.a
Solve equations that have like terms on one side. - 8.AF.2.1
Understand the slope of a line. - 8.AF.2.6
Compare proportional relationships represented in different ways. - 8.AF.2.5
Determine the number of solutions an equation has. - 8.AF.2.4
Solve linear equations and inequalities including multi-step equations and inequalities with the same variable on both sides. - NC.8.EE.7.b
Solve multistep equations and pairs of equations using more than one approach. - 8.AF.2.3
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. - MAFS.8.SP.1.3
Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? - MAFS.8.SP.1.4
Create and identify linear equations with one solution, infinitely many solutions or no solutions. - 8.EEI.C.7a
Solve linear equations and inequalities with rational number coefficients, including equations and inequalities whose solutions require expanding expressions using the distributive property and combining like terms. - 8.EEI.C.7b
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 vertical axis at b. - MAFS.8.EE.2.6
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. - MAFS.8.EE.2.5
Collect, display and interpret data using scatterplots. Use the shape of the scatterplot to informally estimate a line of best fit, make statements about average rate of change, and make predictions about values not in the original data set. Use appropriate titles, labels and units. - PA.D.1.3
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 association. - MAFS.8.SP.1.1
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 data points to the line. - MAFS.8.SP.1.2
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 of the form x = a, a = a, or a = b results (where a and b are different numbers). - MAFS.8.EE.3.7a
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. - MAFS.8.EE.3.7b
Use a sequence of transformations, including dilations, to show that figures are similar. - 8.G.6.7
Identify and find the measures of angles formed by parallel lines and a transversal. - 8.G.6.8
Use a sequence of translations, reflections, and rotations to show that figures are congruent. - 8.G.6.5
The student will compare and order real numbers. - 8.1
Dilate two-dimensional figures. - 8.G.6.6
The student will describe the relationships between the subsets of the real number system. - 8.2
Find the interior and exterior angle measures of a triangle. - 8.G.6.9




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