Organization: SAVVAS
Product Name: envisionmath2.0 Custom Grades 6-8 Grade 8 Virginia
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Curriculum Standards:


The student will construct a three-dimensional model, given the top or bottom, side, and front views. - 8.8
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
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
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
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
Construct a scatter plot and use it to understand the relationship between paired data. - 8.DP.4.1
Use the Pythagorean Theorem to find the distance between two points in the coordinate plane. - 8.G.7.4
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
Find the surface areas of cylinders, cones, and spheres. - 8.G.8.1
Use what I know about finding volumes of rectangular prisms to find the volume of a cylinder. - 8.G.8.2
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
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
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
The student will describe how changing one measured attribute of a rectangular prism affects the volume and surface area. - 8.6b
Find the volumes of cones. - 8.G.8.3
The student will solve problems, including practical problems, involving volume and surface area of cones and square-based pyramids. - 8.6a
Find the volume of a sphere and use it to solve problems. - 8.G.8.4
The student will represent numerical data in boxplots. - 8.12a
The student will make observations and inferences about data represented in boxplots. - 8.12b
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
The student will compare and analyze two data sets using boxplots. - 8.12c
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. - MAFS.8.G.2.8
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
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
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
Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. - M.8.18
The student will given a polygon, apply transformations, to include translations, reflections, and dilations, in the coordinate plane. - 8.7a
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
The student will identify practical applications of transformations. - 8.7b
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
Find the solution to a system of equations using graphs. - 8.AF.5.2
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 number of solutions of a system of equations by inspecting the equations. - 8.AF.5.1
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. (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
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 compare and contrast the probability of independent and dependent events. - 8.11a
The student will verify the Pythagorean Theorem. - 8.9a
The student will apply the Pythagorean Theorem. - 8.9b
The student will determine probabilities for independent and dependent events. - 8.11b
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
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 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
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
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 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
The student will evaluate an algebraic expression for given replacement values of the variables. - 8.14a
The student will simplify algebraic expressions in one variable. - 8.14b
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
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. - MAFS.8.G.1.3
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
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
The student will use a drawing to estimate the line of best fit for data represented in a scatterplot. - 8.13c
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
Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. - PA.A.2.1
Solve problems involving linear functions and interpret results in the original context. - PA.A.2.5
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
Identify, describe, and analyze linear relationships between two variables. - PA.A.2.2
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
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
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
Describe the behavior of a function and write a description to go with its graph. - 8.AF.3.5
Write an equation in the form y = mx + b to describe a linear function. - 8.AF.3.4
Compare linear and nonlinear functions. - 8.AF.3.3
Identify functions by their equations, tables, and graphs. - 8.AF.3.2
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
The student will determine the domain and range of a function. - 8.15b
The student will determine whether a given relation is a function. - 8.15a
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 𝑦-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
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
Calculate the surface area of a rectangular prism using decomposition or nets. Use appropriate measurements such as cm². - PA.GM.2.1
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
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
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
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
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
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. - 8.18
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
The student will solve area and perimeter problems, including practical problems, involving composite plane figures. - 8.10
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
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
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
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 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
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
The student will solve practical problems involving consumer applications. - 8.4
Find the interior and exterior angle measures of a triangle. - 8.G.6.9
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. - 8.5




List of all Files Validated:


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