Organization: SAVVAS
Product Name: enVisionmath2.0  Grades 6-8 Grade 8 2017
Product Version: 1




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Curriculum Standards:


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
Use the Converse of the Pythagorean Theorem to identify right triangles. - 8.G.7.2
Mathematical Modeling: Analyze and Solve Linear Equations - 8.AF.2MM
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 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
The student will estimate and determine the two consecutive integers between which a square root lies. - 8.3a
Compare linear and nonlinear functions. - 8.AF.3.3
The student will determine both the positive and negative square roots of a given perfect square. - 8.3b
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
Mathematical Modeling: Congruence and Similarity - 8.G.6MM
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
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. - 8.G.C.9
Construct a scatter plot and use it to understand the relationship between paired data. - 8.DP.4.1
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
Represent arithmetic sequences using equations, tables, graphs and verbal descriptions, and use them to solve problems. - 8.2.2.4
Represent geometric sequences using equations, tables, graphs and verbal descriptions, and use them to solve problems. - 8.2.2.5
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
Justify steps in generating equivalent expressions by identifying the properties used, including the properties of operations (associative, commutative, and distributive laws) and the order of operations, including grouping symbols. - PA.A.3.2
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
Use substitution to simplify and evaluate algebraic expressions. - PA.A.3.1
Use the Pythagorean Theorem to find the distance between two points in the coordinate plane. - 8.G.7.4
Mathematical Modeling: Use Functions to Model Relationships - 8.AF.3MM
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
Mathematical Modeling: Understand and Apply the Pythagorean Theorem - 8.G.7MM
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
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
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 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
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
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
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 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 geometric sequence is a non-linear function that can be expressed in the form f(x)=abx , where x = 0, 1, 2, 3,…. - 8.2.1.5
Represent, write, solve, and graph problems leading to linear inequalities with one variable in the form px + q > r and px + q < r, where p, q, and r are rational numbers. - PA.A.4.2
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
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
Understand that an arithmetic sequence is a linear function that can be expressed in the form f(x) = mx + b , where x = 0, 1, 2, 3,…. - 8.2.1.4
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
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
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
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. - 8.EE.C.7b
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
Mathematical Modeling: Analyze and Solve Systems of Linear Equations - 8.DP.5MM
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
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). - 8.EE.C.7a
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
Analyze and solve pairs of simultaneous linear equations. - M.8.10
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
Solve systems of equations using elimination. - 8.AF.5.4
Compare and order rational and irrational numbers. - 8.AF.1.3
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
Identify a number that is irrational. - 8.AF.1.2
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 given a polygon, apply transformations, to include translations, reflections, and dilations, in the coordinate plane. - 8.7a
Write repeating decimals as fractions. - 8.AF.1.1
Perform operations with numbers in scientific notation. - 8.AF.1.10
The student will identify practical applications of transformations. - 8.7b
Verify experimentally the properties of rotations, reflections and translations: - M.8.16
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
Write a number with a negative or zero exponent a different way. - 8.AF.1.7
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
Use the properties of exponents to write equivalent expressions. - 8.AF.1.6
Find the solution to a system of equations using graphs. - 8.AF.5.2
Solve equations involving squares or cubes. - 8.AF.1.5
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
Find square roots and cube roots of rational numbers. - 8.AF.1.4
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
Mathematical Modeling: Solve Problems Involving Surface Area and Volume - 8.G.8MM
The student will verify the Pythagorean Theorem. - 8.9a
The student will apply the Pythagorean Theorem. - 8.9b
Lines are taken to lines, and line segments to line segments of the same length. - M.8.16a
Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. - 8.EE.A.2
Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 × 3^-5 = 3^-3 = 1/33 = 1/27. - 8.EE.A.1
Parallel lines are taken to parallel lines. - M.8.16c
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 - 8.EE.A.4
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 times 10^8 and the population of the world as 7 times 10^9, and determine that the world population is more than 20 times larger. - 8.EE.A.3
Angles are taken to angles of the same measure. - M.8.16b
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
Use linear functions to represent and explain real-world and mathematical situations. - PA.A.1.2
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. - 8.G.A.4
Explain a proof of the Pythagorean Theorem and its converse. - M.8.21
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
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. - 8.G.A.5
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
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. - 8.G.A.2
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
Parallel lines are taken to parallel lines. - 8.G.A.1c
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. - 8.G.A.3
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
Angles are taken to angles of the same measure. - 8.G.A.1b
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
Lines are taken to lines, and line segments to line segments of the same length. - 8.G.A.1a
Use linear equations to represent situations involving a constant rate of change, including proportional and non-proportional relationships. - 8.2.4.1
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
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 with equations and inequalities involving the absolute value of a linear expression. Solve such equations and inequalities and graph the solutions on a number line. - 8.2.4.6
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 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 linear inequalities to represent relationships in various contexts. - 8.2.4.4
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
Solve linear inequalities using properties of inequalities. Graph the solutions on a number line. - 8.2.4.5
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
Verify experimentally the properties of rotations, reflections, and translations: - 8.G.A.1
Know the formulas for the volumes of cones, cylinders and spheres and use them to solve real-world and mathematical problems. - M.8.24
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
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. - M.8.23
Rotate a two-dimensional figure. - 8.G.6.3
Understand and apply the relationships between the slopes of parallel lines and between the slopes of perpendicular lines. Dynamic graphing software may be used to examine these relationships. - 8.3.2.1
Describe and perform a sequence of transformations. - 8.G.6.4
Analyze polygons on a coordinate system by determining the slopes of their sides. - 8.3.2.2
Mathematical Modeling: Real Numbers - 8.AF.1MM
Translate two-dimensional figures. - 8.G.6.1
Given a line on a coordinate system and the coordinates of a point not on the line, find lines through that point that are parallel and perpendicular to the given line, symbolically and graphically. - 8.3.2.3
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
Mathematical Modeling: Investigate Bivariate Data - 8.DP.4MM
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
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
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
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
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
Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. - PA.A.2.1
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. - 8.NS.A.1
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. - 8.EE.B.5
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. - 8.EE.B.6
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., pi^2). For example, 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. - 8.NS.A.2
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
Evaluate algebraic expressions, including expressions containing radicals and absolute values, at specified values of their variables. - 8.2.3.1
Identify, describe, and analyze linear relationships between two variables. - PA.A.2.2
Justify steps in generating equivalent expressions by identifying the properties used, including the properties of algebra. Properties include the associative, commutative and distributive laws, and the order of operations, including grouping symbols. - 8.2.3.2
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
Dilate two-dimensional figures. - 8.G.6.6
The student will compare and order real numbers. - 8.1
The student will describe the relationships between the subsets of the real number system. - 8.2
Use angle measures to determine whether two triangles are similar. - 8.G.6.10
Find the interior and exterior angle measures of a triangle. - 8.G.6.9




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