# Virginia State Standards Alignment: 6-8

## This alignment shows the Media4Math resources that support the standards shown below. Click on a grade to see the Virginia Standards for that grade. Then click on a specific standard to see all the Media4Math resources that support it.

### Want to search for resources and create a downloadable CSV of our resources? Check out our __StandardsFinder__ tool.

__StandardsFinder__

## Grade 6 | ## Grade 7 | ## Grade 8 |

## Grade 6

6.NS.1 | The student will reason and use multiple strategies to express equivalency, compare, and order numbers written as fractions, mixed numbers, decimals, and percents. |

6.NS.1.a | Estimate and determine the percent represented by a given model (e.g., number line, picture, verbal description), including percents greater than 100% and less than 1%. |

6.NS.1.b | Represent and determine equivalencies among decimals (through the thousandths place) and percents incorporating the use of number lines, and concrete and pictorial models. |

6.NS.1.c | Represent and determine equivalencies among fractions (proper or improper) and mixed numbers that have denominators that are 12 or less or factors of 100 and percents incorporating the use of number lines, and concrete and pictorial models. |

6.NS.1.d | Represent and determine equivalencies among decimals, percents, fractions (proper or improper), and mixed numbers that have denominators that are 12 or less or factors of 100 incorporating the use of number lines, and concrete and pictorial models. |

6.NS.1.e | Use multiple strategies (e.g., benchmarks, number line, equivalency) to compare and order no more than four positive rational numbers expressed as fractions (proper or improper), mixed numbers, decimals, and percents (decimals through thousandths, fractions with denominators of 12 or less or factors of 100) with and without models. Justify solutions orally, in writing or with a model. Ordering may be in ascending or descending order. |

6.NS.2 | The student will reason and use multiple strategies to represent, compare, and order integers. |

6.NS.2.a | Represent integers (e.g., number lines, concrete materials, pictorial models), including models derived from contextual situations, and identify an integer represented by a point on a number line. |

6.NS.2.b | Compare and order integers using a number line. |

6.NS.2.e | Compare integers, using mathematical symbols (<, >, =). |

6.NS.2.d | Identify and describe the absolute value of an integer as the distance from zero on the number line. |

6.NS.3 | The student will recognize and represent patterns with whole number exponents and perfect squares. |

6.NS.3.a | Recognize and represent patterns with bases and exponents that are whole numbers. |

6.NS.3.b | Recognize and represent patterns of perfect squares not to exceed_ 20_^2, by using concrete and pictorial models. |

6.NS.3.c | Justify if a number between 0 and 400 is a perfect square through modeling or mathematical reasoning. |

6.NS.3.d | Recognize and represent powers of 10 with whole number exponents by examining patterns in place value. |

6.CE.1 | The student will estimate, demonstrate, solve, and justify solutions to problems using operations with fractions and mixed numbers, including those in context. |

6.CE.1.a | Demonstrate/model multiplication and division of fractions (proper or improper) and mixed numbers using multiple representations. |

6.CE.1.b | Multiply and divide fractions (proper or improper) and mixed numbers that include denominators of 12 or less. Answers are expressed in simplest form. |

6.CE.1.c | Investigate and explain the effect of multiplying or dividing a fraction, whole number, or mixed number by a number between zero and one. |

6.CE.1.d | Estimate, determine, and justify the solution to single-step and multistep problems in context that involve addition and subtraction with fractions (proper or improper) and mixed numbers, with and without regrouping, that include like and unlike denominators of 12 or less. Answers are expressed in simplest form. |

6.CE.1.e | Estimate, determine, and justify the solution to single-step and multistep problems in context that involve multiplication and division with fractions (proper or improper) and mixed numbers that include denominators of 12 or less. Answers are expressed in simplest form. |

6.CE.2 | The student will estimate, demonstrate, solve, and justify solutions to problems using operations with integers, including those in context. |

6.CE.2.a | Demonstrate/model addition, subtraction, multiplication, and division of integers using pictorial representations or concrete manipulatives. |

6.CE.2.b | Add, subtract, multiply, and divide two integers. |

6.CE.2.c | Simplify an expression that contains absolute value bars | | and an operation with two integers (e.g., -|5 - 8| or |-12|/8) and represent the result on a number line. |

6.CE.2.d | Estimate, determine, and justify the solution to one and two-step contextual problems, involving addition, subtraction, multiplication, and division with integers. |

6.MG.1 | The student will identify the characteristics of circles and solve problems, including those in context, involving circumference and area. |

6.MG.1.a | Identify and describe chord, diameter, radius, circumference, and area of a circle. |

6.MG.1.b | Investigate and describe the relationship between: i) diameter and radius; ii) radius and circumference; and iii) diameter and circumference. |

6.MG.1.c | Develop an approximation for pi (3.14) by gathering data and comparing the circumference to the diameter of various circles, using concrete manipulatives or technological models. |

6.MG.1.d | Develop the formula for circumference using the relationship between diameter, radius, and pi. |

6.MG.1.e | Solve problems, including those in context, involving circumference and area of a circle when given the length of the diameter or radius. |

6.MG.2 | The student will reason mathematically to solve problems, including those in context, that involve the area and perimeter of triangles, and parallelograms. |

6.MG.2.a | Develop the formula for determining the area of parallelograms and triangles using pictorial representations and concrete manipulatives (e.g., two-dimensional diagrams, grid paper). |

6.MG.2.b | Solve problems, including those in context, involving the perimeter and area of triangles, and parallelograms. |

6.MG.3 | The student will describe the characteristics of the coordinate plane and graph ordered pairs. |

6.MG.3.a | Identify and label the axes, origin, and quadrants of a coordinate plane. |

6.MG.3.b | Identify and describe the location (quadrant or the axis) of a point given as an ordered pair. Ordered pairs will be limited to coordinates expressed as integers. |

6.MG.3.c | Graph ordered pairs in the four quadrants and on the axes of a coordinate plane. Ordered pairs will be limited to coordinates expressed as integers. |

6.MG.3.d | Identify ordered pairs represented by points in the four quadrants and on the axes of the coordinate plane. Ordered pairs will be limited to coordinates expressed as integers. |

6.MG.3.e | Relate the coordinates of a point to the distance from each axis and relate the coordinates of a single point to another point on the same horizontal or vertical line. Ordered pairs will be limited to coordinates expressed as integers. |

6.MG.3.f | Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to determine the length of a side joining points with the same first coordinate or the same second coordinate. Ordered pairs will be limited to coordinates expressed as integers. Apply these techniques in the context of solving contextual and mathematical problems. |

6.MG.4 | The student will determine congruence of segments, angles, and polygons. |

6.MG.4.a | Identify regular polygons. |

6.MG.4.b | Draw lines of symmetry to divide regular polygons into two congruent parts. |

6.MG.4.c | Determine the congruence of segments, angles, and polygons given their properties. |

6.MG.4.d | Determine whether polygons are congruent or noncongruent according to the measures of their sides and angles. |

6.PS.1 | The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on circle graphs. |

6.PS.1.a | Formulate questions that require the collection or acquisition of data with a focus on circle graphs. |

6.PS.1.b | Determine the data needed to answer a formulated question and collect the data (or acquire existing data) using various methods (e.g., observations, measurement, surveys, experiments). |

6.PS.1.c | Determine the factors that will ensure that the data collected is a sample that is representative of a larger population. |

6.PS.1.d | Organize and represent data using circle graphs, with and without the use of technology tools. The number of data values should be limited to allow for comparisons that have denominators of 12 or less or those that are factors of 100 (e.g., in a class of 20 students, 7 choose apples as a favorite fruit, so the comparison is 7 out of 20, 7/20 , or 35%). |

6.PS.1.e | Analyze data represented in a circle graph by making observations and drawing conclusions. |

6.PS.1.f | Compare data represented in a circle graph with the same data represented in other graphs, including but not limited to bar graphs, pictographs, and line plots (dot plots), and justify which graphical representation best represents the data. |

6.PS.2 | The student will represent the mean as a balance point and determine the effect on statistical measures when a data point is added, removed, or changed. |

6.PS.2.a | Represent the mean of a set of data graphically as the balance point represented in a line plot (dot plot). |

6.PS.2.b | Determine the effect on measures of center when a single value of a data set is added, removed, or changed. |

6.PS.2.c | Observe patterns in data to identify outliers and determine their effect on mean, median, mode, or range. |

6.PFA.1 | The student will use ratios to represent relationships between quantities, including those in context. |

6.PFA.1.a | Represent a relationship between two quantities using ratios. |

6.PFA.1.b | Represent a relationship in context that makes a comparison by using the notations a/b, a:b, and a to b. |

6.PFA.1.c | Represent different comparisons within the same quantity or between different quantities (e.g., part to part, part to whole, whole to whole). |

6.PFA.1.d | Create a relationship in words for a given ratio expressed symbolically. |

6.PFA.1.e | Create a table of equivalent ratios to represent a proportional relationship between two quantities, when given a ratio. |

6.PFA.1.f | Create a table of equivalent ratios to represent a proportional relationship between two quantities, when given a contextual situation. |

6.PFA.2 | The student will identify and represent proportional relationships between two quantities, including those in context (unit rates are limited to positive values). |

6.PFA.2.a | Identify the unit rate of a proportional relationship represented by a table of values, a contextual situation, or a graph. |

6.PFA.2.b | Determine a missing value in a ratio table that represents a proportional relationship between two quantities using a unit rate. |

6.PFA.2.c | Determine whether a proportional relationship exists between two quantities, when given a table of values, context, or graph. |

6.PFA.2.d | When given a contextual situation representing a proportional relationship, find the unit rate and create a table of values or a graph. |

6.PFA.2.e | Make connections between and among multiple representations of the same proportional relationship using verbal descriptions, ratio tables, and graphs. |

6.PFA.3 | The student will write and solve one-step linear equations in one variable, including contextual problems that require the solution of a one-step linear equation in one variable. |

6.PFA.3.a | Identify and develop examples of the following algebraic vocabulary: equation, variable, expression, term, and coefficient. |

6.PFA.3.b | Represent and solve one-step linear equations in one variable, using a variety of concrete manipulatives and pictorial representations (e.g., colored chips, algebra tiles, weights on a balance scale). |

6.PFA.3.c | Apply properties of real numbers and properties of equality to solve a one-step equation in one variable. Coefficients are limited to integers and unit fractions. Numeric terms are limited to integers. |

6.PFA.3.d | Confirm solutions to one-step linear equations in one variable using a variety of concrete manipulatives and pictorial representations (e.g., colored chips, algebra tiles, weights on a balance scale). |

6.PFA.3.e | Write a one-step linear equation in one variable to represent a verbal situation, including those in context. |

6.PFA.3.f | Create a verbal situation in context given a one-step linear equation in one variable. |

6.PFA.4 | The student will represent a contextual situation using a linear inequality in one variable with symbols and graphs on a number line. |

6.PFA.4.a | Given the graph of a linear inequality in one variable on a number line, represent the inequality in two equivalent ways (e.g., x < -5 or -5 > x) using symbols. Symbols include <, >, ≤, ≥. |

6.PFA.4.b | Write a linear inequality in one variable to represent a given constraint or condition in context or given a graph on a number line. |

6.PFA.4.c | Given a linear inequality in one variable, create a corresponding contextual situation or create a number line graph. |

6.PFA.4.d | Use substitution or a number line graph to justify whether a given number in a specified set makes a linear inequality in one variable true. |

6.PFA.4.e | Identify a numerical value(s) that is part of the solution set of a given inequality in one variable. |

## Grade 7

7.NS.1 | The student will investigate and describe the concept of exponents for powers of ten and compare and order numbers greater than zero written in scientific notation. |

7.NS.1.a | Investigate and describe powers of 10 with negative exponents by examining patterns. |

7.NS.1.b | Represent a power of 10 with a negative exponent in fraction and decimal form. |

7.NS.1.c | Convert between numbers greater than 0 written in scientific notation and decimals. |

7.NS.1.d | Compare and order no more than four numbers greater than 0 written in scientific notation. Ordering may be in ascending or descending order. |

7.NS.2 | The student will reason and use multiple strategies to compare and order rational numbers. |

7.NS.2.a | Use multiple strategies (e.g., benchmarks, number line, equivalency) to compare (using symbols <, >, =) and order (a set of no more than four) rational numbers expressed as integers, fractions (proper or improper), mixed numbers, decimals, and percents. Fractions and mixed numbers may be positive or negative. Decimals may be positive or negative and are limited to the thousandths place. Ordering may be in ascending or descending order. Justify solutions orally, in writing or with a model. |

7.NS.3 | The student will recognize and describe the relationship between square roots and perfect squares. |

7.NS.3.a | Determine the positive square root of a perfect square from 0 to 400. |

7.NS.3.b | Describe the relationship between square roots and perfect squares. |

7.CE.1 | The student will estimate, solve, and justify solutions to multistep contextual problems involving operations with rational numbers. |

7.CE.1.a | Estimate, solve, and justify solutions to contextual problems involving addition, subtraction, multiplication, and division with rational numbers expressed as integers, fractions (proper or improper), mixed numbers, and decimals. Fractions may be positive or negative. Decimals may be positive or negative and are limited to the thousandths place. |

7.CE.2 | The student will solve problems, including those in context, involving proportional relationships. |

7.CE.2.a | Given a proportional relationship between two quantities, create and use a ratio table to determine missing values. |

7.CE.2.b | Write and solve a proportion that represents a proportional relationship between two quantities to find a missing value, including problems in context. |

7.CE.2.c | Apply proportional reasoning to solve problems in context, including converting units of measurement, when given the conversion factor. |

7.CE.2.d | Estimate and determine the percentage of a given whole number, including but not limited to the use of benchmark percentages. |

7.MG.1 | The student will investigate and determine the volume formula for right cylinders and the surface area formulas for rectangular prisms and right cylinders and apply the formulas in context. |

7.MG.1.a | Develop the formulas for determining the volume of right cylinders and solve problems, including those in contextual situations, using concrete objects, diagrams, and formulas. |

7.MG.1.b | Develop the formulas for determining the surface area of rectangular prisms and right cylinders and solve problems, including those in contextual situations, using concrete objects, two-dimensional diagrams, nets, and formulas. |

7.MG.1.c | Determine if a problem in context, involving a rectangular prism or right cylinder, represents the application of volume or surface area. |

7.MG.1.d | Describe how the volume of a rectangular prism is affected when one measured attribute is multiplied by a scale factor of 1/4, 1/3, 1/2, 2, 3, or 4, including those in contextual situations. |

7.MG.2 | The student will solve problems and justify relationships of similarity using proportional reasoning. |

7.MG.2.a | Identify corresponding congruent angles of similar quadrilaterals and triangles, through the use of geometric markings. |

7.MG.2.b | Identify corresponding sides of similar quadrilaterals and triangles. |

7.MG.2.c | Given two similar quadrilaterals or triangles, write similarity statements using symbols. |

7.MG.2.d | Write proportions to express the relationships between the lengths of corresponding sides of similar quadrilaterals and triangles. |

7.MG.2.e | Recognize and justify if two quadrilaterals or triangles are similar using the ratios of corresponding side lengths. |

7.MG.2.f | Solve a proportion to determine a missing side length of similar quadrilaterals or triangles. |

7.MG.2.g | Given angle measures in a quadrilateral or triangle, determine unknown angle measures in a similar quadrilateral or triangle. |

7.MG.2.h | Apply proportional reasoning to solve problems in context including scale drawings. Scale factors shall have denominators no greater than 12 and decimals no less than tenths. |

7.MG.3 | The student will compare and contrast quadrilaterals based on their properties and determine unknown side lengths and angle measures of quadrilaterals. |

7.MG.3.a | Compare and contrast properties of the following quadrilaterals: parallelogram, rectangle, square, rhombus, and trapezoid: i) parallel/perpendicular sides and diagonals; ii) congruence of angle measures, side, and diagonal lengths; and iii) lines of symmetry. |

7.MG.3.b | Sort and classify quadrilaterals as parallelograms, rectangles, trapezoids, rhombi, and/or squares based on their properties: i) parallel/perpendicular sides and diagonals; ii) congruence of angle measures, side, and diagonal lengths; and iii) lines of symmetry. |

7.MG.3.c | Given a diagram, determine an unknown angle measure in a quadrilateral, using properties of quadrilaterals. |

7.MG.3.d | Given a diagram, determine an unknown side length in a quadrilateral using properties of quadrilaterals. |

7.MG.4 | The student will apply dilations of polygons in the coordinate plane. |

7.MG.4.a | Given a preimage in the coordinate plane, identify the coordinates of the image of a polygon that has been dilated. Scale factors are limited to 1/4, 1/2, 2, 3, or 4. The center of the dilation will be the origin. |

7.MG.4.b | Sketch the image of a dilation of a polygon limited to a scale factor of 1/4, 1/2, 2, 3, or 4. The center of the dilation will be the origin. |

7.MG.4.c | Identify and describe dilations in context including, but not limited to, scale drawings and graphic design. |

7.PS.1 | The student will use statistical investigation to determine the probability of an event and investigate and describe the difference between the experimental and theoretical probability. |

7.PS.1.a | Determine the theoretical probability of an event. |

7.PS.1.b | Given the results of a statistical investigation, determine the experimental probability of an event. |

7.PS.1.c | Describe changes in the experimental probability as the number of trials increases. |

7.PS.1.d | Investigate and describe the difference between the probability of an event found through experiment or simulation versus the theoretical probability of that same event. |

7.PS.2 | The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on histograms. |

7.PS.2.a | Formulate questions that require the collection or acquisition of data with a focus on histograms. |

7.PS.2.b | Determine the data needed to answer a formulated question and collect the data (or acquire existing data) using various methods (e.g., observations, measurement, surveys, experiments). |

7.PS.2.c | Determine how sample size and randomness will ensure that the data collected is a sample that is representative of a larger population. |

7.PS.2.d | Organize and represent numerical data using histograms with and without the use of technology |

7.PS.2.e | Investigate and explain how using different intervals could impact the representation of the data in a histogram. |

7.PS.2.f | Compare data represented in histograms with the same data represented in other graphs, including but not limited to line plots (dot plots), circle graphs, and stem-and-leaf plots, and justify which graphical representation best represents the data. |

7.PS.2.g | Analyze data represented in histograms by making observations and drawing conclusions. Determine how histograms reveal patterns in data that cannot be easily seen by looking at the corresponding given data set. |

7.PFA.1 | The student will investigate and analyze proportional relationships between two quantities using verbal descriptions, tables, equations in y = mx form, and graphs, including problems in context. |

7.PFA.1.a | Determine the slope, m, as the rate of change in a proportional relationship between two quantities given a table of values, graph, or contextual situation and write an equation in the form y = mx to represent the direct variation relationship. Slope may include positive or negative values (slope will be limited to positive values in a contextual situation). |

7.PFA.1.b | Identify and describe a line with a slope that is positive, negative, or zero (0), given a graph. |

7.PFA.1.c | Graph a line representing a proportional relationship, between two quantities given an ordered pair on the line and the slope, m, as rate of change. Slope may include positive or negative values. |

7.PFA.1.d | Graph a line representing a proportional relationship between two quantities given the equation of the line in the form y = mx, where m represents the slope as rate of change. Slope may include positive or negative values. |

7.PFA.1.e | Make connections between and among representations of a proportional relationship between two quantities using problems in context, tables, equations, and graphs. Slope may include positive or negative values (slope will be limited to positive values in a contextual situation). |

7.PFA.2 | The student will simplify numerical expressions, simplify and generate equivalent algebraic expressions in one variable, and evaluate algebraic expressions for given replacement values of the variables. |

7.PFA.2.a | Use the order of operations and apply the properties of real numbers to simplify numerical expressions. Exponents are limited to 1, 2, 3, or 4 and bases are limited to positive integers. Expressions should not include braces { } but may include brackets [ ] and absolute value bars | |. Square roots are limited to perfect squares. |

7.PFA.2.b | Represent equivalent algebraic expressions in one variable using concrete manipulatives and pictorial representations (e.g., colored chips, algebra tiles). |

7.PFA.2.c | Simplify and generate equivalent algebraic expressions in one variable by applying the order of operations and properties of real numbers. Expressions may require combining like terms to simplify. Expressions will include only linear and numeric terms. Coefficients and numeric terms may be positive or negative rational numbers. |

7.PFA.2.d | Use the order of operations and apply the properties of real numbers to evaluate algebraic expressions for given replacement values of the variables. Exponents are limited to 1, 2, 3, or 4 and bases are limited to positive integers. Expressions should not include braces { } but may include brackets [ ] and absolute value bars | |. Square roots are limited to perfect squares. Limit the number of replacements to no more than three per expression. Replacement values may be positive or negative rational numbers. |

7.PFA.3 | The student will write and solve two-step linear equations in one variable, including problems in context, that require the solution of a two-step linear equation in one variable. |

7.PFA.3.a | Represent and solve two-step linear equations in one variable using a variety of concrete materials and pictorial representations. |

7.PFA.3.b | Apply properties of real numbers and properties of equality to solve two-step linear equations in one variable. Coefficients and numeric terms will be rational. |

7.PFA.3.c | Confirm algebraic solutions to linear equations in one variable. |

7.PFA.3.d | Write a two-step linear equation in one variable to represent a verbal situation, including those in context. |

7.PFA.3.e | Create a verbal situation in context given a two-step linear equation in one variable. |

7.PFA.3.f | Solve problems in context that require the solution of a two-step linear equation. |

7.PFA.4 | The student will write and solve one- and two-step linear inequalities in one variable, including problems in context, that require the solution of a one- and two-step linear inequality in one variable. |

7.PFA.4.a | Apply properties of real numbers and the addition, subtraction, multiplication, and division properties of inequality to solve one- and two-step inequalities in one variable. Coefficients and numeric terms will be rational. |

7.PFA.4.b | Investigate and explain how the solution set of a linear inequality is affected by multiplying or dividing both sides of the inequality statement by a rational number less than zero. |

7.PFA.4.c | Represent solutions to one- or two-step linear inequalities in one variable algebraically and graphically using a number line. |

7.PFA.4.d | Write one- or two-step linear inequalities in one variable to represent a verbal situation, including those in context. |

7.PFA.4.e | Create a verbal situation in context given a one or two-step linear inequality in one variable |

7.PFA.4.f | Solve problems in context that require the solution of a one- or two-step inequality. |

7.PFA.4.g | Identify a numerical value(s) that is part of the solution set of as given one- or two-step linear inequality in one variable. |

7.PFA.4.h | Describe the differences and similarities between solving linear inequalities in one variable and linear equations in one variable. |

## Grade 8

8.NS.1 | The student will compare and order real numbers and determine the relationships between real numbers. |

8.NS.1.a | Estimate and identify the two consecutive natural numbers between which the positive square root of a given number lies and justify which natural number is the better approximation. Numbers are limited to natural numbers from 1 to 400. |

8.NS.1.b | Use rational approximations (to the nearest hundredth) of irrational numbers to compare, order, and locate values on a number line. Radicals may include both positive and negative square roots of values from 0 to 400 yielding an irrational number. |

8.NS.1.c | Use multiple strategies (e.g., benchmarks, number line, equivalency) to compare and order no more than five real numbers expressed as integers, fractions (proper or improper), decimals, mixed numbers, percents, numbers written in scientific notation, radicals, and π. Radicals may include both positive and negative square roots of values from 0 to 400. Ordering may be in ascending or descending order. Justify solutions orally, in writing or with a model. |

8.NS.2 | The student will investigate and describe the relationship between the subsets of the real number system. |

8.NS.2.a | Describe and illustrate the relationships among the subsets of the real number system by using representations (e.g., graphic organizers, number lines). Subsets include rational numbers, irrational numbers, integers, whole numbers, and natural numbers. |

8.NS.2.b | Classify and explain why a given number is a member of a particular subset or subsets of the real number system. |

8.NS.2.c | Describe each subset of the set of real numbers and include examples and non-examples. |

8.CE.1 | The student will estimate and apply proportional reasoning and computational procedures to solve contextual problems. |

8.CE.1.a | Estimate and solve contextual problems that require the computation of one discount or markup and the resulting sale price. |

8.CE.1.b | Estimate and solve contextual problems that require the computation of the sales tax, tip and resulting total. |

8.CE.1.c | Estimate and solve contextual problems that require the computation of the percent increase or decrease. |

8.MG.1 | The student will use the relationships among pairs of angles that are vertical angles, adjacent angles, supplementary angles, and complementary angles to determine the measure of unknown angles. |

8.MG.1.a | Identify and describe the relationship between pairs of angles that are vertical, adjacent, supplementary, and complementary. |

8.MG.1.b | Use the relationships among supplementary, complementary, vertical, and adjacent angles to solve problems, including those in context, involving the measure of unknown angles. |

8.MG.2 | The student will investigate and determine the surface area of square-based pyramids and the volume of cones and square-based pyramids. |

8.MG.2.a | Determine the surface area of square-based pyramids by using concrete objects, nets, diagrams, and formulas. |

8.MG.2.b | Determine the volume of cones and square-based pyramids, using concrete objects, diagrams, and formulas. |

8.MG.2.c | Examine and explain the relationship between the volume of cones and cylinders, and the volume of rectangular prisms and square based pyramids. |

8.MG.2.d | Solve problems in context involving volume of cones and square-based pyramids and the surface area of square-based pyramids. |

8.MG.3 | The student will apply translations and reflections to polygons in the coordinate plane. |

8.MG.3.a | Given a preimage in the coordinate plane, identify the coordinates of the image of a polygon that has been translated vertically, horizontally, or a combination of both. |

8.MG.3.b | Given a preimage in the coordinate plane, identify the coordinates of the image of a polygon that has been reflected over the x- or y-axis |

8.MG.3.c | Given a preimage in the coordinate plane, identify the coordinates of the image of a polygon that has been translated and reflected over the x- or y-axis or reflected over the x- or y-axis and then translated. |

8.MG.3.d | Sketch the image of a polygon that has been translated vertically, horizontally, or a combination of both. |

8.MG.3.e | Sketch the image of a polygon that has been reflected over the x- or y-axis. |

8.MG.3.f | Sketch the image of a polygon that has been translated and reflected over the x- or y-axis, or reflected over the x- or y-axis and then translated. |

8.MG.3.g | Identify and describe transformations in context (e.g., tiling, fabric, wallpaper designs, art). |

8.MG.4 | The student will apply the Pythagorean Theorem to solve problems involving right triangles, including those in context. |

8.MG.4.a | Verify the Pythagorean Theorem using diagrams, concrete materials, and measurement. |

8.MG.4.b | Determine whether a triangle is a right triangle given the measures of its three sides. |

8.MG.4.c | Identify the parts of a right triangle (the hypotenuse and the legs) given figures in various orientations. |

8.MG.4.d | Determine the measure of a side of a right triangle, given the measures of the other two sides. |

8.MG.4.e | Apply the Pythagorean Theorem, and its converse, to solve problems involving right triangles in context. |

8.MG.5 | The student will solve area and perimeter problems involving composite plane figures, including those in context. |

8.MG.5.a | Subdivide a plane figure into triangles, rectangles, squares, trapezoids, parallelograms, circles, and semicircles. Determine the area of subdivisions and combine to determine the area of the composite plane figure. |

8.MG.5.b | Subdivide a plane figure into triangles, rectangles, squares, trapezoids, parallelograms, and semicircles. Use the attributes of the subdivisions to determine the perimeter of the composite plane figure. |

8.MG.5.c | Apply perimeter, circumference, and area formulas to solve contextual problems involving composite plane figures. |

8.PS.1 | The student will use statistical investigation to determine the probability of independent and dependent events, including those in context. |

8.PS.1.a | Determine whether two events are independent or dependent and explain how replacement impacts the probability. |

8.PS.1.b | Compare and contrast the probability of independent and dependent events. |

8.PS.1.c | Determine the probability of two independent events. |

8.PS.1.d | Determine the probability of two dependent events. |

8.PS.2 | The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on boxplots. |

8.PS.2.a | Formulate questions that require the collection or acquisition of data with a focus on boxplots. |

8.PS.2.b | Determine the data needed to answer a formulated question and collect the data (or acquire existing data) using various methods (e.g., observations, measurement, surveys, experiments). |

8.PS.2.c | Determine how statistical bias might affect whether the data collected from the sample is representative of the larger population. |

8.PS.2.d | Organize and represent a numeric data set of no more than 20 items, using boxplots, with and without the use of technology. |

8.PS.2.e | Identify and describe the lower extreme (minimum), upper extreme (maximum), median, upper quartile, lower quartile, range, and interquartile range given a data set, represented by a boxplot. |

8.PS.2.f | Describe how the presence of an extreme data point (outlier) affects the shape and spread of the data distribution of a boxplot. |

8.PS.2.g | Analyze data represented in a boxplot by making observations and drawing conclusions. |

8.PS.2.h | Compare and analyze two data sets represented in boxplots. |

8.PS.2.i | Given a contextual situation, justify which graphical representation (e.g., pictographs, bar graphs, line graphs, line plots/dot plots, stem-and-leaf plots, circle graphs, histograms, and boxplots) best represents the data. |

8.PS.2.j | Identify components of graphical displays that can be misleading. |

8.PS.3 | The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on scatterplots. |

8.PS.3.a | Formulate questions that require the collection or acquisition of data with a focus on scatterplots. |

8.PS.3.b | Determine the data needed to answer a formulated question and collect the data (or acquire existing data) of no more than 20 items using various methods (e.g., observations, measurement, surveys, experiments). |

8.PS.3.c | Organize and represent numeric bivariate data using scatterplots with and without the use of technology. |

8.PS.3.d | Make observations about a set of data points in a scatterplot as having a positive linear relationship, a negative linear relationship, or no relationship |

8.PS.3.e | Analyze and justify the relationship of the quantitative bivariate data represented in scatterplots. |

8.PS.3.f | Sketch the line of best fit for data represented in a scatterplot. |

8.PFA.1 | The student will represent, simplify, and generate equivalent algebraic expressions in one variable. |

8.PFA.1.a | Represent algebraic expressions using concrete manipulatives or pictorial representations (e.g., colored chips, algebra tiles), including expressions that apply the distributive property. |

8.PFA.1.b | Simplify and generate equivalent algebraic expressions in one variable by applying the order of operations and properties of real numbers. Expressions may need to be expanded (using the distributive property) or require combining like terms to simplify. Expressions will include only linear and numeric terms. Coefficients and numeric terms may be rational. |

8.PFA.2 | The student will determine whether a given relation is a function and determine the domain and range of a function. |

8.PFA.2.a | Determine whether a relation, represented by a set of ordered pairs, a table, or a graph of discrete points is a function. Sets are limited to no more than 10 ordered pairs. |

8.PFA.2.b | Identify the domain and range of a function represented as a set of ordered pairs, a table, or a graph of discrete points. |

8.PFA.3 | The student will represent and solve problems, including those in context, by using linear functions and analyzing their key characteristics (the value of the y-intercept (b) and the coordinates of the ordered pairs in graphs will be limited to integers). |

8.PFA.3.a | Determine how adding a constant (b) to the equation of a proportional relationship y = mx will translate the line on a graph. |

8.PFA.3.b | Describe key characteristics of linear functions including slope (m), y-intercept (b), and independent and dependent variables. |

8.PFA.3.c | Graph a linear function given a table, equation, or a situation in context. |

8.PFA.3.d | Create a table of values for a linear function given a graph, equation in the form of y = mx + b, or context. |

8.PFA.3.e | Write an equation of a linear function in the form y = mx + b, given a graph, table, or a situation in context. |

8.PFA.3.f | Create a context for a linear function given a graph, table, or equation in the form y = mx + b. |

8.PFA.4 | The student will write and solve multistep linear equations in one variable, including problems in context that require the solution of a multistep linear equation in one variable. |

8.PFA.4.a | Represent and solve multistep linear equations in one variable with the variable on one or both sides of the equation (up to four steps) using a variety of concrete materials and pictorial representations. |

8.PFA.4.b | Apply properties of real numbers and properties of equality to solve multistep linear equations in one variable (up to four steps). Coefficients and numeric terms will be rational. Equations may contain expressions that need to be expanded (using the distributive property) or require combining like terms to solve. |

8.PFA.4.c | Write a multistep linear equation in one variable to represent a verbal situation, including those in context. |

8.PFA.4.d | Create a verbal situation in context given a multistep linear equation in one variable. |

8.PFA.4.e | Solve problems in context that require the solution of a multistep linear equation. |

8.PFA.4.f | Interpret algebraic solutions in context to linear equations in one variable. |

8.PFA.4.g | Confirm algebraic solutions to linear equations in one variable. |

8.PFA.5 | The student will write and solve multistep linear inequalities in one variable, including problems in context that require the solution of a multistep linear inequality in one variable. |

8.PFA.5.a | Apply properties of real numbers and properties of inequality to solve multistep linear inequalities (up to four steps) in one variable with the variable on one or both sides of the inequality. Coefficients and numeric terms will be rational. Inequalities may contain expressions that need to be expanded (using the distributive property) or require combining like terms to solve. |

8.PFA.5.b | Represent solutions to inequalities algebraically and graphically using a number line. |

8.PFA.5.c | Write multistep linear inequalities in one variable to represent a verbal situation, including those in context. |

8.PFA.5.d | Create a verbal situation in context given a multistep linear inequality in one variable. |

8.PFA.5.e | Solve problems in context that require the solution of a multistep linear inequality in one variable. |

8.PFA.5.f | Identify a numerical value(s) that is part of the solution set of a given inequality. |

8.PFA.5.g | Interpret algebraic solutions in context |