Grade 8 Math (Virginia SOL)

Number and Number Sense (NS)

• 8.NS.1 Compare, order, and identify relationships among real numbers.
• Estimate the two consecutive natural numbers a square root lies between, and which is closer.
• Use approximations (to hundredths) of irrational roots to compare, order, and place them on number lines.
• Compare and order up to five real numbers in mixed forms, with justification.
• 8.NS.2 Investigate and describe relationships among subsets of the real number system.
• Illustrate relationships among subsets of real numbers with graphic organizers and number lines.
• Classify numbers into subsets and explain why they belong.
• Describe each subset of real numbers with examples and non-examples.

Computation and Estimation (CE)

• 8.CE.1 Estimate and apply proportional reasoning and computation to solve contextual problems.
• Estimate and solve problems involving one discount or markup and the sale price.
• Estimate and solve problems involving sales tax, tip, and total cost.
• Estimate and solve problems involving percent increase or decrease.

Measurement and Geometry (MG)

• 8.MG.1 Use relationships among vertical, adjacent, supplementary, and complementary angles to find unknown angles.
• Identify and describe vertical, adjacent, supplementary, and complementary angle pairs.
• Use angle relationships to solve problems, including in context, for unknown angle measures.
• 8.MG.2 Find the surface area of square-based pyramids and the volume of cones and square-based pyramids.
• Find square-based pyramid surface area using objects, nets, diagrams, and formulas.
• Find cone and square-based pyramid volume using objects, diagrams, and formulas.
• Explain the volume relationships between cones and cylinders and between pyramids and prisms.
• Solve contextual problems on cone and pyramid volume and pyramid surface area.
• 8.MG.3 Apply translations and reflections to polygons in the coordinate plane.
• Find image coordinates after a vertical, horizontal, or combined translation.
• Find image coordinates after a reflection over the x- or y-axis.
• Find image coordinates after a translation and an axis reflection, in either order.
• Sketch the image after a vertical, horizontal, or combined translation.
• Sketch the image after a reflection over the x- or y-axis.
• Sketch the image after a translation and reflection, in either order.
• Identify and describe transformations in contexts such as tiling and art.
• 8.MG.4 Apply the Pythagorean Theorem and its converse to solve right-triangle problems, including in context.
• Verify the Pythagorean Theorem using diagrams, concrete materials, and measurement.
• Determine whether a triangle with given side lengths is a right triangle.
• Identify the hypotenuse and legs of right triangles in varied orientations.
• Find an unknown side length given the other two.
• Apply the theorem and its converse to contextual right-triangle problems.
• 8.MG.5 Solve area and perimeter problems for composite plane figures, including in context.
• Split composite figures into familiar shapes, find each area, and combine them.
• Split composite figures into familiar shapes and use their attributes to find perimeter.
• Apply perimeter, circumference, and area formulas to contextual composite-figure problems.

Probability and Statistics (PS)

• 8.PS.1 Use statistical investigation to find probabilities of independent and dependent events, including in context.
• Determine whether events are independent or dependent and how replacement affects probability.
• Compare and contrast probabilities of independent and dependent events.
• Determine the probability of two independent events.
• Determine the probability of two dependent events.
• 8.PS.2 Apply the data cycle with boxplots.
• Formulate questions requiring data collection or acquisition, with a boxplot focus.
• Determine needed data and collect or acquire it using various methods.
• Determine how statistical bias may affect whether a sample represents the population.
• Organize and display a numerical data set of up to 20 items as a boxplot.
• Identify minimum, maximum, median, quartiles, range, and interquartile range from a boxplot.
• Describe how an outlier affects a boxplot's shape and spread.
• Analyze boxplot data by making observations and drawing conclusions.
• Compare and analyze two data sets shown as boxplots.
• Justify the best graph type for a given context.
• Identify graph features that can be misleading.
• 8.PS.3 Apply the data cycle with scatterplots.
• Formulate questions requiring data collection or acquisition, with a scatterplot focus.
• Determine needed data and collect or acquire up to 20 items.
• Organize and display bivariate numerical data as scatterplots, with or without technology.
• Describe scatterplot patterns as positive linear, negative linear, or no relationship.
• Analyze and justify relationships in bivariate scatterplot data.
• Sketch a line of best fit for scatterplot data.

Patterns, Functions, and Algebra (PFA)

• 8.PFA.1 Represent, simplify, and generate equivalent one-variable algebraic expressions.
• Represent expressions with manipulatives or pictures, including the distributive property.
• Simplify and generate equivalent one-variable expressions using order of operations and properties.
• 8.PFA.2 Determine whether a relation is a function and identify its domain and range.
• Decide whether a relation (up to 10 ordered pairs, a table, or discrete points) is a function.
• Identify domain and range from ordered pairs, a table, or discrete points.
• 8.PFA.3 Represent and solve problems, including in context, using linear functions and their key characteristics.
• Explain how adding a constant b to y = mx shifts the line on a graph.
• Describe slope, y-intercept, and independent and dependent variables of linear functions.
• Graph a linear function from a table, equation, or situation.
• Create a table of values for a linear function from a graph, equation, or context.
• Write y = mx + b from a graph, table, or situation.
• Create a context for a linear function given its graph, table, or equation.
• 8.PFA.4 Write and solve multistep linear equations in one variable, including in context.
• Represent and solve equations of up to four steps using concrete and pictorial models.
• Apply properties of real numbers and equality to solve equations of up to four steps.
• Write a multistep linear equation for a verbal or contextual situation.
• Create a verbal situation for a given multistep linear equation.
• Solve contextual problems that require multistep linear equations.
• Interpret algebraic solutions in context.
• Confirm algebraic solutions of linear equations.
• 8.PFA.5 Write and solve multistep linear inequalities in one variable, including in context.
• Apply properties to solve inequalities of up to four steps, with variables on one or both sides.
• Represent inequality solutions algebraically and on a number line.
• Write multistep inequalities for verbal or contextual situations.
• Create a verbal situation for a given multistep linear inequality.
• Solve contextual problems that require multistep linear inequalities.
• Identify a value in an inequality's solution set.
• Interpret algebraic inequality solutions in context.