Grade 7 Math (Virginia SOL)

Number and Number Sense (NS)

• 7.NS.1 Investigate negative powers of ten and compare and order positive numbers in scientific notation.
• Find patterns in powers of ten with negative exponents.
• Write negative powers of ten as fractions and decimals.
• Convert between positive numbers in scientific notation and decimals.
• Compare and order up to four positive numbers in scientific notation.
• 7.NS.2 Use multiple strategies to reason about, compare, and order rational numbers.
• Compare and order up to four rational numbers in various forms, justifying answers.
• 7.NS.3 Recognize and describe how square roots relate to perfect squares.
• Find positive square roots of perfect squares from 0 to 400.
• Describe the relationship between square roots and perfect squares.

Computation and Estimation (CE)

• 7.CE.1 Estimate, solve, and justify multistep contextual problems with operations on rational numbers.
• Estimate, solve, and justify contextual problems using all four operations on rational numbers.
• 7.CE.2 Solve problems, including in context, involving proportional relationships.
• Build and use ratio tables to find missing values in proportional relationships.
• Write and solve proportions to find missing values, including in context.
• Apply proportional reasoning, including unit conversions with a given conversion factor.
• Estimate and find percentages of whole numbers using benchmark percentages.

Measurement and Geometry (MG)

• 7.MG.1 Develop formulas for cylinder volume and prism and cylinder surface area, and apply them in context.
• Develop the cylinder volume formula and solve problems with objects, diagrams, and formulas.
• Develop surface area formulas for prisms and cylinders using nets and solve related problems.
• Decide whether a prism or cylinder problem calls for volume or surface area.
• Describe how prism volume changes when one attribute is scaled by given factors.
• Describe how prism surface area changes when one attribute is halved or doubled.
• 7.MG.2 Solve problems and justify similarity using proportional reasoning.
• Identify corresponding congruent angles in similar quadrilaterals and triangles using markings.
• Identify corresponding sides of similar quadrilaterals and triangles.
• Write similarity statements for similar quadrilaterals or triangles using symbols.
• Write proportions relating corresponding side lengths of similar figures.
• Recognize and justify similarity using ratios of corresponding side lengths.
• Solve proportions to find missing side lengths of similar figures.
• Find unknown angles in similar figures from given angle measures.
• Apply proportional reasoning in context, including scale drawings with limited scale factors.
• 7.MG.3 Compare quadrilaterals by their properties and find unknown side lengths and angles.
• Compare quadrilateral properties: parallel/perpendicular sides and diagonals, congruence, lines of symmetry.
• Sort and classify quadrilaterals by these properties.
• Find an unknown angle in a quadrilateral using its properties.
• Find an unknown side length in a quadrilateral using its properties.
• 7.MG.4 Apply dilations of polygons in the coordinate plane.
• Find image coordinates of polygons dilated about the origin with specified scale factors.
• Sketch images of polygons dilated about the origin with specified scale factors.
• Identify and describe dilations in contexts such as scale drawings and graphic design.

Probability and Statistics (PS)

• 7.PS.1 Use statistical investigation to find probabilities and compare experimental with theoretical results.
• Determine the theoretical probability of an event.
• Determine experimental probability from investigation results.
• Describe how experimental probability changes as the number of trials increases.
• Compare experimental or simulated probability with theoretical probability.
• 7.PS.2 Apply the data cycle with histograms.
• Formulate questions that require collecting or acquiring data, with a histogram focus.
• Determine needed data and collect or acquire it using various methods.
• Explain how sample size and randomness make data representative of a population.
• Organize and represent numerical data in histograms, with or without technology.
• Investigate how different interval choices change a histogram's appearance.
• Compare histograms with other graphs and justify the best representation.
• Analyze histograms to draw conclusions and reveal patterns hidden in raw data.

Patterns, Functions, and Algebra (PFA)

• 7.PFA.1 Analyze proportional relationships using words, tables, y = mx equations, and graphs.
• Find slope as rate of change and write y = mx from tables, graphs, or contexts.
• Identify and describe lines with positive, negative, or zero slope from graphs.
• Graph a proportional line from an ordered pair on the line and the slope.
• Graph a proportional line from its y = mx equation.
• Connect contexts, tables, equations, and graphs of proportional relationships.
• 7.PFA.2 Simplify numerical expressions and generate and evaluate equivalent algebraic expressions.
• Simplify numerical expressions using order of operations and number properties, within stated limits.
• Show equivalent one-variable expressions using manipulatives and pictorial models.
• Simplify one-variable linear expressions by combining like terms and applying properties.
• Evaluate expressions for up to three rational replacement values.
• 7.PFA.3 Write and solve two-step linear equations in one variable, including in context.
• Solve two-step equations using concrete materials and pictorial representations.
• Solve two-step equations using properties of real numbers and equality.
• Confirm algebraic solutions to one-variable linear equations.
• Write two-step equations representing verbal or contextual situations.
• Create a verbal context matching a given two-step equation.
• Solve contextual problems that require two-step linear equations.
• 7.PFA.4 Write and solve one- and two-step linear inequalities in one variable, including in context.
• Solve one- and two-step inequalities using properties of real numbers and inequality.
• Explain how multiplying or dividing by a negative number changes the solution set.
• Represent inequality solutions algebraically and on a number line.
• Write inequalities representing verbal or contextual situations.
• Create a verbal context matching a given inequality.
• Solve contextual problems that require one- or two-step inequalities.
• Identify numerical values in an inequality's solution set.
• Describe similarities and differences between solving inequalities and solving equations.