Grade 5 Math (Virginia SOL)

Number and Number Sense (NS)

• 5.NS.1 Identify equivalences between fractions (thirds, eighths, factors of 100) and decimals; compare and order them.
• Represent these fractions as equivalent decimals using models.
• Represent decimals as equivalent fractions using models.
• Identify equivalent decimal and fraction relationships, with or without models.
• Compare and order up to four decimals, fractions, and mixed numbers, justifying results.
• 5.NS.2 Understand prime and composite numbers and find prime factorizations of numbers up to 100.
• Show with a representation whether a number up to 100 is prime or composite, and justify.
• Classify, compare, and contrast numbers up to 100 as prime or composite.
• Determine the prime factorization of a whole number up to 100.

Computation and Estimation (CE)

• 5.CE.1 Estimate, solve, and justify single- and multistep whole-number problems with all four operations.
• Estimate sums, differences, products, and quotients in contextual problems.
• Solve problems using strategies and algorithms within the stated digit and divisor limits.
• Interpret quotients and remainders in context.
• 5.CE.2 Add and subtract fractions with like and unlike denominators; multiply a whole number by a proper fraction.
• Find the least common multiple to get a least common denominator.
• Estimate and compute sums and differences of fractions and mixed numbers, simplifying.
• Solve single- and multistep contextual fraction addition and subtraction problems in simplest form.
• Solve contextual problems multiplying a whole number (12 or less) by a proper fraction, using models.
• 5.CE.3 Estimate, solve, and justify problems with decimal operations.
• Use estimation strategies to judge reasonable decimal answers.
• Estimate and compute decimal products within the stated digit limits.
• Estimate and compute decimal quotients within the stated limits.
• Solve single- and multistep contextual decimal addition, subtraction, and multiplication problems.
• Solve single-step contextual decimal division problems.
• 5.CE.4 Simplify numerical expressions with whole numbers using the order of operations.
• Simplify expressions within stated limits, with at most one set of parentheses.
• Describe which operation is done first, second, and third in an expression.

Measurement and Geometry (MG)

• 5.MG.1 Solve problems involving metric length, mass, and liquid volume.
• Choose the most appropriate metric unit in a contextual problem.
• Estimate and measure metric length, mass, and liquid volume.
• Convert within the metric system given one equivalent measure.
• 5.MG.2 Use multiple representations to solve perimeter, area, and volume problems.
• Investigate and develop the formula for the area of a right triangle.
• Find right-triangle areas from whole-number base and height, with units.
• Describe volume as capacity and give contextual examples.
• Develop the rectangular prism volume formula using concrete objects.
• Find rectangular prism volume using objects, diagrams, and formulas.
• Identify whether perimeter, area, or volume fits a situation.
• Solve contextual perimeter, area, and volume problems in standard units.
• 5.MG.3 Classify and measure angles and triangles, and solve related problems.
• Classify angles as right, acute, obtuse, or straight, with justification.
• Classify triangles by angles and by sides, with justification.
• Mark congruent sides and right angles with geometric markings.
• Compare and contrast properties of triangles.
• Identify tools for measuring and drawing angles.
• Measure angles in degrees with appropriate tools.
• Use models to show the angles of a triangle sum to 180 degrees; find unknown angles.
• Solve addition and subtraction problems for unknown angles on diagrams.

Probability and Statistics (PS)

• 5.PS.1 Apply the data cycle with line plots (dot plots) and stem-and-leaf plots.
• Formulate questions that require collecting or acquiring data.
• Determine needed data and collect or acquire it (30 or fewer data points).
• Make line plots with title, labeled axes, and key.
• Make stem-and-leaf plots with title and key, in ascending order.
• Analyze line plots and stem-and-leaf plots and communicate results.
• 5.PS.2 Solve contextual problems using measures of center and the range.
• Describe the mean as fair share.
• Describe and determine the mean in context.
• Describe and determine the median in context.
• Describe and determine the mode in context.
• Describe and determine the range as a measure of spread.
• 5.PS.3 Find probability using a sample space and the Fundamental Counting Principle.
• Build a sample space (24 or fewer equally likely outcomes) to find probability.
• Count possible outcomes using the Fundamental Counting Principle.

Patterns, Functions, and Algebra (PFA)

• 5.PFA.1 Identify, describe, extend, and create patterns with whole numbers, fractions, and decimals.
• Identify, describe, extend, and create patterns using various representations, including function machines.
• Find the rule, extend, or find missing terms in single-operation patterns.
• Solve contextual problems using single-operation input and output rules.
• 5.PFA.2 Investigate and use variables in contextual problems.
• Describe a variable as a symbol representing an unknown quantity.
• Write a one-variable, one-operation equation from a context.
• Write an expression with a variable for a one-operation verbal phrase.
• Write a word problem matching a one-variable, one-operation equation.