The Virginia SOL Grade 5 math assessment marks an important transition point. Fifth grade is where students move from working primarily with whole numbers to working fluently with fractions, decimals, and percentages — skills that directly support pre-algebra and beyond. Students who master Grade 5 SOL content are well-prepared for the more rigorous math that follows in middle school.
This study guide covers the key topics on the Virginia SOL Grade 5 math test, provides mini-practice problems for each domain, and offers a structured 4-week preparation plan.
ViewMath is not affiliated with or endorsed by the Virginia Department of Education (VDOE) or any Virginia school division. Visit doe.virginia.gov for the most current SOL information.
Virginia SOL Grade 5 Math: Key Topics
Number and Number Sense: Fractions, Decimals, and Percents
This is the most tested domain in Grade 5. Students must:
- Identify, compare, and order fractions, decimals, and percents
- Represent equivalences among fractions, decimals, and percents (e.g., 1/4 = 0.25 = 25%)
- Identify the absolute value of integers on a number line
- Solve practical problems using estimation with fractions and decimals
Practice problem: Order from least to greatest: 0.6, 3/5, 58%. (Answer: 3/5 = 0.6 = 60%; 58% = 0.58 < 60%, so order is: 58%, 3/5, 0.6 — but 3/5 = 0.6, so 58% < 3/5 = 0.6)
Computation and Estimation
Fifth graders perform all four operations with fractions (including unlike denominators) and decimals. They find common multiples and least common multiples to add and subtract fractions with different denominators. Division of fractions by whole numbers and multiplication of fractions by fractions are also tested. Order of operations (no exponents) is introduced.
Practice problems:
- 2/3 + 3/4 = ___ (Answer: 8/12 + 9/12 = 17/12 = 1 5/12)
- 3/5 × 2/7 = ___ (Answer: 6/35)
- 4.5 × 2.3 = ___ (Answer: 10.35)
- 12 ÷ 0.4 = ___ (Answer: 30)
Measurement and Geometry
Students convert between units in both customary and metric systems, work with perimeter and area of triangles, rectangles, and other polygons, and find the volume of rectangular prisms by counting unit cubes or using V = l × w × h. The coordinate plane is introduced: students plot and identify ordered pairs in the first quadrant.
Practice problem: A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 4 cm. What is its volume? (Answer: 5 × 3 × 4 = 60 cm³)
Probability and Statistics
Students determine all possible outcomes of a simple probability experiment and find the probability of an event as a fraction. They also create and interpret stem-and-leaf plots, line graphs, and circle graphs — answering questions that require reading data, making comparisons, and computing the mean (average) of a data set.
Practice problem: A bag contains 3 red marbles, 4 blue marbles, and 3 green marbles. What is the probability of picking a blue marble? (Answer: 4/10 = 2/5)
Topic Checklist for Virginia SOL Grade 5 Math
Use this checklist to track which skills are ready and which still need work:
- ☐ Identify and compare fractions, decimals, and percents
- ☐ Add and subtract fractions with unlike denominators
- ☐ Multiply and divide fractions
- ☐ Add, subtract, multiply, and divide decimals
- ☐ Apply order of operations (no exponents)
- ☐ Convert between customary units (inches/feet/yards, ounces/pounds)
- ☐ Convert between metric units (mm/cm/m, g/kg, mL/L)
- ☐ Find area of rectangles and triangles
- ☐ Find volume of rectangular prisms
- ☐ Plot and identify ordered pairs on a coordinate plane (first quadrant)
- ☐ Find the mean of a data set
- ☐ Interpret stem-and-leaf plots and circle graphs
- ☐ Determine probability of a simple event
Common Grade 5 SOL Math Mistakes
- Finding a common denominator incorrectly: Students sometimes add denominators instead of finding the LCM. Always list multiples of each denominator until a common multiple appears: for 3 and 4, that’s 12.
- Decimal multiplication errors: Forgetting to count total decimal places in the product is the most common mistake. Multiply as whole numbers, then count the decimal places in both factors and place the decimal point.
- Volume vs. area confusion: Area uses square units (cm²); volume uses cubic units (cm³). Keeping units in the answer helps catch this mistake.
- Coordinate plane axis mix-up: Students plot (x, y) as (y, x). Remind students: x comes first and goes left/right; y comes second and goes up/down. The mnemonic “x is across” helps.
- Mean calculation errors: Students sometimes forget to divide by the number of values after adding. Write the formula: Mean = sum ÷ count.
A 4-Week Virginia SOL Grade 5 Math Prep Plan
Week 1: Fractions, Decimals, and Percents
Work through fraction-decimal-percent equivalences using a reference chart (1/4 = 0.25 = 25%, 1/2 = 0.5 = 50%, 3/4 = 0.75 = 75%, etc.). Practice ordering mixed sets of fractions, decimals, and percents on a number line. Review the LCM method for adding fractions with unlike denominators.
Week 2: Computation — Fraction and Decimal Operations
Daily practice: 5 fraction problems and 5 decimal problems. Include all four operations. Focus on the most error-prone: adding fractions with unlike denominators, multiplying decimals (decimal placement), and dividing decimals by decimals. Use estimation to check each answer for reasonableness.
Week 3: Measurement, Geometry, and Coordinate Plane
Review customary and metric conversions using a conversion chart. Practice area of rectangles and triangles (A = ½ × b × h). Work through 5–8 volume problems using V = l × w × h. Plot 10 ordered pairs on a coordinate plane and practice identifying points from a graph. Connect to real-world map reading contexts.
Week 4: Probability, Statistics, and Mixed Review
Review probability as a fraction, experiment with a simple spinner or bag of colored counters. Read stem-and-leaf plots and circle graphs and answer multi-step questions. Practice computing the mean. End the week with a full 30-question mixed practice test under timed conditions.
Virginia Grade 5 SOL Math Resources
ViewMath offers Grade 5 math practice test books, workbooks, and study guides covering all the topics assessed on the Virginia SOL. Each resource includes full answer keys and is organized by topic for easy targeted review. Browse the Grade 5 catalog in the sidebar.
ViewMath is an independent publisher. Our materials are not official Virginia SOL or VDOE resources.
