The Pennsylvania System of School Assessment (PSSA) is Pennsylvania’s annual state standardized test in mathematics and English Language Arts. Grade 3 math is one of the earliest testing years, and it assesses whether students have mastered the foundational concepts expected by the end of third grade. For students, parents, and teachers preparing for PSSA season, understanding what the test covers — and practicing it systematically — is the most effective approach.
This guide covers the PSSA Grade 3 math reporting categories, provides practice problems in each area with solutions, and offers a study plan for the weeks leading up to the test.
ViewMath is not affiliated with or endorsed by the Pennsylvania Department of Education (PDE). Always visit education.pa.gov for official PSSA information, testing windows, and sample materials.
PSSA Grade 3 Math: What’s Tested
The PSSA is aligned to Pennsylvania’s academic standards, which are based on the Common Core State Standards (CCSS). The Grade 3 math test covers five major reporting categories:
- Numbers and Operations
- Algebraic Concepts
- Geometry
- Measurement and Data
- Data Analysis and Probability
The test consists of multiple-choice and open-ended questions. Students are scored at four performance levels: Advanced, Proficient, Basic, and Below Basic. The Proficient level indicates grade-level readiness.
Category 1: Numbers and Operations
This is the largest category in Grade 3. Students demonstrate understanding of place value to the thousands, fluency with multiplication and division within 100, understanding of fractions as parts of a whole, and the ability to compare fractions with the same numerator or denominator.
Practice 1: What is the value of the digit 7 in the number 2,735?
Answer: 700 — the 7 is in the hundreds place.
Practice 2: What is 6 × 9?
Answer: 54.
Practice 3: There are 48 students and each table seats 6. How many tables are needed?
Answer: 48 ÷ 6 = 8 tables.
Practice 4: Which fraction is greater: 3/4 or 3/8?
Answer: 3/4. Same numerator — larger denominator means smaller pieces, so 3/8 is less. 3/4 is greater.
Practice 5: Write a fraction to represent the shaded part: a rectangle divided into 5 equal parts with 2 shaded.
Answer: 2/5.
Category 2: Algebraic Concepts
Grade 3 algebra includes understanding properties of multiplication (commutative, associative, distributive), interpreting multiplication as equal groups or arrays, and identifying and extending patterns in arithmetic.
Practice 6: Complete the pattern: 4, 8, 12, 16, ___, ___
Answer: 20, 24 — adding 4 each time.
Practice 7: Use the distributive property to find 6 × 7 by breaking it into 6 × 5 + 6 × 2.
Answer: 6 × 5 = 30, 6 × 2 = 12. 30 + 12 = 42.
Practice 8: If 4 × □ = 32, what is □?
Answer: 8, because 4 × 8 = 32.
Category 3: Geometry
Grade 3 geometry involves recognizing and classifying two-dimensional shapes (triangles, quadrilaterals, hexagons, etc.) by their attributes (number of sides, angles), understanding that shapes in different categories can share attributes, and partitioning shapes into equal areas to understand fractions geometrically.
Practice 9: A shape has 4 sides and all 4 angles are right angles, but not all sides are equal. What shape is it?
Answer: A rectangle.
Practice 10: How many sides does a hexagon have?
Answer: 6.
Practice 11: A square is divided into 4 equal parts. Each part represents what fraction of the whole square?
Answer: 1/4.
Category 4: Measurement and Data
Students solve problems involving time (to the nearest minute), liquid volumes (liters), and masses (grams and kilograms). They measure lengths to the nearest 1/2 inch, represent data in scaled picture graphs and bar graphs, and find areas and perimeters of rectangles.
Practice 12: A movie starts at 2:15 PM and ends at 3:50 PM. How long is the movie?
Answer: 1 hour and 35 minutes.
Practice 13: A rectangle is 7 cm long and 4 cm wide. What is its area? What is its perimeter?
Answer: Area = 7 × 4 = 28 cm². Perimeter = 2 × (7 + 4) = 22 cm.
Practice 14: A container holds 5 liters of water. Another holds 3 liters. How many liters are there in total?
Answer: 5 + 3 = 8 liters.
Category 5: Data Analysis and Probability
Grade 3 students read and interpret scaled picture graphs and bar graphs, draw graphs from given data, and solve problems based on the information in graphs. Basic data analysis at this level centers on comparing values and understanding what questions graphs can and cannot answer.
Practice 15: A bar graph shows that the class voted for their favorite fruit: Apple = 8, Orange = 5, Banana = 7, Grape = 4. How many more students voted for Apple than Grape?
Answer: 8 − 4 = 4 more students.
Practice 16: In the same survey, how many students voted in total?
Answer: 8 + 5 + 7 + 4 = 24 students.
Practice 17: A picture graph uses one star symbol to represent 3 books read. If a student’s row shows 4 stars, how many books did that student read?
Answer: 4 × 3 = 12 books.
Word Problems Combining Multiple Skills
Practice 18: Ms. Brown puts 35 crayons into boxes of 5. She then gives each of 7 students one box. Are there enough boxes for all students?
Answer: 35 ÷ 5 = 7 boxes. Yes, there are exactly enough for 7 students.
Practice 19: A garden is 8 feet long and 3 feet wide. What is the area? What is the perimeter?
Answer: Area = 8 × 3 = 24 square feet. Perimeter = 2 × (8 + 3) = 22 feet.
Practice 20: Jamie has 1/4 of a pizza and Sarah has 2/4 of a pizza. Who has more? How much do they have together?
Answer: Sarah has more. Together: 1/4 + 2/4 = 3/4 of a pizza.
Common PSSA Grade 3 Math Mistakes
- Fraction comparison direction: When comparing fractions with the same numerator (like 3/4 vs. 3/8), students sometimes choose the one with the larger denominator. Larger denominator = smaller pieces = smaller fraction.
- Confusing area and perimeter: Area is measured in square units (multiply side × side). Perimeter is measured in linear units (add all sides). Students frequently mix up which formula applies.
- Forgetting to scale in picture graphs: When a symbol represents more than one item (e.g., 1 star = 3 books), students must multiply by the scale factor, not just count symbols.
- Multiplication fact fluency under test pressure: Students who know their facts but haven’t automated them may slow down significantly and make arithmetic errors during the test. Regular timed practice on multiplication facts (1–10) builds both accuracy and speed.
3-Week PSSA Grade 3 Math Study Plan
Week 1: Numbers and Operations
Practice multiplication and division facts each day (aim for fluency on 1–10 by the end of the week). Cover place value to thousands, fraction identification, and fraction comparison. Complete 15 practice problems per day.
Week 2: Geometry, Measurement, and Algebraic Concepts
Review 2D shape attributes (sides, angles, names). Practice area and perimeter of rectangles. Cover time to the nearest minute, liquid volume, and mass. Work with patterns and the distributive property. Complete 15 practice problems per day.
Week 3: Data Analysis and Mixed Review
Read and interpret picture graphs and bar graphs (include scaled graphs). Take a 25-problem mixed practice test. Identify missed topics and do 10 targeted problems in each area before test day. End each session on 5 correctly solved problems to build confidence.
PSSA Grade 3 Math Resources from ViewMath
ViewMath offers Grade 3 math workbooks and practice test books organized by topic, with full answer keys and step-by-step solutions. Each book covers the full range of Grade 3 math skills tested on state assessments aligned to Common Core standards — the same foundation as the PSSA. Explore the Grade 3 collection in the sidebar.
ViewMath is an independent publisher. Our materials are not official PSSA or PDE materials.
