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Free Practice Questions for PSSA Grade 5 Mathematics

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Key Facts: PSSA Grade 5 Mathematics Exam

Official assessment body: Pennsylvania Department of Education (PDE).

Aligned to PA Core Standards for Grade 5 Mathematics.

40% Numbers & Operations, 20% Algebraic Concepts, 20% Geometry, 20% Data Analysis.

Untimed test format administered in two testing sessions.

Includes real-world word problems and step-by-step computational questions.

The PSSA Grade 5 Mathematics test is Pennsylvania's annual state assessment for 5th graders, aligned to PA Core Standards. It covers 4 domains with 40% emphasis on Numbers and Operations and 20% on each of Algebraic Concepts, Geometry, and Data Analysis. This bank contains 100 full-length practice questions with step-by-step solutions.

Sample PSSA Grade 5 Mathematics Practice Questions

Try these sample questions to review concepts for the PSSA Grade 5 Mathematics exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1What is the value of the digit 7 in the number 4.375?
A.7 tens
B.7 tenths
C.7 hundredths
D.7 thousandths
Explanation: In 4.375, the digit 4 is in the ones place, 3 is in the tenths place (0.3), 7 is in the hundredths place (0.07), and 5 is in the thousandths place (0.005). Thus, the digit 7 has a value of 7 hundredths.
2Which of the following shows 5.208 written in expanded form?
A.5 + (2 × 1/10) + (8 × 1/100)
B.5 + (2 × 1/10) + (8 × 1/1000)
C.5 + (2 × 1/100) + (8 × 1/1000)
D.5 + (2 × 1) + (8 × 1/10)
Explanation: 5.208 consists of 5 ones, 2 tenths, 0 hundredths, and 8 thousandths. In expanded notation using fractions, this is represented as 5 + (2 × 1/10) + (8 × 1/1000).
3Which comparison statement is true?
A.0.458 > 0.46
B.0.458 = 0.460
C.0.458 < 0.46
D.0.46 < 0.409
Explanation: Comparing 0.458 and 0.46 (which equals 0.460), both have 4 in the tenths place. In the hundredths place, 5 is less than 6. Therefore, 0.458 < 0.46.
4What is 18.347 rounded to the nearest hundredth?
A.18.3
B.18.34
C.18.35
D.18.4
Explanation: The digit in the hundredths place is 4. Look at the digit to its right in the thousandths place, which is 7. Since 7 is 5 or greater, round the hundredths digit up from 4 to 5, resulting in 18.35.
5What is the product of 4.56 and 10^3?
A.45.6
B.456
C.4,560
D.45,600
Explanation: 10^3 equals 1,000. Multiplying a decimal by 10^3 shifts the decimal point 3 places to the right: 4.56 × 1,000 = 4,560.
6What is 73.2 divided by 10^2?
A.0.732
B.7.32
C.732
D.7,320
Explanation: 10^2 equals 100. Dividing a decimal by 10^2 shifts the decimal point 2 places to the left: 73.2 ÷ 100 = 0.732.
7A bag of apples weighs 4.863 pounds. What is the weight of the bag rounded to the nearest tenth of a pound?
A.4.8 lbs
B.4.86 lbs
C.4.9 lbs
D.5.0 lbs
Explanation: The tenths place is 8. The adjacent digit in the hundredths place is 6. Since 6 ≥ 5, round up the tenths digit to 9, giving 4.9 pounds.
8Which list of decimals is ordered from least to greatest?
A.0.305, 0.35, 0.309, 0.53
B.0.305, 0.309, 0.35, 0.53
C.0.35, 0.305, 0.309, 0.53
D.0.53, 0.35, 0.309, 0.305
Explanation: Pad each decimal with zeros to thousandths: 0.305, 0.309, 0.350, 0.530. Comparing the values: 305 < 309 < 350 < 530. Thus, the correct order is 0.305, 0.309, 0.35, 0.53.
9A scientist measures a chemical sample mass as (3 × 10^1) + (4 × 1) + (5 × 1/10) + (2 × 1/1000) grams. What is this mass in standard decimal form?
A.34.52
B.34.502
C.34.052
D.345.2
Explanation: Calculate each part: 3 × 10 = 30; 4 × 1 = 4; 5 × 1/10 = 0.5; 2 × 1/1000 = 0.002. Summing these values gives 30 + 4 + 0.5 + 0.002 = 34.502 grams.
10In which number is the value of the digit in the hundredths place equal to 1/10 the value of the digit in the tenths place?
A.0.444
B.0.626
C.0.505
D.0.808
Explanation: In 0.444, the digit in the tenths place is 4 (value 0.4) and the digit in the hundredths place is 4 (value 0.04). Since 0.04 is 1/10 of 0.4, the hundredths digit is 1/10 the value of the tenths digit.

About the PSSA Grade 5 Mathematics Exam

The PSSA Grade 5 Mathematics assessment measures 5th-grade student achievement relative to the Pennsylvania Core Standards for Mathematics. The exam evaluates mathematical fluency, conceptual understanding, and problem-solving skills across four major domains: Numbers and Operations (decimal place value, multi-digit whole number and decimal arithmetic, fraction operations), Algebraic Concepts (numerical expressions, order of operations with grouping symbols, pattern relationships), Geometry (coordinate plane graphing, 2D figure classification, volume of rectangular prisms), and Data Analysis and Probability (line plots with fractions, unit conversions).

Exam sponsor: Pennsylvania Department of Education (PDE). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Two sections of 24 multiple-choice/technology-enhanced items and 2 open-ended items each. PDE's 2025 blueprint reports Grade 5 as Numbers and Operations in Base Ten 24-28%, Numbers and Operations - Fractions 26-30%, Operations and Algebraic Thinking 14-17%, Geometry 14-17%, and Measurement and Data 17-21%. Calculators are permitted on designated sections.

Time Limit

Untimed; PDE's test design plans two sections with an estimated 78 minutes of testing each. Delivered online only beginning with the Spring 2026 administration.

Passing Score

Students receive a scaled score placed into one of four performance levels: Below Basic, Basic, Proficient, or Advanced. Proficient represents grade-level mastery of PA Core Standards.

Exam / Certification Fees

$0 (State-funded assessment for public school students in Pennsylvania)

Exam sponsor website

Reported exam pass rate: Approximately 50%–60% of Pennsylvania 5th grade students achieve Proficient or Advanced.. This describes exam candidates, not OpenExamPrep users or results from using our resources. Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

40%

Numbers and Operations

Understanding place value to thousandths, powers of 10, operations with multi-digit whole numbers and decimals, and fraction arithmetic (addition, subtraction, multiplication, and division).

20%

Algebraic Concepts

Evaluating multi-step expressions using order of operations and grouping symbols (parentheses, brackets), translating word phrases to expressions, and comparing numerical patterns.

20%

Geometry

Plotting ordered pairs in quadrant I of the coordinate grid, classifying 2D shapes by attributes and hierarchy, and calculating volume of rectangular prisms using unit cubes and formulas.

20%

Data Analysis and Probability

Interpreting data on line plots involving fractional units (1/2, 1/4, 1/8) and converting measurement units within standard customary and metric systems.

Preparing for the PSSA Grade 5 Mathematics Exam

What You Need to Know

  • Passing score: Students receive a scaled score placed into one of four performance levels: Below Basic, Basic, Proficient, or Advanced. Proficient represents grade-level mastery of PA Core Standards.
  • Assessment: Two sections of 24 multiple-choice/technology-enhanced items and 2 open-ended items each. PDE's 2025 blueprint reports Grade 5 as Numbers and Operations in Base Ten 24-28%, Numbers and Operations - Fractions 26-30%, Operations and Algebraic Thinking 14-17%, Geometry 14-17%, and Measurement and Data 17-21%. Calculators are permitted on designated sections.
  • Time limit: Untimed; PDE's test design plans two sections with an estimated 78 minutes of testing each. Delivered online only beginning with the Spring 2026 administration.
  • Exam / certification fees: $0 (State-funded assessment for public school students in Pennsylvania) Official sources

Using Our Practice Resources

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
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PSSA Grade 5 Mathematics: Suggested Study Strategy

1Practice multi-digit multiplication and long division algorithms until comfortable without a calculator.
2Master finding common denominators for adding and subtracting fractions and mixed numbers with unlike denominators.
3Pay strict attention to the order of operations (PEMDAS) when evaluating expressions with parentheses and brackets.
4Remember the volume formula V = length × width × height and V = base area × height for rectangular prisms.
5Review customary conversions (inches, feet, yards; ounces, pounds; cups, quarts, gallons) and metric conversions (mm, cm, m, km; g, kg; mL, L).

Frequently Asked Questions

What is the PSSA Grade 5 Mathematics exam?

The PSSA Grade 5 Math exam is a statewide assessment administered annually to public school 5th graders in Pennsylvania to evaluate proficiency in the PA Core Standards for Mathematics.

How many questions are on the PSSA Grade 5 Math exam?

The official state test contains 72 total items across multiple-choice and open-ended formats. Our practice question bank features 100 questions covering topics from the official assessment blueprint.

Are calculators allowed on the Grade 5 PSSA Math test?

Calculators are permitted on designated sections of the PSSA Grade 5 Math test, while non-calculator sections assess basic mental math and standard computational algorithms.

How are PSSA Grade 5 Math scores categorized?

Student performance is reported as a scaled score falling into four levels: Below Basic, Basic, Proficient, and Advanced. Proficient indicates full grade-level standard mastery.

What topics carry the highest weight on the exam?

Numbers and Operations is the largest reporting category, accounting for 40% of the exam weight, followed by 20% each for Algebraic Concepts, Geometry, and Data Analysis and Probability.