A rope 9.6 meters long is cut into 8 equal pieces. How long is each piece?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-T.2.1.3
In 3,385, how does the value of the 3 in the hundreds place compare with the value of the 3 in the thousands place?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-T.1.1.1
What is 4.8 × 1.5?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-T.2.1.3
What is 6.2 × 10³?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-T.1.1.2
What is 12.6 − 4.85?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-T.2.1.3
What is 18.746 rounded to the nearest tenth?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-T.1.1.5
What is 47.5 ÷ 10²?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-T.1.1.2
Show all 45 questions (38 more)
Numbers and Operations in Base Ten, continued
What is 418 × 37?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-T.2.1.1
What is 4,536 ÷ 24?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-T.2.1.2
Which numeral is four and thirty-seven thousandths?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-T.1.1.3
Which of these four comparisons of decimals is true?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-T.1.1.4
Numbers and Operations – Fractions 12
7 pounds of clay are shared equally among 3 students. How much clay does each student get?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-F.2.1.1
A jar holds 2 1/2 cups of juice. Then 1 2/3 cups are poured out. How much juice is left?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-F.1.1.1
A photo 45 centimeters wide is resized to 4/3 of its width. How does the new width compare with 45 centimeters?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-F.2.1.3
A rope 11 feet long is cut into 4 equal lengths. How long is each one?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-F.2.1.1
How many 1/3-cup servings are in 6 cups of rice?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-F.2.1.4
Ty walks 3/4 mile to the park and then 2/3 mile to the store. How far does he walk in all?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-F.1.1.1
What is 1/7 ÷ 4?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-F.2.1.4
What is 2 1/4 × 1 1/3?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-F.2.1.2
What is 5 1/3 − 2 3/4?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-F.1.1.1
What is 5/6 + 5/8?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-F.1.1.1
What is 7/10 × 5/14?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-F.2.1.2
Without multiplying, which product is greater than 5/6?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.A-F.2.1.3
Operations and Algebraic Thinking 7
A pattern starts at 0 and follows the rule "add 12". What is its fifth term?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.B-O.2.1.1
Pattern X starts at 0 and adds 3. Pattern Y starts at 0 and adds 9. How does each term of Y compare with the matching term of X?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.B-O.2.1.2
Rule 1 starts at 0 and adds 5. Rule 2 starts at 0 and adds 10. Which ordered pair is made from matching terms, (Rule 1, Rule 2)?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.B-O.2.1.2
What is 3 × [16 − (4 + 2)] + 5?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.B-O.1.1.1
What is {2 × [9 + (12 ÷ 4)]} − 6?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.B-O.1.1.1
Which expression means "subtract 4 from 30, then divide by 2"?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.B-O.1.1.2
Without calculating, how does 5 × (4,318 + 276) compare with 4,318 + 276?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.B-O.1.1.2
Geometry 7
A graph plots hours worked on the x-axis and dollars earned on the y-axis. What does the point (4, 60) mean?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.C-G.1.1.2
A parallelogram is a quadrilateral with two pairs of parallel sides. A rhombus has two pairs of parallel sides and four equal sides. Which statement must be true?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.C-G.2.1.1
A park map uses a coordinate grid. The gate is at (2, 4) and the fountain is at (9, 4). Each unit is 10 meters. How far apart are they?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.C-G.1.1.2
A point is at (7, 2). Which describes how to reach it from the origin?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.C-G.1.1.1
The points (2, 1), (2, 6) and (8, 1) are three corners of a rectangle. Where is the fourth corner?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.C-G.1.1.2
What are the coordinates of the origin on a coordinate plane?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.C-G.1.1.1
Which statement about rectangles and parallelograms is true?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.C-G.2.1.1
Measurement and Data 8
A line plot shows how much trail mix five hikers carry: 1/4 pound, 1/2 pound, 1/2 pound, 3/4 pound and 3/4 pound. What is the difference between the most and the least?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.D-M.2.1.1
A line plot shows six pieces of wire: four are 3/8 foot long and two are 1/4 foot long. What is their total length?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.D-M.2.1.1
An L-shaped block is built from two rectangular prisms. One is 5 cm long, 3 cm wide and 2 cm high. The other is 3 cm long, 3 cm wide and 4 cm high. What is the volume of the block?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.D-M.3.1.2
In a pictograph, each ball stands for 4 students. The row for soccer has 5 1/2 balls. How many students chose soccer?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.D-M.2.1.2
One gallon is 4 quarts and one quart is 2 pints. How many pints are in 3 gallons?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.D-M.1.1.1
One meter is 100 centimeters. How many meters is 45 centimeters?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.D-M.1.1.1
One pound is 16 ounces. A 5-pound bag of rice is split into 8-ounce servings. How many servings is that?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.D-M.1.1.1
Use V = l × w × h. A box is 12 inches long, 5 inches wide and 4 inches high. What is its volume?Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 5 (April 2014), eligible content M05.D-M.3.1.1
Unofficial practice for Pennsylvania's grade 5 PSSA mathematics test. Each of the 45 questions was written for this site from one line of the state's eligible content; none is a sampler item. Not affiliated with the Pennsylvania Department of Education.
Read the full guide
What the 5th grade math PSSA covers
At least half of the grade 5 core is number work. Pennsylvania's test design gives fractions 26 to 30 percent and base ten 24 to 28 percent: adding and subtracting unlike fractions, multiplying fractions, dividing with unit fractions, powers of 10 and decimals to thousandths. Measurement and Data, with unit conversions, line plots and volume, has 17 to 21 percent. Geometry and Operations and Algebraic Thinking have 14 to 17 percent each. The 45 questions here keep those shares.
Reading a missed question
Under each answer are the steps and an eligible content code, such as M05.A-F.2.1.4. The code points to one line of the state's assessment anchors.
The anchors say a table of equivalencies is provided for unit conversions, and the volume formulas are provided too.
Questions and answers
How many questions are on the 5th grade math PSSA?
The core is 43 items worth 52 points: 40 multiple-choice or technology-enhanced items at one point each and 3 open-ended items at four points each. A form adds 9 items for field testing and psychometric use. This page has 45 questions.
How long is the PSSA math test in grade 5?
The test design has two sections, each with 24 multiple-choice or technology-enhanced items and 2 open-ended items, and it estimates 78 minutes of testing for each. That is an estimate, and the design names no time limit.
Can 5th graders use a calculator on the math PSSA?
On part of it. The test design says calculators are not allowed in grade 3, and that in grades 4 to 8 just part of the test is non-calculator. The state's calculator policy lists the devices that are barred.
Are there PSSA practice tests for 5th grade math from the state?
The department publishes a grade 5 item and scoring sampler, with scoring guidelines and formula sheets, on its PSSA page. The box under the questions links to that page. The questions here are separate and unofficial.