A pattern starts at 3 and adds 6 each time. What is the fifth term?Common Core State Standards for Mathematics, 5.OA.B.3: generate two numerical patterns from two rules and relate their terms
Pattern A starts at 0 and adds 4 each time. Pattern B starts at 0 and adds 12 each time. How do the terms of pattern B compare with the matching terms of pattern A?Common Core State Standards for Mathematics, 5.OA.B.3: generate two numerical patterns from two rules and relate their terms
Pattern X starts at 0 and adds 2 each time. Pattern Y starts at 0 and adds 7 each time. Which ordered pair (X, Y) is made from the fourth terms?Common Core State Standards for Mathematics, 5.OA.B.3: generate two numerical patterns from two rules and relate their terms
What is the value of 6 × (4 + 5) − 10?Common Core State Standards for Mathematics, 5.OA.A.1: use parentheses, brackets or braces in numerical expressions, and evaluate them
What is the value of 48 ÷ [2 × (9 − 5)]?Common Core State Standards for Mathematics, 5.OA.A.1: use parentheses, brackets or braces in numerical expressions, and evaluate them
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Operations and Algebraic Thinking, continued
What is the value of {2 + [3 × (10 − 4)]} × 5?Common Core State Standards for Mathematics, 5.OA.A.1: use parentheses, brackets or braces in numerical expressions, and evaluate them
Which expression means "divide the sum of 12 and 18 by 6"?Common Core State Standards for Mathematics, 5.OA.A.2: write simple expressions and interpret them without evaluating
Which expression means "subtract 4 from 20, then multiply by 3"?Common Core State Standards for Mathematics, 5.OA.A.2: write simple expressions and interpret them without evaluating
Without working it out, how does 5 × (672 + 89) compare with 672 + 89?Common Core State Standards for Mathematics, 5.OA.A.2: write simple expressions and interpret them without evaluating
Number and Operations in Base Ten 20
A baker packs 2,170 muffins into boxes of 35. How many boxes are filled?Common Core State Standards for Mathematics, 5.NBT.B.6: find whole-number quotients with up to four-digit dividends and two-digit divisors
A school orders 125 boxes of pencils. Each box holds 48 pencils. How many pencils is that?Common Core State Standards for Mathematics, 5.NBT.B.5: fluently multiply multi-digit whole numbers
Ana buys 3 notebooks that cost $2.75 each. How much does she pay?Common Core State Standards for Mathematics, 5.NBT.B.7: add, subtract, multiply and divide decimals to hundredths
How does the value of the 7 in 0.07 compare with the value of the 7 in 0.7?Common Core State Standards for Mathematics, 5.NBT.A.1: a digit in one place is 10 times what it is in the place to its right
How is the number 3.058 read?Common Core State Standards for Mathematics, 5.NBT.A.3.a: read and write decimals to thousandths
In the number 5,555, the 5 in the hundreds place has how many times the value of the 5 in the tens place?Common Core State Standards for Mathematics, 5.NBT.A.1: a digit in one place is 10 times what it is in the place to its right
What is 0.9 × 0.8?Common Core State Standards for Mathematics, 5.NBT.B.7: add, subtract, multiply and divide decimals to hundredths
What is 3.249 rounded to the nearest tenth?Common Core State Standards for Mathematics, 5.NBT.A.4: use place value understanding to round decimals to any place
What is 4.2 × 10³?Common Core State Standards for Mathematics, 5.NBT.A.2: patterns when multiplying or dividing by powers of 10
What is 4.85 + 13.6?Common Core State Standards for Mathematics, 5.NBT.B.7: add, subtract, multiply and divide decimals to hundredths
What is 6 − 2.38?Common Core State Standards for Mathematics, 5.NBT.B.7: add, subtract, multiply and divide decimals to hundredths
What is 8.4 ÷ 0.7?Common Core State Standards for Mathematics, 5.NBT.B.7: add, subtract, multiply and divide decimals to hundredths
What is 12.346 rounded to the nearest hundredth?Common Core State Standards for Mathematics, 5.NBT.A.4: use place value understanding to round decimals to any place
What is 57.3 ÷ 100?Common Core State Standards for Mathematics, 5.NBT.A.2: patterns when multiplying or dividing by powers of 10
What is 246 × 37?Common Core State Standards for Mathematics, 5.NBT.B.5: fluently multiply multi-digit whole numbers
What is 1,794 ÷ 26?Common Core State Standards for Mathematics, 5.NBT.B.6: find whole-number quotients with up to four-digit dividends and two-digit divisors
Which comparison of decimals to thousandths is true?Common Core State Standards for Mathematics, 5.NBT.A.3.b: compare two decimals to thousandths
Which list of decimals runs from least to greatest?Common Core State Standards for Mathematics, 5.NBT.A.3.b: compare two decimals to thousandths
Which number is 6 × 10 + 2 × 1 + 4 × (1/10) + 9 × (1/1000)?Common Core State Standards for Mathematics, 5.NBT.A.3.a: read and write decimals to thousandths
Which number is equal to 10⁴?Common Core State Standards for Mathematics, 5.NBT.A.2: patterns when multiplying or dividing by powers of 10
Number and Operations: Fractions 20
A 25-foot rope is cut into 4 equal pieces. How long is each piece?Common Core State Standards for Mathematics, 5.NF.B.3: interpret a fraction as division of the numerator by the denominator
A jug holds 3 1/4 cups of juice. Ben pours out 1 1/2 cups. How much juice is left?Common Core State Standards for Mathematics, 5.NF.A.2: solve word problems on adding and subtracting fractions and judge if an answer is reasonable
A recipe needs 2 1/2 cups of flour. Ty makes 1 1/2 times the recipe. How much flour does he need?Common Core State Standards for Mathematics, 5.NF.B.6: solve real world problems involving multiplication of fractions and mixed numbers
A rug is 5/6 yard long and 3/4 yard wide. What is its area?Common Core State Standards for Mathematics, 5.NF.B.4.b: find the area of a rectangle with fractional side lengths
Four friends share 1/5 of a pan of brownies equally. What fraction of the whole pan does each friend get?Common Core State Standards for Mathematics, 5.NF.B.7.c: solve real world problems on dividing with unit fractions
Four pizzas are shared equally among 6 friends. How much pizza does each friend get?Common Core State Standards for Mathematics, 5.NF.B.3: interpret a fraction as division of the numerator by the denominator
How many 1/8-pound burgers can be made from 3 pounds of meat?Common Core State Standards for Mathematics, 5.NF.B.7.c: solve real world problems on dividing with unit fractions
Kai walks 3/8 mile to the park and then 1/2 mile to the store. How far does he walk?Common Core State Standards for Mathematics, 5.NF.A.2: solve word problems on adding and subtracting fractions and judge if an answer is reasonable
Mia says that 1/2 + 3/5 = 4/7. How can you tell she is wrong without adding?Common Core State Standards for Mathematics, 5.NF.A.2: solve word problems on adding and subtracting fractions and judge if an answer is reasonable
Plants cover 3/5 of a garden. Beans grow on 1/2 of the planted part. What fraction of the whole garden grows beans?Common Core State Standards for Mathematics, 5.NF.B.6: solve real world problems involving multiplication of fractions and mixed numbers
What is 1/7 ÷ 5?Common Core State Standards for Mathematics, 5.NF.B.7.a: divide a unit fraction by a non-zero whole number
What is 2 1/3 + 1 3/4?Common Core State Standards for Mathematics, 5.NF.A.1: add and subtract fractions with unlike denominators, including mixed numbers
What is 2/3 × 24?Common Core State Standards for Mathematics, 5.NF.B.4.a: multiply a fraction or whole number by a fraction
What is 2/5 × 3/7?Common Core State Standards for Mathematics, 5.NF.B.4.a: multiply a fraction or whole number by a fraction
What is 3/5 + 2/7?Common Core State Standards for Mathematics, 5.NF.A.1: add and subtract fractions with unlike denominators, including mixed numbers
What is 6 1/4 − 3 2/3?Common Core State Standards for Mathematics, 5.NF.A.1: add and subtract fractions with unlike denominators, including mixed numbers
What is 7 ÷ 1/3?Common Core State Standards for Mathematics, 5.NF.B.7.b: divide a whole number by a unit fraction
What is 7/9 − 1/6?Common Core State Standards for Mathematics, 5.NF.A.1: add and subtract fractions with unlike denominators, including mixed numbers
Which product is greater than 60?Common Core State Standards for Mathematics, 5.NF.B.5.b: multiplying by a fraction greater than 1 or less than 1
Without multiplying, what is true about 7/8 × 500?Common Core State Standards for Mathematics, 5.NF.B.5.a: compare the size of a product to the size of one factor without multiplying
Measurement and Data 13
A bag of flour weighs 40 ounces. How many pounds is that? (1 pound = 16 ounces)Common Core State Standards for Mathematics, 5.MD.A.1: convert among different-sized standard measurement units within one system. Conversion factor: NIST Handbook 44 (2026), Appendix C, Avoirdupois Units of Mass
A box is packed with 30 unit cubes with no gaps and no overlaps. What is the volume of the box?Common Core State Standards for Mathematics, 5.MD.C.3.b: a solid packed with n unit cubes has a volume of n cubic units
A cooler holds 3 gallons of water. How many quarts is that? (1 gallon = 4 quarts)Common Core State Standards for Mathematics, 5.MD.A.1: convert among different-sized standard measurement units within one system. Conversion factor: NIST Handbook 44 (2026), Appendix C, Units of Liquid Volume
A fish tank is 20 inches long, 10 inches wide and 12 inches tall. What is its volume?Common Core State Standards for Mathematics, 5.MD.C.5.b: apply the formulas V = l × w × h and V = b × h for rectangular prisms
A line plot shows the lengths of six ribbons: three are 1/4 foot, two are 1/2 foot and one is 3/4 foot. What is the total length of the ribbons?Common Core State Standards for Mathematics, 5.MD.B.2: use operations on fractions to solve problems with data on line plots
A rectangular prism has a base with an area of 15 square centimeters and a height of 4 centimeters. What is its volume?Common Core State Standards for Mathematics, 5.MD.C.5.a: volume as edge lengths multiplied, or the height times the area of the base
A shelf is 42 inches long. How long is it in feet? (1 foot = 12 inches)Common Core State Standards for Mathematics, 5.MD.A.1: convert among different-sized standard measurement units within one system. Conversion factor: NIST Handbook 44 (2026), Appendix C, Units of Length
A solid is built from 3 layers of unit cubes. Each layer has 8 cubes. What is the volume of the solid?Common Core State Standards for Mathematics, 5.MD.C.4: measure volumes by counting unit cubes
A solid is made of two rectangular prisms joined side by side. One is 5 by 2 by 3 units and the other is 2 by 2 by 3 units. What is the total volume?Common Core State Standards for Mathematics, 5.MD.C.5.c: recognize volume as additive
A storage box has a volume of 96 cubic feet. It is 8 feet long and 4 feet wide. How tall is it?Common Core State Standards for Mathematics, 5.MD.C.5.b: apply the formulas V = l × w × h and V = b × h for rectangular prisms
A table is 3.2 meters long. How long is it in centimeters? (1 meter = 100 centimeters)Common Core State Standards for Mathematics, 5.MD.A.1: convert among different-sized standard measurement units within one system. Conversion factor: NIST Handbook 44 (2026), Appendix C, Units of Length
Lena runs 1.5 kilometers each day for 4 days. How many meters does she run in all? (1 kilometer = 1,000 meters)Common Core State Standards for Mathematics, 5.MD.A.1: convert among different-sized standard measurement units within one system. Conversion factor: NIST Handbook 44 (2026), Appendix C, Units of Length
On a line plot of pencil lengths, the longest pencil is 7 1/2 inches and the shortest is 5 3/4 inches. What is the difference?Common Core State Standards for Mathematics, 5.MD.B.2: use operations on fractions to solve problems with data on line plots
Geometry 7
A graph shows hours on the x-axis and miles walked on the y-axis. What does the point (4, 7) mean?Common Core State Standards for Mathematics, 5.G.A.2: graph points in the first quadrant and interpret coordinate values
A shape has four right angles and four equal sides. Which statement is true?Common Core State Standards for Mathematics, 5.G.B.4: classify two-dimensional figures in a hierarchy based on properties
Every rectangle has two pairs of parallel sides. A square is a rectangle. What does this tell you about every square?Common Core State Standards for Mathematics, 5.G.B.3: attributes of a category of figures belong to all of its subcategories
On a coordinate plane, what is the name of the point (0, 0), where the two axes cross?Common Core State Standards for Mathematics, 5.G.A.1: axes, the origin and ordered pairs of a coordinate system
On a town map drawn on a coordinate grid, the library is at (2, 6) and the school is at (2, 1). How many units apart are they?Common Core State Standards for Mathematics, 5.G.A.2: graph points in the first quadrant and interpret coordinate values
Starting at the origin, how do you reach the point (3, 5)?Common Core State Standards for Mathematics, 5.G.A.1: axes, the origin and ordered pairs of a coordinate system
Which shape is always a rectangle?Common Core State Standards for Mathematics, 5.G.B.4: classify two-dimensional figures in a hierarchy based on properties
How this list was compiled: Our own questions. Outline: the Common Core State Standards for Mathematics, grade 5, https://www.thecorestandards.org/Math/Content/5/introduction/, with the five domain pages (Operations and Algebraic Thinking, Number and Operations in Base Ten, Number and Operations: Fractions, Measurement and Data, Geometry), read 2026-10-10 there and in the standards’ own file, https://learning.ccsso.org/wp-content/uploads/2022/11/ADA-Compliant-Math-Standards.pdf; thecorestandards.org is an unofficial site that carries the same text by domain. Each question names the standard it practices and links to that domain page. Every answer is arithmetic or reasoning on the numbers the question prints, and each one was worked out again on 2026-10-10. The five conversion factors (100 centimeters in 1 meter, 1,000 meters in 1 kilometer, 12 inches in 1 foot, 4 quarts in 1 gallon, 16 ounces in 1 pound) are printed in their questions and were read in NIST Handbook 44 (2026), Appendix C, https://www.nist.gov/document/2026-nist-handbook-44-appendix-c, on 2026-10-10. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from a state test, a released form, a sample item, a textbook or another practice test, and no example printed in the standards is used as a question.
How it works
Unofficial fifth grade math practice: 69 questions written for this page to the five domains of the Common Core grade 5 standards. No school's or state's test is followed or copied, so no test length or pass mark is implied.
Read the full guide
What the 69 questions cover
Fractions and Base Ten have 20 questions each, Measurement and Data 13, Operations and Algebraic Thinking 9, and Geometry 7. The weight follows the three critical areas the standards name for the grade: fractions; decimals and division by two-digit numbers; and volume.
How far fraction division goes
Grade 5 divides only a unit fraction by a whole number, or a whole number by a unit fraction, such as 1/7 ÷ 5 or 7 ÷ 1/3. The standards leave dividing one fraction by another to grade 6, so it is not asked here.
Before adding fractions, rename them with the same denominator. Never add the denominators.
Line up the decimal points before adding or subtracting decimals.
Volume is counted in cubic units, area in square units.
Questions and answers
Can I print these free grade 5 practice math tests?
Yes. The questions print as a paper test, with or without the answer key, and Save as PDF in the print window keeps a copy. There is nothing to sign up for.
What math should a 5th grader know?
By the Common Core: adding and subtracting fractions with unlike denominators, multiplying fractions, dividing with unit fractions, decimals to thousandths, dividing by two-digit numbers, and the volume of rectangular prisms. Graphing points and classifying shapes are taught as well.
Is this the same as a state grade 5 math test?
No. It follows the national standards and no single test. For one test's own design, try the STAAR, MCAS, PSSA or New York grade 5 math pages.