Free 5th Grade Math Placement Test

The diagnostic compares decimals, fraction operations, volume, coordinate reasoning, and multi-step problems against a 5th grade starting point.

Start the free math preview. No account or email is required.

Skills this preview checks

• decimal place value
• fraction operations
• volume
• coordinate plane
• multi-step problems

All 6 questions with answers

1. Which number is greatest?

   1. 4.205
   2. 4.25
   3. 4.052
   4. 4.025
   Answer and explanation

   Answer: B. Four and twenty-five hundredths is greater than the other decimals.

   Skill checked: Decimal place value

2. What is 2/3 + 1/6?

   1. 3/9
   2. 1/2
   3. 5/6
   4. 3/6
   Answer and explanation

   Answer: C. Two thirds is four sixths. Four sixths plus one sixth equals five sixths.

   Skill checked: Fraction operations

3. A rectangular prism is 4 cm long, 3 cm wide, and 5 cm high. What is its volume?

   1. 12 cm³
   2. 20 cm³
   3. 47 cm³
   4. 60 cm³
   Answer and explanation

   Answer: D. Multiply length × width × height: 4 × 3 × 5 = 60 cubic centimeters.

   Skill checked: Volume

4. Point P is at (2, 5). Which number tells how far to move right from the origin?

   1. 2
   2. 3
   3. 5
   4. 7
   Answer and explanation

   Answer: A. The first coordinate, 2, gives the horizontal move to the right.

   Skill checked: Coordinate plane

5. A class collected $18.75 on Monday and $24.50 on Tuesday. It spent $12.25. How much remains?

   1. $18.75
   2. $31.00
   3. $36.50
   4. $55.50
   Answer and explanation

   Answer: B. Add $18.75 and $24.50 to get $43.25, then subtract $12.25 to get $31.00.

   Skill checked: Multi-step problems

6. What is 3 × 2 1/4?

   1. 5 1/4
   2. 6 1/4
   3. 6 3/4
   4. 7 1/2
   Answer and explanation

   Answer: C. Three groups of 2 1/4 equal 6 3/4.

Free printable worksheet

Download the 5th Grade math practice worksheet. It includes a separate set of practice items and an answer key.

Continue to the full diagnostic

This short preview provides an initial signal. The 25-question diagnostic checks more skills and produces a more dependable starting point.

Take the full diagnostic

5th Grade math placement questions

What math should a 5th grader know?

Fifth grade math usually includes multi-digit operations, decimals through thousandths, fraction addition and multiplication, volume, coordinate graphs, numerical patterns, and multi-step problems.

Does this test cover every 5th grade standard?

No. This preview samples a small set of high-leverage skills. Continue to the full diagnostic for broader coverage and a skill-by-skill report.

Should a calculator be used?

No calculator is needed for these questions. Scratch paper is useful, and written work often shows more than the final answer alone.