What this diagnostic measures
Fourth-grade work moves quickly into larger numbers, multi-digit multiplication, and deeper fraction reasoning. This diagnostic checks whether students can draw on the core third-grade meanings beneath those procedures.
Free beginning-of-year diagnostic
4th Grade Back-to-School Math Diagnostic
A printable 24-question 4th grade math diagnostic covering operations, multiplication, division, fractions, measurement, geometry, data, and multi-step word problems.
24 questions6 skill areasAbout 45 minutesAnswer key and scoring guide
Download the free diagnostic PDFAdministration note
Students should work without a multiplication chart on the first attempt. If fact recall is slow but strategies are accurate, note fluency as a practice goal rather than marking the larger concept as missing.
Preview all 24 questions
Give one point per correct answer. Also record each section score out of three so the follow-up plan stays specific.
Place value and operations
Section score: ____ / 4
Use place value to compute, compare, and round.
- 1Find 1,846 + 975.
- 2Find 3,002 - 1,687.
- 3Round 6,472 to the nearest hundred.
- 4Write [[4,305]] in expanded form.
Multiplication and division
Section score: ____ / 4
Use facts and interpret equal groups, arrays, and sharing.
- 5Find 8 x 7 and [[\frac{56}{8}]].
- 6Write a multiplication equation for 6 rows of 9 chairs.
- 7Forty-five markers are shared equally among 5 tables. How many per table?
- 8Find the missing factor: [[7\times n=63]].
Fractions
Section score: ____ / 4
Locate, compare, and build equivalent unit fractions.
- 9Which is greater: [[\frac{3}{8}]] or [[\frac{5}{8}]]?
- 10Name a fraction equivalent to [[\frac{2}{3}]].
- 11A number line from 0 to 1 is split into 6 equal intervals. What number is at the fourth mark after 0?
- 12Order [[\frac{1}{4}]], [[\frac{3}{4}]], and [[\frac{2}{4}]] from least to greatest.
Measurement
Section score: ____ / 4
Work with time, mass, perimeter, and area.
- 13A lesson begins at 9:35 and lasts 50 minutes. When does it end?
- 14Find the perimeter of a rectangle 8 cm by 5 cm.
- 15A rectangle has 4 rows of 7 unit squares. Find its area.
- 16A ribbon is [[2]] meters [[35]] centimeters long. How many centimeters is that?
Geometry and data
Section score: ____ / 4
Classify shapes and interpret a small data set.
- 17Name a quadrilateral with four equal sides and four right angles.
- 18How many right angles does a rectangle have?
- 19The scores are 6, 8, 8, 9, and 9. What score occurs most often?
- 20A pictograph uses one star for [[4]] votes. How many votes do [[6]] stars represent?
Word problems
Section score: ____ / 4
Choose operations and organize two-step reasoning.
- 21Five buses carry 8 students each. Six students leave. How many remain?
- 22A shop has 72 balloons. It sells 29 and then receives 18. How many balloons now?
- 23Twenty-four apples are packed equally into 4 bags. Two more apples are added to each bag. How many apples total now?
- 24A library has [[7]] shelves with [[9]] books each and adds [[15]] books. How many books are there now?
Open the answer key
Equivalent forms and clearly justified open-ended responses should receive credit.
Place value and operations
1. 2,821
2. 1,315
3. 6,500
4. [[4,000+300+5]]
Multiplication and division
5. 56 and 7
6. 6 x 9 = 54
7. 9 markers
8. [[n=9]]
Fractions
9. [[\frac{5}{8}]]
10. Answers vary; for example, [[\frac{4}{6}]]
11. [[\frac{4}{6}]], or [[\frac{2}{3}]]
12. [[\frac{1}{4}<\frac{2}{4}<\frac{3}{4}]]
Measurement
13. 10:25
14. 26 cm
15. 28 square units
16. [[235]] centimeters
Geometry and data
17. A square
18. 4
19. 8 and 9; the data are bimodal
20. [[24]] votes
Word problems
21. 34 students
22. 61 balloons
23. 32 apples
24. [[78]] books
Readiness score
Turn the answer key into a next step.
Count one point for each correct answer. Partial understanding is best noted beside the problem rather than counted as half a point.