Free beginning-of-year diagnostic

6th Grade Back-to-School Math Diagnostic

A 24-question 6th grade readiness diagnostic covering fraction and decimal operations, expressions, volume, coordinates, data, and multi-step applications.

24 questions6 skill areasAbout 60 minutesAnswer key and scoring guide
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What this diagnostic measures

The transition to middle school brings ratios, variables, and more independent problem solving. Students are best prepared when fraction and decimal computation is stable enough to support—not interrupt—their reasoning.

Administration note

Do not require mental calculation for every problem. Scratch work is expected. Pay attention to whether the student lines up decimal places, finds common denominators, and labels quantities with units.

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.

Whole numbers and expressions

Section score: ____ / 4

Use the order of operations and multi-digit algorithms.

  1. 1Find 3,406 x 28.
  2. 2Find 8,736 / 32.
  3. 3Evaluate 7 + 4 x (13 - 8).
  4. 4Evaluate [[48\div(2^{2}+2)+3(5-1)]].

Decimal operations

Section score: ____ / 4

Add, subtract, multiply, and divide decimals accurately.

  1. 5Find 14.86 + 7.095.
  2. 6Find 30 - 8.647.
  3. 7Find 4.2 x 0.35.
  4. 8Find [[15.75\div3.5]].

Fraction operations

Section score: ____ / 4

Compute with unlike denominators and interpret multiplication and division.

  1. 9Find [[\frac{2}{3}]] + [[\frac{5}{8}]].
  2. 10Find 3 [[\frac{1}{4}]] - 1 [[\frac{5}{6}]].
  3. 11Find [[\frac{5}{6}]] x [[\frac{9}{10}]].
  4. 12Find [[2\frac{1}{4}\div\frac{3}{8}]].

Coordinates and geometry

Section score: ____ / 4

Use the coordinate plane and volume formulas.

  1. 13In which quadrant is (-4, 7)?
  2. 14Find the distance between (2, 3) and (2, -5).
  3. 15Find the volume of a prism measuring 7 cm by 4 cm by 2.5 cm.
  4. 16Find the area of a triangle with base [[13]] cm and height [[8]] cm.

Data and patterns

Section score: ____ / 4

Summarize a data set and describe a numerical rule.

  1. 17Find the mean of 7, 9, 10, 10, and 14.
  2. 18Find the median of 4, 6, 8, 11, 13, 15.
  3. 19The rule is y = 3x - 2. Find y when x = 6.
  4. 20The values are [[4,6,6,9,15]]. Find the range and mode.

Applications

Section score: ____ / 4

Use rates, fractions, and equations in context.

  1. 21Five pounds of apples cost $11.25. Find the cost per pound.
  2. 22A 16-gallon tank is [[\frac{3}{8}]] full. How many gallons are in it?
  3. 23A number divided by 5, then increased by 7, equals 15. Find the number.
  4. 24A recipe uses [[2\frac{1}{2}]] cups for [[4]] batches. How many cups are needed for [[10]] batches?
Open the answer key

Equivalent forms and clearly justified open-ended responses should receive credit.

Whole numbers and expressions

1. 95,368

2. 273

3. 27

4. [[20]]

Decimal operations

5. 21.955

6. 21.353

7. 1.47

8. [[4.5]]

Fraction operations

9. 1 [[\frac{7}{24}]]

10. 1 [[\frac{5}{12}]]

11. [[\frac{3}{4}]]

12. [[6]]

Coordinates and geometry

13. Quadrant II

14. 8 units

15. 70 cubic cm

16. [[52]] square cm

Data and patterns

17. 10

18. 9.5

19. 16

20. Range [[11]]; mode [[6]]

Applications

21. $2.25

22. 6 gallons

23. 40

24. [[6\frac{1}{4}]] cups

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.

All back-to-school diagnostics5th Grade Back-to-School Math Diagnostic7th Grade Back-to-School Math DiagnosticFull-length summer review packetsTarget one prerequisite skill