Sample questions · Grade 6 math

Sample math questions that show you how students think.

Real items, exactly as they appear in Vecole Studio. Each one is aligned to a specific standard, checked by code, and paired with distractors built from common misconceptions — so every answer choice gives you something to act on.

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Aligned to the exact standard

Every question is generated against one Common Core standard, at the right grade and depth of knowledge — not a loose topic tag.

Wrong answers that mean something

Each distractor is built from a specific student misconception, so a wrong choice tells you why a student is stuck.

Math checked by code

Answers, numbers and figures are computed and verified by code before you see them. AI writes the words; it never invents the math.

Real figures, ready to teach

Tables, nets, dot plots, prisms and balance models are drawn precisely and export cleanly to PDF, QTI and Google Forms.

Question 1 of 5

6.RP.A.3aDOK 1 Multiple choice question with answer

StandardMake tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

DOK 1: Recall & reproduction

Vecole Studio · answer key view

Multiple choice·6.RP.A.3a·DOK 1·~2 min

In a recipe, the ratio of tomatoes to onions is 9:7. A student adds 3 to each entry to scale the recipe and proposes (12, 10). Which explanation is correct?

AAdding the same amount preserves this ratio; both entries increase by 3, so the new pair is equivalent.

BAdding the same amount preserves this ratio; the first entry remains 2 greater than the second entry.

Adding the same amount does not preserve this ratio; multiply both entries by the same scale factor.

DAdding the same amount does not preserve this ratio; multiply only the first entry by the scale factor.

Targeted misconceptions

Each wrong answer is there for a reason. Here's what a student who picks it is probably thinking.

AAdding the same amount preserves this ratio; both entries increase by 3, so the new pair is equivalent.
Equal additions preserve ratios
The student treats adding the same number to both quantities as interchangeable with multiplying both by the same factor, accepting (12, 10).
BAdding the same amount preserves this ratio; the first entry remains 2 greater than the second entry.
Equal differences mean equivalent ratios
The student checks the difference between quantities instead of their multiplicative relationship. Since both 9 − 7 and 12 − 10 equal 2, the student concludes that the ratios are equivalent.
DAdding the same amount does not preserve this ratio; multiply only the first entry by the scale factor.
Scale only the target quantity
The student recognizes that addition is inappropriate but thinks only the quantity with a target value needs scaling. This would change 9 to 27 while leaving 7 unchanged, rather than scaling both quantities.

Why the correct answer works

Equivalent ratios are formed by multiplying both quantities by the same factor. Adding 3 gives 12:10, which simplifies to 6:5, not 9:7. Keeping the difference between the quantities equal to 2 does not preserve their ratio. To scale the recipe from 9 tomatoes to 27 tomatoes, multiply by 3; the number of onions must also be multiplied by 3, giving 21 onions.

Question 2 of 5

6.EE.B.7DOK 1 Select all that apply question with answer

StandardSolve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

DOK 1: Recall & reproduction

Vecole Studio · answer key view

Multi-select·6.EE.B.7·DOK 1·~2 min

Keep both sides equal as you isolate the unknown. Solve by isolating x in the equation. $(2) \times x = 18$ Select all equations that preserve the solution and have a left side that simplifies to x.

Targeted misconceptions

Each wrong answer is there for a reason. Here's what a student who picks it is probably thinking.

A $x = (18) \times (2)$
Multiplying instead of dividing
The student multiplies the right side by the coefficient instead of using division to undo multiplication. This gives x = 36 rather than x = 9.
C $x = (18) - (2)$
Treating a factor as an addend
The student treats 2 * x as though it were x + 2 and subtracts 2 to isolate x. This gives x = 16.

Why the correct answer works

To undo multiplication by 2, divide both sides by 2: (2 * x) / 2 = 18 / 2. The left side simplifies to x, giving x = 9. Thus, both B and D preserve the solution and have a left side that simplifies to x. Multiplying 18 by 2 or subtracting 2 from 18 does not undo multiplication by 2.

Question 3 of 5

6.G.A.2DOK 2 Multiple choice question with answer

StandardFind the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

DOK 2: Skills & concepts

Vecole Studio · answer key view

Multiple choice·6.G.A.2·DOK 2·~3 min

A company packs small cube-shaped gift boxes into a rectangular container. Consider how the size of each box affects the packed volume. The right rectangular prism is completely packed without gaps or overlaps using cubes with edge length $\frac{1}{3}$ cm. Hidden cubes are included. A student counts 12 cubes and reports a volume of 12 cubic centimetres. Which calculation correctly gives the prism volume? Use the labeled dimensions; do not measure the drawing.

A cubic centimetres

B cubic centimetres

cubic centimetres

D cubic centimetres

Targeted misconceptions

Each wrong answer is there for a reason. Here's what a student who picks it is probably thinking.

A $12 \times (\frac{1}{3})^{2} = \frac{4}{3}$ cubic centimetres
This uses the area of a cube face, not its volume.
B $12 \times (\frac{1}{3})^{1} = 4$ cubic centimetres
This uses cube edge length, not cube volume.
D $12 = 12$ cubic centimetres
A fractional cube is smaller than one cubic unit; a count alone is not volume.

Why the correct answer works

The student correctly counts 3 × 2 × 2 = 12 cubes, including hidden cubes, but incorrectly treats each cube as one cubic centimetre. Each cube has volume (1/3) × (1/3) × (1/3) = 1/27 cubic centimetre. Therefore, the prism’s volume is 12 × (1/3)^3 = 4/9 cubic centimetre. This matches multiplying the prism’s dimensions: 1 × (2/3) × (2/3) = 4/9 cubic centimetre. Multiplying the cube count by an edge length or a face area does not give volume.

Question 4 of 5

6.SP.A.3DOK 1 Select all that apply question with answer

StandardRecognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

DOK 1: Recall & reproduction

Vecole Studio · answer key view

Multi-select·6.SP.A.3·DOK 1·~3 min

Two soccer teams, labeled Group A and Group B, record their training-session durations in the dot plots shown. The investigation records practice duration for sessions in minutes. Select all correct comparisons of Groups A and B.

ABoth groups have the same range.

Both groups have the same median.

Group B has the greater range.

DGroup B has the greater median.

Targeted misconceptions

Each wrong answer is there for a reason. Here's what a student who picks it is probably thinking.

ABoth groups have the same range.
Counting distinct values instead of measuring range
The student counts five distinct practice durations in each group and treats this count as the range. Range instead measures the difference between the greatest and least durations.
DGroup B has the greater median.
Using the maximum to compare medians
The student assumes Group B's greater maximum means it also has a greater median. The two middle observations are 8 minutes in both groups.

Why the correct answer works

Each group has eight recorded durations, so its median is the average of the fourth and fifth values in order. Those values are both 8 minutes in each group, so both medians are 8 minutes. Group A’s range is 10 − 6 = 4 minutes, while Group B’s range is 14 − 2 = 12 minutes. Thus, both groups have the same median, but Group B has the greater range. Range measures the difference between the greatest and least values, not the number of distinct values. A greater maximum does not necessarily mean a greater median.

Question 5 of 5

6.G.A.4DOK 2 Select all that apply question with answer

StandardRepresent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

DOK 2: Skills & concepts

Vecole Studio · answer key view

Multi-select·6.G.A.4·DOK 2·~3 min

A bakery is comparing box designs shaped like a closed square pyramid. Each plan is intended to fold into the same closed square pyramid. Each labeled outline is one whole face. Faces must meet along full matching edges without gaps or overlapping interiors. Select all valid nets.

Net A

Net B

CNet C

DNet D

Targeted misconceptions

Each wrong answer is there for a reason. Here's what a student who picks it is probably thinking.

CNet C
Accepting an incomplete net
The student checks that the shown faces can fold together but does not verify that they enclose the solid. A closed square pyramid requires one square base and four triangular faces; this net is missing a required face.
DNet D
Ignoring face dimensions
The student recognizes the expected face shapes but does not check their sizes or matching edge lengths. One attached face is too small to form the required pyramid.

Why the correct answer works

A valid net must include one square base and four triangular faces of the correct sizes. Its faces must meet along full matching edges and fold into a closed pyramid without gaps or overlapping interiors. Nets A and B meet these requirements. Net C is missing a required face, so it cannot close the pyramid. Net D has an attached face that is too small, so its edges do not match the required faces.

Questions shown exactly as generated in Vecole Studio, before teacher edits. Teachers review, edit or regenerate every item before it reaches students. Standard wording: Common Core State Standards for Mathematics, NGA Center and CCSSO, 2010. These are original Vecole questions, not official test items. Want more for one standard? See the standards library.

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Sample math questions that show you how students think.

Aligned to the exact standard

Wrong answers that mean something

Math checked by code

Real figures, ready to teach

Bring a standard. Leave with an assessment like these.

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