For Teachers: Standards-Aligned Math Assessments

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Straight from Vecole Studio: aligned to one standard, math verified by code, and distractors built from the misconceptions students actually have.

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.

See all 5 sample math questions with answers

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