What the standard asks
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g. by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
Standard wording: Common Core State Standards for Mathematics, National Governors Association Center for Best Practices and Council of Chief State School Officers, 2010. The sample questions and explanations below are original Vecole examples, not official Common Core test items.
Typical depth: DOK 1–3, with most classroom items landing at DOK 2.
Sample ratio and rate assessment
Use these 5 examples to discuss the reasoning behind an answer, not just the final number. They sample the standard's strands rather than establish mastery or comprehensive coverage. Answers and explanations are available below without an account; review suitability for your class before use.
6.RP.A.3a · Equivalent-ratio table
Question 1
A paint mixture uses 2 cups of blue paint for every 6 cups of white paint. Complete the table so every batch has the same color. How many cups of white paint belong in the last row?
| Blue paint (cups) | White paint (cups) |
|---|---|
| 2 | 6 |
| 5 | 15 |
| 8 | ? |
6.RP.A.3b · Unit-price comparison
Question 2
Pack A contains 6 notebooks for $15. Pack B contains 10 notebooks for $22. The notebooks are identical and there are no additional charges. Which pack costs less per notebook, and by how much per notebook?
- A. Pack A, by $7.00 per notebook
- B. Pack B, by $0.30 per notebook
- C. Pack A, by $0.30 per notebook
- D. The packs have the same cost per notebook
6.RP.A.3c · Find a percentage
Question 3
A library display has 60 books. Of these, 18 are biographies. What percentage of the books on the display are biographies?
6.RP.A.3c · Find the whole from a percentage
Question 4
A club has sold 24 tickets, which is 30% of all its available tickets. How many tickets were available in total?
6.RP.A.3d · Measurement conversion
Question 5
A ribbon is 4.5 yards long. Use 1 yard = 3 feet to find its length in feet.
Answer key and explanations
Question 1: 24 cups of white paint.
Each cup of blue paint needs 3 cups of white paint because 6 ÷ 2 = 3. For 8 cups of blue paint, 8 × 3 = 24 cups of white paint preserves the ratio. Equivalently, multiply both quantities in the first row by 4.
What to discuss: An answer of 12 may come from preserving the difference of 4 instead of the multiplicative relationship. Ask the student to compare 2/6 and 8/12 before deciding what caused the error.
Back to question 1Question 2: B. Pack B costs $0.30 less per notebook.
Pack A costs $15 ÷ 6 = $2.50 per notebook. Pack B costs $22 ÷ 10 = $2.20 per notebook. The difference is $2.50 − $2.20 = $0.30 per notebook, so Pack B has the lower unit price.
What to discuss: Choice A compares package prices without accounting for the different quantities. Choice C reverses the result after finding the difference. Ask students to label each quotient in dollars per notebook.
Back to question 2Question 3: 30%.
The fraction is 18/60 = 3/10. Expressed per 100, 3/10 = 30/100, so 30% of the books are biographies.
What to discuss: An answer of 18% treats a count as a percentage without using the whole. Ask what 100% represents here and how many books would make up 10%.
Back to question 3Question 4: 80 tickets.
If 30% is 24 tickets, 10% is 24 ÷ 3 = 8 tickets. Then 100% is 8 × 10 = 80 tickets. Check: 30% of 80 is 24.
What to discuss: Multiplying 24 by 0.30 finds 30% of the part, not the whole. Compare this question with the previous one to discuss which quantity represents 100%.
Back to question 4Question 5: 13.5 feet.
Multiply 4.5 yards by 3 feet per yard: 4.5 × 3 = 13.5 feet. The same length has a larger numerical measure in feet because a foot is a smaller unit than a yard.
What to discuss: Dividing by 3 gives 1.5, which applies the conversion in the wrong direction. Ask whether the number of smaller units should be greater or smaller before calculating.
Back to question 5Misconceptions worth testing
These are possible error patterns, not diagnoses based on a single wrong answer. Ask students to explain their reasoning before choosing a follow-up activity.
- Additive thinking — treating 3 : 1 as a difference, so 6 : 4 looks equivalent
- Reversal — mapping the wrong quantity to the wrong role in the ratio
- Part–whole confusion — using 3/4, the first part's share of the total in a 3 : 1 mixture, when the question asks for the ratio of the first part to the second, which is 3/1
- Unit-rate slip — computing a correct rate, then applying it to the wrong quantity
Item types that measure it honestly
- Multiple choice comparing unit rates, with explanations of the alternatives
- Numeric questions about equivalent ratios, percentages, and measurement conversion
- Tables, double number lines, and other representations chosen to fit the reasoning being assessed
Notes for the classroom
- Students who can scale a table forward often cannot work backwards from a total — assess both directions.
- Keep numbers small so the item measures ratio reasoning rather than arithmetic stamina.
- Use a double number line alongside an equation to discuss which quantities and units each number represents.
Create your own math assessment
Explore standards-aligned assessment authoring in Vecole to see how standards, question formats, figures, and teacher review fit together. For digital delivery, learn how to create Google Forms math quizzes and share them through Classroom.
State-specific standards support is available on demand. Contact the Vecole team to confirm your grade, course, and access requirements. No account is needed to read these sample questions.