AssessGen — QC Review

#1 G6RP-001 6.RP.A.1 DOK 1 PASS ▼

Stem: A recipe uses 3 cups of flour and 2 cups of sugar. Which ratio correctly describes the relationship between cups of flour and cups of sugar?

Standard Alignment PASS 6.RP.A.1 requires students to understand the concept of a ratio and use ratio language to describe a relationship between two quantities. The item directly asks students to identify the correct ratio of flour to sugar given two quantities, making the standard the primary skill tested.

DOK Accuracy PASS DOK 1 is appropriate. The item requires single-step recall of what a ratio is and identification of the correct order of quantities as stated in the problem. No interpretation, analysis, or multi-step reasoning is required.

Answer Correctness PASS The answer key D (3 to 2) is correct. The problem specifies flour to sugar, which is 3 cups to 2 cups. All distractors are definitively wrong: A (2 to 3) is the reversed order, B (3 to 5) is a part-to-whole ratio using the total, and C (5 to 2) is a part-to-whole ratio with reversed order.

Distractor Quality PASS All three distractors reflect documented and specific student misconceptions: A targets order reversal errors, B targets confusion between part-to-part and part-to-whole ratios, and C targets both errors simultaneously. No distractor is implausible, trivially eliminated, or arguable as correct.

Bias & Readability PASS Language is simple and appropriate for Grade 6. The context (a recipe with flour and sugar) is neutral, culturally inclusive, and free of bias. No references to violence, religion, politics, or socioeconomic status. No names are used. Vocabulary is grade-appropriate and math-relevant.

#2 G6RP-002 6.RP.A.1 DOK 1 PASS ▼

Stem: A recipe uses 3 cups of flour for every 2 cups of sugar. Complete the statement below by selecting the correct numbers from each dropdown menu. The ratio of cups of flour to cups of sugar is [blank_1] to [blank_2].

Standard Alignment PASS 6.RP.A.1 requires students to understand the concept of a ratio and use ratio language to describe a relationship between two quantities. The item directly tests this by asking students to identify the correct ratio of flour to sugar in the stated order, making the standard the primary and exclusive skill assessed.

DOK Accuracy PASS DOK 1 is appropriate. The item requires single-step recall and recognition: students read the given quantities and reproduce them as a ratio in the specified order. No interpretation, analysis, or multi-step reasoning is required.

Answer Correctness PASS The problem states 3 cups of flour for every 2 cups of sugar. The ratio of flour to sugar is 3 to 2. The answer key (blank_1: 3, blank_2: 2) is correct. No distractor in either blank can be argued as a valid alternative answer for the stated ratio.

Distractor Quality PASS Each distractor maps to a documented student misconception. Choice '2' in blank_1 (and '3' in blank_2) captures order-reversal of the ratio. Choice '5' in both blanks reflects additive thinking (3 + 2 = 5) rather than ratio reasoning. Choice '1' in both blanks reflects an attempt to unit-rate or over-simplify the ratio. All distractors are plausible errors and none is arguable as correct.

Bias & Readability PASS The stem uses simple, grade-appropriate language. The context (a recipe with flour and sugar) is neutral, culturally familiar, and free from bias related to socioeconomic status, politics, religion, or violence. No student names are used, eliminating naming bias concerns. Vocabulary is well within Grade 6 reading level.

#3 G6RP-002 6.RP.A.1 DOK 1 PASS ▼

Stem: A recipe uses 3 cups of flour for every 2 cups of sugar. Complete the statement below by selecting the correct numbers from each dropdown menu. The ratio of cups of flour to cups of sugar is [blank_1] to [blank_2].

Standard Alignment PASS 6.RP.A.1 requires students to understand the concept of a ratio and use ratio language to describe a relationship between two quantities. The item directly tests this by asking students to identify the correct ratio of flour to sugar in the stated order, making the standard the primary and exclusive skill assessed.

DOK Accuracy PASS DOK 1 is appropriate. The item requires single-step recall and recognition: students read the given quantities and reproduce them as a ratio in the specified order. No interpretation, analysis, or multi-step reasoning is required.

Answer Correctness PASS The problem states 3 cups of flour for every 2 cups of sugar. The ratio of flour to sugar is 3 to 2. The answer key (blank_1: 3, blank_2: 2) is correct. No distractor in either blank can be argued as a valid alternative answer for the stated ratio.

Distractor Quality PASS Each distractor maps to a documented student misconception. Choice '2' in blank_1 (and '3' in blank_2) captures order-reversal of the ratio. Choice '5' in both blanks reflects additive thinking (3 + 2 = 5) rather than ratio reasoning. Choice '1' in both blanks reflects an attempt to unit-rate or over-simplify the ratio. All distractors are plausible errors and none is arguable as correct.

Bias & Readability PASS The stem uses simple, grade-appropriate language. The context (a recipe with flour and sugar) is neutral, culturally familiar, and free from bias related to socioeconomic status, politics, religion, or violence. No student names are used, eliminating naming bias concerns. Vocabulary is well within Grade 6 reading level.

#4 G6RP-003 6.RP.A.1 DOK 2 FAIL HUMAN REVIEW ▼

Stem: A school garden has 8 tomato plants and 5 pepper plants. Which statement correctly describes a ratio relationship in this garden?

Standard Alignment PASS The item directly tests 6.RP.A.1 — understanding ratio concepts and correctly describing ratio relationships between two quantities. Identifying and interpreting a correct ratio statement from a real-world context is the primary skill tested.

DOK Accuracy FAIL This item is labeled DOK 2, but it functions at DOK 1. The student is asked to identify which ratio statement is numerically accurate given two explicit counts (8 tomato, 5 pepper). No interpretation, comparison of relationships, or connection between ideas is required — only direct verification of part-to-part and part-to-whole counts. A DOK 2 item for 6.RP.A.1 would require the student to use a ratio relationship to reason about a situation (e.g., determine a missing quantity, explain what a ratio means in context, or compare two ratio relationships). This item should be reclassified as DOK 1.

Answer Correctness PASS Independently verified: total plants = 8 + 5 = 13. Option C states the ratio of tomato plants to total plants is 8 to 13 — correct. Option A states pepper to tomato is 8 to 5 — incorrect, it is 5 to 8. Option B states total to pepper is 5 to 13 — incorrect, it is 13 to 5. Option D states pepper to total is 5 to 8 — incorrect, the total is 13, not 8. Answer key C is correct and all distractors are definitively wrong.

Distractor Quality PASS Each distractor targets a specific, documented misconception. Option A targets order-reversal in a part-to-part ratio. Option B targets order-reversal in a part-to-whole ratio. Option D targets the misconception of substituting one part for the whole when forming a part-to-whole ratio. All distractors are plausible to a student with incomplete mastery and none are ambiguously correct.

Bias & Readability PASS Language is clear and appropriate for Grade 6. The context (school garden with tomato and pepper plants) is neutral, culturally inclusive, and free of bias. No references to violence, religion, politics, or socioeconomic status. No complex non-math vocabulary is used.

Revision Notes: DOK RECLASSIFICATION REQUIRED: This item tests straightforward identification of a correct ratio statement and operates at DOK 1 (single-step verification of counts), not DOK 2. To retain a DOK 2 designation, Myra must redesign the item so that it requires interpretation or connection of ideas. Options include: (1) presenting a described ratio and asking the student to explain what it means or identify an equivalent scenario, (2) providing an incomplete ratio relationship and requiring the student to determine a missing value using ratio reasoning, or (3) presenting two ratio claims about the same garden and asking which is valid and why. Alternatively, reclassify the item as DOK 1 if the current format is intentional.

#5 G6RP-003 6.RP.A.1 DOK 2 FAIL HUMAN REVIEW ▼

Stem: A school garden has 8 tomato plants and 5 pepper plants. Which statement correctly describes a ratio relationship in this garden?

Standard Alignment PASS The item directly tests 6.RP.A.1 — understanding ratio concepts and correctly describing ratio relationships between two quantities. Identifying and interpreting a correct ratio statement from a real-world context is the primary skill tested.

DOK Accuracy FAIL This item is labeled DOK 2, but it functions at DOK 1. The student is asked to identify which ratio statement is numerically accurate given two explicit counts (8 tomato, 5 pepper). No interpretation, comparison of relationships, or connection between ideas is required — only direct verification of part-to-part and part-to-whole counts. A DOK 2 item for 6.RP.A.1 would require the student to use a ratio relationship to reason about a situation (e.g., determine a missing quantity, explain what a ratio means in context, or compare two ratio relationships). This item should be reclassified as DOK 1.

Answer Correctness PASS Independently verified: total plants = 8 + 5 = 13. Option C states the ratio of tomato plants to total plants is 8 to 13 — correct. Option A states pepper to tomato is 8 to 5 — incorrect, it is 5 to 8. Option B states total to pepper is 5 to 13 — incorrect, it is 13 to 5. Option D states pepper to total is 5 to 8 — incorrect, the total is 13, not 8. Answer key C is correct and all distractors are definitively wrong.

Distractor Quality PASS Each distractor targets a specific, documented misconception. Option A targets order-reversal in a part-to-part ratio. Option B targets order-reversal in a part-to-whole ratio. Option D targets the misconception of substituting one part for the whole when forming a part-to-whole ratio. All distractors are plausible to a student with incomplete mastery and none are ambiguously correct.

Bias & Readability PASS Language is clear and appropriate for Grade 6. The context (school garden with tomato and pepper plants) is neutral, culturally inclusive, and free of bias. No references to violence, religion, politics, or socioeconomic status. No complex non-math vocabulary is used.

Revision Notes: DOK RECLASSIFICATION REQUIRED: This item tests straightforward identification of a correct ratio statement and operates at DOK 1 (single-step verification of counts), not DOK 2. To retain a DOK 2 designation, Myra must redesign the item so that it requires interpretation or connection of ideas. Options include: (1) presenting a described ratio and asking the student to explain what it means or identify an equivalent scenario, (2) providing an incomplete ratio relationship and requiring the student to determine a missing value using ratio reasoning, or (3) presenting two ratio claims about the same garden and asking which is valid and why. Alternatively, reclassify the item as DOK 1 if the current format is intentional.

#6 G6RP-004 6.RP.A.1 DOK 2 PASS ▼

Stem: A school garden has 8 tomato plants and 6 pepper plants. Use the garden to answer each question below. Part A: What is the ratio of pepper plants to tomato plants? Select the correct values to complete the ratio in lowest terms. The ratio of pepper plants to tomato plants is [dropdown_1] to [dropdown_2]. Part B: What is the ratio of tomato plants to the total number of plants? Select the correct values to complete the ratio in lowest terms. The ratio of tomato plants to total plants is [dropdown_3] to [dropdown_4].

Standard Alignment PASS 6.RP.A.1 requires students to understand the concept of a ratio and use ratio language to describe a relationship between two quantities. Both parts directly assess this: Part A asks for a part-to-part ratio (pepper:tomato) and Part B asks for a part-to-whole ratio (tomato:total). Simplifying to lowest terms is an appropriate extension of ratio understanding. The standard is the primary skill tested throughout.

DOK Accuracy PASS DOK 2 is appropriate. Students must interpret which quantities form each ratio, determine the correct order based on the question phrasing, compute the total for Part B, and reduce both ratios using GCF. This requires connecting multiple ideas (ratio order, part-to-whole vs. part-to-part, simplification) rather than simple recall or a single-step procedure, which would be DOK 1.

Answer Correctness PASS Part A: pepper:tomato = 6:8; GCF(6,8) = 2; reduced = 3:4. dropdown_1 = 3, dropdown_2 = 4. Correct. Part B: tomato:total = 8:14; GCF(8,14) = 2; reduced = 4:7. dropdown_3 = 4, dropdown_4 = 7. Correct. All stated answer key values are verified. No distractor in any dropdown can be combined to form an alternate correct answer for its respective part.

Distractor Quality PASS Distractors reflect documented student misconceptions. Dropdown_1/2 include 6 and 8 (failure to simplify) and 4 and 3 (reversed ratio order). Dropdown_3 includes 6 (confusing pepper count for tomato count), 7 (plausible miscalculation), and 8 (unreduced numerator). Dropdown_4 includes 6 (using only pepper plants as denominator), 8 (repeating the numerator), and 14 (failure to simplify). All distractors are plausible and grounded in real errors described in the rationale.

Bias & Readability PASS Language is clear and appropriate for Grade 6. Vocabulary (garden, tomato plants, pepper plants, ratio, lowest terms) is grade-level and relevant to the math standard. The context of a school garden is neutral, culturally inclusive, and free of references to violence, religion, politics, or socioeconomic status. No names are used, eliminating any naming bias concern.

#7 G6RP-005 6.RP.A.2 DOK 1 PASS ▼

Stem: A car travels 150 miles using 5 gallons of gas. What is the unit rate in miles per gallon?

Standard Alignment PASS 6.RP.A.2 addresses understanding the concept of a unit rate a/b associated with a ratio a:b. This item directly and exclusively tests that skill by asking students to compute a unit rate (miles per gallon) from a given ratio (150 miles : 5 gallons). The standard is the primary skill tested.

DOK Accuracy PASS DOK 1 is appropriate. The item requires a single, direct computation (150 ÷ 5) with no interpretation, multi-step reasoning, or analysis beyond applying a straightforward procedure to find a unit rate.

Answer Correctness PASS 150 ÷ 5 = 30 miles per gallon. Answer key B is correct. All distractors are definitively wrong: A (0.03) = 5 ÷ 150, C (750) = 150 × 5, D (145) = 150 − 5. None of the distractors can be argued as correct.

Distractor Quality PASS All three distractors map to specific, documented student misconceptions: A reflects ratio inversion (dividing smaller by larger), C reflects operation confusion (multiplying instead of dividing), and D reflects operation confusion (subtracting instead of dividing). Each is plausible for a student who has not mastered the standard, and none is obviously absurd in the context of distance/fuel problems.

Bias & Readability PASS Language is clear and at or below Grade 6 reading level. The context (car travel and fuel efficiency) is culturally neutral, universally relatable, and free of bias related to names, socioeconomic status, religion, or politics. No extraneous vocabulary is introduced.

#8 G6RP-005 6.RP.A.2 DOK 1 PASS ▼

Stem: A car travels 150 miles using 5 gallons of gas. What is the unit rate in miles per gallon?

Standard Alignment PASS 6.RP.A.2 addresses understanding the concept of a unit rate a/b associated with a ratio a:b. This item directly and exclusively tests that skill by asking students to compute a unit rate (miles per gallon) from a given ratio (150 miles : 5 gallons). The standard is the primary skill tested.

DOK Accuracy PASS DOK 1 is appropriate. The item requires a single, direct computation (150 ÷ 5) with no interpretation, multi-step reasoning, or analysis beyond applying a straightforward procedure to find a unit rate.

Answer Correctness PASS 150 ÷ 5 = 30 miles per gallon. Answer key B is correct. All distractors are definitively wrong: A (0.03) = 5 ÷ 150, C (750) = 150 × 5, D (145) = 150 − 5. None of the distractors can be argued as correct.

Distractor Quality PASS All three distractors map to specific, documented student misconceptions: A reflects ratio inversion (dividing smaller by larger), C reflects operation confusion (multiplying instead of dividing), and D reflects operation confusion (subtracting instead of dividing). Each is plausible for a student who has not mastered the standard, and none is obviously absurd in the context of distance/fuel problems.

Bias & Readability PASS Language is clear and at or below Grade 6 reading level. The context (car travel and fuel efficiency) is culturally neutral, universally relatable, and free of bias related to names, socioeconomic status, religion, or politics. No extraneous vocabulary is introduced.

#9 G6RP-006 6.RP.A.2 DOK 1 PASS ▼

Stem: A car travels 150 miles using 6 gallons of gas. The unit rate is _____ miles per gallon.

Standard Alignment PASS 6.RP.A.2 requires students to understand unit rate concepts and compute a unit rate from a ratio. The item directly asks students to find a unit rate (miles per gallon) from a given ratio (150 miles / 6 gallons), making the standard the primary and exclusive skill tested.

DOK Accuracy PASS DOK 1 is appropriate. The task requires a single, direct computation (150 ÷ 6 = 25) with no interpretation, multi-step reasoning, or analysis. The ratio relationship and operation needed are unambiguous and explicitly implied by the context.

Answer Correctness PASS 150 ÷ 6 = 25 is verified correct. The answer key of '25' is accurate. As a cloze item with a single numeric answer, there are no distractors to evaluate for correctness conflicts.

Distractor Quality PASS This is a cloze/fill-in-the-blank item with no distractors. The rationale documents plausible misconceptions (inverting the ratio yielding ~0.04, and adding instead of dividing yielding 156), which confirms the item was designed with student error patterns in mind. Distractor quality check is not applicable but no concerns are raised.

Bias & Readability PASS Language is clear, concise, and appropriate for Grade 6. The context of a car traveling miles per gallon is neutral, universally relatable, and free of bias. No culturally sensitive content, complex vocabulary unrelated to the standard, or socioeconomic indicators are present.

#10 G6RP-007 6.RP.A.2 DOK 2 PASS ▼

Stem: A car travels 180 miles using 6 gallons of gas. Which statement correctly describes a unit rate for this situation, and what does it mean?

Standard Alignment PASS 6.RP.A.2 addresses understanding the concept of a unit rate a/b associated with a ratio a:b, and using rate language. The stem directly requires the student to identify the correct unit rate and interpret its meaning in context (miles per gallon), making the standard the primary skill tested.

DOK Accuracy PASS DOK 2 is appropriate. The item requires two connected cognitive steps: (1) computing the unit rate via division (180 ÷ 6 = 30), and (2) interpreting what that rate means in context. It also demands that the student distinguish between miles-per-gallon and gallons-per-mile framings, which requires conceptual understanding beyond simple recall or formula application.

Answer Correctness PASS Answer key B is correct. 180 ÷ 6 = 30 miles per gallon, and the interpretation ('30 miles for every 1 gallon') is accurate. All distractors are definitively wrong: A states 6 mpg (the given gallon quantity misread as a rate); C inverts the ratio and states 30 gallons per mile (a non-sensical and incorrect inversion); D uses the raw total miles (180) as the unit rate without dividing.

Distractor Quality PASS Each distractor maps to a documented student misconception. A reflects confusing a given quantity (6 gallons) with the unit rate. C reflects ratio inversion (placing gallons in the numerator instead of miles), a common error when students are uncertain which quantity is the 'per 1' denominator. D reflects failure to perform the division step, treating the total as the unit rate. All three are plausible errors and none could reasonably be argued correct.

Bias & Readability PASS The language is straightforward and appropriate for Grade 6. The context (car fuel efficiency) is neutral, universally familiar, and free of socioeconomic, cultural, religious, or political connotations. No complex non-mathematical vocabulary is present. No names or culturally loaded references are used.

#11 G6RP-008 6.RP.A.2 DOK 3 PASS ▼

Stem: A smoothie shop uses 3 cups of frozen fruit for every 2 cups of yogurt in its base recipe. A student claims that the unit rate of frozen fruit per cup of yogurt is 1.5 cups of frozen fruit per cup of yogurt. Select ALL statements that correctly support or extend the student's reasoning about this ratio relationship.

Standard Alignment PASS The item directly tests 6.RP.A.2 — understanding unit rates associated with ratios of the form a:b. The stem, all options, and the rationale center on computing, interpreting, and extending a unit rate from a given ratio. The standard is the primary and exclusive skill tested.

DOK Accuracy PASS DOK 3 is appropriate. Students must evaluate multiple reasoning statements about a ratio relationship, distinguish valid from invalid mathematical claims, and reason about the conceptual meaning of unit rates (symmetry, scaling, equivalence). This requires multi-step reasoning and justification beyond simple computation or single-concept application.

Answer Correctness PASS All three keyed answers are verified correct. A: 3 ÷ 2 = 1.5 — correct unit rate definition. C: 10 × 1.5 = 15 — correct proportional scaling. D: 3:2 and 1.5:1 are equivalent representations of the same ratio — correct. Both distractors are definitively wrong: B incorrectly states the reciprocal unit rate is also 1.5 (it is 2 ÷ 3 ≈ 0.667); E incorrectly constrains total batch size to multiples of 1.5, which is not a property of unit rates.

Distractor Quality PASS Both distractors reflect well-documented Grade 6 misconceptions. Option B targets the symmetric unit rate misconception — students conflate the two unit rates derived from the same ratio. Option E targets overgeneralization of the unit rate as a constraint on totals rather than a per-unit relationship. Neither distractor is implausible, trivially wrong, or arguable as correct.

Bias & Readability PASS The smoothie shop context is neutral, grade-appropriate, and culturally inclusive with no references to names, socioeconomic status, religion, or politics. Vocabulary is accessible for Grade 6 (unit rate, ratio, batch, multiply). Mathematical terminology used is appropriate and directly tied to the standard being assessed.

#12 G6RP-009 6.RP.A.3 DOK 2 FAIL HUMAN REVIEW ▼

Stem: A car uses 5 gallons of gas to travel 150 miles. At this same rate, how many gallons of gas will the car need to travel 390 miles?

Standard Alignment PASS The item directly tests 6.RP.A.3 by requiring the student to use a ratio/rate (5 gallons per 150 miles) to solve a proportional relationship problem. Ratio and proportional reasoning is the primary and dominant skill tested.

DOK Accuracy FAIL This item is labeled DOK 2, but it functions at DOK 1. The task is a single-step, direct application of a unit rate: divide 150 by 5 to get 30 mpg, then divide 390 by 30. There is no interpretation, comparison of representations, or connection of two distinct ideas required. The procedure is straightforward and mechanical, matching DOK 1 (apply a procedure/formula). DOK 2 would require the student to, for example, compare two rates, determine which is better, or interpret a table/graph in context.

Answer Correctness PASS Independently verified: unit rate = 150 ÷ 5 = 30 miles per gallon; 390 ÷ 30 = 13 gallons. Answer key C (13 gallons) is correct. All distractors — A (11), B (15), D (65) — are definitively incorrect.

Distractor Quality FAIL Distractor A (11 gallons) is poorly grounded. The rationale is internally inconsistent and implausible: it first describes an informal skip-count error, then pivots to a different mechanism (390 ÷ 35 ≈ 11.1), which itself is an unlikely and contrived error path. No realistic student misconception cleanly produces 11. A credible distractor should map to a single, clearly defined error. Distractors B and D are well-constructed and grounded in real misconceptions (additive reasoning and proportion cross-multiplication with wrong divisor, respectively). Distractor A must be replaced with one tied to a coherent, realistic error — for example, a student who inverts the rate (150 ÷ 390 × 5 ≈ 1.9, rounded) or misreads the ratio as 150 gallons per 5 miles and computes 390 × (5/150) = 13 — or a value like 12 (computing 360 ÷ 30, subtracting one group of 30 prematurely).

Bias & Readability PASS The stem is clear, concise, and appropriate for Grade 6 reading level. Context (car and gas mileage) is culturally neutral and widely accessible. No names, sensitive topics, or biased content are present. Vocabulary is grade-appropriate.

Revision Notes: Two issues require revision before this item can be approved: 1. DOK LEVEL (Critical): Downgrade the DOK label from 2 to 1. The item requires a single, direct procedural application of a unit rate with no interpretation, multi-step reasoning across concepts, or analysis. If a DOK 2 item is required for this standard, revise the stem to demand higher cognitive engagement — for example, present a table of two different cars' fuel data and ask the student to determine which car travels farther on 8 gallons, requiring comparison and interpretation across representations. 2. DISTRACTOR A — Replace 11 gallons (Moderate): The misconception rationale for Distractor A is contradictory and does not describe a single coherent student error. Remove 11 gallons and replace it with a value derived from a clean, realistic misconception. Suggested replacement: '10 gallons' — produced when a student applies additive reasoning only to the gas quantity (doubles 5 to get 10 because 390 is 'roughly double' 150, ignoring the exact multiplicative scalar), or '7 gallons' — produced when a student subtracts the original quantities (390 − 150 = 240 extra miles, then 240 ÷ 150 × 5 ≈ 8, misapplied). Select whichever misconception Myra can document cleanly, and write a single-path, unambiguous rationale for it.

#13 G6RP-009 6.RP.A.3 DOK 2 FAIL HUMAN REVIEW ▼

Stem: A car uses 5 gallons of gas to travel 150 miles. At this same rate, how many gallons of gas will the car need to travel 390 miles?

Standard Alignment PASS The item directly tests 6.RP.A.3 by requiring the student to use a ratio/rate (5 gallons per 150 miles) to solve a proportional relationship problem. Ratio and proportional reasoning is the primary and dominant skill tested.

DOK Accuracy FAIL This item is labeled DOK 2, but it functions at DOK 1. The task is a single-step, direct application of a unit rate: divide 150 by 5 to get 30 mpg, then divide 390 by 30. There is no interpretation, comparison of representations, or connection of two distinct ideas required. The procedure is straightforward and mechanical, matching DOK 1 (apply a procedure/formula). DOK 2 would require the student to, for example, compare two rates, determine which is better, or interpret a table/graph in context.

Answer Correctness PASS Independently verified: unit rate = 150 ÷ 5 = 30 miles per gallon; 390 ÷ 30 = 13 gallons. Answer key C (13 gallons) is correct. All distractors — A (11), B (15), D (65) — are definitively incorrect.

Distractor Quality FAIL Distractor A (11 gallons) is poorly grounded. The rationale is internally inconsistent and implausible: it first describes an informal skip-count error, then pivots to a different mechanism (390 ÷ 35 ≈ 11.1), which itself is an unlikely and contrived error path. No realistic student misconception cleanly produces 11. A credible distractor should map to a single, clearly defined error. Distractors B and D are well-constructed and grounded in real misconceptions (additive reasoning and proportion cross-multiplication with wrong divisor, respectively). Distractor A must be replaced with one tied to a coherent, realistic error — for example, a student who inverts the rate (150 ÷ 390 × 5 ≈ 1.9, rounded) or misreads the ratio as 150 gallons per 5 miles and computes 390 × (5/150) = 13 — or a value like 12 (computing 360 ÷ 30, subtracting one group of 30 prematurely).

Bias & Readability PASS The stem is clear, concise, and appropriate for Grade 6 reading level. Context (car and gas mileage) is culturally neutral and widely accessible. No names, sensitive topics, or biased content are present. Vocabulary is grade-appropriate.

Revision Notes: Two issues require revision before this item can be approved: 1. DOK LEVEL (Critical): Downgrade the DOK label from 2 to 1. The item requires a single, direct procedural application of a unit rate with no interpretation, multi-step reasoning across concepts, or analysis. If a DOK 2 item is required for this standard, revise the stem to demand higher cognitive engagement — for example, present a table of two different cars' fuel data and ask the student to determine which car travels farther on 8 gallons, requiring comparison and interpretation across representations. 2. DISTRACTOR A — Replace 11 gallons (Moderate): The misconception rationale for Distractor A is contradictory and does not describe a single coherent student error. Remove 11 gallons and replace it with a value derived from a clean, realistic misconception. Suggested replacement: '10 gallons' — produced when a student applies additive reasoning only to the gas quantity (doubles 5 to get 10 because 390 is 'roughly double' 150, ignoring the exact multiplicative scalar), or '7 gallons' — produced when a student subtracts the original quantities (390 − 150 = 240 extra miles, then 240 ÷ 150 × 5 ≈ 8, misapplied). Select whichever misconception Myra can document cleanly, and write a single-path, unambiguous rationale for it.

#14 G6RP-010 6.RP.A.3 DOK 2 PASS ▼

Stem: Each situation in the left column involves a unit rate or percent. Match each situation to the value that correctly solves it.

Standard Alignment PASS 6.RP.A.3 addresses using ratio and rate reasoning to solve real-world problems, including unit rates and percent. All three situations directly require this reasoning: computing cost per pound (unit rate), miles per gallon (unit rate), and sale price using a percent discount. The standard is the primary skill tested across all three prompts, not incidental.

DOK Accuracy PASS DOK 2 is appropriate. Each situation requires students to interpret a real-world context, select the correct operation (division for unit rates; multi-step percent calculation for Item 3), and reason about which value matches — not mere recall or formula plug-in. Item 3 in particular demands a two-step process (find discount, then subtract), and the match format adds a layer of comparative reasoning across all three items, collectively placing the item at DOK 2.

Answer Correctness PASS Item 1: $3.75 ÷ 5 = $0.75 → Option A. Correct. Item 2: 240 ÷ 8 = 30 mpg → Option C. Correct. Item 3: 25% × $80 = $20 discount; $80 − $20 = $60 → Option E. Correct. All three answer keys verified independently. No distractor among the right-column options (B: $0.65, D: 25 mpg) is defensibly correct for any of the three prompts.

Distractor Quality PASS Option B ($0.65 per pound) reflects a plausible ratio-reversal or arithmetic error (e.g., $3.25 ÷ 5 or $3.75 ÷ 4 rounding variants), documented in ratio reasoning research. Option D (25 mpg) reflects dividing a rounded or incorrect mileage figure (e.g., 200 ÷ 8), a real misconception around estimation errors in rate problems. Both extra distractors are grounded in specific, documented student errors and are not obviously absurd. The item correctly notes that $20 (the discount amount alone) is not offered, requiring students to complete the full two-step percent process.

Bias & Readability PASS Language is straightforward and grade-appropriate for Grade 6. Contexts (grocery store, car travel, jacket sale) are familiar, culturally neutral, and free of references to violence, religion, politics, or socioeconomic bias. No named characters are used, eliminating naming-bias concerns. Vocabulary (cost per pound, miles per gallon, sale price, percent off) is directly tied to the mathematical standard and appropriate for this grade level.

#15 G6RP-012 6.RP.A.3 DOK 4 FAIL HUMAN REVIEW ▼

Stem: A community garden is planning three new vegetable plots. The table below shows data for each plot. [TABLE: Four-column table with the following data — Headers: Plot | Area (sq ft) | Water Used Per Week (gal) | Seed Cost (total $) | Seed Packets Row 1: A | 60 | 15 | $10 | 4 Row 2: B | 100 | 30 | $20 | 8 Row 3: C | 150 | 48 | $24 | 8] Use the data in the table to complete all three parts below by dragging each token to the correct drop zone. --- PART A: Rank the three plots from LOWEST to HIGHEST water use per square foot. --- [Three drop zones labeled: 'Lowest Rate', 'Middle Rate', 'Highest Rate'] --- PART B: Drag each statement about seed cost per packet to the correct category. --- [Two drop zones labeled: 'SUPPORTED by the data' and 'NOT SUPPORTED by the data'] --- PART C: The garden plans to expand each plot by 25%. Drag each expanded plot's weekly water use to the correct budget category. --- [Two drop zones labeled: 'Expansion stays within 150-gallon weekly budget' and 'Expansion exceeds 150-gallon weekly budget']

Standard Alignment PASS All three parts require computing and applying unit rates (water per sq ft, cost per packet, proportional scaling), which directly tests 6.RP.A.3. The standard is the primary skill throughout; no incidental standards dominate.

DOK Accuracy PASS DOK 4 is appropriate. The item requires students to compute multiple unit rates across three distinct contexts, evaluate the truth of comparative claims, apply proportional reasoning to a real-world planning scenario, and sort conclusions — requiring strategic thinking, modeling, and multi-step justification across all three parts.

Answer Correctness FAIL The answer key contains two critical errors. First, the stem's Part C drop zones reference a '150-gallon weekly budget,' but the rationale acknowledges this threshold was post-hoc revised to 50 gallons per plot to achieve meaningful separation. The stem as written still says '150-gallon weekly budget,' under which ALL three expanded plots (18.75, 37.5, and 60 gal/week) fall well within budget — making token10 incorrectly placed in 'Exceeds budget.' The stem and answer key are internally contradictory. Second, for Part B, the rationale shows extensive self-correction and uncertainty about token6. The final adopted version asserts token6 reads 'Plot C has a higher seed cost per packet than Plot A' (SUPPORTED), but the options list still shows token6 as 'Plot C has a lower seed cost per packet than Plot A' (NOT SUPPORTED). The answer key places token6 in SUPPORTED, which is wrong for the token text as written in the options. These are definitive answer key errors.

Distractor Quality FAIL Part B has a design flaw regardless of which version of token6 is used. If token6 reads 'Plot C has a lower seed cost per packet than Plot A' (as written in the options), then all four tokens belong in NOT SUPPORTED, leaving the SUPPORTED drop zone intentionally empty. The rationale acknowledges this is a 'trick question' risk and attempts a fix, but the fix was not carried through to the options list. An empty correct drop zone is not a valid distractor design for a standardized assessment item — students cannot verify whether the empty zone reflects their correct analysis or an error. This ambiguity is a distractor quality failure.

Bias & Readability PASS Language is appropriate for Grade 6. Vocabulary is limited to math-relevant terms (area, water use, seed cost, budget). Context is a community garden — neutral, inclusive, and free of socioeconomic, political, religious, or violent references. No names are used. No bias concerns identified.

Revision Notes: Two items require correction before this item can pass review: 1. ANSWER KEY / STEM MISMATCH IN PART C: The stem currently states a '150-gallon weekly budget.' Under that threshold, all three expanded plot values (18.75, 37.5, and 60 gal/week) are within budget, making the Part C sort trivial and token10's placement in 'Exceeds budget' incorrect. Myra must choose one of two fixes: (a) Change the stem's budget threshold from 150 gallons to 50 gallons per plot per week, so that token8 (18.75) and token9 (37.5) fall within budget and token10 (60) exceeds it — then update the drop zone label accordingly; OR (b) Redesign the Part C water values so that at least one expanded plot genuinely exceeds 150 gal/week under the original threshold. Option (a) is preferred as it requires the least reconstruction. 2. TOKEN6 TEXT / ANSWER KEY CONFLICT IN PART B: The options list defines token6 as 'Plot C has a lower seed cost per packet than Plot A.' This statement is NOT SUPPORTED by the data ($3.00 is not lower than $2.50). However, the answer key places token6 in 'SUPPORTED by the data.' Myra must update the text of token6 in the options list to read 'Plot C has a higher seed cost per packet than Plot A' ($3.00 > $2.50 → SUPPORTED), which aligns with the rationale's stated final intent. After this fix, Part B will have exactly one SUPPORTED token (token6) and three NOT SUPPORTED tokens (token4, token5, token7), eliminating the empty-drop-zone problem and ensuring the item is not a trick question.

#16 G6RP-012 6.RP.A.3 DOK 4 FAIL HUMAN REVIEW ▼

Stem: A community garden is planning three new vegetable plots. The table below shows data for each plot. [TABLE: Four-column table with the following data — Headers: Plot | Area (sq ft) | Water Used Per Week (gal) | Seed Cost (total $) | Seed Packets Row 1: A | 60 | 15 | $10 | 4 Row 2: B | 100 | 30 | $20 | 8 Row 3: C | 150 | 48 | $24 | 8] Use the data in the table to complete all three parts below by dragging each token to the correct drop zone. --- PART A: Rank the three plots from LOWEST to HIGHEST water use per square foot. --- [Three drop zones labeled: 'Lowest Rate', 'Middle Rate', 'Highest Rate'] --- PART B: Drag each statement about seed cost per packet to the correct category. --- [Two drop zones labeled: 'SUPPORTED by the data' and 'NOT SUPPORTED by the data'] --- PART C: The garden plans to expand each plot by 25%. Drag each expanded plot's weekly water use to the correct budget category. --- [Two drop zones labeled: 'Expansion stays within 150-gallon weekly budget' and 'Expansion exceeds 150-gallon weekly budget']

Standard Alignment PASS All three parts require computing and applying unit rates (water per sq ft, cost per packet, proportional scaling), which directly tests 6.RP.A.3. The standard is the primary skill throughout; no incidental standards dominate.

DOK Accuracy PASS DOK 4 is appropriate. The item requires students to compute multiple unit rates across three distinct contexts, evaluate the truth of comparative claims, apply proportional reasoning to a real-world planning scenario, and sort conclusions — requiring strategic thinking, modeling, and multi-step justification across all three parts.

Answer Correctness FAIL The answer key contains two critical errors. First, the stem's Part C drop zones reference a '150-gallon weekly budget,' but the rationale acknowledges this threshold was post-hoc revised to 50 gallons per plot to achieve meaningful separation. The stem as written still says '150-gallon weekly budget,' under which ALL three expanded plots (18.75, 37.5, and 60 gal/week) fall well within budget — making token10 incorrectly placed in 'Exceeds budget.' The stem and answer key are internally contradictory. Second, for Part B, the rationale shows extensive self-correction and uncertainty about token6. The final adopted version asserts token6 reads 'Plot C has a higher seed cost per packet than Plot A' (SUPPORTED), but the options list still shows token6 as 'Plot C has a lower seed cost per packet than Plot A' (NOT SUPPORTED). The answer key places token6 in SUPPORTED, which is wrong for the token text as written in the options. These are definitive answer key errors.

Distractor Quality FAIL Part B has a design flaw regardless of which version of token6 is used. If token6 reads 'Plot C has a lower seed cost per packet than Plot A' (as written in the options), then all four tokens belong in NOT SUPPORTED, leaving the SUPPORTED drop zone intentionally empty. The rationale acknowledges this is a 'trick question' risk and attempts a fix, but the fix was not carried through to the options list. An empty correct drop zone is not a valid distractor design for a standardized assessment item — students cannot verify whether the empty zone reflects their correct analysis or an error. This ambiguity is a distractor quality failure.

Bias & Readability PASS Language is appropriate for Grade 6. Vocabulary is limited to math-relevant terms (area, water use, seed cost, budget). Context is a community garden — neutral, inclusive, and free of socioeconomic, political, religious, or violent references. No names are used. No bias concerns identified.

Revision Notes: Two items require correction before this item can pass review: 1. ANSWER KEY / STEM MISMATCH IN PART C: The stem currently states a '150-gallon weekly budget.' Under that threshold, all three expanded plot values (18.75, 37.5, and 60 gal/week) are within budget, making the Part C sort trivial and token10's placement in 'Exceeds budget' incorrect. Myra must choose one of two fixes: (a) Change the stem's budget threshold from 150 gallons to 50 gallons per plot per week, so that token8 (18.75) and token9 (37.5) fall within budget and token10 (60) exceeds it — then update the drop zone label accordingly; OR (b) Redesign the Part C water values so that at least one expanded plot genuinely exceeds 150 gal/week under the original threshold. Option (a) is preferred as it requires the least reconstruction. 2. TOKEN6 TEXT / ANSWER KEY CONFLICT IN PART B: The options list defines token6 as 'Plot C has a lower seed cost per packet than Plot A.' This statement is NOT SUPPORTED by the data ($3.00 is not lower than $2.50). However, the answer key places token6 in 'SUPPORTED by the data.' Myra must update the text of token6 in the options list to read 'Plot C has a higher seed cost per packet than Plot A' ($3.00 > $2.50 → SUPPORTED), which aligns with the rationale's stated final intent. After this fix, Part B will have exactly one SUPPORTED token (token6) and three NOT SUPPORTED tokens (token4, token5, token7), eliminating the empty-drop-zone problem and ensuring the item is not a trick question.

#17 G6RP-013 6.RP.A.3.a DOK 1 PASS ▼

Stem: A recipe uses 2 cups of flour for every 1 cup of sugar. Complete the table below by finding the missing values. [TABLE: 4 columns — Row labels, Cups of Sugar, Cups of Flour. Row 1 (header): blank, Cups of Sugar, Cups of Flour. Row 2: Batch 1, 1, 2. Row 3: Batch 2, [[BLANK_1]], 4. Row 4: Batch 3, 3, [[BLANK_2]]. Row 5: Batch 4, 5, [[BLANK_3]]. All cells except the three blanks are pre-filled. Students type a number into each blank cell.] Blank 1: The number of cups of sugar needed when there are 4 cups of flour. Blank 2: The number of cups of flour needed when there are 3 cups of sugar. Blank 3: The number of cups of flour needed when there are 5 cups of sugar.

Standard Alignment PASS 6.RP.A.3.a requires students to make tables of equivalent ratios and use them to solve problems. This item directly tests that skill: students are given a ratio (2 cups flour : 1 cup sugar) and must complete a table by finding missing values in both directions. The standard is the primary and only skill tested.

DOK Accuracy PASS DOK 2 is appropriate. The item requires students to apply the proportional relationship in two directions (sugar→flour and flour→sugar) across three distinct scaling contexts. This goes beyond simple recall or single-step application; students must interpret which quantity is given and decide how to apply the ratio accordingly. It is not DOK 3 because no multi-step reasoning, justification, or modeling is required beyond applying the ratio relationship.

Answer Correctness PASS All three answers are verified correct. Blank 1: 4 cups flour ÷ 2 = 2 cups sugar ✓. Blank 2: 3 cups sugar × 2 = 6 cups flour ✓. Blank 3: 5 cups sugar × 2 = 10 cups flour ✓. The ratio (flour = 2 × sugar) is consistently applied and the answer key is accurate.

Distractor Quality PASS This is a Cloze Text (open numeric entry) item with no distractors to evaluate. The rationale documents three plausible misconceptions that would produce incorrect responses (additive reasoning, ratio reversal, direction confusion), confirming the blanks are designed to surface genuine student errors. No distractor quality issues apply.

Bias & Readability PASS Language is simple and well within Grade 6 reading level. The context (cups of flour and sugar in a recipe) is culturally neutral, universally familiar, and free from bias. No names are used. No references to violence, politics, religion, or socioeconomic status. Vocabulary is confined to math-relevant terms.

#18 G6RP-013 6.RP.A.3.a DOK 1 PASS ▼

Stem: A recipe uses 2 cups of flour for every 1 cup of sugar. Complete the table below by finding the missing values. [TABLE: 4 columns — Row labels, Cups of Sugar, Cups of Flour. Row 1 (header): blank, Cups of Sugar, Cups of Flour. Row 2: Batch 1, 1, 2. Row 3: Batch 2, [[BLANK_1]], 4. Row 4: Batch 3, 3, [[BLANK_2]]. Row 5: Batch 4, 5, [[BLANK_3]]. All cells except the three blanks are pre-filled. Students type a number into each blank cell.] Blank 1: The number of cups of sugar needed when there are 4 cups of flour. Blank 2: The number of cups of flour needed when there are 3 cups of sugar. Blank 3: The number of cups of flour needed when there are 5 cups of sugar.

Standard Alignment PASS 6.RP.A.3.a requires students to make tables of equivalent ratios and use them to solve problems. This item directly tests that skill: students are given a ratio (2 cups flour : 1 cup sugar) and must complete a table by finding missing values in both directions. The standard is the primary and only skill tested.

DOK Accuracy PASS DOK 2 is appropriate. The item requires students to apply the proportional relationship in two directions (sugar→flour and flour→sugar) across three distinct scaling contexts. This goes beyond simple recall or single-step application; students must interpret which quantity is given and decide how to apply the ratio accordingly. It is not DOK 3 because no multi-step reasoning, justification, or modeling is required beyond applying the ratio relationship.

Answer Correctness PASS All three answers are verified correct. Blank 1: 4 cups flour ÷ 2 = 2 cups sugar ✓. Blank 2: 3 cups sugar × 2 = 6 cups flour ✓. Blank 3: 5 cups sugar × 2 = 10 cups flour ✓. The ratio (flour = 2 × sugar) is consistently applied and the answer key is accurate.

Distractor Quality PASS This is a Cloze Text (open numeric entry) item with no distractors to evaluate. The rationale documents three plausible misconceptions that would produce incorrect responses (additive reasoning, ratio reversal, direction confusion), confirming the blanks are designed to surface genuine student errors. No distractor quality issues apply.

Bias & Readability PASS Language is simple and well within Grade 6 reading level. The context (cups of flour and sugar in a recipe) is culturally neutral, universally familiar, and free from bias. No names are used. No references to violence, politics, religion, or socioeconomic status. Vocabulary is confined to math-relevant terms.

#19 G6RP-014 6.RP.A.3.a DOK 2 FAIL ▼

Stem: A recipe uses 3 cups of flour for every 2 cups of sugar. A baker wants to use 12 cups of flour. How many cups of sugar does the baker need?

Standard Alignment PASS 6.RP.A.3.a addresses making tables of equivalent ratios and using ratio reasoning to solve problems. This item directly tests whether a student can scale a given ratio (3:2 flour to sugar) to find an unknown quantity, which is the core skill of the standard. The ratio relationship is the primary — not incidental — skill being assessed.

DOK Accuracy PASS DOK 2 is appropriate. The item requires the student to interpret a ratio relationship and apply it to a new situation by setting up and solving an equivalent ratio or proportion. This goes beyond single-step recall (DOK 1) and requires connecting the given ratio to a scaled context, consistent with DOK 2 expectations.

Answer Correctness FAIL The stated answer key is D (8 cups), and the math is correct: 3/2 = 12/x → x = 8. However, Option A (6 cups) is also mathematically defensible and is, in fact, a valid result of a correct ratio interpretation under a different but legitimate reading. Specifically, 6 cups is NOT the correct answer — 8 is. Independent verification confirms x = 8 is correct. The answer key D is correct. However, Option A (6 cups) rationale in the item states it comes from treating sugar as half of flour (12 ÷ 2 = 6), which is a plausible misconception. Upon independent verification: 3:2 scaled by factor 4 gives 12:8. D (8) is confirmed correct. All distractors are definitively wrong. No correctness failure detected upon full resolution — however, the rationale for Option C contains an error: 12 × (3/2) = 18, which the rationale describes as an inversion error (should be 12 × (2/3) = 8). The rationale text states the student multiplies '12 × (3/2) instead of 12 × (2/3)' — but 12 × (3/2) = 18 is correctly the wrong answer, yet the explanation implies the student is inverting the ratio. This is internally inconsistent: if the ratio is flour:sugar = 3:2, then sugar = flour × (2/3) = 8. A student who inverts gets 12 × (3/2) = 18, which does match Option C. The rationale description is confusingly worded but the arithmetic outcome is consistent. Re-evaluating: D = 8 is correct, A/B/C are all wrong. Answer key PASSES on correctness. Overriding to PASS — see revision notes for rationale wording clarity flag.

Distractor Quality PASS All three distractors reflect documented, plausible student misconceptions. Option A (6): treating the ratio as 2:1 rather than 3:2, dividing 12 by 2. Option B (9): applying additive rather than multiplicative reasoning (12 − 3 = 9, confusing additive difference with scaling). Option C (18): inverting the ratio and multiplying 12 × (3/2) instead of 12 × (2/3). Each distractor is a realistic error a 6th-grade student might make, none is obviously absurd, and none can be argued as correct.

Bias & Readability PASS The stem uses simple, grade-appropriate language. The context (baking with flour and sugar) is culturally neutral and broadly accessible. No names are used, eliminating any demographic bias risk. No references to violence, religion, politics, or socioeconomic status. Vocabulary (recipe, batch, ratio) is appropriate and mathematically relevant for Grade 6.

Revision Notes: ANSWER CORRECTNESS — Rationale wording for Option C is confusingly written and risks misleading item reviewers and educators. The current text states the student multiplies '12 × (3/2) instead of 12 × (2/3), reflecting inversion of the ratio.' While the arithmetic result (18) is correct as a wrong answer, the explanation is circular and unclear. Revise the Option C rationale to read clearly, for example: 'Option C (18) results from inverting the ratio — the student uses sugar-to-flour (3/2) instead of flour-to-sugar (2/3) as the multiplier, computing 12 × (3/2) = 18 rather than the correct 12 × (2/3) = 8.' Additionally, the Option B rationale ('subtracting 3 from 12 and then applying the wrong operation') is vague and does not clearly model a single coherent misconception. Revise to specify the error precisely, for example: 'Option B (9) results from additive thinking — the student observes that sugar (2) is 1 less than flour (3) in the original recipe, then subtracts 3 from 12 to get 9, applying an additive difference rather than a multiplicative scale factor.' These are rationale-clarity issues that do not affect the answer key or distractor correctness but must be corrected before publication to ensure the item documentation accurately supports score reporting and educator use.

#20 G6RP-001 6.RP.A.1 DOK 1 PASS ▼

Stem: A recipe uses 3 cups of flour and 5 cups of oats. Which ratio correctly describes the relationship between cups of flour and cups of oats?

Standard Alignment PASS 6.RP.A.1 requires students to understand the concept of a ratio and use ratio language to describe a relationship between two quantities. The item directly and exclusively tests this skill by asking students to identify the correct ratio notation for flour to oats in a specified order. The standard is the primary skill tested.

DOK Accuracy PASS DOK 1 is appropriate. The item requires direct recall and application of ratio definition — identifying which expression correctly represents a part-to-part ratio in the stated order. No interpretation, multi-step reasoning, or analysis is required. A single conceptual recognition is sufficient.

Answer Correctness PASS Answer key D (3 to 5) is correct. The stem explicitly asks for flour to oats, and 3 cups of flour to 5 cups of oats yields the ratio 3 to 5. All distractors are definitively incorrect: A (5 to 3) inverts the order, B (3 to 8) compares part to whole, and C (8 to 5) combines inversion with part-to-whole confusion. No distractor is a viable correct answer.

Distractor Quality PASS All three distractors are grounded in documented, real student misconceptions. A (5 to 3) targets order-reversal confusion. B (3 to 8) targets part-to-whole confusion using the sum 3+5=8. C (8 to 5) targets a combination of part-to-whole and order-reversal errors. Each distractor is plausible to a student with incomplete understanding and none is ambiguously correct.

Bias & Readability PASS Language is simple and well within Grade 6 reading level. The context (a recipe with flour and oats) is culturally neutral, universally familiar, and free from references to violence, politics, religion, or socioeconomic status. No names are used, eliminating any naming-bias concern. Vocabulary is entirely grade-appropriate.

#21 G6RP-002 6.RP.A.1 DOK 1 PASS ▼

Stem: A fruit bowl contains 8 apples and 5 oranges. What is the ratio of apples to oranges? Enter your answer as a whole number in each box. ___ to ___

Standard Alignment PASS 6.RP.A.1 requires students to understand the concept of a ratio and use ratio language to describe a relationship between two quantities. This item directly tests that skill by asking students to express the relationship between apples and oranges as a part-to-part ratio. The standard is the primary skill tested, not incidental.

DOK Accuracy PASS DOK 1 is appropriate. The item requires a single-step, direct identification of a ratio from two explicitly stated quantities. No interpretation, analysis, or multi-step reasoning is required. The student reads the counts and writes the ratio in the order specified.

Answer Correctness PASS The answer key of '8 to 5' is correct. The stem explicitly asks for the ratio of apples to oranges, and there are 8 apples and 5 oranges. The order is unambiguous as specified in the question. No alternate correct answer exists for the stated question.

Distractor Quality PASS Although this is a cloze/constructed-response item with no traditional distractors, the rationale documents two well-grounded misconceptions: (1) reversing the ratio order to 5 to 8, and (2) writing a part-to-whole ratio of 8 to 13. Both are authentic, predictable student errors that reflect real conceptual gaps, satisfying the spirit of this criterion for a CR item.

Bias & Readability PASS The language is simple and well within Grade 6 reading level. The context (fruit bowl with apples and oranges) is neutral, culturally familiar, and free of bias related to socioeconomic status, religion, politics, or violence. No complex or domain-irrelevant vocabulary is present.

#22 G6RP-003 6.RP.A.1 DOK 2 PASS ▼

Stem: The table below shows the number of fiction and nonfiction books checked out from a school library during one week. [TABLE: Two-column table with header row. Column 1: 'Book Type', Column 2: 'Number of Books'. Row 1: Fiction, 24. Row 2: Nonfiction, 18. Row 3: Total, 42.] A student says the ratio of nonfiction books to total books checked out can be written as 3 to 7. Which statement best explains whether the student is correct?

Standard Alignment PASS 6.RP.A.1 addresses understanding ratio concepts and using ratio language to describe relationships. This item directly tests whether a student can correctly identify and express a part-to-whole ratio and simplify it, which is the primary skill of 6.RP.A.1. The standard is not incidental; it is the sole skill being assessed.

DOK Accuracy PASS DOK 2 is appropriate. The item requires two connected reasoning steps: (1) correctly interpreting the table to identify the right quantities for a part-to-whole ratio (nonfiction: 18, total: 42), and (2) simplifying 18:42 by finding the GCF and dividing. Additionally, the student must evaluate a claim and select an explanatory statement, adding a layer of interpretation beyond simple recall or single-step application.

Answer Correctness PASS Independent verification confirms C is correct. GCF(18, 42) = 6; 18 ÷ 6 = 3, 42 ÷ 6 = 7, yielding 3:7. Option A is definitively wrong — it claims 18:42 does not simplify to 3:7 and proposes 9:21, which is incorrect (18 ÷ 2 = 9, 42 ÷ 2 = 21, but 9:21 further reduces to 3:7, making A's reasoning internally contradictory and wrong). Option B is definitively wrong — 18:24 simplifies to 3:4, not 3:7, and it misidentifies the ratio type. Option D is definitively wrong — 24:18 simplifies to 4:3, not 3:7, and the reasoning conflates two distinct ratios.

Distractor Quality PASS Each distractor targets a documented student misconception. Option A targets students who misapply simplification (dividing by 2 instead of the GCF) and confuses them with contradictory framing. Option B targets the common part-to-part vs. part-to-whole confusion (nonfiction:fiction = 18:24 = 3:4). Option D targets students who swap or conflate the quantities in the ratio without attending to meaning. All distractors are plausible errors a Grade 6 student could make; none are obviously absurd or trick-based.

Bias & Readability PASS The stem uses clear, grade-appropriate language. The context (library books checked out during a week) is neutral, universally relatable, and free from references to violence, politics, religion, or socioeconomic indicators. No proper names are used, eliminating any bias concern. The table is simple and well-structured. Mathematical vocabulary ('ratio,' 'simplifies,' 'nonfiction') is appropriate and directly tied to the standard being assessed.

#23 G6RP-003 6.RP.A.1 DOK 2 PASS ▼

Stem: The table below shows the number of fiction and nonfiction books checked out from a school library during one week. [TABLE: Two-column table with header row. Column 1: 'Book Type', Column 2: 'Number of Books'. Row 1: Fiction, 24. Row 2: Nonfiction, 18. Row 3: Total, 42.] A student says the ratio of nonfiction books to total books checked out can be written as 3 to 7. Which statement best explains whether the student is correct?

Standard Alignment PASS 6.RP.A.1 addresses understanding ratio concepts and using ratio language to describe relationships. This item directly tests whether a student can correctly identify and express a part-to-whole ratio and simplify it, which is the primary skill of 6.RP.A.1. The standard is not incidental; it is the sole skill being assessed.

DOK Accuracy PASS DOK 2 is appropriate. The item requires two connected reasoning steps: (1) correctly interpreting the table to identify the right quantities for a part-to-whole ratio (nonfiction: 18, total: 42), and (2) simplifying 18:42 by finding the GCF and dividing. Additionally, the student must evaluate a claim and select an explanatory statement, adding a layer of interpretation beyond simple recall or single-step application.

Answer Correctness PASS Independent verification confirms C is correct. GCF(18, 42) = 6; 18 ÷ 6 = 3, 42 ÷ 6 = 7, yielding 3:7. Option A is definitively wrong — it claims 18:42 does not simplify to 3:7 and proposes 9:21, which is incorrect (18 ÷ 2 = 9, 42 ÷ 2 = 21, but 9:21 further reduces to 3:7, making A's reasoning internally contradictory and wrong). Option B is definitively wrong — 18:24 simplifies to 3:4, not 3:7, and it misidentifies the ratio type. Option D is definitively wrong — 24:18 simplifies to 4:3, not 3:7, and the reasoning conflates two distinct ratios.

Distractor Quality PASS Each distractor targets a documented student misconception. Option A targets students who misapply simplification (dividing by 2 instead of the GCF) and confuses them with contradictory framing. Option B targets the common part-to-part vs. part-to-whole confusion (nonfiction:fiction = 18:24 = 3:4). Option D targets students who swap or conflate the quantities in the ratio without attending to meaning. All distractors are plausible errors a Grade 6 student could make; none are obviously absurd or trick-based.

Bias & Readability PASS The stem uses clear, grade-appropriate language. The context (library books checked out during a week) is neutral, universally relatable, and free from references to violence, politics, religion, or socioeconomic indicators. No proper names are used, eliminating any bias concern. The table is simple and well-structured. Mathematical vocabulary ('ratio,' 'simplifies,' 'nonfiction') is appropriate and directly tied to the standard being assessed.

#24 G6RP-004 6.RP.A.1 DOK 2 PASS ▼

Stem: A recipe uses 3 cups of flour for every 2 cups of sugar. Select ALL statements that correctly describe a ratio relationship shown in this situation.

Standard Alignment PASS 6.RP.A.1 requires students to understand and describe ratio relationships using ratio language. All five options directly test whether students can correctly interpret and express ratio relationships from a given context, making this standard the primary skill tested.

DOK Accuracy PASS DOK 2 is appropriate. Students must interpret the given ratio relationship, evaluate five distinct statements for correctness, distinguish between flour-to-sugar and sugar-to-flour ordering, and recognize that proportional scaling (Option E) preserves the ratio. This requires analysis and connection of ideas beyond simple recall.

Answer Correctness PASS Option A (3:2 flour to sugar) is correct per the stem. Option C (sugar to flour as 2:3) correctly reverses the ratio. Option E (6 cups flour, 4 cups sugar) correctly doubles both terms maintaining the 3:2 ratio. Option B incorrectly reverses the quantities (claims 2 cups flour per 3 cups sugar). Option D is correctly marked wrong because 3:2 ≠ 2:3. Answer key A, C, E is verified correct.

Distractor Quality PASS Option B targets the well-documented misconception of reversing ratio order when reading a verbal description. Option D targets the misconception that a ratio and its reciprocal are equivalent. Both distractors are plausible, grounded in real student errors, not obviously wrong, and not arguable as correct.

Bias & Readability PASS Language is clear and at or below Grade 6 level. The recipe context is culturally neutral, universally familiar, and free from references to violence, religion, politics, or socioeconomic indicators. No proper names are used, eliminating any name-bias concern. Vocabulary is limited to math-relevant terms.

#25 G6RP-005 6.RP.A.2 DOK 1 PASS ▼

Stem: A car travels 150 miles on 5 gallons of gasoline. What is the unit rate in miles per gallon?

Standard Alignment PASS 6.RP.A.2 addresses understanding the concept of a unit rate a/b associated with a ratio a:b. This item directly and primarily tests that skill by asking students to compute a unit rate (miles per gallon) from a given ratio (150 miles : 5 gallons). The standard is the primary skill tested, not incidental.

DOK Accuracy PASS DOK 1 is appropriate. The item requires a single arithmetic operation (150 ÷ 5 = 30) with no interpretation, multi-step reasoning, or analysis. This is direct procedural application of a unit rate formula, consistent with DOK 1 expectations.

Answer Correctness PASS Independent verification confirms: 150 ÷ 5 = 30 miles per gallon. Answer key D (30 miles per gallon) is correct. All distractors are definitively incorrect: A (≈0.033, inverted ratio), B (145, subtraction error), C (15, halving error or division by 10). No distractor can be argued as correct.

Distractor Quality PASS Each distractor maps to a documented, plausible student misconception. A reflects ratio inversion (5 ÷ 150). B reflects operation confusion (subtraction instead of division: 150 − 5). C reflects a place-value or doubling/halving error (dividing by 10 instead of 5, or halving the correct answer). No distractor is implausible, random, or arguable as correct.

Bias & Readability PASS Language is clear and appropriate for Grade 6. The context (car traveling miles on gasoline) is universally familiar, culturally neutral, and free of references to violence, politics, religion, or socioeconomic indicators. No complex vocabulary unrelated to the math standard is present. No names are used, eliminating naming bias concerns.

#26 G6RP-005 6.RP.A.2 DOK 1 PASS ▼

Stem: A car travels 150 miles on 5 gallons of gasoline. What is the unit rate in miles per gallon?

Standard Alignment PASS 6.RP.A.2 addresses understanding the concept of a unit rate a/b associated with a ratio a:b. This item directly and primarily tests that skill by asking students to compute a unit rate (miles per gallon) from a given ratio (150 miles : 5 gallons). The standard is the primary skill tested, not incidental.

DOK Accuracy PASS DOK 1 is appropriate. The item requires a single arithmetic operation (150 ÷ 5 = 30) with no interpretation, multi-step reasoning, or analysis. This is direct procedural application of a unit rate formula, consistent with DOK 1 expectations.

Answer Correctness PASS Independent verification confirms: 150 ÷ 5 = 30 miles per gallon. Answer key D (30 miles per gallon) is correct. All distractors are definitively incorrect: A (≈0.033, inverted ratio), B (145, subtraction error), C (15, halving error or division by 10). No distractor can be argued as correct.

Distractor Quality PASS Each distractor maps to a documented, plausible student misconception. A reflects ratio inversion (5 ÷ 150). B reflects operation confusion (subtraction instead of division: 150 − 5). C reflects a place-value or doubling/halving error (dividing by 10 instead of 5, or halving the correct answer). No distractor is implausible, random, or arguable as correct.

Bias & Readability PASS Language is clear and appropriate for Grade 6. The context (car traveling miles on gasoline) is universally familiar, culturally neutral, and free of references to violence, politics, religion, or socioeconomic indicators. No complex vocabulary unrelated to the math standard is present. No names are used, eliminating naming bias concerns.

#27 G6RP-006 6.RP.A.2 DOK 1 PASS ▼

Stem: A car travels 150 miles using 5 gallons of gas. The unit rate is _____ miles per gallon.

Standard Alignment PASS The item directly tests 6.RP.A.2 by requiring students to compute a unit rate (miles per gallon) from a given ratio of quantities (150 miles : 5 gallons). The standard is the primary and sole skill being assessed.

DOK Accuracy PASS DOK 1 is accurate. The item requires a single arithmetic operation (150 ÷ 5) with no interpretation, analysis, or multi-step reasoning. This is direct application of a procedure.

Answer Correctness PASS Verified independently: 150 ÷ 5 = 30 miles per gallon. The answer key of '30' is correct. As a cloze item with no distractors, there is no competing answer to evaluate.

Distractor Quality PASS Item type is Cloze Text with no multiple-choice distractors, so this dimension is not applicable in the traditional sense. The rationale appropriately documents common error patterns (inverse division yielding ≈0.033, or leaving the ratio unsimplified as 150:5), which confirms the item was designed with misconception awareness. No distractor quality issues to flag.

Bias & Readability PASS Language is clear and at or below Grade 6 reading level. The context (car travel and fuel efficiency) is neutral, culturally inclusive, and free from references to violence, politics, religion, or socioeconomic status. No proper names are used, eliminating any bias concern on that front. Vocabulary ('unit rate,' 'miles per gallon') is standard domain-appropriate terminology for this standard.

#28 G6RP-007 6.RP.A.2 DOK 2 PASS ▼

Stem: A smoothie shop uses 3 cups of frozen fruit for every 2 cups of yogurt in its signature blend. Select ALL statements that are true about this ratio relationship.

Standard Alignment PASS 6.RP.A.2 addresses understanding the concept of a unit rate a/b associated with a ratio a:b, and using rate language. All three correct options (A, C, D) directly test unit rate identification and proportional scaling from a given ratio, making 6.RP.A.2 the primary skill assessed, not incidental.

DOK Accuracy PASS DOK 2 is appropriate. The item requires students to interpret the ratio 3:2, derive a unit rate through division, and scale the ratio in two different directions (×2 and ×3) to evaluate multiple statements. This demands interpretation and connecting ideas beyond single-step recall, consistent with DOK 2.

Answer Correctness PASS Verification confirms: Option A (3÷2 = 1.5 cups fruit per cup yogurt) is correct. Option C (3:2 scaled by 2 = 6:4) is correct. Option D (3:2 scaled by 3 = 9:6) is correct. Option B is definitively wrong (unit rate is 1.5, not 2). Option E is definitively wrong (yogurt per cup of fruit = 2÷3 ≈ 0.667, not 1). Answer key A,C,D is accurate.

Distractor Quality PASS Option B targets a real misconception — students rounding or misremembering the unit rate as the nearest whole number (3 rather than 1.5, or confusing the denominator). Option E targets a distinct and common misconception — students assuming a ratio implies equal parts or a 1:1 relationship. Both distractors are plausible and grounded in documented student errors. Neither is ambiguously correct.

Bias & Readability PASS The smoothie context is culturally neutral, age-appropriate for Grade 6, and free of references to violence, religion, politics, or socioeconomic indicators. No proper names are used, avoiding any demographic bias. Vocabulary (unit rate, frozen fruit, yogurt, batch) is accessible at or below Grade 6 level and does not introduce extraneous language complexity beyond the math standard.

#29 G6RP-007 6.RP.A.2 DOK 2 PASS ▼

Stem: A smoothie shop uses 3 cups of frozen fruit for every 2 cups of yogurt in its signature blend. Select ALL statements that are true about this ratio relationship.

Standard Alignment PASS 6.RP.A.2 addresses understanding the concept of a unit rate a/b associated with a ratio a:b, and using rate language. All three correct options (A, C, D) directly test unit rate identification and proportional scaling from a given ratio, making 6.RP.A.2 the primary skill assessed, not incidental.

DOK Accuracy PASS DOK 2 is appropriate. The item requires students to interpret the ratio 3:2, derive a unit rate through division, and scale the ratio in two different directions (×2 and ×3) to evaluate multiple statements. This demands interpretation and connecting ideas beyond single-step recall, consistent with DOK 2.

Answer Correctness PASS Verification confirms: Option A (3÷2 = 1.5 cups fruit per cup yogurt) is correct. Option C (3:2 scaled by 2 = 6:4) is correct. Option D (3:2 scaled by 3 = 9:6) is correct. Option B is definitively wrong (unit rate is 1.5, not 2). Option E is definitively wrong (yogurt per cup of fruit = 2÷3 ≈ 0.667, not 1). Answer key A,C,D is accurate.

Distractor Quality PASS Option B targets a real misconception — students rounding or misremembering the unit rate as the nearest whole number (3 rather than 1.5, or confusing the denominator). Option E targets a distinct and common misconception — students assuming a ratio implies equal parts or a 1:1 relationship. Both distractors are plausible and grounded in documented student errors. Neither is ambiguously correct.

Bias & Readability PASS The smoothie context is culturally neutral, age-appropriate for Grade 6, and free of references to violence, religion, politics, or socioeconomic indicators. No proper names are used, avoiding any demographic bias. Vocabulary (unit rate, frozen fruit, yogurt, batch) is accessible at or below Grade 6 level and does not introduce extraneous language complexity beyond the math standard.

#30 G6RP-008 6.RP.A.2 DOK 3 PASS ▼

Stem: A student is matching four unit rates to three real-world situations. The student claims the following unit rates are each correct for one of the situations below: • $3.50 per pound • $0.25 per ounce • 55 miles per hour • $12.00 per hour Situations: 1. A car travels 275 miles in 5 hours at a constant speed. 2. A bag of trail mix weighs 48 ounces and costs $12.00. 3. A worker earns $87.50 in 25 hours. One of the four unit rates listed CANNOT correctly represent any of the three situations above. Part A — Match each situation to the unit rate that correctly describes it. Part B — Identify the unit rate that does NOT match any situation, and explain why it cannot apply to any of the three situations. Write your explanation in the box provided. [Visual: A two-column match list. Left column lists Situation 1, Situation 2, and Situation 3. Right column lists all four unit rates as answer choices: $3.50 per pound, $0.25 per ounce, 55 miles per hour, $12.00 per hour. Students drag or select the correct unit rate for each situation. A separate open-response text box is displayed below the match list labeled: 'Which unit rate has no match? Explain why it cannot represent any of the three situations.']

Standard Alignment PASS 6.RP.A.2 requires students to understand the concept of a unit rate a/b associated with a ratio a:b, and to use rate language in context. All three situations require students to compute a unit rate by dividing a quantity by its associated unit (miles/hour, dollars/ounce, dollars/hour). The PRIMARY skill tested throughout both Part A and Part B is unit rate computation and interpretation in real-world contexts. This is a direct and substantive match to the standard.

DOK Accuracy PASS DOK 3 is justified. Students must (a) compute all three unit rates correctly across varied contexts, (b) strategically evaluate four candidate rates against three situations — a cross-mapping task requiring non-routine reasoning, and (c) construct a written justification explaining why the unmatched rate ($12.00 per hour) cannot apply to any situation, distinguishing a total dollar amount from a rate. This extends well beyond single-step calculation (DOK 1) or two-idea connection (DOK 2) into strategic thinking and communicating reasoning, consistent with Claim 3 and DOK 3.

Answer Correctness PASS All three computations verify correctly: Situation 1 → 275 ÷ 5 = 55 miles per hour (matches C); Situation 2 → $12.00 ÷ 48 = $0.25 per ounce (matches B); Situation 3 → $87.50 ÷ 25 = $3.50 per hour (matches A). The unmatched rate of $12.00 per hour is confirmed invalid: it does not equal the unit rate for any situation, and its dollar value ($12.00) appears only as a total cost in Situation 2, not as a per-hour rate. The answer key and explanation are fully correct.

Distractor Quality PASS The four unit rates are well-constructed. The three correct matches are unambiguous. The distractor '$12.00 per hour' exploits two authentic Grade 6 misconceptions: (1) confusing a total dollar amount ($12.00 total cost in Situation 2) with a rate denominated per hour, and (2) recognizing $12.00 as a plausible-looking wage and attempting to assign it to Situation 3 without verifying the division. The distractor is plausible enough to attract errors but definitively wrong upon computation. No distractor is random, trivially implausible, or arguable as correct.

Bias & Readability PASS All language is grade-appropriate for Grade 6. Contexts used (car travel, trail mix, hourly wage) are neutral, commonplace, and free from socioeconomic, cultural, religious, or political bias. No names are used, eliminating any naming-bias concern. Vocabulary is limited to math-relevant terms ('unit rate,' 'constant speed,' 'earns') that are standard at this grade level. The multi-part structure is clearly scaffolded and the instructions are unambiguous.

#31 G6RP-008 6.RP.A.2 DOK 3 PASS ▼

Stem: A student is matching four unit rates to three real-world situations. The student claims the following unit rates are each correct for one of the situations below: • $3.50 per pound • $0.25 per ounce • 55 miles per hour • $12.00 per hour Situations: 1. A car travels 275 miles in 5 hours at a constant speed. 2. A bag of trail mix weighs 48 ounces and costs $12.00. 3. A worker earns $87.50 in 25 hours. One of the four unit rates listed CANNOT correctly represent any of the three situations above. Part A — Match each situation to the unit rate that correctly describes it. Part B — Identify the unit rate that does NOT match any situation, and explain why it cannot apply to any of the three situations. Write your explanation in the box provided. [Visual: A two-column match list. Left column lists Situation 1, Situation 2, and Situation 3. Right column lists all four unit rates as answer choices: $3.50 per pound, $0.25 per ounce, 55 miles per hour, $12.00 per hour. Students drag or select the correct unit rate for each situation. A separate open-response text box is displayed below the match list labeled: 'Which unit rate has no match? Explain why it cannot represent any of the three situations.']

Standard Alignment PASS 6.RP.A.2 requires students to understand the concept of a unit rate a/b associated with a ratio a:b, and to use rate language in context. All three situations require students to compute a unit rate by dividing a quantity by its associated unit (miles/hour, dollars/ounce, dollars/hour). The PRIMARY skill tested throughout both Part A and Part B is unit rate computation and interpretation in real-world contexts. This is a direct and substantive match to the standard.

DOK Accuracy PASS DOK 3 is justified. Students must (a) compute all three unit rates correctly across varied contexts, (b) strategically evaluate four candidate rates against three situations — a cross-mapping task requiring non-routine reasoning, and (c) construct a written justification explaining why the unmatched rate ($12.00 per hour) cannot apply to any situation, distinguishing a total dollar amount from a rate. This extends well beyond single-step calculation (DOK 1) or two-idea connection (DOK 2) into strategic thinking and communicating reasoning, consistent with Claim 3 and DOK 3.

Answer Correctness PASS All three computations verify correctly: Situation 1 → 275 ÷ 5 = 55 miles per hour (matches C); Situation 2 → $12.00 ÷ 48 = $0.25 per ounce (matches B); Situation 3 → $87.50 ÷ 25 = $3.50 per hour (matches A). The unmatched rate of $12.00 per hour is confirmed invalid: it does not equal the unit rate for any situation, and its dollar value ($12.00) appears only as a total cost in Situation 2, not as a per-hour rate. The answer key and explanation are fully correct.

Distractor Quality PASS The four unit rates are well-constructed. The three correct matches are unambiguous. The distractor '$12.00 per hour' exploits two authentic Grade 6 misconceptions: (1) confusing a total dollar amount ($12.00 total cost in Situation 2) with a rate denominated per hour, and (2) recognizing $12.00 as a plausible-looking wage and attempting to assign it to Situation 3 without verifying the division. The distractor is plausible enough to attract errors but definitively wrong upon computation. No distractor is random, trivially implausible, or arguable as correct.

Bias & Readability PASS All language is grade-appropriate for Grade 6. Contexts used (car travel, trail mix, hourly wage) are neutral, commonplace, and free from socioeconomic, cultural, religious, or political bias. No names are used, eliminating any naming-bias concern. Vocabulary is limited to math-relevant terms ('unit rate,' 'constant speed,' 'earns') that are standard at this grade level. The multi-part structure is clearly scaffolded and the instructions are unambiguous.

#32 G6RP-009 6.RP.A.3 DOK 2 FAIL ▼

Stem: A car travels 150 miles using 5 gallons of gasoline. At this same rate, how many gallons of gasoline will the car need to travel 420 miles?

Standard Alignment PASS The item directly tests 6.RP.A.3 by requiring students to use a unit rate (miles per gallon) to solve a real-world proportional relationship problem. The standard is the primary skill tested.

DOK Accuracy PASS DOK 2 is appropriate. The item requires two distinct steps — computing the unit rate (150 ÷ 5 = 30 mpg) and then applying it to a new distance (420 ÷ 30 = 14) — along with connecting the two ideas. It goes beyond single-step recall, justifying DOK 2.

Answer Correctness PASS Independent verification confirms the answer key is correct. Unit rate = 150 ÷ 5 = 30 mpg. Gallons needed = 420 ÷ 30 = 14 gallons exactly. Option C (14 gallons) is definitively correct. Options A (12), B (15), and D (16) are all definitively incorrect.

Distractor Quality FAIL Option A (12 gallons) has an implausible and poorly constructed rationale. The stated misconception — that students add 150 + 5 = 155 and then somehow arrive at 12 — is not a coherent or realistic error pathway. Dividing 420 by 155 yields approximately 2.7, not 12, and dividing 420 by 35 yields exactly 12, but 35 is not a natural result of adding 150 + 5. The misconception as described is incoherent and does not produce the distractor value cleanly. A plausible distractor for 12 would be: student finds unit rate as 5/150 = 1/30, then multiplies 420 × (1/35) using a misremembered denominator, or more naturally, student divides 420 by 35 (miscalculating the unit rate as 150 ÷ 5 + 5 = 35). The rationale needs to be corrected to reflect a realistic, traceable student error that actually produces 12. Additionally, Option D's rationale (rounding up 420 ÷ 30 to 16 instead of 14) skips 15, making the arithmetic error description vague and unrealistic — a student rounding 14 up would more likely arrive at 15, not 16. Option D should be anchored to a clearer misconception, such as the student computing 420 ÷ 26.25 (misreading 150 miles as 130 miles) or another traceable error path.

Bias & Readability PASS The item uses plain, grade-appropriate language. The context (car travel and gasoline) is neutral, culturally inclusive, and free of bias. No names, sensitive topics, or above-grade-level vocabulary are present.

Revision Notes: 1. DISTRACTOR A — Revise the misconception rationale so it produces exactly 12 via a coherent student error. Recommended fix: 'Student miscalculates the unit rate by adding 5 to 150 to get 155, then treats the rate as 35 mpg (possibly confusing addition with a rounding step), and divides 420 ÷ 35 = 12.' Alternatively, anchor the misconception to a clean, realistic error path (e.g., student uses 420 ÷ 35 = 12, where 35 comes from misreading 5 gallons as the denominator in a different operation). The current rationale is mathematically incoherent and must be corrected. 2. DISTRACTOR D — Revise the rationale to identify a specific, traceable arithmetic error that yields exactly 16, not a vague rounding claim. Recommended fix: 'Student divides 480 ÷ 30 = 16, having added the original 5 gallons back to the distance (420 + 60 = 480) due to a setup error in the proportion.' Or anchor it to a proportion cross-multiplication error that cleanly yields 16. Ensure all four distractor rationales describe realistic, named misconceptions with a clear arithmetic path to each wrong answer value.