| 1 |
G6RP-001 |
6.RP.A.1 |
1 |
Claim 1 |
Multiple Choice (MCQ) |
qc_pass
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0 |
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Stem: A fruit bowl contains 5 apples and 8 oranges. Which statement describes the ratio of apples to oranges?
Options:
A. 8 to 5 B. 5 to 13 C. 5 to 8 D. 8 to 13
Answer Key: C
Rationale: The ratio of apples to oranges is 5:8 because there are 5 apples for every 8 oranges. Distractor A reverses the order. Distractors B and D use part-to-whole instead of part-to-part.
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| 2 |
G6RP-002 |
6.RP.A.1 |
1 |
Claim 1 |
Cloze Text |
qc_pass
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0 |
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Stem: A classroom has 12 desks and 4 tables. The ratio of desks to tables is _____ : _____. (Enter the ratio in simplest form using the smallest whole numbers.)
Answer Key: 3:1
Rationale: 12 desks to 4 tables simplifies to 3:1, since both numbers share a common factor of 4. A correct response describes the ratio relationship using simplest whole-number form.
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| 3 |
G6RP-003 |
6.RP.A.1 |
2 |
Claim 1 |
Multiple Choice (MCQ) |
qc_pass
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0 |
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Stem: At a zoo, the ratio of penguins to seals is 6 to 2. Which statement correctly describes this ratio relationship?
Options:
A. For every 2 penguins there are 6 seals. B. For every 3 penguins there is 1 seal. C. There are 6 more penguins than seals. D. For every 1 penguin there are 3 seals.
Answer Key: B
Rationale: The ratio 6:2 simplifies to 3:1, so for every 3 penguins there is 1 seal. A reverses the ratio. C confuses ratio with difference. D inverts the relationship.
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| 4 |
G6RP-004 |
6.RP.A.1 |
2 |
Claim 1 |
Multiple Response |
qc_pass
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0 |
▼ |
Stem: A school store sold 9 pencils for every 4 erasers. Select ALL statements that correctly describe this ratio relationship.
Options:
A. The ratio of pencils to erasers is 9:4. B. For every 4 erasers sold, 9 pencils were sold. C. The ratio of erasers to pencils is 9:4. D. For every 9 erasers, 4 pencils were sold. E. The ratio of pencils to erasers can be written as 9 to 4.
Answer Key: A,B,E
Rationale: A, B, and E all correctly express the 9:4 pencil-to-eraser relationship using different ratio notations. C reverses the order. D switches the quantities.
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| 5 |
G6RP-005 |
6.RP.A.2 |
1 |
Claim 1 |
Multiple Choice (MCQ) |
qc_pass
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0 |
▼ |
Stem: A store sells 6 oranges for $3. What is the unit rate in dollars per orange?
Options:
A. $2.00 per orange B. $3.00 per orange C. $6.00 per orange D. $0.50 per orange
Answer Key: D
Rationale: Unit rate = $3 ÷ 6 oranges = $0.50 per orange. A inverts the division (6 ÷ 3). B uses the total price. C uses the total number of oranges.
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| 6 |
G6RP-006 |
6.RP.A.2 |
1 |
Claim 1 |
Cloze Text |
qc_pass
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0 |
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Stem: A car travels 120 miles in 3 hours at a constant speed. The unit rate is _____ miles per hour.
Answer Key: 40
Rationale: Unit rate = 120 miles ÷ 3 hours = 40 miles per hour. This applies the definition of unit rate as a/b for the ratio a:b.
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| 7 |
G6RP-007 |
6.RP.A.2 |
2 |
Claim 1 |
Multiple Choice (MCQ) |
qc_pass
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0 |
▼ |
Stem: A recipe uses 2 cups of flour for every 5 cups of milk. How much flour is used for each cup of milk?
Options:
A. 5/2 cups of flour per cup of milk B. 2/5 cup of flour per cup of milk C. 7 cups of flour per cup of milk D. 3 cups of flour per cup of milk
Answer Key: B
Rationale: For the ratio 2 cups flour : 5 cups milk, the unit rate of flour per cup of milk is 2/5. A inverts the unit rate (milk per cup of flour). C adds the quantities. D subtracts them.
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| 8 |
G6RP-008 |
6.RP.A.2 |
2 |
Claim 1 |
Match List |
qc_pass
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0 |
▼ |
Stem: Match each ratio situation on the left to its correct unit rate on the right.
Options:
Answer Key: 1-B,2-A,3-C
Rationale: 1) $24 ÷ 6 = $4 per sandwich (B). 2) 150 ÷ 5 = 30 mph (A). 3) 8 ÷ 4 = 2 cups per orange (C). D and E are common errors from misordered division.
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| 9 |
G6RP-009 |
6.RP.A.3 |
2 |
Claim 2 |
Cloze Text |
qc_pass
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0 |
▼ |
Stem: A double number line shows that 4 pounds of grapes cost $10. [Double number line: top line marked with pounds 0, 2, 4, 6, 8; bottom line marked with dollars 0, ?, 10, ?, ?]. Use the diagram to find: 6 pounds of grapes will cost $_____.
Answer Key: 15
Rationale: The unit rate is $10 ÷ 4 = $2.50 per pound. For 6 pounds: 6 × $2.50 = $15. Students can also extend the double number line: 2 lb = $5, 4 lb = $10, 6 lb = $15.
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| 10 |
G6RP-010 |
6.RP.A.3 |
3 |
Claim 4 |
Match List |
qc_pass
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0 |
▼ |
Stem: Match each real-world situation on the left to the representation on the right that best models its ratio relationship.
Options:
Answer Key: 1-D,2-C,3-A
Rationale: 1) A double number line aligns two changing quantities like pounds and dollars (D). 2) A two-column table best displays multiple equivalent ratios (C). 3) A tape diagram with 4 equal sections shows equal groupings (A). B and E are unrelated or inappropriate representations.
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| 11 |
G6RP-011 |
6.RP.A.3 |
4 |
Claim 4 |
Drag and Drop |
human_review
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0 |
▼ |
Stem: A juice mix uses 3 cups of orange juice for every 2 cups of pineapple juice. A school needs to make 30 cups of this mix for an event. Drag each value into the correct box to complete the model. [Visual: a tape diagram with 5 equal sections — 3 labeled 'OJ' and 2 labeled 'Pineapple' — followed by two answer boxes: 'Cups of OJ needed: ___' and 'Cups of Pineapple needed: ___'. Below, a two-row equivalent-ratio table with columns OJ and Pineapple has rows (3,2), (6,4), (___,___) showing the row that totals 30 cups.]
Options:
token1. 18 token2. 12 token3. 15 token4. 10 token5. 20
Answer Key: Cups of OJ needed: token1; Cups of Pineapple needed: token2
Rationale: Total parts = 3 + 2 = 5. Each part = 30 ÷ 5 = 6 cups. OJ = 3 × 6 = 18 (token1). Pineapple = 2 × 6 = 12 (token2). Tokens 3, 4, and 5 are common errors (using half of 30, splitting 30 evenly, or misreading the ratio).
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| 12 |
G6RP-012 |
6.RP.A.3.a |
1 |
Claim 1 |
Multiple Choice (MCQ) |
qc_pass
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0 |
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Stem: The table shows equivalent ratios of cups of water to cups of rice. [Table with columns: Water (cups) | Rice (cups). Rows: 2 | 1; 4 | 2; 6 | ?; 8 | 4]. What value completes the third row?
Options:
A. 5 B. 3 C. 6 D. 2
Answer Key: B
Rationale: The ratio of water to rice is 2:1, so each cup of rice pairs with 2 cups of water. For 6 cups of water, rice = 6 ÷ 2 = 3. A adds a constant difference. C copies the water value. D repeats a value already in the table.
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| 13 |
G6RP-013 |
6.RP.A.3.a |
2 |
Claim 1 |
Multiple Choice (MCQ) |
qc_pass
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0 |
▼ |
Stem: Two trail mixes use these ratios of nuts to raisins. [Mix A table: Nuts | Raisins → 2|3, 4|6, 6|9. Mix B table: Nuts | Raisins → 3|4, 6|8, 9|12]. Which statement compares the two mixes correctly?
Options:
A. Both mixes have the same ratio of nuts to raisins. B. Mix A has more nuts per raisin than Mix B. C. Mix B has more nuts per raisin than Mix A. D. Neither mix shows a constant ratio.
Answer Key: C
Rationale: Mix A unit rate: 2/3 ≈ 0.67 nuts per raisin. Mix B unit rate: 3/4 = 0.75 nuts per raisin. Mix B has more nuts per raisin. A misses the difference between 2:3 and 3:4. B reverses the comparison. D ignores that both tables show equivalent ratios.
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| 14 |
G6RP-014 |
6.RP.A.3.a |
2 |
Claim 1 |
Match List |
qc_pass
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0 |
▼ |
Stem: A ratio table shows pairs (x, y) where y = 3x. [Table: x | y → 1|3, 2|6, 3|9, 4|12]. Match each x-value on the left to the correct coordinate pair on the right that would be plotted on the coordinate plane.
Options:
Answer Key: 1-C,2-A,3-B
Rationale: Each ordered pair (x, y) plots x on the horizontal axis and y on the vertical axis. 1→(1,3) is C. 2→(2,6) is A. 3→(4,12) is B. D reverses the coordinates. E uses an additive (not multiplicative) relationship.
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| 15 |
G6RP-015 |
6.RP.A.3.a |
3 |
Claim 3 |
Drag and Drop |
qc_pass
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0 |
▼ |
Stem: Drag each ordered pair into the correct category to show whether it belongs to the same ratio relationship as the table. [Table of equivalent ratios: x | y → 2|5, 4|10, 6|15]. Categories: 'Belongs to the ratio' and 'Does NOT belong to the ratio'.
Options:
token1. (8, 20) token2. (10, 25) token3. (3, 7) token4. (12, 30) token5. (5, 10)
Answer Key: Belongs to the ratio: token1, token2, token4; Does NOT belong to the ratio: token3, token5
Rationale: The ratio is 2:5, so y = 2.5x (or y/x = 5/2). token1 (8,20): 20/8 = 5/2 ✓. token2 (10,25): 25/10 = 5/2 ✓. token4 (12,30): 30/12 = 5/2 ✓. token3 (3,7): 7/3 ≠ 5/2 ✗. token5 (5,10): 10/5 = 2 ≠ 5/2 ✗.
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| 16 |
G6RP-016 |
6.RP.A.3.a |
4 |
Claim 4 |
Multiple Response |
human_review
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0 |
▼ |
Stem: A bakery records ingredients for two cookie recipes. [Recipe X table: Sugar (cups) | Flour (cups) → 1|3, 2|6, 3|9. Recipe Y table: Sugar (cups) | Flour (cups) → 2|5, 4|10, 6|15]. Select ALL true statements about the recipes.
Options:
A. Recipe X uses 1/3 cup of sugar for each cup of flour. B. Recipe Y uses 2/5 cup of sugar for each cup of flour. C. Recipe Y has more sugar per cup of flour than Recipe X. D. If both recipes use 30 cups of flour, Recipe X uses more sugar. E. The point (6, 18) belongs to Recipe X on a coordinate plot.
Answer Key: A,B,C
Rationale: A: Recipe X is 1:3 sugar to flour → 1/3 ✓. B: Recipe Y is 2:5 → 2/5 ✓. C: 2/5 = 0.40 > 1/3 ≈ 0.33 ✓. D: With 30 cups flour, X uses 10 sugar, Y uses 12 sugar — Y uses more, so D is false. E: For Recipe X, x = sugar, y = flour, so (6, 18) only fits if we plot (sugar, flour); however the table column order is sugar then flour, and 6 sugar → 18 flour, but typical convention asks (flour, sugar) when comparing. Either way the listed point doesn't match a row in the table (3, 9). Misconception flag.
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| 17 |
G6RP-017 |
6.RP.A.3.b |
1 |
Claim 1 |
Multiple Choice (MCQ) |
qc_pass
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0 |
▼ |
Stem: A printer prints 60 pages in 5 minutes at a constant rate. What is the unit rate in pages per minute?
Options:
A. 12 pages per minute B. 5 pages per minute C. 300 pages per minute D. 55 pages per minute
Answer Key: A
Rationale: Unit rate = 60 ÷ 5 = 12 pages per minute. B reuses the time. C multiplies instead of dividing. D subtracts the values.
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| 18 |
G6RP-018 |
6.RP.A.3.b |
2 |
Claim 1 |
Multiple Response |
qc_pass
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0 |
▼ |
Stem: A bicycle travels 24 miles in 3 hours at a constant speed. Select ALL statements that are true.
Options:
A. The unit rate is 8 miles per hour. B. In 6 hours, the bicycle travels 48 miles. C. In 1 hour, the bicycle travels 8 miles. D. The unit rate is 24 miles per hour. E. In 2 hours, the bicycle travels 12 miles.
Answer Key: A,B,C
Rationale: Unit rate = 24 ÷ 3 = 8 mph (A, C). In 6 hours: 6 × 8 = 48 miles (B). D ignores time. E uses 24/4 instead of multiplying the unit rate.
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| 19 |
G6RP-019 |
6.RP.A.3.b |
2 |
Claim 1 |
Cloze Text |
qc_pass
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0 |
▼ |
Stem: A grocery store sells 4 cans of soup for $5. At this unit price, 12 cans of soup would cost $_____.
Answer Key: 15
Rationale: Unit price = $5 ÷ 4 = $1.25 per can. 12 × $1.25 = $15. Alternatively, 12 cans is 3 × 4 cans, so cost = 3 × $5 = $15.
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| 20 |
G6RP-020 |
6.RP.A.3.b |
3 |
Claim 2 |
Multiple Choice (MCQ) |
qc_pass
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0 |
▼ |
Stem: It takes 7 hours to mow 4 lawns at a constant rate. At this rate, how many lawns can be mowed in 35 hours?
Options:
A. 28 lawns B. 32 lawns C. 5 lawns D. 20 lawns
Answer Key: D
Rationale: Rate = 4 lawns / 7 hours. In 35 hours: (4/7) × 35 = 20 lawns. A multiplies 4 × 7. B adds 28 + 4. C divides 35 ÷ 7 (giving hours-multiplier, not lawns).
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| 21 |
G6RP-021 |
6.RP.A.3.b |
4 |
Claim 3 |
Match List |
human_review
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0 |
▼ |
Stem: Three runners run at constant speeds. Runner 1 runs 6 miles in 1 hour. Runner 2 runs 15 miles in 3 hours. Runner 3 runs 12 miles in 2 hours. Match each runner to the statement that best justifies their relative speed.
Options:
Answer Key: 1-B,2-A,3-D
Rationale: Runner 1: 6/1 = 6 mph (middle, B). Runner 2: 15/3 = 5 mph (slowest, A). Runner 3: 12/2 = 6 mph (same as Runner 1, D). C uses total distance not rate. E divides incorrectly. F is fabricated.
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| 22 |
G6RP-022 |
6.RP.A.3.c |
2 |
Claim 1 |
Multiple Choice (MCQ) |
qc_pass
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0 |
▼ |
Stem: What is 30% of 80? [Visual: a percent bar split into 10 equal sections, with 3 of 10 sections shaded; the full bar is labeled 80.]
Options:
A. 50 B. 24 C. 30 D. 240
Answer Key: B
Rationale: 30% of 80 = (30/100) × 80 = 24. A subtracts 30 from 80. C confuses the percent with the answer. D ignores the decimal placement (multiplies 30 × 8).
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| 23 |
G6RP-023 |
6.RP.A.3.c |
2 |
Claim 1 |
Multiple Response |
qc_pass
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0 |
▼ |
Stem: Select ALL expressions that are equal to 25% of 60.
Options:
A. (25/100) × 60 B. 0.25 × 60 C. 60 ÷ 4 D. 25 × 60 E. 60 ÷ 25
Answer Key: A,B,C
Rationale: 25% = 25/100 = 0.25 = 1/4. A, B, and C all equal 15. D treats the percent as a whole number. E divides incorrectly.
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| 24 |
G6RP-024 |
6.RP.A.3.c |
3 |
Claim 3 |
Cloze Text |
qc_pass
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0 |
▼ |
Stem: A part of a number is 18, and that part is 30% of the whole. Use ratio reasoning: since 30% corresponds to 18, then 10% corresponds to _____ , and the whole (100%) is _____ .
Answer Key: 6;60
Rationale: If 30% = 18, then 10% = 18 ÷ 3 = 6. The whole (100%) = 10 × 6 = 60. This uses ratio reasoning to find the whole given a part and percent.
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| 25 |
G6RP-025 |
6.RP.A.3.c |
3 |
Claim 2 |
Multiple Response |
qc_pass
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0 |
▼ |
Stem: A jacket originally costs $80. The store offers a 25% discount. Select ALL true statements.
Options:
A. The discount amount is $20. B. The sale price is $60. C. The sale price is 75% of the original price. D. The sale price is $55. E. The discount is $25 because the percent is 25.
Answer Key: A,B,C
Rationale: 25% of $80 = $20 (A). Sale price = $80 − $20 = $60 (B). After 25% off, 75% remains, so sale price = 75% of $80 = $60 (C). D miscalculates. E confuses the percent with dollars.
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| 26 |
G6RP-026 |
6.RP.A.3.c |
4 |
Claim 4 |
Drag and Drop |
human_review
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0 |
▼ |
Stem: A school survey asked 200 students about their favorite lunch. The results are shown in the percent bar. [Visual: 100-section grid where 40 sections are labeled 'Pizza', 25 sections labeled 'Tacos', 20 sections labeled 'Salad', and 15 sections labeled 'Pasta'.] Drag the correct number of students into each box. Boxes: 'Pizza: ___', 'Tacos: ___', 'Salad: ___', 'Pasta: ___'.
Options:
token1. 80 token2. 50 token3. 40 token4. 30 token5. 25 token6. 20
Answer Key: Pizza: token1; Tacos: token2; Salad: token3; Pasta: token4
Rationale: Pizza: 40% of 200 = 80 (token1). Tacos: 25% of 200 = 50 (token2). Salad: 20% of 200 = 40 (token3). Pasta: 15% of 200 = 30 (token4). Distractors 5 and 6 reflect students confusing the percent with the number of students.
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| 27 |
G6RP-027 |
6.RP.A.3.d |
2 |
Claim 1 |
Match List |
qc_pass
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0 |
▼ |
Stem: Use the conversion facts: 1 foot = 12 inches; 1 pound = 16 ounces; 1 meter = 100 centimeters. Match each measurement on the left to its equivalent on the right.
Options:
Answer Key: 1-C,2-A,3-B
Rationale: 1) 3 × 12 = 36 inches (C). 2) 2 × 16 = 32 ounces (A). 3) 4 × 100 = 400 centimeters (B). D applies the wrong conversion. E uses 10 cm per meter incorrectly.
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| 28 |
G6RP-028 |
6.RP.A.3.d |
3 |
Claim 3 |
Multiple Choice (MCQ) |
qc_pass
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0 |
▼ |
Stem: A student wrote: '5 liters = 5 × 1,000 = 5,000 milliliters because 1 liter = 1,000 milliliters.' Which statement BEST explains why the student multiplied by 1,000?
Options:
A. Because milliliters are smaller, more of them are needed to equal the same amount, so we multiply when going from liters to milliliters. B. Because milliliters are larger units, we always multiply to convert. C. Because the number must always get bigger when converting units. D. Because dividing would give a fraction, and conversions cannot use fractions.
Answer Key: A
Rationale: Going to a smaller unit means more of them fit in the same amount, so we multiply by the conversion factor. B reverses the unit-size logic. C is a misconception that ignores direction of conversion. D is false reasoning.
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| 29 |
G6RP-029 |
6.RP.A.3.d |
4 |
Claim 2 |
Drag and Drop |
human_review
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0 |
▼ |
Stem: A rectangular garden is 4 yards long and 6 feet wide. Use the conversions: 1 yard = 3 feet; 1 foot = 12 inches. Drag the correct values into each box. Boxes: 'Length in feet: ___', 'Length in inches: ___', 'Perimeter in feet: ___', 'Area in square feet: ___'.
Options:
token1. 12 token2. 144 token3. 36 token4. 72 token5. 10 token6. 48
Answer Key: Length in feet: token1; Length in inches: token2; Perimeter in feet: token3; Area in square feet: token4
Rationale: Length: 4 yd × 3 = 12 ft (token1). Length in inches: 12 ft × 12 = 144 in (token2). Perimeter: 2(12 + 6) = 36 ft (token3). Area: 12 × 6 = 72 sq ft (token4). token5 reflects adding length + width once. token6 reflects multiplying 4 × 12.
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| 30 |
G6RP-030 |
6.RP.A.3.d |
4 |
Claim 3 |
Drag and Drop |
human_review
|
0 |
▼ |
Stem: A juice carton holds 2 liters. Use the conversions: 1 liter = 1,000 milliliters; 1 cup = 250 milliliters. Drag each value into the correct box to justify the steps of the conversion. Boxes: 'Total milliliters: ___', 'Conversion factor used (mL per cup): ___', 'Total cups: ___', 'Operation used to find cups: ___'.
Options:
token1. 2,000 token2. 250 token3. 8 token4. division token5. multiplication token6. 500
Answer Key: Total milliliters: token1; Conversion factor used (mL per cup): token2; Total cups: token3; Operation used to find cups: token4
Rationale: 2 L × 1,000 = 2,000 mL (token1). 1 cup = 250 mL (token2). 2,000 ÷ 250 = 8 cups (token3). Going from smaller units (mL) to larger units (cups) requires division (token4). token5 reflects misconception about always multiplying. token6 reflects miscomputing 2,000 ÷ 4.
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