Compare Lengths of Two Objects - 2nd Grade Math

1. Keisha's ribbon is 24 inches and Yuki's ribbon is 19 inches. How much shorter is Yuki's ribbon?
   Answer: 5 inches shorter Yuki's ribbon is 5 inches shorter, because $24 - 19 = 5$. Choice A (4 inches) comes from subtracting incorrectly by one too many. Choice B (6 inches) comes from subtracting incorrectly by one too few. Choice D (43 inches) comes from adding the two lengths instead of subtracting.
2. Put these in order from shortest to longest: 3 in, 8 in, 5 in.
   Answer: 3 in, 5 in, 8 in The correct answer is 3 in, 5 in, 8 in, because ordering the lengths from smallest to largest gives shortest to longest. Choice A (8 in, 5 in, 3 in) lists the lengths backward, longest to shortest. Choice B (5 in, 3 in, 8 in) and Choice C (3 in, 8 in, 5 in) are both out of order and don't go from smallest to largest.
3. Keisha jumped 19 inches and Amir jumped 23 inches. Who jumped farther?
   Answer: Amir Amir jumped 23 inches and Keisha jumped 19 inches. Since $23 > 19$, Amir jumped farther. Choice A picks the shorter distance. Choice B is incorrect because 19 and 23 are different numbers. Choice C is incorrect because both distances are already given, so nothing more is needed to compare them.
4. Jake measures his toy car as 6 inches long. His sister's doll is 4 inches long. Jake then gets a toy truck that is 2 inches longer than his car. How much longer is the truck than the doll?
   Answer: 4 inches longer The truck is 4 inches longer than the doll, since the truck is 6 plus 2, or 8 inches long, and 8 minus 4 equals 4. Choosing 8 inches longer confuses the truck's total length with the difference between the truck and the doll. Choosing 2 inches longer is the difference between the truck and the car, not the doll. Choosing 6 inches longer mixes up the car's length with the actual difference needed.
5. Emma measured three objects: a book that is 11 centimeters long, an eraser that is 5 centimeters long, and a marker that is 9 centimeters long. How much longer is the book than the eraser?
   Answer: 6 centimeters longer The book is 11 centimeters and the eraser is 5 centimeters, so the book is 11 minus 5, or 6 centimeters, longer than the eraser. Getting 4 centimeters mixes up the marker's length with the eraser's. Getting 2 centimeters mixes up the marker's length with the book's. Getting 5 centimeters just restates the eraser's own length instead of finding the difference between the book and the eraser.
6. Chen measured two books: one is 10 inches long and the other is 12 inches long. Which book is longer?
   Answer: The 12-inch book Since 12 inches is greater than 10 inches, the 12-inch book is longer, making A correct. Choice B is wrong because the two lengths are different, not equal. Choice C reverses the comparison and picks the shorter book. Choice D is wrong because both lengths are given, so the comparison can be made.
7. Look at the number line where each mark represents 1 inch. A pencil spans from the 3-inch mark to the 10-inch mark. A pen spans from the 5-inch mark to the 9-inch mark. How much longer is the pencil than the pen?
   Answer: 3 inches longer because 7 minus 4 equals 3 Pencil length = 10 - 3 = 7 inches. Pen length = 9 - 5 = 4 inches. Difference = 7 - 4 = 3 inches. Choice A uses endpoints incorrectly (10 - 9). Choice C shows an arithmetic error. Choice D gives only the pencil's length, not the comparison.
8. Sofia cut string A to 30 inches and string B to 22 inches. How much longer is string A than string B?
   Answer: 8 inches longer String A is 8 inches longer, because $30 - 22 = 8$. Choice A (10 inches) comes from a subtraction error, likely rounding 22 down to 20 before subtracting. Choice B (52 inches) comes from adding the two lengths instead of subtracting. Choice C (7 inches) comes from subtracting incorrectly by one.
9. Lisa has a jump rope that measures 15 feet. Her friend has a jump rope that measures 9 feet. Lisa cuts her rope to make it exactly 2 feet longer than her friend's rope. How many feet did Lisa cut off her rope?
   Answer: 4 feet Lisa's rope must end up 2 feet longer than her friend's 9-foot rope, so it should be 11 feet long. Since her rope started at 15 feet, she cut off 15 minus 11, or 4 feet. Choice A confuses the 2-foot difference with the amount cut. Choice B subtracts 9 from 15 but forgets to account for the extra 2 feet. Choice D adds instead of subtracting, mixing up the final length with the amount removed.
10. A pencil is 7 inches. A crayon is 4 inches. Which is shorter?
    Answer: The crayon The crayon is 4 inches, which is shorter than the pencil's 7 inches. Choice B is wrong because the pencil is the longer of the two objects. Choice C is wrong because both lengths are given, so the answer can be determined. Choice D is wrong because 4 inches and 7 inches are not equal.
11. Keisha's jump was 34 inches. Carlos's jump was 29 inches. Who jumped farther?
    Answer: Keisha Keisha jumped 34 inches, which is farther than Carlos's 29 inches, so Keisha jumped farther. Carlos jumped a shorter distance at 29 inches. The two distances are different, so they are not the same. Since one distance is greater than the other, one of them did jump farther.
12. A book is 10 inches, a ruler is 12 inches, and a notebook is 9 inches. Which object is the longest?
    Answer: The ruler The ruler is 12 inches, which is longer than the book at 10 inches and the notebook at 9 inches. Choice A is wrong because the three objects have different lengths. Choice C is wrong because the notebook is the shortest of the three. Choice D is wrong because the book is shorter than the ruler.
13. Order these from shortest to longest: eraser 2 inches, marker 5 inches, pencil 7 inches.
    Answer: Eraser, Marker, Pencil This question tests 2nd grade understanding of comparing lengths of two objects by direct comparison or by comparing measurements (CCSS 2.MD.A.4: Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit). To compare lengths of two objects, you can line them up side-by-side (start at the same point) and see which extends farther—that one is longer; or, if both are measured in the same units, compare the numbers: the bigger number means longer length; to find how much longer, subtract the smaller measurement from the larger measurement; longer means greater length (extends farther, bigger measurement); shorter means lesser length (doesn't extend as far, smaller measurement); if asked 'how much longer', subtract to find the difference. In this problem, objects are given with measurements (eraser 2 inches, marker 5 inches, pencil 7 inches), and the task is to order from shortest to longest. To find the answer, order by size of measurements (2 < 5 < 7). Choice A is correct because ordering 2, 5, 7 from smallest to largest gives eraser (2), marker (5), pencil (7) = shortest to longest; this demonstrates understanding of ordering by length. Choice C represents wrong ordering sequence (longest to shortest instead of shortest to longest); this error typically happens when students can't order numbers or confuse shortest with longest. To help students: Practice direct visual comparison first—line up objects at one end and observe; then add measurement, sort numbers first: 2, 5, 7 (smallest to largest), match to objects; model subtraction for differences; use number line; practice language: shortest, longest; watch for wrong ordering.
14. Emma is 48 inches tall. Jamal is 46 inches tall. How much taller is Emma than Jamal?
    Answer: 2 inches Emma is 2 inches taller than Jamal, since 48 minus 46 equals 2. Choosing 4 inches or 6 inches does not match the actual difference between their heights. Adding 48 and 46 gives 94, which is their combined height, not the difference between them.
15. A marker is 5 inches, a pencil is 7 inches, and an eraser is 2 inches. Which is longest?
    Answer: The pencil The pencil is the longest, at 7 inches, since $7 > 5$ and $7 > 2$. Choice B (the eraser) is only 2 inches, the shortest of the three. Choice C is incorrect because the three items are not the same length (5, 7, and 2 inches). Choice D (the marker) is 5 inches, shorter than the pencil.
16. Study the diagram showing three ribbons measured against a centimeter ruler. The blue ribbon goes from 0 to 8 cm, the red ribbon goes from 2 to 9 cm, and the green ribbon goes from 1 to 5 cm. How much longer is the red ribbon than the green ribbon?
    Answer: 3 centimeters longer The red ribbon is 9 minus 2, or 7 centimeters long, and the green ribbon is 5 minus 1, or 4 centimeters long, and 7 minus 4 is 3, so the red ribbon is 3 centimeters longer, matching A. B uses only the red ribbon's endpoints and ignores the green ribbon's length. C compares the wrong pair of endpoints instead of finding each ribbon's actual length first. D compares the blue ribbon's endpoints, which are not part of this comparison.
17. A blue ribbon is 19 inches. A red ribbon is 11 inches. How much shorter is the red ribbon?
    Answer: 8 inches shorter The red ribbon is 8 inches shorter, because $19 - 11 = 8$. Choice A (11 inches) repeats the red ribbon's own length instead of finding the difference. Choice C (7 inches) comes from subtracting incorrectly by one. Choice D (30 inches) comes from adding the two lengths instead of subtracting.
18. Chen measured two sticks: 16 inches and 9 inches. How much shorter is the 9-inch stick?
    Answer: 7 inches shorter The correct answer is 7 inches shorter, because 16 - 9 = 7. Choice B (8 inches shorter) is off by one from the correct difference. Choice C (25 inches shorter) adds the two lengths instead of subtracting. Choice D (6 inches shorter) is one inch less than the correct difference.
19. Maya measured two ribbons: 18 inches and 25 inches. Which is longer?
    Answer: The 25-inch ribbon The 25-inch ribbon is longer because 25 is a greater number of inches than 18. The ribbons are not the same length, since 25 and 18 are different numbers. The 18-inch ribbon is the shorter one, not the longer one.
20. Marcus jumped 36 inches and Emma jumped 29 inches. Who jumped farther?
    Answer: Marcus The correct answer is Marcus, because 36 inches is greater than 29 inches. Choice A (Emma) picks the person who jumped the shorter distance. Choices B (Neither one) and C (They jumped the same distance) don't apply, since 36 and 29 are different numbers.

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