Solve Length Word Problems - 2nd Grade Math

1. Using the ruler shown, Anna measures her book as $23$ centimeters long and her notebook as $18$ centimeters long. If she places them end-to-end, what is the total length?
   Answer: $41$ centimeters total length Adding the lengths end-to-end: $23 + 18 = 41$ centimeters. Choice B shows subtraction error ($23 - 18$). Choice C shows addition error missing 1. Choice D shows addition error adding 1 extra.
2. Maya places 3 identical desks in a row to make one long desk. Each desk is 4 feet long. What is the total length of the row of desks now?
   Answer: 12 feet Each of the 3 desks is 4 feet long, so the total length is 3 times 4, or 12 feet. Choice A only counts one desk. Choice B only counts two desks. Choice D adds a fourth desk that isn't part of the row.
3. Marcus jumps 53 inches. Yuki jumps 38 inches. How much farther did Marcus jump than Yuki?
   Answer: 15 53 minus 38 equals 15, so Marcus jumped 15 inches farther. 38 inches is Yuki's own jump distance, not the difference between the two. 91 inches would result from adding the two distances instead of subtracting. 16 inches is 1 more than the correct difference.
4. Marcus measured two boards. One board is 63 inches long and the other is 48 inches long. What is the difference in their lengths?
   Answer: 15 inches The difference in length is 15 inches, because $63 - 48 = 15$. Choice A (111 inches) comes from adding the two lengths instead of subtracting. Choice C (16 inches) comes from a subtraction error, off by one. Choice D (48 inches) repeats one of the given lengths instead of finding the difference.
5. Keisha has 48 inches of ribbon. She uses 15 inches, then uses 9 inches more. How many inches of ribbon are left?
   Answer: 24 inches Starting with 48 inches, using 15 inches leaves 33, and using 9 more leaves 24 inches. Choice A, 72 inches, comes from adding the amounts used instead of subtracting them. Choice C, 15 inches, only reflects the first amount used, not what remains. Choice D, 33 inches, stops after subtracting the first 15 inches and forgets the second use of 9 inches.
6. A desk is 4 feet long. Maya adds a 3-foot extension to it. What is the total length of the desk now?
   Answer: 7 feet Adding the 3-foot extension to the 4-foot desk gives a total length of 7 feet. Choice A, 12 feet, is much too long for this addition. Choice B, 6 feet, does not match adding 4 and 3. Choice D, 1 foot, looks like a subtraction of 4 minus 3 instead of addition.
7. Marcus tapes together three strips of paper: 12 inches, 16 inches, and 9 inches. What is the total length of the strips together?
   Answer: 37 inches This question tests 2nd grade understanding of solving word problems involving addition and subtraction of lengths, including finding totals, differences, and remaining amounts (CCSS 2.MD.B.5: Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units). To solve a length word problem, first identify what operation is needed. If combining lengths (taping ribbons together, adding distances walked), use addition. If finding difference (how much longer, how much taller), use subtraction (larger - smaller). If finding remaining (after cutting, after using some), use subtraction (start - used = left). Then set up the equation, calculate, and state the answer with units. Addition keywords: total, altogether, combined, in all, both, together. Subtraction keywords: how much more, how much longer/taller, difference (comparison), or left, remaining, left over (take away). In this problem, three strips of paper measuring 12 inches, 16 inches, and 9 inches are taped together. To solve, add the three lengths (12 + 16 + 9 = 37 inches total). The answer must include units (inches). Choice B is correct because adding 12 + 16 + 9 = 37 inches, which is the total combined length of the strips together. The answer 37 inches correctly states the result with proper units. Choice C represents incomplete multi-step (added first two but forgot third number: 12 + 16 = 28 instead of 12 + 16 + 9 = 37). This error typically happens when students don't identify correct operation from keywords, make arithmetic mistakes, don't complete all steps, use wrong numbers, forget to include units, misunderstand what question is asking for. To help students: Teach keyword identification—underline keywords that indicate operation (total/altogether = add, how much more/longer/left = subtract). Model thinking aloud: 'Tapes together three strips—that means combine, so add. 12 + 16 + 9.' Use visual models: draw ribbons or number line showing lengths. Practice setting up equations: identify numbers and operation, write equation (12 + 16 + 9 = ?), solve, state answer with units. For comparison/difference problems, emphasize: bigger number - smaller number (48 - 35, not 35 - 48). For remaining problems, emphasize: start - used = left (50 - 18 = 32 left). Use consistent problem structure: read problem, identify operation, identify numbers, write equation, calculate, answer with units. Practice checking: Does my answer make sense? (If combining 12, 16, 9, answer should be bigger than each; if cutting 18 from 50, answer should be less than 50). Watch for: wrong operation selected, calculation errors (especially with regrouping), using only one number, forgetting units, answering different question than asked, subtraction direction errors, incomplete multi-step problems.
8. Keisha tapes together three strips of paper: 12 inches, 15 inches, and 9 inches. How long is the paper strip altogether?
   Answer: 36 inches Adding 12, 15, and 9 inches together gives a total of 36 inches. 24 inches leaves out one of the three strips. 37 inches is 1 inch too high for the correct sum. 27 inches leaves out the 9-inch strip.
9. Carlos has 3 feet of wood for a project. He adds 2 more feet. What is the total length of the wood now?
   Answer: 5 feet The correct answer is 5 feet, because 3 + 2 = 5. Choice A (3 feet) repeats only the starting amount and ignores the wood Carlos added. Choice C (1 foot) is far too short to be the total. Choice D (6 feet) adds one foot too many.
10. Tommy walks $34$ feet from his house to the mailbox, then $19$ feet from the mailbox to his friend's house. His friend's house is $28$ feet from the park. How many feet does Tommy walk if he goes from his house to the park by way of the mailbox and his friend's house?
    Answer: 81 feet Tommy walks 81 feet in all, because $34 + 19 + 28 = 81$. Choice A (47 feet) adds only the last two legs of the trip ($19 + 28$), skipping the walk from the house to the mailbox. Choice B (53 feet) adds only the first two legs ($34 + 19$), leaving out the walk from the friend's house to the park. Choice C (62 feet) adds only the first and last legs ($34 + 28$), skipping the middle leg entirely.
11. Emma has 72 meters of rope. She cuts off 25 meters to tie boxes. How many meters of rope remain?
    Answer: 47 meters 72 minus 25 equals 47, so 47 meters of rope remain. 97 meters would result from adding instead of subtracting. 46 meters is 1 short of the correct difference. 25 meters is just the amount cut off, not what remains.
12. Yuki tapes together three strips of paper that are 12 inches, 15 inches, and 9 inches long. What is the total length of the strips together?
    Answer: 36 inches The correct answer is 36 inches, because 12 + 15 + 9 = 36. Choice A (15 inches) is just the length of one strip, not the total. Choice B (27 inches) adds only the first two strips and forgets the third. Choice C (24 inches) comes from an addition mistake when combining the three lengths.
13. Alex has a $58$ inch rope. He cuts off a $19$ inch piece and a $23$ inch piece. Then he cuts $4$ more inches off the rest. How long is the rope now?
    Answer: $12$ inches The rope started at 58 inches. After cutting off 19 inches and 23 inches, 58 - 19 - 23 = 16 inches are left. Cutting 4 more inches off leaves 16 - 4 = 12 inches, so Choice C is correct. Choice A is wrong because it does not subtract enough. Choice B is wrong because it stops before the last cut. Choice D is wrong because it adds instead of subtracting.
14. Sofia has an 18-inch ribbon and a 27-inch ribbon. She tapes them together to make one long ribbon. How long is the combined ribbon altogether?
    Answer: 45 inches 18 inches plus 27 inches equals 45 inches when the two ribbons are taped together. 44 inches comes from a small addition error in the ones place. 9 inches would come from subtracting instead of adding the two lengths. 27 inches is only the length of one ribbon, not the combined length of both.
15. One plant is 46 cm tall. Another plant is 31 cm tall. How much taller is the 46 cm plant?
    Answer: 15 cm taller The difference between 46 cm and 31 cm is 46 - 31 = 15 cm, so Choice B is correct. Choice A is wrong because it is 1 centimeter too few. Choice C is wrong because it just repeats the height of the taller plant instead of finding the difference. Choice D is wrong because it adds the two heights instead of subtracting.
16. Maya has a 70-inch piece of string. She uses 28 inches to tie a package. How many inches of string remain?
    Answer: 42 inches This question tests 2nd grade understanding of solving word problems involving addition and subtraction of lengths, including finding totals, differences, and remaining amounts (CCSS 2.MD.B.5: Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units). To solve a length word problem, first identify what operation is needed. If combining lengths (taping ribbons together, adding distances walked), use addition. If finding difference (how much longer, how much taller), use subtraction (larger - smaller). If finding remaining (after cutting, after using some), use subtraction (start - used = left). Then set up the equation, calculate, and state the answer with units. Addition keywords: total, altogether, combined, in all, both, together. Subtraction keywords: how much more, how much longer/taller, difference (comparison), or left, remaining, left over (take away). In this problem, Maya has a 70-inch piece of string and uses 28 inches to tie a package, asking how many inches remain. To solve, subtract to find remaining (70 - 28 = 42 inches left). The answer must include units (inches). Choice A is correct because subtracting 70 - 28 = 42 inches, which is the amount of string remaining after using 28 inches. The answer 42 inches correctly states the result with proper units. Choice C represents using only one number from problem (answered 28 instead of calculating remaining). This error typically happens when students don't identify correct operation from keywords, make arithmetic mistakes, don't complete all steps, use wrong numbers, forget to include units, misunderstand what question is asking for. To help students: Teach keyword identification—underline keywords that indicate operation (total/altogether = add, how much more/longer/left = subtract). Model thinking aloud: 'Uses some string, how many remain—that means take away, so subtract. 70 - 28.' Use visual models: draw string or number line showing lengths. Practice setting up equations: identify numbers and operation, write equation (70 - 28 = ?), solve, state answer with units. For comparison/difference problems, emphasize: bigger number - smaller number (48 - 35, not 35 - 48). For remaining problems, emphasize: start - used = left (70 - 28 = 42 left). Use consistent problem structure: read problem, identify operation, identify numbers, write equation, calculate, answer with units. Practice checking: Does my answer make sense? (If combining 15 and 22, answer should be bigger than both; if using 28 from 70, answer should be less than 70). Watch for: wrong operation selected, calculation errors (especially with regrouping), using only one number, forgetting units, answering different question than asked, subtraction direction errors, incomplete multi-step problems.
17. Yuki has a 35 cm jump rope. Her brother has a 50 cm jump rope. What is the difference in length between the two ropes?
    Answer: 15 cm 50 minus 35 equals 15, so the difference in length is 15 cm. 14 cm is 1 short of the correct difference. 35 cm is Yuki's own rope length, not the difference between the two. 85 cm would result from adding the two lengths instead of subtracting.
18. A runner goes 29 meters, then 34 meters more. How many meters did the runner go in total?
    Answer: 63 meters This question tests 2nd grade understanding of solving word problems involving addition and subtraction of lengths, including finding totals, differences, and remaining amounts (CCSS 2.MD.B.5: Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units). To solve a length word problem, first identify what operation is needed. If combining lengths (taping ribbons together, adding distances walked), use addition. If finding difference (how much longer, how much taller), use subtraction (larger - smaller). If finding remaining (after cutting, after using some), use subtraction (start - used = left). Then set up the equation, calculate, and state the answer with units. Addition keywords: total, altogether, combined, in all, both, together. Subtraction keywords: how much more, how much longer/taller, difference (comparison), or left, remaining, left over (take away). In this problem, a runner goes 29 meters, then 34 meters more, asking how many meters the runner went in total. To solve, add the two distances (29 + 34 = 63 meters total). The answer must include units (meters). Choice A is correct because adding 29 + 34 = 63 meters, which is the total distance the runner went. The answer 63 meters correctly states the result with proper units. Choice B represents a calculation error (29 - 34 = -5, but absolute or miscalculation to 5). This error typically happens when students don't identify correct operation from keywords, make arithmetic mistakes, don't complete all steps, use wrong numbers, forget to include units, misunderstand what question is asking for. To help students: Teach keyword identification—underline keywords that indicate operation (total/altogether = add, how much more/longer/left = subtract). Model thinking aloud: 'Goes some then more, in total—that means combine, so add. 29 + 34.' Use visual models: draw path or number line showing distances. Practice setting up equations: identify numbers and operation, write equation (29 + 34 = ?), solve, state answer with units. For comparison/difference problems, emphasize: bigger number - smaller number (48 - 35, not 35 - 48). For remaining problems, emphasize: start - used = left (50 - 18 = 32 left). Use consistent problem structure: read problem, identify operation, identify numbers, write equation, calculate, answer with units. Practice checking: Does my answer make sense? (If combining 29 and 34, answer should be bigger than both; if cutting 18 from 50, answer should be less than 50). Watch for: wrong operation selected, calculation errors (especially with regrouping), using only one number, forgetting units, answering different question than asked, subtraction direction errors, incomplete multi-step problems.
19. Maria has a ribbon that is 27 inches long. She cuts off 9 inches to make a bow. Then she cuts the remaining ribbon into 2 equal pieces. How long is each piece?
    Answer: 9 inches After cutting off 9 inches for the bow, Maria has 18 inches of ribbon left, and splitting that evenly into 2 pieces gives 9 inches each. Choice B, 18 inches, is the full remaining length before it is split into two pieces. Choice C, 13 inches, comes from dividing the original 27 inches by 2 instead of the 18 inches that remained after the cut. Choice D, 4 inches, comes from dividing the 9-inch piece that was cut off instead of the remaining ribbon.
20. One plant is 28 cm tall. Another plant is 41 cm tall. How much taller is the 41 cm plant?
    Answer: 13 cm taller The 41 cm plant is 13 cm taller, because $41 - 28 = 13$. Choice A (12 cm) comes from subtracting incorrectly by one. Choice B (28 cm) repeats the shorter plant's height instead of finding the difference. Choice C (69 cm) comes from adding the two heights instead of subtracting.

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