Length word problems within 100
Solve word problems involving lengths within 100, using addition and subtraction with drawings and equations
What a learner can do afterwards
- Solve addition and subtraction word problems about lengths within 100, including missing parts and two changes
- Interpret a supplied number-line model or hop description for a length word problem
- Choose or check an equation with a symbol for the unknown that represents a length word problem
1 · Read
Use the same unit for every length; cm means centimetres. Join pieces end to end without overlap: add their lengths. Cut a piece off: subtract its length to find what is left. For two-digit calculations, split the added or removed length into tens and ones. Work with the tens, then the ones. To compare lengths, subtract the shorter length from the longer one.
Mia places a 62 cm ribbon and a 15 cm ribbon end to end without overlap. Add: 62 + 15 = 77. The total length is 77 cm. Subtracting would find the difference between the two lengths, not their total.
For a number-line drawing, mark the starting length. Hop right to add a piece or left to remove one. Label the hop with the piece's length. The landing point shows the new length. To find a missing hop, subtract the smaller endpoint from the larger one. A hop from 54 to 38 removes 54 - 38 = 16 cm.
A letter, such as n or p, or the symbol ? can stand for a missing length in centimetres. For a cut, write start - piece = left. A rope starts at 80 cm and has 55 cm left: 80 - n = 55. Find the removed piece by subtracting: 80 - 55 = 25, so n = 25.
To find a missing added piece, subtract the start from the total. A strip grows from 26 cm to 44 cm. The added piece is 44 - 26 = 18 cm long. To find the start before a cut, add the cut piece to what is left. If 32 cm remains after a 14 cm cut, the start was 32 + 14 = 46 cm.
For two changes, work in story order. A 20 cm strip gains 13 cm, then loses 7 cm: 20 + 13 = 33, then 33 - 7 = 26. For two cuts, subtract the first cut, then subtract the second cut from what is left. Write the unit with your answer.
Both sides of an equals sign have the same value. You can write n = 50 - 12 or 50 - 12 = n. To find a missing second cut, find the length after the first cut. From 80 cm, cut 20 cm to leave 60 cm. If 37 cm remains after another cut, that cut was 60 - 37 = 23 cm.
Use the story to choose addition or subtraction. Show the lengths with an equation or number line, solve, and write the unit.
Lesson, questions and flashcards written for this dataset.
Questions, readings and flashcards written for this dataset. The linked video, "Measuring lengths (cm, m)", is by Khan Academy.
More to read
Find what the question asks
Two lengths can be used in different ways. Suppose two strips measure 28 cm and 19 cm. Placing them end to end gives a total of 47 cm. Comparing them gives a difference of 9 cm. Read the question before calculating. A total combines the pieces. A difference tells how far apart their measurements are.
Find the length before a cut
A cut separates one length into two parts. If 11 cm was cut off and 42 cm remains, both parts belonged to the starting piece. Add them: 42 + 11 = 53 cm. Check the result by subtracting the removed length again: 53 - 11 = 42. This matches the length left.
Make the hops show the story
A 57 cm strip loses 16 cm. Draw a number line with equal spaces. Start at 57, hop left 10 to 47, then left 6 to 41. Write the amount removed above each hop. The landing point, 41, gives the centimetres left. Your line can show just the part you need. It does not have to begin at zero.
Keep track after each change
A strip starts at 50 cm. A 12 cm piece is removed, leaving 38 cm. Another piece, 15 cm long, is then placed at the end without overlap. Add it to 38, giving 53 cm. Use the length after the first change when you begin the second calculation. A short list of lengths can help: 50 cm, then 38 cm, then 53 cm.
Explore more
2 · Watch
En anglaisTake it off screen
Where it sits
Learn first
Optional connections
This opens up
Where this leads
17 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.