Grade 2 · Measurement · MAT-02-MEAS-004
Add and Subtract Lengths
Add and subtract lengths expressed in the same unit.
Learning objectives
What you should be able to do
- Add and subtract lengths expressed in the same unit.
- Solve length word problems within 100.
- Represent measurement changes with equations and number lines.
Prerequisite check
Make sure the foundation is ready.
Checks measurement and arithmetic foundations.
Learn
Build the idea from meaning, not memorization.
Lengths can be combined when units match
If one ribbon is24 cm and another is18 cm, together they measure42 cm. The shared unit allows direct addition.
Subtraction can find remaining length or difference
If a50 cm strip loses17 cm,33 cm remain. If one object is50 cm and another33 cm, subtraction also finds their17 cm difference.
Keep the unit through the calculation
24 cm+18 cm=42 cm. The unit is part of the quantity and must appear in the result.
Number lines model distance relationships
A length addition can be shown as forward jumps and subtraction as backward jumps or distance between two points.
Interactive math lab
Change it. See what stays true.
Number Line Explorer
Move along the number line.
4 is one less. 5 and 6 is one more.
- combine segments
- remove segment
- find difference
- inverse check
Worked examples
Twenty different ways to see the concept work.
24cm+18cm
42cmSame units add.
50cm−17cm
33cmSame units subtract.
35in+22in
57inCombine inches.
60in−25in
35inRemove inches.
3ft+4ft
7ftCombine feet.
9ft−3ft
6ftSubtract feet.
40cm and55cm difference.
15cm55−40.
Ribbon28cm +12cm.
40cmLength join.
Board75cm cut20cm.
55cmLength removed.
Path30m+45m.
75mSame meter units.
90m−35m.
55mRemaining distance.
18in+18in.
36inDouble length.
48cm−8cm.
40cmSubtract8.
Start32cm, add15cm.
47cmForward jump.
Start70cm, remove26cm.
44cmBackward difference.
Can20cm+3in combine directly?
NoConvert first.
Why result keeps cm?
Sum is still a length measured in cmUnit persists.
Which is longer by how much:62cm vs49cm?
13cm62−49.
Two segments25cm and30cm total.
55cmSegment addition.
Explain42cm−18cm=24cm check.
24cm+18cm=42cmInverse verifies.
Practice
Guided practice with hints
0123cm+19cm
Hint: Same units.
Answer: 42cm
0265cm−28cm
Hint: Subtract.
Answer: 37cm
0340in vs27in difference
Hint: Subtract smaller.
Answer: 13in
045ft+6ft
Hint: Combine.
Answer: 11ft
05Why can't addcm andin directly?
Hint: Units differ.
Answer: Convert first
06Check52cm−19cm=33cm.
Hint: Add back19.
Answer: 33+19=52
Practice
Independent practice
0118cm+27cm
Answer: 45cm
0270cm−26cm
Answer: 44cm
0333in+15in
Answer: 48in
0450in−18in
Answer: 32in
056ft+5ft
Answer: 11ft
0612ft−7ft
Answer: 5ft
07Difference80cm and63cm
Answer: 17cm
08Why label unit?
Answer: It identifies measured quantity scale.
Common mistakes
Learn to catch the error, not just the answer.
Carry the measurement unit through the equation.
Convert to a common unit first.
Identify whether problem combines lengths or compares/removes them.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Combine craft-material lengths.
- Find remaining rope, board, or travel distance.
Challenge problems
Two pieces total80cm; one is35cm. Other?
45cm
One board is12cm longer than48cm board. Length?
60cm
Why can number line model length?
Distance corresponds to numerical interval.
How can inverse operations check measurement arithmetic?
Add difference back or subtract addend from total.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Length Builder
Combine and cut virtual segments to reach target lengths.
Practice
Mastery check
0126cm+17cm
Answer: 43cm
0260cm−24cm
Answer: 36cm
03Difference55in,39in
Answer: 16in
044ft+7ft
Answer: 11ft
05Can cm+in add directly?
Answer: No
06Why preserve units?
Answer: The result remains a measurement.
07Check43−17=26
Answer: 26+17=43
08How does number line help?
Answer: It shows combined or removed distance as jumps.
Terminology
Words to know
- length
- Distance from one endpoint to another.
- difference
- How far apart two measurements are numerically.
- segment
- A part of a measured length.
- unit consistency
- Using matching units in a calculation unless converted.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — 2.MD.B.5–6
Length addition/subtraction and number-line representation.