PSLE Mathematics Learning Guide · Guide 43
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A length problem can contain metres, centimetres and sometimes kilometres in the same story. The arithmetic is not ready until the units agree.
Choose one working unit, convert every relevant length into that unit, perform the calculation, then convert the final answer only if the question asks for another form.
Guide 2 owns the general rule that units must agree. This page is a focused application workshop for length: total lengths, differences, repeated pieces, missing dimensions and practical interpretation.
The MOE Primary Mathematics syllabus updated October 2025 provides curriculum context. All examples below are original eduKate teaching material.
Core metric relationships
1 m = 100 cm.
1 km = 1000 m.
Therefore 2.35 m = 235 cm, and 450 cm = 4.5 m.
Use the unit required by the calculation, not the unit that looks shorter to write.
Add mixed lengths only after conversion
2 m 35 cm + 1 m 80 cm.
Method 1: work in centimetres.
235 cm + 180 cm = 415 cm = 4 m 15 cm.
Method 2: add metres and centimetres, then regroup 115 cm as 1 m 15 cm. Both methods agree.
Subtraction may need regrouping
5 m 10 cm − 2 m 75 cm.
Convert to centimetres: 510 − 275 = 235 cm = 2 m 35 cm.
This avoids awkward regrouping across the metre boundary.
Difference means compare two lengths
A rope is 3.8 m long and another is 245 cm.
3.8 m = 380 cm.
Difference = 380 − 245 = 135 cm = 1.35 m.
Subtracting 3.8 − 245 would mix units and produce a meaningless numeral.
Repeated equal pieces use multiplication
Six strips are each 75 cm long.
Total = 6 × 75 = 450 cm = 4.5 m.
Keep the unit attached to the repeated value.
Equal cutting uses division
A 4.8 m ribbon is cut into 6 equal pieces.
4.8 m ÷ 6 = 0.8 m = 80 cm per piece.
Check: 6 × 80 cm = 480 cm.
Recover a missing length from a total
Three pieces total 5 m. Two are 1.45 m and 2.1 m.
Known total = 3.55 m.
Missing = 5 − 3.55 = 1.45 m.
Length units also control perimeter
A rectangle is 1.2 m by 75 cm.
Convert 1.2 m = 120 cm.
Perimeter = 2(120 + 75) = 390 cm = 3.9 m.
Use Guide 29 when the main difficulty is the area/perimeter relationship rather than the unit conversion.
Distance travelled is also length
A walker covers 1.4 km and then 850 m.
1.4 km = 1400 m.
Total = 2250 m = 2.25 km.
The same unit discipline applies whether the length is a ribbon, room, road or journey segment.
Do not confuse a drawing length with real length unless a scale is given
A line printed 4 cm long on a page is not automatically a 4 cm real-world object. If the task is a scale drawing, the stated scale determines the actual length.
If no scale relationship is supplied, do not invent one from the physical size of the printed diagram.
Main worked workshop: sixteen original length problems
1.
2.7 m to cm.
Answer: 270 cm.
2.
635 cm to m.
Answer: 6.35 m.
3.
3 m 45 cm + 2 m 80 cm.
Answer: 6 m 25 cm.
4.
7 m − 2 m 65 cm.
Answer: 4 m 35 cm.
5.
4.2 m − 175 cm.
Answer: 245 cm = 2.45 m.
6.
Eight pieces of 45 cm.
Answer: 360 cm = 3.6 m.
7.
6.3 m divided into 9 equal pieces.
Answer: 0.7 m = 70 cm each.
8.
Total 9 m; known pieces 2.4 m, 175 cm and 3.1 m. Find missing.
Reasoning: 2.4 m + 1.75 m + 3.1 m = 7.25 m; missing = 1.75 m.
9.
Compare 1.85 m and 190 cm.
Answer: 190 cm is longer by 5 cm.
10.
2.6 km + 750 m.
Answer: 3.35 km.
11.
5 km − 1.35 km.
Answer: 3.65 km.
12.
A learner adds 2 m + 35 cm and writes 37 m.
Repair: 2 m = 200 cm; total = 235 cm = 2.35 m.
13.
A learner says 80 cm is larger than 1.2 m because 80 > 1.2.
Repair: 1.2 m = 120 cm, so 1.2 m is larger.
14.
A square has side 85 cm. Perimeter?
Answer: 340 cm = 3.4 m.
15.
A rectangular path is 2 m by 150 cm. Perimeter?
Answer: 2 m = 200 cm; perimeter = 700 cm = 7 m.
16.
A 10 m roll has 2.35 m and 4.8 m cut away. Remaining?
Answer: 2.85 m.
Three useful checks
Unit check: Have all values been expressed in compatible units before arithmetic?
Size check: If two positive lengths are added, the total must exceed each part.
Inverse check: Add a removed length back to the remainder and recover the original total.
Common mixed-length errors
Error 1: treat 1 m as 10 cm.
Error 2: add metres directly to centimetres.
Error 3: compare numerals without converting units.
Error 4: confuse endpoint position on a ruler with object length.
Error 5: convert the final answer but forget to relabel the unit.
Independent transfer check
- 3.85 m to cm.
- 920 cm to m.
- 4 m 75 cm + 2 m 60 cm.
- 8 m 20 cm − 3 m 85 cm.
- Seven pieces of 65 cm. Find total in metres.
- 5.4 m cut into 6 equal pieces. Find each length in cm.
- Compare 2.05 m and 198 cm.
- Explain why all lengths should be converted before a mixed-unit difference is found.
Independent-check answers
1. 385 cm.
2. 9.2 m.
3. 7 m 35 cm.
4. 4 m 35 cm.
5. 455 cm = 4.55 m.
6. 90 cm.
7. 2.05 m = 205 cm, so it is longer by 7 cm.
8. The numerical values refer to different-sized units, so direct arithmetic would combine unlike quantities.
Parent and tutor guide
Ask the learner to circle every unit before calculating. Then choose one working unit for the whole problem.
If the child converts correctly but chooses the wrong operation, separate the two jobs: first unit alignment, then the relationship—total, difference, equal sharing or missing part.
The learner’s final card
What length unit is each number using? Which one unit will I work in? Am I finding a total, difference, equal piece or missing part? Does my final unit answer what the question asked?
Continue through Batch 11
Use Guide 41 and Guide 42. Continue with Guide 44: Mass Problems in Kilograms and Grams.
Return to the PSLE Learning Guide Mathematics route.
Sources and boundaries
MOE Primary Mathematics syllabus, updated October 2025; SEAB 2026 PSLE formats.
All examples and solutions are original eduKate teaching material. This focused length workshop routes to the general units owner rather than replacing it.