PSLE Mathematics Learning Guide · Guide 20
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The unitary method is one of the most transferable ideas in Primary Mathematics. If several equal units have a known total value, find the value of one unit first. Once one unit is known, scale to any required number of units.
Six notebooks cost $15. One notebook costs $15 ÷ 6 = $2.50. Nine notebooks cost 9 × $2.50 = $22.50.
The method is simple, but difficult word problems can hide the unit inside packs, kilograms, litres, time intervals, repeated groups or ratios. This guide uses one working habit: name the unit, find one unit only when the situation is truly proportional, keep the unit attached to the value, then scale to the required quantity.
The MOE Primary Mathematics syllabus updated October 2025 provides the curriculum context, while the SEAB 2026 PSLE examination-format page links the current Mathematics syllabus. All examples here are original eduKate teaching material.
The unitary method starts with one unit
Five identical pens cost $12.50.
Cost of 1 pen = 12.50 ÷ 5 = $2.50.
Cost of 8 pens = 8 × 2.50 = $20.
The intermediate value $2.50 per pen is the bridge between the known and required quantities.
Write what one unit actually is
“One unit” could mean one pen, one kilogram, one litre, one minute, one packet, one person or one equal ratio part. The label matters.
For 4 kg of rice costing $18, one unit is 1 kg, not one bag unless the problem says one bag contains 4 kg.
Unit labels prevent a correct division from being applied to the wrong object.
Scale up after finding the unit value
Three metres of fabric cost $21.
1 m costs $7.
8 m costs 8 × 7 = $56.
The relationship is proportional because each metre has the same price in the simplified problem.
Sometimes the target is smaller than one stated group
Six litres of juice fill 24 identical bottles.
Amount per bottle = 6 ÷ 24 = 0.25 L.
Ten bottles require 10 × 0.25 = 2.5 L.
The unitary method can scale down to one small unit and back up to a different group size.
A rate is a value attached to another unit
$4 per kilogram, 60 km per hour and 3 litres per minute are rates.
The word per means “for each one unit of”.
At $4 per kilogram, 2.5 kg costs $10.
At 3 L/min for 4 minutes, 12 litres are transferred.
The unitary method and rate thinking are closely connected: finding one unit often creates a rate.
Compare value by converting to the same unit
Shop A sells 6 notebooks for $15. Shop B sells 8 notebooks for $18.40.
Shop A unit price = 15 ÷ 6 = $2.50 per notebook.
Shop B unit price = 18.40 ÷ 8 = $2.30 per notebook.
Shop B has the lower price per notebook.
Comparing only the total prices would be misleading because the pack sizes differ.
Do not confuse pack rate with item rate
Four packs contain 6 markers each and cost $28 altogether.
There are 24 markers total.
Cost per pack = $7.
Cost per marker = 28 ÷ 24 = $1.1666…
These are different rates. The correct one depends on what the question asks.
Use the unitary method only when equal scaling is justified
If a taxi fare contains a fixed starting charge plus a distance charge, total cost is not directly proportional to distance. Dividing total fare by distance to find a universal “cost per kilometre” can be misleading because the fixed charge is mixed into the total.
Similarly, a bulk discount may make the unit price change when quantity changes. The unitary method works directly only when the stated relationship is proportional over the relevant range.
Ask: If the number of units doubles, should the total double? If not, inspect the pricing or relationship structure before scaling.
Ratio unit value is a specialised unitary idea
If A : B = 3 : 5 and 8 ratio units represent 64 items, one ratio unit is 8 items. Then A = 24 and B = 40.
This is unitary reasoning inside a ratio model. Guide 3 develops it fully: Turn Ratio Units Into Actual Quantities Without Losing the Unit Value.
Speed is also a rate
60 km/h means 60 kilometres per one hour. The unitary interpretation is visible in the unit itself.
Guide 13 develops journey-specific rate reasoning: Build Speed Problems From Distance ÷ Time.
Main worked workshop: sixteen original unitary-method problems
1.
5 pencils cost $7.50. Find the cost of 1 pencil.
Answer: $1.50.
2.
Using Problem 1, find cost of 12 pencils.
Answer: $18.
3.
8 kg of rice cost $28. Find cost per kg.
Answer: $3.50/kg.
4.
At $3.50/kg, find cost of 2.4 kg.
Answer: $8.40.
5.
6 L fill 24 bottles. Find amount per bottle.
Answer: 0.25 L.
6.
At 0.25 L per bottle, how much for 18 bottles?
Answer: 4.5 L.
7.
4 workers make 120 items in equal-output simplified conditions. How many items per worker?
Answer: 30 items.
8.
At the same simplified rate, 7 workers make how many items?
Answer: 210 items.
9.
15 metres of ribbon cost $27. Find cost of 8 metres.
Reasoning: $1.80/m; 8 m costs $14.40.
10.
12 identical boxes hold 90 kg altogether. Find mass per box.
Answer: 7.5 kg.
11.
Shop A: 5 items for $12. Shop B: 8 items for $18. Which has lower unit price?
Reasoning: A=$2.40/item; B=$2.25/item. Shop B.
12.
A pump moves 18 L in 3 min. Find litres per minute.
Answer: 6 L/min.
13.
At 6 L/min, how much in 7.5 min?
Answer: 45 L.
14.
3 packs contain 8 cards each. The 3 packs cost $18. Find cost per card.
Reasoning: 24 cards total; 18÷24=$0.75/card.
15.
A service charges $5 fixed fee plus $2 per item. A learner divides a $25 total for 10 items and claims the rate is always $2.50/item.
Repair: The fixed fee breaks direct proportionality. Variable rate is $2/item plus one $5 fixed charge.
16.
6 equal ratio units represent 42 objects. Find value of 1 unit and 9 units.
Answer: 7 objects/unit; 9 units = 63 objects.
Work backwards from a target total when useful
If one item costs $2.40, how many items can be bought for $19.20?
19.20 ÷ 2.40 = 8 items.
The unit rate supports scaling in both directions.
Unitary reasoning can produce fractional quantities
If 4 metres cost $10, 1 metre costs $2.50. Half a metre costs $1.25.
The unit does not need to remain a whole count. Rates can scale to fractional measures when the context permits them.
Keep compound units visible
$3/kg, L/min and km/h tell you which quantity belongs in the numerator and denominator.
If a rate is $3/kg and mass is in grams, convert the mass to kilograms or convert the rate consistently before calculating. Guide 2 covers this unit alignment in detail.
Common unitary-method errors
Error 1: Divide by the wrong number because “one unit” was not named.
Error 2: Compare pack totals without converting to a common unit.
Error 3: Treat a fixed-fee relationship as directly proportional.
Error 4: Find cost per pack when the question asks cost per item.
Error 5: Scale the numerical value but drop or change the unit.
Error 6: Use unitary method where output per worker or time is not actually constant in the stated situation.
Independent transfer check
- 7 pens cost $17.50. Find cost per pen.
- At that rate, find cost of 12 pens.
- 9 kg of flour cost $31.50. Find cost per kg.
- 20 bottles contain 5 L altogether. Find amount per bottle.
- Shop A sells 4 items for $9.60; Shop B sells 6 for $13.80. Which is cheaper per item?
- A machine produces 48 items in 6 minutes at a constant simplified rate. Find items per minute.
- A fare is $4 fixed plus $1.50 per kilometre. Explain why total fare ÷ kilometres is not a constant rate across different journey lengths.
- Explain how the unitary method is related to ratio unit value.
Independent-check answers
1. $2.50.
2. $30.
3. $3.50/kg.
4. 0.25 L.
5. A=$2.40/item; B=$2.30/item, so B.
6. 8 items/min.
7. The fixed $4 is spread across different distances, so average fare per kilometre changes even though the variable rate stays $1.50/km.
8. Both find the value of one equal unit first, then scale to the number of units required.
Parent and tutor guide
Ask “one what?” before allowing division. Make the learner attach the unit to the intermediate value: $/item, kg/box, L/bottle.
For comparison shopping, require both options to be expressed in the same unit before deciding. For fixed-fee situations, draw the fixed and variable parts separately.
After a successful direct problem, reverse it: give the unit rate and a total, then ask for the number of units.
The learner’s final card
What is one unit? Is the relationship truly proportional? What is the value per one unit? What unit belongs to that value? How do I scale from one unit to the amount the question asks for?
Continue through the PSLE Mathematics Learning Guide
Use Guide 17: Whole-Number Place Value, Guide 18: Fraction Operations, and Guide 19: Decimal Operations.
Return to the PSLE Learning Guide.
Sources and boundaries
Official references: SEAB 2026 PSLE formats and MOE Primary Mathematics syllabus, updated October 2025.
Teaching boundary: All examples and suggested solutions are original eduKate teaching material. Proportional examples explicitly assume constant unit rates where required.