Mathematics Tutor Singapore | PSLE Unitary Method

Mathematics Tutor Singapore | PSLE Maths unitary-method questions are straightforward when the price of one item is known, but they become harder when the question gives the price of several items. A child may divide by the wrong quantity, compare pack prices instead of price per unit, or assume that a fixed delivery fee is charged once for every item.

Did you know that the cheaper-looking packet may actually be worse value? A six-item pack costing $12.60 costs $2.10 per item, while a ten-item pack costing $19.50 costs $1.95 per item. The larger total price is not evidence of worse value when the amount purchased differs.

This Singapore Primary Mathematics guide teaches the unitary method—finding the value of one unit and then calculating other amounts—through original worked shopping and rate problems. It includes unit conversions, ratio tables, fixed-fee exceptions and independent checks. The examples are classroom models rather than advertisements for any real products.

Browse unitary-method and value-comparison lessons

The unitary method goes from many units to one
Choose which rate you actually need
Worked example: eight notebooks from a pack of three
Worked best-value comparison: two snack packs
Convert grams and kilograms before comparing prices
Unit rates also describe pages, distance and time
A ratio table and a one-unit table can agree
Find how many items a budget can purchase
Constant-rate assumptions must be stated
A fixed charge can invalidate direct proportionality
Comparing sale prices against quantity
Decimal money and rounding
What a reasonableness check should test
Choose unitary, bar, ratio table or equation
Nine common errors in PSLE unit-price problems
Sixteen worked unitary-method questions
Ten short sessions for Primary 5 and PSLE preparation
How to judge whether a tutor has taught the relationship
Common parent questions
MOE syllabus and connected Maths articles

The unitary method goes from many units to one

Suppose three identical notebooks cost $7.50. If each notebook has the same price and there is no separate charge, we can find the price of one notebook: $7.50÷3=$2.50. Once one unit is known, eight notebooks cost 8×$2.50=$20.

The method has two moves: divide to get the amount per one item, then multiply by the new number of items. The order matters. Dividing by eight first would not tell us the original notebook price because the $7.50 belonged to three notebooks.

Step	Working	Meaning
Given	3 notebooks cost $7.50	Three equal price units
Find one	$7.50÷3	$2.50 per notebook
Find eight	$2.50×8	$20
Check ratio	$20÷8	$2.50 per notebook

An honest unit rate names both the numerator and denominator units.

A useful sentence is ‘For one notebook, the cost is …’. That sentence checks whether the answer really is a cost per item rather than a total, number of items or leftover amount.

Choose which rate you actually need

A rate relates two measured quantities. Unit price typically expresses dollars per item or dollars per kilogram. But we could also calculate items per dollar, which has a different use: it estimates how much quantity one dollar buys under the model.

For three notebooks at $7.50, the unit price is $2.50 per notebook. The reciprocal rate is 3÷7.5=0.4 notebook per dollar. Both are mathematically consistent, but a question asking ‘How much does each notebook cost?’ calls for the first.

Question	Useful division	Unit
Cost of one of 3 notebooks priced $7.50	7.50÷3	Dollars/notebook
Pages per minute from 84 pages in 7 minutes	84÷7	Pages/minute
Minutes per page for the same printer	7÷84	Minutes/page
Kilograms per dollar from 4 kg at $12	4÷12	kg/dollar
Dollars per kilogram from the same pack	12÷4	Dollars/kg

The rate’s unit should answer the wording of the question.

Students sometimes divide ‘small number by big number’ as a general rule. That is not safe. Use units to decide which quantity belongs in the numerator and which in the denominator.

Worked example: eight notebooks from a pack of three

An invented stationery offer sells three identical exercise books for $7.50. A teacher wants eight books and can purchase any number at the same proportional price. How much do eight cost?

Find one: 750 cents÷3=250 cents. Find eight: 250×8=2,000 cents=$20.00. Working in cents or dollars gives the same answer.

The question’s assumption matters. If the shop sells books only in sealed packs of three, then eight separate books cannot necessarily be bought at that per-item price. The teacher would need three complete packs costing $22.50 to obtain at least eight books. The original $20 solution relies on individual purchase at the same rate.

Purchase condition	Mathematical model	Cost for at least 8 books
Any quantity at proportional unit price	8×$2.50	$20.00
Only sealed packs of 3	3 packs×$7.50	$22.50

A packaging restriction changes what the word problem is asking.

A good tutor highlights this distinction instead of teaching a memorised unitary calculation that would produce the wrong real-world purchase decision.

Worked best-value comparison: two snack packs

Two fictional snack packs contain identical snack portions. Pack A has six portions and costs $12.60. Pack B has ten portions and costs $19.50. Which offers a lower price per portion?

Pack A costs $12.60÷6=$2.10 per portion. Pack B costs $19.50÷10=$1.95 per portion. Thus Pack B offers a lower unit price by $0.15 per portion, assuming identical quality, size and no additional charges.

Pack	Portions	Total price	Price per portion
A	6	$12.60	$2.10
B	10	$19.50	$1.95

Only unit prices provide a like-for-like value comparison.

A student may conclude Pack A is cheaper because its total price is smaller. That is true as a cash-outlay comparison, but it answers a different question. The term ‘better value’ here means lower cost per comparable portion. A buyer with only thirteen dollars could buy A but not B; affordability and unit value are different decisions.

For exactly thirty portions, and if whole packs must be purchased, five A packs cost $63.00, while three B packs cost $58.50. This second check supports the unit-price conclusion for a common attainable quantity.

Convert grams and kilograms before comparing prices

A hypothetical food packet of 750 g costs $6.00. Another packet of 1.2 kg costs $9.00. Comparing $6 with $9 directly is not fair because the masses differ.

Convert 750 g to 0.75 kg. The smaller pack’s rate is $6.00÷0.75=$8.00 per kilogram. The larger pack’s rate is $9.00÷1.2=$7.50 per kilogram. The larger pack offers the lower cost per kilogram under the stated comparison.

Packet	Mass in kg	Price	Price per kg
Small	0.75	$6.00	$8.00
Large	1.2	$9.00	$7.50

Use the same mass unit before dividing.

An arithmetic trap arises if a pupil calculates $6÷750 and calls the answer dollars per kilogram. That produces dollars per gram, not per kilogram. Units are not decoration; they reveal which comparison has been computed.

Unit rates describe pages, distance and time

The unitary method is not limited to shopping. If a printer produces eighty-four pages in seven minutes at a constant rate, the number per minute is 84÷7=12 pages. At that rate, eleven minutes produce 12×11=132 pages.

Another problem might give a cyclist travelling 36 km in two hours at constant speed, leading to 18 km/h. This is rate reasoning, though real journeys may involve changing speeds; a constant-rate assumption must be present.

Context	Given	Unit rate	Follow-up
Printer	84 pages in 7 min	12 pages/min	132 in 11 min
Cyclist model	36 km in 2 h	18 km/h	54 km in 3 h
Bottling model	48 bottles in 6 min	8 bottles/min	80 in 10 min

A unit rate helps compare and predict under constant conditions.

Speed, work and unit-price questions share the unitary structure but not always the same physical assumptions. A unit-rate label tells the reader exactly which quantities are being compared.

A ratio table and a one-unit table can agree

Suppose five identical pens cost $8.50. One pen costs $1.70. A student can calculate fifteen pens as 15×$1.70=$25.50. Alternatively, fifteen is three groups of five, so three original packs cost 3×$8.50=$25.50. Both methods agree.

Pen count	Scaling factor from five pens	Total price
5	1	$8.50
10	2	$17.00
15	3	$25.50
1	1/5	$1.70

A proportional ratio table and unitary method represent the same relationship.

Choosing the shortcut depends on the target. If the required number is a convenient multiple of the original quantity, scaling may be faster than calculating one. If it is not, a per-unit rate may be clearer.

Find how many items a budget can purchase

If one item costs $2.50 and a buyer has $18.00, then $18.00÷$2.50=7.2. If the item must be purchased whole and there is no partial-item option, the buyer can afford at most seven items. Seven cost $17.50 and leave $0.50.

The answer is not 7.2 items in a whole-object purchasing story. The numerical quotient describes how many unit prices fit into the available money continuously; the practical restriction changes the final count.

Quantity	Calculation	Result
Budget	Given	$18.00
Unit cost	Given	$2.50
Unrestricted quotient	18÷2.5	7.2
Maximum whole items	7×$2.50	$17.50 spent
Money remaining	18−17.5	$0.50

Discreteness changes interpretation without changing the underlying rate.

Constant-rate assumptions must be stated

A unitary method applies directly when each unit contributes the same amount. If the first six items cost a fixed amount but additional items receive a discount, the cost per item is no longer necessarily constant across the order.

Likewise, a printer may stop for maintenance or slow down. A constant-rate model is useful because the problem specifies it or because it is an agreed approximation, not because all real-world processes are perfectly proportional.

A fixed charge can invalidate simple proportionality

A fictional delivery service charges a one-time $5 booking fee plus $3 per parcel. Sending two parcels costs 5+2×3=$11, while sending four costs 5+4×3=$17. The second order is not twice the first cost.

A learner who divides the two-parcel total by two obtains an average of $5.50 per parcel, but this includes a share of the fixed fee. Multiplying $5.50 by four predicts $22, not the stated $17. That is why the apparent unit cost changes as fixed fees are shared across different quantities.

Parcels	Variable charge	Fixed fee	Total
2	$6	$5	$11
4	$12	$5	$17
6	$18	$5	$23

Total cost is not proportional to the number of parcels when a fixed fee is present.

This can be an enrichment bridge into Secondary linear functions, where the rule would be written C=3n+5 rather than C=kn. At Primary level, a simple table is often enough to expose the difference.

Comparing sale prices and quantities

Suppose one fictional four-pack costs $12 before a 25% discount. The discounted cost is 75% of $12, or $9, so the unit price becomes $9÷4=$2.25. A six-pack sold for $13.80 without discount costs $13.80÷6=$2.30 per item.

Under equal-item conditions, the discounted four-pack has a slightly lower unit price, even though it contains fewer items. For a fair comparison we use final payable cost divided by comparable quantity, not the original price printed on a sticker.

If taxes, membership fees or delivery charges apply differently, those also belong in a realistic total-cost comparison. In school questions the necessary conditions should be provided; do not invent missing charges.

Decimal money and rounding

Calculating a unit price can produce a recurring decimal. If three items cost $10, the mathematical unit rate is $10/3, approximately $3.333… per item. Rounding the unit rate to $3.33 and multiplying by three gives $9.99, one cent below the stated total.

For an exact proportional calculation, keep $10/3 until the final operation where possible. Then apply any required currency rounding at the appropriate point stated by the question.

Do not assume a physical retail transaction will sell an indivisible item at a fractional cent. The school proportional model and actual pricing practices can differ. The student should follow the problem’s stated precision and payment conditions.

A reasonableness check should test the units and direction

If ten items cost $20, one item should cost $2, not $200. If a packet of 0.75 kg costs six dollars, its per-kilogram price should be greater than six dollars because one kilogram is larger than 0.75 kg. These magnitude checks catch a reversed division.

The same reasoning works for rates: if 84 pages are produced in seven minutes, pages per minute should be less than 84 and positive, not 588. A calculation is not finished until the unit and size are sensible.

Choose unitary, bar, ratio table or equation

For a Primary pupil who knows multiplication facts, a ratio table may be easiest when the target is an exact multiple of the given quantity. For a non-multiple target, finding one unit is often natural. For a two-step purchasing story, a bar or clear action table can prevent forgetting a fixed charge.

The best Maths tutor does not insist on one visual layout in every word problem. They teach learners how to choose a representation and explain why its assumptions fit the question.

Nine common PSLE unit-price errors

First incorrect move	Underlying gap	Better next question
Compares pack totals rather than per-unit prices	Quantity difference ignored	How much does one comparable item cost?
Divides item count by cost when asked dollars per item	Rate direction reversed	Which unit should the answer have?
Uses grams in one rate and kilograms in another	Units inconsistent	Convert both masses first
Calls 0.4 item per dollar a dollar price	Reciprocal rate mislabeled	What quantity is in the numerator?
Multiplies sealed-pack unit cost by any number of items	Packaging restriction ignored	Can partial packs be bought?
Uses average cost with booking fee as constant rate	Fixed fee unrecognised	Does the total double when quantity doubles?
Rounds $10/3 too early	Rounding error propagated	Keep exact fraction until final
Reports 7.2 whole boxes as purchase count	Discrete units ignored	Can part of a box be purchased?
Says cheaper pack always affordable	Value and cash budget confused	Can the buyer actually pay the total?

Diagnose the first mathematical or contextual mismatch.

One student may be fluent with arithmetic but forget to convert kilograms. Another may understand units but lack a clear sense of fixed charges. Those are different gaps and need different follow-up lessons.