PSLE Mathematics Learning Guide · Guide 28
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Money problems are rarely difficult because the arithmetic is unfamiliar. They become difficult when the learner confuses unit price with total cost, amount paid with money owned, discount with change, or cents with decimal parts of a dollar.
This guide uses one working habit: name the transaction state—price, quantity, total cost, amount paid, change or remaining money—make dollars and cents consistent, calculate in the direction the story requires, and check that the final amount fits the real transaction.
The MOE Primary Mathematics syllabus updated October 2025 provides curriculum context, while the SEAB 2026 PSLE examination-format page links the current Mathematics syllabus. All examples and suggested solutions here are original eduKate teaching material.
Separate price, total cost, amount paid and change
A notebook costs $3.20. Three notebooks cost $9.60. If $10 is paid, the change is $0.40.
Those numbers have different jobs:
- $3.20 = unit price;
- $9.60 = total cost;
- $10.00 = amount paid;
- $0.40 = change returned.
A correct answer requires the correct state, not merely a correct calculation somewhere in the chain.
One dollar is 100 cents
$4.07 means 4 dollars and 7 cents, not 4 dollars and 70 cents.
407 cents = $4.07.
40 cents = $0.40.
When column addition or subtraction is used, align decimal points so dollars match dollars and cents match cents.
Total cost = price per item × number of identical items
Five pens cost $1.80 each.
Total cost = 5 × 1.80 = $9.00.
The unitary method can work in reverse when a pack total is given. Guide 20 develops that rate relationship: Use the Unitary Method to Find One Unit Before Scaling.
A basket with different items needs subtotals
Two books at $6.40 each and three pens at $1.25 each:
Books = 2 × 6.40 = $12.80.
Pens = 3 × 1.25 = $3.75.
Total = $16.55.
Calculating subtotals separately reduces the chance of multiplying a price by the wrong quantity.
Change = amount paid − total cost
A purchase costs $17.65 and the customer pays $20.
Change = 20.00 − 17.65 = $2.35.
Check forward: 17.65 + 2.35 = 20.00.
The inverse check reconstructs the amount paid.
Affordability is a comparison before it is a subtraction
A pupil has $15. A set costs $16.20.
The pupil cannot afford it because $15 < $16.20.
If the question asks how much more is needed, calculate 16.20 − 15.00 = $1.20.
Do not subtract in the wrong direction and report negative “change” when the real issue is insufficient money.
Remaining money is not the same as change unless money is actually paid
A child has $30 and spends $18.40. Remaining money = $11.60.
If the child hands a cashier a $20 note for an $18.40 purchase, change = $1.60. The child may still have other money elsewhere. “Remaining money” and “change” describe different states.
Discount changes the price before payment and change
A $50 bag is discounted by 20%.
Discount = $10.
Sale price = $40.
If $50 is paid, change = $10.
The $10 discount and $10 change happen to have the same numerical value here, but they are different quantities. In another transaction they need not match.
Guide 21 develops percentage changes fully: Percentage Change, Discount and Final Value.
Multi-buy offers require the stated pricing structure
Offer: 3 notebooks for $7.50. Six notebooks cost two offer groups = $15.00.
If seven notebooks are needed and the seventh is sold individually at $2.80, total = $15.00 + $2.80 = $17.80.
Do not assume the 3-for-$7.50 rate automatically applies proportionally to one notebook unless the offer states that it does.
Budget problems combine totals and inequalities
A pupil has $25 and wants a $12.80 book plus pens costing $2.40 each.
Money after book = 25 − 12.80 = $12.20.
Maximum whole pens = 12.20 ÷ 2.40 = 5 full pens, with $0.20 remaining.
Six pens would cost $14.40 and exceed the remaining budget.
Sharing a bill requires the question to define equality
A $48 bill is shared equally among 6 people.
Each pays $8.
If one person pays an extra fixed item or if different people ordered different amounts, equal sharing may no longer model the situation. Use the relationship actually stated.
Do not round money prematurely when exact cents are available
Three items at $2.47 cost $7.41 exactly.
Rounding each item to $2.50 first gives $7.50—useful as an estimate, but not the exact cost.
Guide 16 explains this boundary: Round and Estimate Without Replacing the Exact Question.
Main worked workshop: sixteen original money problems
1.
Four files cost $2.35 each.
Answer: $9.40.
2.
Two books at $8.90 and three pencils at $0.75.
Answer: $17.80 + $2.25 = $20.05.
3.
Total cost $13.65; pay $20.
Change: $6.35.
4.
Total cost $48.70; pay $50.
Change: $1.30.
5.
A child has $24 and spends $7.85 then $6.40.
Answer: total spent $14.25; remaining $9.75.
6.
Convert 735 cents to dollars.
Answer: $7.35.
7.
Convert $12.08 to cents.
Answer: 1,208 cents.
8.
A $60 item has 25% discount.
Sale price: $45.
9.
Pay $50 for the item in Problem 8.
Change: $5.
10.
Offer: 4 drinks for $6.80. Buy 8 drinks.
Answer: $13.60.
11.
A pupil has $20. A toy costs $22.45. How much more is needed?
Answer: $2.45.
12.
$36 is shared equally among 8 pupils.
Answer: $4.50 each.
13.
A child has $30 after receiving $12. How much before receiving it?
Answer: $18.
14.
Three identical items and a $2 fixed fee cost $17. Find item price.
Reasoning: items total $15; each $5.
15.
A learner says $3.5 means $3 and 5 cents.
Repair: $3.50 means $3 and 50 cents; $3.05 means $3 and 5 cents.
16.
A learner reports $4.20 change from a $10 payment for a $6.20 item.
Repair: 10.00 − 6.20 = $3.80. Check: 6.20 + 3.80 = 10.00.
A transaction-control table
| Quantity | Typical relationship |
|---|---|
| total cost | sum of subtotals |
| subtotal | unit price × quantity |
| change | amount paid − total cost |
| remaining money | money owned − money spent |
| amount needed | required total − money available |
| unit price | group cost ÷ number of equal units, when proportional |
Common money errors
Error 1: Misalign dollars and cents.
Error 2: Confuse discount with change.
Error 3: Confuse remaining money with cashier change.
Error 4: Multiply one item’s price by the total number of mixed items.
Error 5: Apply a bundle offer proportionally when the offer does not state a unit rate.
Error 6: Round prices before an exact total is required.
Independent transfer check
- Five pens cost $1.85 each. Find total.
- Two books at $7.40 and four erasers at $0.65. Find total.
- Pay $30 for a $24.75 purchase. Find change.
- A pupil has $18 and wants an item costing $20.35. How much more is needed?
- Convert 1,425 cents to dollars.
- A $40 item has 15% discount. Find sale price.
- Explain the difference between discount and change.
- Explain why $5.08 and $5.80 are very different amounts.
Independent-check answers
1. $9.25.
2. $14.80 + $2.60 = $17.40.
3. $5.25.
4. $2.35.
5. $14.25.
6. $34.
7. Discount reduces the listed price before payment; change is money returned after the amount paid exceeds the final cost.
8. The hundredths place represents cents: $5.08 is 5 dollars 8 cents, while $5.80 is 5 dollars 80 cents.
Parent and tutor guide
Ask the learner to label each money number before calculating: unit price, subtotal, total, paid, change, remaining or needed. Many “careless” money errors are actually state errors.
Use inverse checks for change: cost + change should reconstruct amount paid. For budgets, compare available money and required cost before subtracting.
The learner’s final card
What does each money amount represent? Are dollars and cents aligned? What is the subtotal and total? Am I finding change, remaining money or money needed? Can I reconstruct the transaction to check?
Continue through the PSLE Mathematics Learning Guide
Use Guide 25: Elapsed Time, Guide 26: Triangle Area, and Guide 27: Compare and Order Fractions.
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. Money arithmetic is treated as cumulative Primary Mathematics knowledge relevant to PSLE preparation.