Primary 3 money problems are an early lesson in decimal notation, place value and real-world quantitative reasoning. Students already know that one dollar is made of one hundred cents, but they now have to preserve that relationship inside written calculations, multi-step questions and unfamiliar purchasing situations. The arithmetic may look simple; the real challenge is keeping dollars, cents, totals, differences and change attached to the correct roles.
This is Guide 13 in the Primary 3 Mathematics Learning Hub. It deepens the money strand from Guide 2 and connects decimal notation to place value, estimation, word-problem structure and verification.
Money is not a separate kind of arithmetic. It is place value with a unit and a real-world relationship between dollars and cents.
One Dollar Is One Hundred Cents
The relationship $1 = 100¢ is the foundation of Primary 3 money work. The decimal notation $4.35 means 4 dollars and 35 cents. The decimal point separates whole dollars from the cents part of the amount.
| Money notation | Meaning |
|---|---|
| $7.04 | 7 dollars and 4 cents |
| $7.40 | 7 dollars and 40 cents |
| $0.85 | 85 cents |
| $12.00 | 12 dollars exactly |
The difference between $7.04 and $7.40 is a useful diagnostic. A learner who reads both as “seven dollars and four” may not yet be preserving the cents place accurately.
Decimal Notation Must Stay Aligned
When money amounts are added or subtracted in decimal notation, align the decimal points. This places dollars under dollars, tenths of a dollar under tenths, and hundredths under hundredths.
Example: $8.75 + $2.60.
The exact total is $11.35. The decimal-point alignment protects the place values throughout the calculation.
Align decimal points, not merely the visible digits.
Why the Zero in $6.80 Is Useful
Mathematically, $6.8 and $6.80 represent the same numerical value. In money notation, writing two decimal places helps make the 80 cents explicit and keeps written calculations easier to align.
Students should understand the equality rather than believe the extra zero changes the amount.
Adding Money
Worked Example: A book costs $12.75 and a pen costs $3.80. Find the total cost.
$12.75 + $3.80 = $16.55.
A quick estimate gives about $13 + $4 = $17, so $16.55 is plausible.
Subtracting Money
Worked Example: Find the difference between $15.20 and $8.65.
$15.20 − $8.65 = $6.55.
Estimate first: about $15 − $9 = $6. The exact answer is close to the estimate.
Regrouping Across One Dollar
When there are not enough cents to subtract, one dollar can be regrouped as 100 cents.
Example: $10.00 − $3.68.
Regroup part of the $10.00 so that cents are available. The answer is $6.32. The regrouping is justified by the relationship $1 = 100¢.
Total Cost
A total-cost problem combines two or more prices.
Example: A notebook costs $4.25, a ruler costs $1.60 and a file costs $3.90. Find the total.
$4.25 + $1.60 + $3.90 = $9.75.
The learner should be able to state that the result represents the amount spent before moving to any later change calculation.
Price Difference
If one item costs $13.80 and another costs $9.25, the price difference is found by subtraction:
$13.80 − $9.25 = $4.55.
The phrase “how much more expensive” describes a comparison relationship, not a new arithmetic rule.
Change
Change is the amount paid minus the total cost. If several items are purchased, the total cost must be found first.
Worked Example: A book costs $8.75 and a pen costs $2.60. Jia pays with $20.
- Total cost = $8.75 + $2.60 = $11.35.
- Change = $20.00 − $11.35 = $8.65.
The intermediate answer $11.35 is not yet the final answer. It is the new state required before the change can be found.
Estimate Change Before Calculating
If the total cost is a little over $11 and the shopper pays $20, the change should be a little under $9. This creates a useful expectation before exact subtraction.
An answer of $18.65 would be impossible because the shopper did not spend only $1.35.
Repeated Equal Prices
Money can also create multiplicative relationships.
Example: One notebook costs $3.25. Four identical notebooks cost 4 × $3.25 = $13.00.
The student should recognise the equal-price structure rather than add unrelated prices mechanically.
Reverse Money Problems
Some questions give the change and ask for the total cost or original amount.
Example: Mei pays $20 and receives $6.45 change. What was the total cost?
Total cost = $20.00 − $6.45 = $13.55.
The word “change” does not always mean the final operation is subtraction from the cost. Identify which amount is unknown.
Missing Price Problems
Example: Two items cost $12.40 altogether. One item costs $5.75. Find the other price.
$12.40 − $5.75 = $6.65.
This is a part–whole structure written in money notation.
Money and Part–Whole Models
A bar model can show a total cost split into known and unknown item prices. It can also show an amount paid split into total cost and change. The representation is useful when the direction is unclear.
Worked Multi-Step Money Problem
Question: A family buys 3 identical drinks at $2.40 each and one sandwich for $5.75. They pay with $20. How much change do they receive?
- Cost of drinks = 3 × $2.40 = $7.20.
- Total cost = $7.20 + $5.75 = $12.95.
- Change = $20.00 − $12.95 = $7.05.
Three different relationships appear: equal groups, total cost and change. Each intermediate answer should be labelled before the next step.
Compare Two Shopping Choices
Example: Shop A sells a set for $14.80. Shop B sells the same set for $16.25. How much cheaper is Shop A?
$16.25 − $14.80 = $1.45.
The word “cheaper” describes the direction of the comparison. The difference is still found by subtracting the smaller price from the larger price.
Reasonableness in Money
- A total should usually be larger than each individual positive price.
- Change should be smaller than the amount paid.
- A price difference should not exceed the larger price.
- Four identical positive-priced items should cost more than one item.
- Decimal-point mistakes often create answers ten or one hundred times too large or small.
Common Money Misconceptions
- Reading $4.05 as $4.50. The cents places are being confused.
- Aligning digits rather than decimal points. Place values no longer match.
- Thinking $6.8 and $6.80 are different amounts. The trailing zero does not change the value.
- Finding change before total cost. The dependency sequence is wrong.
- Forgetting the dollar sign. The unit is part of the answer.
- Using addition whenever “more expensive” appears. Comparison usually asks for a difference.
Error Analysis Example
A student calculates $12.50 − $7.85 and writes $5.65. Rather than call this careless, inspect the decimal columns and regrouping. The first wrong step may reveal weak hundredths/tenths alignment or an incorrect regroup across one dollar. Repair the place-value relationship, then rerun the money question.
Diagnostic Questions
- Read $7.04 and $7.40 aloud.
- Which is larger: $8.09 or $8.90?
- Add $6.75 and $4.80.
- Find the difference between $15.20 and $8.65.
- Find the change from $20 after spending $13.55.
- Three identical items cost $2.40 each. Find the total.
- A total is $18.60 and one item costs $7.95. Find the missing price.
- Estimate the answer before solving one multi-step shopping problem.
How to Practise Money Well
Use realistic menus, receipts and simple price lists. Mix total cost, difference, equal-price multiplication, missing-price and change problems. Ask for an estimate before exact calculation so the student develops a sense of financial scale.
A Short Money Practice Cycle
- read two decimal money amounts;
- compare two prices;
- add two or three prices;
- subtract to find a difference;
- find change;
- solve one equal-price multiplication;
- solve one multi-step shopping problem;
- estimate and verify.
Exam Craft | Protect the Decimal Point and the Story
Align decimal points, write two decimal places where useful, label intermediate totals and reread whether the question asks for total cost, difference, missing price or change. Before moving on, check whether the final amount is plausible relative to the amount paid and prices given.
Read the money role → align the decimal point → calculate → estimate → state the amount with its unit.
Checkpoint | Is Money Control Stable?
- Can the learner convert between dollars and cents conceptually?
- Can the student read decimal money notation accurately?
- Can the learner align decimal points?
- Can the student add and subtract money with regrouping?
- Can the learner distinguish total cost, difference and change?
- Can the student solve reverse money problems?
- Can the learner combine multiplication with money?
- Can the student estimate and reject impossible financial answers?
How This Connects to the Primary 3 Mathematics System
This guide deepens Guide 2: Fractions and Money, uses place-value control from Guide 9, and applies the problem-sequencing and checking routines from Guide 4 and Guide 5.
Final Thought
Money gives students a familiar setting for a powerful mathematical lesson: notation, unit and relationship must stay aligned. Once dollars and cents are treated as place value rather than decoration, multi-step money problems become far more controllable.
Know what the amount represents before deciding what to do with it.
Return to the Primary 3 Mathematics Learning Hub.
