“Per” is a small word that carries an important relationship. A price per notebook connects money with notebooks. A number of pages per day connects reading with time. To use either relationship, a child must know which quantity is being shared and what one unit means.
For primary families studying Mathematics in Punggol, per-unit examples offer a practical way to build multiplication and division reasoning. Use questions appropriate to the pupil’s current learning. The examples here teach the unitary method through prices and stated equal amounts; they do not require a claim about every year level studying every type of rate.
Read the two quantities together
If 4 identical notebooks cost $12, the cost of one notebook is $12 ÷ 4 = $3.
The result is $3 per notebook. The words explain what the number measures. Multiplying $3 by a number of notebooks gives their total cost under the same pricing arrangement.
Reversing the division would answer a different question. Four notebooks divided by $12 describes notebooks per dollar, not dollars per notebook. Before pressing ahead with arithmetic, say the desired unit aloud.
This also clarifies why the relevant objects must be comparable. A bundle containing a large notebook, a small notebook and two pens does not provide the individual notebook price unless more information is given. Dividing a bundle’s price by its number of objects is not automatically an appropriate comparison.
Worked example: compare two offers fairly
Consider these fictional stationery offers. Both sell the same type of exercise book, with no extra fees.
Offer A: 6 books for $15.
Offer B: 8 books for $18.
Which offer has the lower cost per book?
For Offer A, one book costs $15 ÷ 6 = $2.50.
For Offer B, one book costs $18 ÷ 8 = $2.25.
Offer B has the lower unit cost. The difference is $2.50 − $2.25 = $0.25 per book.
The higher bundle price does not make Offer B more expensive per book. It contains more books, so the original totals are not yet on an equal basis. Dividing by the number of books makes the comparison useful.
However, choosing what to buy is a separate question. If a family needs 6 books for the task and must buy complete bundles, Offer A requires $15 while Offer B requires $18 and leaves 2 extra books. A lower unit cost does not always mean a lower amount paid for the actual need.
Use one unit to rebuild a total
Suppose a question states that identical folders cost $2.40 each. Find the cost of 7 folders.
Total cost = 7 × $2.40 = $16.80.
A child can explain the multiplication as seven equal costs combined. This is stronger than saying, “I multiplied because the question said each.” The relationship, rather than one keyword, justifies the operation.
Now reverse the task. A pupil spends $16.80 on these folders. How many were bought?
Number of folders = $16.80 ÷ $2.40 = 7.
The numerical division finds how many equal $2.40 groups fit into $16.80. Check by returning to 7 × $2.40 = $16.80.
A common mistake: using an average as a promise
A fictional reading log records 48 pages across 4 days. Dividing gives an average of 12 pages per day. That calculation does not show that the child read exactly 12 pages on every day.
One possible record is 8, 10, 14 and 16 pages. These amounts total 48, although none is 12. Nor does the average guarantee that tomorrow’s reading will be 12 pages.
If a question says, “The pupil reads 12 pages each day,” equal daily amounts are given. If it says, “The pupil read 48 pages over 4 days,” equal daily amounts are not given. Both may involve division, but the conclusions differ.
Check which conditions are stated
A straightforward unitary-method question often gives identical items, equal quantities or an unchanged price. Retain those conditions when explaining the answer.
If a question says that 3 identical packets contain 72 counters in equal amounts, each packet contains 72 ÷ 3 = 24 counters. Without the statement about equal amounts, 24 is only the average per packet. The packets could contain different numbers.
A useful habit is to underline the phrase that permits equal grouping. If it is missing, avoid silently adding it to the question.
Try it independently
Five identical rolls of ribbon cost $17.50 altogether. At the same price per roll, how much do 8 rolls cost? How many rolls can be bought for $24.50?
One roll costs $17.50 ÷ 5 = $3.50.
Eight rolls cost 8 × $3.50 = $28.
The number bought for $24.50 is $24.50 ÷ $3.50 = 7 rolls.
Check the first given total: 5 × $3.50 = $17.50. Check the final answer: 7 × $3.50 = $24.50. Both checks use the same stated unit price, so the quantities fit together.
A pupil who calculates $17.50 × 8 has multiplied the price of 5 rolls by 8. That would correspond to 40 rolls, not 8. Labelling the intermediate amount prevents this mistake.
A useful connection with Science
Reading tables and graphs requires the same attention to quantities and intervals. A total change divided by elapsed time describes an average over that interval. It does not establish an unchanged rate within the interval or predict the next reading. Mathematics describes the recorded relationship; further observations support further conclusions.
A parent prompt that keeps the meaning visible
Ask, “What does one mean in this question, and what is the unit of your answer?” The pupil might answer one book, one packet or one day. Then ask them to use their one-unit result to reconstruct the given total.
Keep units in the explanation even when the arithmetic is short. A bare answer of 3 is hard to interpret. An answer of $3 per notebook tells the reader exactly what the child has found.
Continue learning
Return to the Mathematics in Punggol study guide.
Related practice: Ratios: Compare Quantities Using Equal Units · Compare Choices: Unit Price, Total Cost and Practical Limits.
