A unit price is cost for one fixed amount, such as dollars per kilogram or cents per item. It removes pack size from the immediate comparison. If one pack contains twice as much as another, their checkout prices alone do not tell us which charges less for the same quantity.

Write the unit in the heading before calculating. ‘Dollars per 100 g’ is a different number from ‘dollars per kilogram’, although both can describe the same offer. Comparing one pack’s price per 100 g with another’s price per kilogram would create a false difference. The numbers need matching meanings as well as matching currency.

For the 600 g pack, $4.20 divided by six gives $0.70 per 100 g. For the 900 g pack, $5.85 divided by nine gives $0.65 per 100 g. Therefore the second pack charges five cents less per 100 g. We have compared equal quantities, not equal packs.

An alternative is dollars per kilogram: 4.20/0.6 = 7 and 5.85/0.9 = 6.50. The ordering stays the same. The unit changes the displayed number, not which rate is lower. Show your child these two equivalent descriptions to check whether the denominator is understood rather than memorised.

Cost divided by quantity gives cost per quantity. For $4.20 and 600 g, 4.20/600 = 0.007 dollars per gram. Quantity divided by cost gives a different rate: grams per dollar. Both calculations can be meaningful, but they answer reciprocal questions.

If comparing cost per gram, lower is cheaper. If comparing grams per dollar, higher gives more quantity for the same money. Do not mix one rate with the other or keep the same higher-is-better rule for both. Write a sentence after the number: ‘Each dollar buys …’ or ‘Each 100 g costs …’.

Convert before comparing. Suppose 750 g costs $6 and 1.2 kg costs $9. The first costs $8 per kilogram because 750 g is 0.75 kg. The second costs $7.50 per kilogram. Dividing six by 750 and nine by 1.2 without naming their units would produce incomparable rates.

Alternatively, convert both quantities to grams and work in cents per 100 g. Consistent units are the important condition. Keep enough precision to distinguish close rates, then round only for a final display. Rounding an early intermediate value can conceal a small difference that the question expects the student to identify.

Yes. Scale both packs to a common quantity. Two 600 g packs contain 1,200 g and cost $8.40. A 1,200 g equivalent at the second pack’s rate costs $7.80. This confirms the lower rate of the 900 g offer, although fractional-pack equivalents are a mathematical comparison rather than a promise that a shop sells them.

Cross-multiplication is another equivalent check when quantities and costs are positive and consistently measured. But a younger learner should still explain what is being compared. A short unit-rate calculation is often clearer than an unexplained rule that happens to give the right ordering.

No. Lower unit price describes a rate. A person may have a fixed budget, need only a small amount, lack storage or waste the extra quantity. Different quality or included accessories can also make a purely numerical comparison incomplete. Keep mathematical conclusions within their assumptions.

In a textbook question stating identical products and asking for better value per unit, compare the rates. In a broader decision question, state both the rate and the relevant constraint. Do not invent costs, product equivalence or future use. Good mathematical reasoning can support a decision without pretending to determine every preference.

Question 1: six identical notebooks cost $9; ten cost $14. Which has lower cost per notebook? Question 2: 400 g costs $3.20 and 1 kg costs $7.50. Compare per kilogram. Question 3: one bottle costs $2.40 for 800 ml. Find dollars per litre. Question 4: does a lower unit price guarantee a lower checkout price?

Answers: 1) $1.50 versus $1.40; the ten-pack has the lower rate. 2) $8/kg versus $7.50/kg; the kilogram pack has the lower rate. 3) $3 per litre. 4) No; checkout price depends on total quantity purchased. Ask for the unit alongside every numerical answer.

Bring an example where your child compared prices without noticing quantities. Ask whether they can identify the required unit, convert quantities and explain the direction of comparison. In a small-group 3-pax lesson, students can compare the same fictional offers using cost per kilogram and grams per dollar, then explain why the ordering agrees.

For parents considering Secondary 1 Mathematics tuition in Punggol, a useful home prompt is ‘What equal amount are we comparing?’ Once your child answers that independently, change the units or the pack sizes. The learning goal is a stable relationship between cost and quantity, not simply choosing the larger pack.