Unit rate and the word ‘per’ after PSLE is a useful post-PSLE Mathematics bridge because it connects familiar Primary ideas to the more formal language students meet in Secondary 1. The goal is not to race ahead. It is to make the relationship clear enough that a new symbol or formula still feels connected to something the child already understands.
The wider route begins with After PSLE — Should My Child Start Secondary 1 Maths Early?. If a difficulty keeps repeating, use the Punggol Mathematics diagnostic guide to separate fluency, interpretation, strategy and execution before simply adding more practice.
At eduKatePunggol, Mathematics is taught in focused small groups of up to three students in 1.5-hour lessons near Punggol MRT. A small class makes the student’s setup, explanation and checking visible, so the tutor can repair the first weak link rather than only the final answer.
WhatsApp eduKatePunggol about a post-PSLE Mathematics transition plan
The short answer: ‘per’ usually compares one quantity for one unit of another
Sixty kilometres per hour means 60 kilometres for each one hour. Four dollars per kilogram means $4 for each one kilogram. Fifteen pages per day means 15 pages for each one day.
Unit rate turns a comparison into a one-unit relationship.
Why division is usually involved
Suppose 5 kg of fruit costs $20. To find dollars per kilogram, divide total cost by total kilograms:
20 ÷ 5 = 4.
The unit rate is $4/kg.
The division answers the question: how much belongs to one kilogram?
Read the requested rate before dividing
Order matters. If a cyclist travels 90 km in 3 h, kilometres per hour means distance ÷ time: 90 ÷ 3 = 30 km/h.
Hours per kilometre is the reciprocal comparison: 3 ÷ 90 = 1/30 h/km.
Both are valid rates, but they answer different questions.
Units tell you which way the division should go
If the requested unit is dollars per item, put dollars in the numerator and items in the denominator.
If the requested unit is kilometres per hour, put kilometres over hours.
This is one reason units should be written during the setup, not added at the end from memory.
Worked example: price per 100 g
A 500 g packet costs $7.50. What is the cost per 100 g?
There are five lots of 100 g in 500 g. So $7.50 ÷ 5 = $1.50 per 100 g.
This is a unit-rate idea even though the chosen unit is 100 g rather than 1 g. The reference quantity is made convenient for the context.
Worked example: pages per minute
A student reads 42 pages in 35 minutes. Average rate = 42 ÷ 35 = 1.2 pages per minute.
At the same average rate, 10 minutes corresponds to 12 pages.
The phrase “at the same rate” is important. Without it, the later amount is not guaranteed by the first observation.
Unit rate and direct proportion
When a unit rate remains constant and there is no fixed starting amount, the relationship is often directly proportional.
If apples cost exactly $3 per kilogram with no additional fee, total cost C can be modelled as C = 3m, where m is mass in kilograms.
This connects directly to Direct Proportion After PSLE.
A rate can contain compound units
Speed in km/h combines distance and time. Fuel efficiency may be expressed in km/L. Density may be expressed in g/cm³. Unit price may be $/kg.
The slash can be read as “per” and as division. That language helps students interpret formulas instead of treating units as labels.
Do not compare rates before matching the units
Suppose one runner moves at 5 m/s and another at 15 km/h. The numbers 15 and 5 cannot be compared directly because the units differ.
Convert first. Five metres per second is 18 km/h, so the first runner is faster.
This connects unit rate to Units and Conversion After PSLE.
Use a unit rate to check reasonableness
If 4 identical items cost $12, the rate is $3 per item. A claim that 10 items cost $25 under the same proportional price should look suspicious because $25 ÷ 10 = $2.50 per item.
The changing unit rate reveals that either the situation is not proportional or the calculation is wrong.
A unit-rate routine
- Read the phrase containing “per”.
- Write the desired numerator unit.
- Write the desired denominator unit.
- Divide in that order.
- Simplify to one reference unit where useful.
- Use the rate only if the context says it remains constant.
Independent practice with answers
- $18 for 6 notebooks: find dollars per notebook.
- 120 km in 2.5 h: find km/h.
- 750 g costs $9: find cost per 250 g.
- 48 pages in 40 min: find pages per minute.
- Which is faster: 10 m/s or 30 km/h?
Answers: $3/notebook; 48 km/h; $3 per 250 g; 1.2 pages/min; 10 m/s is faster because it equals 36 km/h.
How a 3-pax class helps
A student may perform the division accurately but reverse the units. Another may find the unit rate but use it in a situation where the rate changes. A third may struggle with unit conversion rather than rate itself.
These are different mathematical jobs and should be diagnosed separately.
Frequently asked questions
Does ‘per’ always mean divide?
In school Mathematics, “per” commonly represents a rate or quotient relationship. The precise setup still depends on which quantity is per which other quantity.
Why is km/h a division?
It means kilometres for each hour, so distance is compared with time by division.
Is unit rate the same as ratio?
A unit rate is a ratio expressed relative to one unit of the second quantity. It is one particularly useful form of a ratio.
Why review this after PSLE?
Because rates appear in speed, price, density, graphs, Science and algebraic models. Understanding the units makes later formulas much easier to interpret.
Continue through the Post-PSLE to Secondary 1 Mathematics route
- After PSLE — Should My Child Start Secondary 1 Maths Early?
- Secondary 1 Math Readiness Checklist After PSLE
- Speed, Rate and Units After PSLE
- Ratio, Rate and Percentage After PSLE
Mathematics Tuition in Punggol: keep the relationship visible
Students become more independent when they can say what the quantities mean, why a method is valid and what kind of answer should appear before pressing a calculator.
That is a better transition target than merely finishing more chapters before January.
