I only understood how much ratio mattered when my elder girl hit P6. She was wrestling with a percentage problem — the kind where a quantity changes and you have to find the new percentage — and after twenty minutes of frustration she said something that stopped me: "I don't get what the 100 is for."
We backtracked. The percentage was fine. The multiplication was fine. What was missing was the thing underneath: the ability to see two quantities in proportion to each other, and to carve a problem into equal units. In other words — ratio. A topic she had "finished" in P5, with decent marks, a year earlier.
That is the strange thing about ratio. It arrives in P5 looking like one more chapter in the queue, somewhere between fractions and averages. It does not announce itself. But it is quietly the load-bearing wall of upper primary math: percentage, speed, and a big share of P6 problem sums are all ratio wearing different clothes. A child who truly gets ratio finds P6 oddly familiar. A child who memorised ratio finds P6 a wall of new topics that are secretly the same old gap.
So this post is about making sure it is really understood — at home, without turning the dining table into a tuition centre.
Ratio Is a Relationship, Not a Recipe
Start with what ratio actually says, because this is where the shaky version begins.
When we write that the ratio of Ali's marbles to Ben's is 2 : 3, we are not saying Ali has 2 marbles. We are saying: for every 2 marbles Ali has, Ben has 3. They might have 2 and 3. They might have 20 and 30, or 14 and 21. The ratio does not tell us the amounts — it tells us the relationship between the amounts.
That "for every" phrasing is the heart of it, and it is worth saying out loud, often, until it becomes your child's default translation. Ratio 5 : 1 between adults and children on an outing? For every 5 adults, 1 child. Ratio of flour to sugar 3 : 1? For every 3 spoons of flour, 1 spoon of sugar.
Two small but important habits ride along:
- Ratios have no units. We do not write 2 kg : 3 kg as the final ratio — we write 2 : 3. But both quantities must be in the same unit before comparing: 500 g to 2 kg is 500 : 2000, which simplifies to 1 : 4, not 500 : 2.
- Order matters. The ratio of cats to dogs being 3 : 4 is a different statement from 4 : 3. Half of careless-mistake territory in this topic is just reading order sloppily.
Draw It: Bar Models Turn Ratio Into Something You Can See
Singapore math gives us the perfect tool for this topic, and by P5 your child already knows it: the bar model. Ratio 2 : 3 becomes two equal boxes for Ali, three equal boxes for Ben. Same-sized boxes — that is the whole point. Each box is one unit.
Suddenly everything about ratio is visible:
- The relationship: Ben's bar is longer, by exactly one box.
- The total: 5 boxes altogether.
- The difference: 1 box.
This is the unitary method, and it is not a trick for one chapter. Find one unit, then scale up: that same move solves percentage problems, speed comparisons, and half the problem sums in P6. When your child works a ratio question, listen for the sentence "one unit is…". If it never appears, the method has not landed yet, even if the answer is right.
My honest home rule, borrowed from a teacher friend: for two weeks, draw the bar for every ratio question, even the easy ones. Children resist — "I can do it in my head!" — and for the easy ones they can. But the drawing habit is being built for the hard ones, where heads run out of room. The children who draw at P5 are the ones still standing in P6.
Equivalent Ratios: The Same Relationship in Different Sizes
The next pillar is equivalence: 2 : 3, 4 : 6, and 20 : 30 are the same ratio, the way 1/2 and 5/10 are the same fraction. Multiply or divide both sides by the same number and the relationship is unchanged.
Children usually learn the mechanics fast. What is worth checking is whether they understand it, and the kitchen is the best place to check. If a cordial recipe is 1 part syrup to 4 parts water, and you make a big jug using 3 cups of syrup, how much water? A child who gets equivalence says 12 cups without breaking stride — the relationship scales. A child who does not will ask "plus how much?" — and that is your cue that ratio still feels like arithmetic on two random numbers rather than a relationship being preserved.
Simplifying is the same idea run backwards: 12 : 18 becomes 2 : 3 by dividing both by 6. Encourage the habit of simplifying early in a problem — small numbers are kinder to tired brains — and always giving final ratios in simplest form.
The Classic Problem Families
P5 ratio questions cluster into recognisable families. It helps enormously when a child can name what kind of problem they are looking at, because each family has a natural first move.
Family one: sharing a total. "Share $63 between two children in the ratio 4 : 5." Draw 4 boxes and 5 boxes, total 9 units, one unit is $7, answers follow. First move: total ÷ total units.
Family two: given the difference. "The ratio of Sam's cards to Wei's is 5 : 2. Sam has 12 more cards than Wei. How many has Wei?" Now the 12 is not the total — it is the gap between the bars: 3 units. One unit is 4, Wei has 8. First move: ask which units the given number actually covers. This family exists mostly to punish children who divide by the total on autopilot, so it is a wonderful one to practise slowly.
Family three: given one quantity. "The ratio of red to blue beads is 3 : 7. There are 21 red beads. How many blue?" The 21 sits on 3 units, so one unit is 7, blue is 49. Same discipline: locate the number on the bar before touching the calculator in your head.
Family four: before-and-after. The boss level, and the bridge to P6. Something changes — beads are given away, money is spent, students join — and the ratio changes with it. For example: Ken and Maya had stickers in the ratio 3 : 1. After Ken gave Maya 8 stickers, they had the same number. How many stickers do they have altogether?
The key insight: giving stickers to each other changes each person's share but not the total. Before: 3 units and 1 unit, total 4 units. After, equal shares means 2 units each. Ken went from 3 units to 2 — he gave away 1 unit, and we are told that was 8 stickers. So one unit is 8 and the total is 32. The whole solution turns on spotting what stayed constant — sometimes the total, sometimes the difference, sometimes one person's untouched amount. Drawing before-and-after bars, one above the other, makes the constant thing visible.
Do not rush family four. One slow, drawn, discussed problem is worth ten rushed ones. This exact structure — find what is unchanged, anchor units to it — is the engine of some of the hardest P6 questions.
Why Weak Ratio Resurfaces in P6
Here is the part I wish someone had told me a year earlier. In P6, ratio does not politely stay in its chapter. It comes back wearing costumes:
- Percentage is ratio with 100 as the base. "30% of the pupils" is the ratio 30 : 100 — 3 units out of every 10. Children who can flex between ratio, fraction and percentage views of the same situation find P6 percentage manageable; children who learned each as a separate recipe meet what feels like three unrelated topics and juggle badly.
- Speed is proportional reasoning with time in the mix. Two cars covering the same distance, journeys compared, "how many times as fast" — under every one of these sits for-every thinking and the hunt for one unit.
- P6 problem sums love changing ratios: two people's ages, money before and after spending, transfers between groups. These are family four grown up, with bigger numbers and more steps.
- Even fractions of a remainder — that P6 staple — is unit-hunting: the remainder becomes a new whole to be cut into units.
Building Ratio Sense at Home
None of this needs worksheets stacked to the ceiling. What builds ratio sense is small, frequent, concrete contact.
- Cook something with parts. Rice and water. Cordial and water. A marinade of 2 spoons soya sauce to 1 spoon sesame oil. Then double it, halve it, triple it — and let your child do the scaling. This is equivalent ratios with a snack at the end.
- Share things unequally on purpose. "You and your brother share these 15 grapes in the ratio 3 : 2, since you're older." Watch the negotiation. Ratio is never more interesting than when dessert depends on it.
- Play "what's one unit?" Take any ratio statement from daily life — 2 : 3, this drink is 1 part syrup to 6 parts water — and fire the one question: if the total is 24, what is one unit? Thirty seconds, done. It keeps the central move warm.
- Ask for the bar. When homework has a ratio question, ask your child to draw and explain it to you as if you don't know the method. Teaching a slightly clueless parent is a genuinely effective way to consolidate — and you get to see exactly where the understanding thins out.
- A little, often. Five questions spread over a week beats thirty-five on a Sunday. If it helps to have this ready-made, the P5 math chapters on BrightBit include ratio practice in ten-question bites, which is about the length of one MRT ride or one before-dinner slot — enough to keep the muscle warm without a fight.
The Quiet Investment
Ratio will never be the topic parents whisper about at the school gate. It has none of the drama of PSLE composition or the terror of speed-time problems. But it is the P5 topic with the longest reach — the one whose quality quietly decides how P6 feels.
So when it comes around, give it more than its chapter's share of attention. Ask the for-every question. Insist on the bars. Sit with one before-and-after problem until it actually makes sense. Your child will not thank you at the time — mine certainly didn't — but somewhere in P6, a percentage problem will unfold politely instead of exploding, and you will know exactly which P5 evening paid for it.