The Term Every P1 Parent Hears and Half of Them Misunderstand
Somewhere in Term 1 of P1, your child comes home with a worksheet that looks like a little cherry. A circle at the top with a number in it, two circles below joined by short lines, each holding a smaller number. The teacher calls it a number bond. Most parents glance at it, decide it is just addition wearing a costume, and move on to drilling "sums".
That is the overlook. And it is the single most expensive mistake in early Singapore maths.
A number bond is not a sum. A sum asks "what is 4 plus 3?" and expects one answer. A number bond holds a whole and its parts in the child's mind at the same time — 7 is made of 4 and 3, and also 5 and 2, and also 6 and 1. It is part-part-whole thinking, and it is the structure that MOE's syllabus deliberately builds Primary 1 around. Addition, subtraction, the "make 10" strategy, mental arithmetic, and — years later — the bar models that dominate PSLE word problems all grow from this one root.
A sum is a question with an answer. A number bond is a relationship the child can take apart and put back together in any direction. The first is a fact. The second is a tool.
A child who has memorised "4 + 3 = 7" knows one fact. A child who owns the bond of 7 knows that 7 − 3 = 4, that 7 − 4 = 3, that 3 + 4 = 7, and that if you have 7 and lose 2 you have 5 — without recalculating any of it. One child has a fact. The other has flexibility. P1 maths rewards the second child quietly all year, and P5 word problems reward them loudly.
What a Number Bond Actually Is
Strip away the cherry diagram and a number bond is just this: a whole, split into parts, that you can recombine freely.
Take 8. Its bonds are:
- 8 and 0
- 7 and 1
- 6 and 2
- 5 and 3
- 4 and 4
This is why the syllabus introduces bonds before it introduces the subtraction symbol with any force. Subtraction in P1 is not really a new operation — it is a number bond with one part missing. "8 take away 3" is just "8 is 3 and what?". A child fluent in bonds finds subtraction almost free. A child who only drilled "plus" sums hits subtraction as a brand-new, frightening thing in Term 2 and the wheels come off.
Why Bonds, Not Sums, Build Mental Maths
Here is the part most parents never see coming. The point of number bonds is not to answer the questions on the bond worksheet. It is to make the child's brain stop counting.
Watch a P1 child add 6 + 7. Two completely different children, and they look the same from across the kitchen table.
Child A counts on. They hold 6 in their head and tick up — "seven, eight, nine, ten, eleven, twelve, thirteen" — usually on fingers, slowly, often losing track once. They get 13. Eventually.
Child B uses a bond. They think: "7 needs 3 to make 10. I'll take 3 from the 6, that leaves 3. So 10 and 3 is 13." Instantly. No fingers. No counting.
Child B is doing the make 10 strategy, and it is entirely built on number bonds — specifically the bonds of 10. They knew instantly that 7 and 3 make 10 (a bond), and that the 6 splits into 3 and 3 (another bond). Two recalled bonds, no counting, done. This is the strategy MOE explicitly teaches for addition and subtraction within 20, and it is unusable by a child who has not first internalised the bonds of 10.
"Make 10" is not a trick to memorise on top of bonds. It IS bonds, applied. A child who does not have bond fluency cannot run it, no matter how many times you demonstrate the steps.
So when a P1 parent says "my child can do their sums, they just count on their fingers" — that is the warning sign, not the reassurance it sounds like. Counting on works at 6 + 7. It collapses at 28 + 47, and it is hopeless against the multi-step word problems from P3. By the second half of P1, you want bonds doing the work, not counting.
The Bridge to Bar Models and PSLE
Let me jump ahead five years, because this is where the overlook gets expensive.
The bar model — the rectangular part-whole diagram every Singapore child draws to crack PSLE word problems — is a number bond grown up. The "whole bar" split into parts is exactly the cherry diagram, just drawn as rectangles and scaled to handle 240 and 185 instead of 4 and 3.
A typical PSLE problem: "Aisha had \$240. She spent some and had \$185 left. How much did she spend?" The child who internalised part-part-whole in P1 sees it instantly — whole is 240, one part is 185, find the other part. Same structure as "8 is 3 and what?", just bigger numbers and a story wrapped around it. The child who never built bond intuition stares at the words and guesses whether to add or subtract.
This is not a stretch — it is the designed progression of the Singapore maths curriculum. Number bonds in P1, bar models from P3, and the bar model is the load-bearing skill in roughly half of the PSLE maths paper. The P1 number bond is the seed of the PSLE bar model. Skip the seed and you spend P5 and P6 retrofitting a structure that should have been laid down at age seven.
The "Make 10" Strategy, Step by Step
Because this is the keystone, here is exactly how to show it at home with objects — not symbols.
Use a ten-frame (a 2x5 grid, ten cells) and some counters — buttons, raisins, LEGO studs, anything. To add 8 + 5:
- Fill the ten-frame with 8 counters. The child sees the frame is two cells short of full.
- Ask: "How many more to fill the frame?" The answer is 2 — and that is the bond of 10 doing its job (8 and 2).
- Take 2 from the 5 and slide them in. The frame is now full: 10.
- Ask: "How many are left over?" 3. (The 5 split into 2 and 3 — another bond.)
- "So we have a full ten and 3 more. That's 13."
The non-negotiable prerequisite: the child must own the bonds of 10 cold. 9 and 1, 8 and 2, 7 and 3, 6 and 4, 5 and 5. If your child cannot rattle these off without thinking, that is the first job. Everything else waits.
Common Misconceptions That Trip Parents Up
Three beliefs sabotage well-meaning Singapore parents at this exact stage.
"Bonds are just easy sums, so we'll skip to harder sums." No. Bonds are not easy sums — they are a different kind of knowledge. A sum is recall of one answer. A bond is a flexible relationship the child can run in four directions. Skipping bonds to drill bigger sums builds a child who is fast at the questions on the page and helpless the moment the question is phrased differently. Depth on small numbers beats range on big ones, every time, at this age.
"My child knows 4 + 3 = 7, so they know the bond." Not necessarily. Test the reverse: cover one part — "7 is 4 and what?" If they have to recount, they have the fact but not the bond. The bond is only real when it runs backwards as easily as forwards.
"Fingers mean they haven't learned it." Fingers are fine — at first. Finger use in early arithmetic actually predicts later ability; the old "stop using your fingers" advice was always wrong. The thing to watch is not whether fingers appear, but whether they are still counting up one at a time by late P1. Fingers flashing a known bond (7 as 5-and-2) are great. Fingers ticking "8, 9, 10, 11..." are the counting-on trap. Same hands, completely different maths.
What to Realistically Expect in P1
P1 runs the whole year, and bonds develop across it. Calibrate so you neither panic nor coast.
By mid-P1 (around June), a healthy child should:
- Know all the bonds of numbers up to 10, in both directions.
- Use a ten-frame to show a bond without prompting.
- Be starting — not mastering — the "make 10" strategy with counters.
- Recognise that subtraction is a bond with a missing part.
- Bonds of 10 recalled instantly, no counting.
- "Make 10" used to add and subtract within 20, mostly without objects.
- Comfortable moving between a bond and its matching sums and differences.
- Beginning to handle simple one-step word problems by thinking part-part-whole.
Building Bond Fluency at Home
None of this needs an app or a worksheet pack. Bonds are built in small, physical, repeatable moments.
- The "hidden part" game. Count out 8 raisins together. Cover some with your hand. "There are 8. I'm hiding some. You can see 5. How many am I hiding?" Reveal. This drills bonds backwards, which is the half most worksheets neglect.
- Ten-frames everywhere. Draw a 2x5 grid on paper, or use an egg carton trimmed to ten cups. Filling it daily makes "how many more to make 10" automatic — and that bond is the engine of mental maths.
- Finger flashes. Call a number; the child throws it up on two hands instantly — 7 as a full hand plus two. Then ask "how many fingers are down?" That is the bond to 10, on their own hands, for free.
- Household splits. "We have 6 dumplings and two of us. How did you split 6?" 3 and 3, or 4 and 2, or 5 and 1 — every split is a lived number bond.
- Dominoes and coins. A domino is a bond made physical: two halves are the parts, the total is the whole. And "I have 10 cents, here's 4 — how much more makes 10?" turns Singapore coins into a pocket-sized bonds-of-10 trainer.
Red Flags: Counting-On Instead of Recalling
The core thing to catch is a child who is counting when they should be recalling. It hides well, because the answers are still right — just slow, and built on sand. Watch for these:
- Fingers tick upward one at a time for sums the child has "done" many times. 5 + 3 should be instant by late P1. If they are still counting "six, seven, eight" every time, the bond never formed — they re-derive it from scratch each go. A two- or three-second stall, even with no visible fingers, means the same counting is happening internally.
- Can do "4 + 3 = 7" but freezes on "7 − 3 = ?". The bond does not run backwards — they have a forward fact, not a relationship, and subtraction will keep feeling alien.
- Cannot fill in a missing part. Show 9 as the whole, 6 as one part, blank for the other — and they are stuck. This is the bond from the angle every word problem will eventually demand.
- Re-counts the whole thing when you change the order. Knows 3 + 5 but treats 5 + 3 as a fresh problem. The bond is not yet a single flexible object in their mind.
What to Do This Week
Pick one number to "own" each week — start with 5, then 6, then up to 10. For the week's number, every day:
- Build it on a ten-frame with counters, and ask the child to show you two ways to split it.
- Play one round of the hidden-part game with that number.
- Once, ask the matching subtraction: "If the whole is 7 and one part is 4, what's the other part?"
For families who want that bonds-first sequence structured digitally — ten-frames, hidden-part puzzles, and "make 10" practice ordered the way P1 actually needs — BrightBit's P1 Maths module is built around part-part-whole fluency rather than sum drilling.
The One-Sentence Version
Sums give your child one answer; number bonds give them a tool they can run in every direction — and that tool is the same one, grown larger, that cracks bar models at PSLE. Build the bonds of 10 until they are instant and counting-on disappears. Everything in Singapore primary maths is downstream of this, and almost no amount of later tuition fixes it as cleanly as a jar of buttons and ten quiet minutes a day in P1.