Number Bonds

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1. 1

   Start with bonds to 10

   0+10, 1+9, 2+8, 3+7, 4+6, 5+5

   There are only six pairs to learn, and their reverses. Ten is the anchor because our whole number system is built on it, so every later bond and every carrying decision routes back through these six facts.

2. 2

   Learn each bond as a family, not a fact

   6 + 4 = 10 · 4 + 6 = 10 · 10 − 6 = 4 · 10 − 4 = 6

   One relationship produces four statements. Teaching them as four separate things to memorise quadruples the work and hides the structure. Teaching the family means subtraction arrives already known rather than as a new topic.

3. 3

   Extend to 20 by reusing the ten

   7 + 3 = 10, so 7 + 13 = 20 and 17 + 3 = 20

   Bonds to twenty are not twenty new facts. They are the bonds to ten with a ten attached, and a child who sees that learns them in an afternoon instead of a term.

4. 4

   Bridge through ten for anything harder

   8 + 5 → 8 + 2 = 10, then 10 + 3 = 13

   Any addition crossing ten can be split at ten using a bond. This is the strategy that replaces counting on fingers, and it works because the bond is instant — if it is not instant, the strategy is slower than counting and the child correctly abandons it.

5. 5

   Test for recall, not for correctness

   Ask "what goes with 7 to make 10?" — the answer should take under two seconds

   A child who arrives at 3 by counting has the right answer and not the skill. The distinction matters enormously later: recall costs no working memory, and counting costs all of it at exactly the moment a carried digit needs remembering.

Why this small topic decides so much

Number bonds look like the most trivial content in primary maths, and they are the most load-bearing. Every written method — column addition, subtraction with exchange, long multiplication, long division — assumes the single-digit facts are free. When they are not, the child spends their working memory computing 7 + 6 and has none left for the carry, and the method fails in a way that looks like carelessness.

This is why a Grade 7 student making "silly mistakes" in algebra so often turns out to have a bonds problem. The algebra is understood. The arithmetic underneath is consuming the attention the algebra needed.

• Bonds to 10 — the six pairs everything else routes through
• Bonds to 20 — the same six with a ten attached
• Each bond is a family of four facts, not one
• Fluent means under two seconds, not merely correct

Correct is not the same as fluent

A child counting on their fingers to reach 3 from 7 is producing correct answers, and a parent watching will reasonably conclude the topic is secure. It is not. The purpose of bonds is to free attention, and a bond that has to be computed frees nothing. Speed here is not a performance metric; it is the entire point of the skill.

The honest test is a mixed, out-of-order verbal quiz. Bonds practised in sequence get recalled by pattern rather than by fact, so a child can recite 1+9, 2+8, 3+7 flawlessly and stall completely on "what goes with 6".

How fluency is actually built

Short and frequent beats long and occasional. Three minutes daily builds recall considerably faster than half an hour once a week, because what is being built is retrieval speed rather than understanding — and retrieval speed responds to repetition spacing, not to session length.

Games work better than worksheets at this specific job, because they add the time pressure that forces recall over counting. Anything requiring a fast answer will do: cards, dice, calling bonds across a room.

How we teach number bonds

We check bonds in the first demo class for any primary student, and for any older student whose written methods are unreliable. It takes two minutes and it changes what the following term looks like, because a bonds gap diagnosed as a bonds gap is a fortnight of work and a bonds gap diagnosed as carelessness is a year of frustration.

When bonds are the issue we do not pause the syllabus to fix them. We run three minutes of bond recall at the start of every class alongside the normal content, because the recall needs frequency rather than airtime, and stopping a Grade 7 student's algebra to do Grade 1 work is neither necessary nor good for them.