MISSION · Number sense
Number Bonds and Making Ten
The pairs that make ten, and why they unlock everything after
LEVEL 1 · EXPLORE
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LEVEL 2 · LEARN
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The idea in one sentence
Every number can be split into two parts, and knowing the splits by heart is what makes arithmetic fast instead of laborious.
Parts and wholes
Seven is 5 and 2. It’s also 6 and 1, 4 and 3, 7 and 0. Each of those pairs is a number bond — two parts that make the whole.
Seeing it this way makes addition and subtraction the same picture rather than two separate skills. From the parts 4 and 3 with the whole 7, four true statements follow at once:
\[4 + 3 = 7 \qquad 3 + 4 = 7 \qquad 7 - 3 = 4 \qquad 7 - 4 = 3\]That set is called a fact family. Learn one bond and you have four facts, which is why this is worth more than memorising sums one at a time.
The bonds to ten
Ten matters more than any other number, because our whole number system is built in tens. These are the pairs worth knowing without thinking:
\[0 + 10 \quad 1 + 9 \quad 2 + 8 \quad 3 + 7 \quad 4 + 6 \quad 5 + 5\]Six pairs. Once they’re instant, a large amount of later arithmetic gets easier, because so many methods reach for ten as a stepping stone.
Bridging through ten
Here’s where the pairs earn their keep. To work out \(8 + 5\), don’t count on five times. Split the 5 into what 8 needs to reach ten, and what’s left:
\[8 + 5 = 8 + 2 + 3 = 10 + 3 = 13\]Two jumps instead of five counts, and no fingers. Subtraction works the same way in reverse: \(13 - 5\) becomes \(13 - 3 - 2\), dropping to ten first and then down.
This is the method that scales. Later you’ll use it on \(68 + 5\) by bridging to 70, and on \(3.8 + 0.5\) by bridging to 4. The number changes; the move doesn’t.
Doubles help too
Doubles stick in the memory easily — \(6 + 6 = 12\), \(7 + 7 = 14\) — and near-doubles come free. \(6 + 7\) is one more than \(6 + 6\), so 13. \(8 + 7\) is one less than \(8 + 8\), so 15.
Between the bonds to ten and the doubles, most single-digit sums are one small step from a fact you already know.
Common mix-ups
- Counting on from one every time. Start from the bigger number, or better, use a bond.
- Forgetting zero counts. \(7 + 0 = 7\) is a bond like any other.
- Treating addition and subtraction as unrelated. One bond gives you both.
- Splitting the wrong part when bridging. Work out what the first number needs to reach ten, then break the second number around that.
Check yourself
What is \(9 + 6\), bridged through ten? And name the fact family for the bond 4 and 6.
\(9\) needs 1, so \(9 + 1 + 5 = 15\). The family is \(4 + 6 = 10\), \(6 + 4 = 10\), \(10 - 4 = 6\), and \(10 - 6 = 4\).
LEVEL 3 · REFLECT
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