Number Bonds to 10
Imagine you have ten shiny stickers and you want to share them
between your two hands. You could hold 7 in one hand and
3 in the other. Or 6 and
4. Every time, the two piles join back up to make ten. Those
special pairs have a name: they are number bonds.
A number bond is a pair of numbers that add together to make a
particular total. The most useful ones make 10, because
ten is the number our whole counting system is built around — it is the friendly number
you can always lean on.
Think of 10 as a single whole that splits into two
parts. If one part is a, the other part is
whatever is left over to fill the ten:
a + (10 - a) = 10
This is just addition
seen the other way round: instead of asking "what is the total?", we fix the total at
ten and ask "what two parts make it?".
See ten split apart
Watch a row of ten cells split into two coloured parts. The left part is
a and the right part is 10 - a —
together they always fill the whole ten. Step through it. Each visit shows a different bond.
The ten-frame
Here is another way to picture a bond: a ten-frame — two rows of five
boxes, ten in all. Drop a counter into some of the boxes and a bond appears all by
itself. The filled boxes are one part, the empty boxes
are the other part, and the frame is exactly full when you have ten.
+
▢▢▢
Seven apples and three empty boxes: 7 + 3 = 10.
Press Refresh on the ten-frame below for a fresh split, and read the
bond it shows.
Two groups of counters
A third way to see a bond is to take ten counters and push them into two groups. However
you split them, the two groups still add up to ten. Here are six on the left and four on
the right:
|
6 + 4 = 10
The bar, the ten-frame and the two groups are three pictures of the very same idea. Once
you can see a bond in any of them, you can see it everywhere.
The bonds to 10
There are only a handful of them, and they come in mirror pairs — once you know
3 + 7 you also know 7 + 3:
0+10 \quad 1+9 \quad 2+8 \quad 3+7 \quad 4+6 \quad 5+5
Look closely at the pattern. As the first part climbs up
0, 1, 2, 3, 4, 5, the second part slides down
10, 9, 8, 7, 6, 5. One goes up by one, the other goes down by
one — that is why they always stay balanced at ten. Right in the middle the two parts
meet at 5 + 5.
Learning these by heart is worth the effort: once the bonds to ten are instant, much
of mental addition becomes fast, because you can always lean on a friendly ten.
A number bond is a pair that makes the target — the order does not
matter:
- 6 + 4 = 10, and so does 4 + 6 = 10.
It is the same bond, just turned around.
- So every bond gives you two addition facts for the price of one
(except 5 + 5, which looks the same both ways).
A surprising amount! One little bond is really a whole family of facts. From
7 + 3 = 10 you also know straight away:
- 3 + 7 = 10 — the same bond turned around.
- 10 - 7 = 3 — take one part away, the other is left.
- 10 - 3 = 7 — take the other part away instead.
That is four facts from one bond. Bonds are not just for adding — they unlock
subtraction
too.
Because ten is such a tidy number to count in. Suppose you want
8 + 5 and you get stuck. You can borrow from a bond: split the
5 into 2 + 3, give the
2 to the 8 to make a friendly ten,
and then it is just 10 + 3 = 13. Knowing that
8 + 2 = 10 turned a hard sum into an easy one. That trick is
everywhere in mental maths.
Almost every bond has a mirror twin — 2 + 8 flips to
8 + 2. But one bond is its own twin, because both parts are
the same:
|
5 + 5 = 10 — five frogs and five frogs. Splitting ten right
down the middle.
Stretching to 20
The same idea works for any whole. The bonds to 20 split twenty into
two parts in exactly the same way:
a + (20 - a) = 20
So 13 + 7 = 20 and 15 + 5 = 20.
If you already know a bond to ten, you can often find the matching bond to twenty by
adding ten to one of the parts: 3 + 7 = 10 grows into
13 + 7 = 20. The friendly ten just gets a friendly twenty for
company.
See it explained
Sal Khan shows the different ways of making ten by filling in the missing part.