Early maths
Number Bonds to Ten: The Nine Facts Worth Knowing by Heart
Six and four. Seven and three. A handful of number pairs do a surprising amount of work in later arithmetic. Why they matter and how to practise.
If you ask a primary teacher which number facts matter most in the first years of school, the pairs that make ten will be near the top of the list. Schools often call them number bonds. There are only a few of them, and they are used constantly for years afterwards.
What they are
They are the pairs of whole numbers that add up to ten:
- 1 and 9
- 2 and 8
- 3 and 7
- 4 and 6
- 5 and 5
Turn the first four round and you have 9 and 1, 8 and 2, 7 and 3, and 6 and 4. That makes nine facts, though a child who understands that the order does not matter really only has five to learn.
Why ten?
We write numbers in tens. After nine we run out of digits and start again with a one in a new column. Almost every method of mental arithmetic uses ten as a stepping stone.
Take 8 + 5. A child who counts on from eight needs five careful steps and a spare hand. A child who knows that eight needs two more to make ten can think: eight and two is ten, and there are three left over, so thirteen. Teachers call this bridging through ten, and it only works if the bonds come to mind instantly.
The same facts come back, scaled up, all through school. 60 and 40 make 100. 700 and 300 make 1,000. Change from a ten-pound note. Minutes left in an hour is the same kind of thinking, with sixty.
Knowing, not working out
There is a difference between being able to work out that six and four make ten, and simply knowing it. The first is where every child begins. The second is the goal.
That does not mean chanting without understanding. A child should first see why six and four make ten, with objects, fingers and pictures. Then practise until the answer arrives without effort. Understanding comes first, and speed follows.
The ten frame
The best picture for this is a ten frame: two rows of five squares. Put six counters in and four squares are empty. The answer is there to be seen.
Our game Make Ten uses exactly this. A frame appears with some counters in it and the question reads, for example, "6 and ? make 10". Your child can count the empty squares at first. Over time they stop needing to.
You can make a ten frame at home with an egg box cut down to ten cups, or by drawing a grid on paper.
Six ways to practise away from the screen
Fingers. Hold up some fingers. "How many are down?" Ten fingers are the most convenient ten frame there is.
Ten in a cup. Count ten small objects into a cup. Tip some out onto the table. "How many are still in the cup?"
Cards. Take the picture cards out of a pack. Turn one over and race to say its partner to ten. Later, play pairs where a match is two cards that make ten.
Up the stairs. If you have ten or more stairs, stand on the sixth. "How many more to ten?"
Say it both ways. "Seven and three make ten. Three and seven make ten."
Turn it round. Once the pairs are secure, ask the take-away: "Ten take away seven?" It is the same fact seen from the other side.
Start with five
Many children find bonds to ten easier once they are sure of the pairs that make five: 1 and 4, 2 and 3. These fit on one hand. If ten is a struggle, go back to five for a week.
How long does it take?
Longer than adults expect. Many children are introduced to these pairs at five or six and are not fully fluent for another year or more. That is normal. A minute or two a day, in passing, does more than a long session at the weekend.
Signs that it is going in:
- Your child stops counting the empty squares one by one.
- They answer the easy ones, 9 and 1, 5 and 5, straight away.
- They start using ten in other sums without being told.
What the game adds
Make Ten has only nine possible questions and asks eight of them in a round. So the same facts come round again and again, in a different order each time. That repetition is the whole purpose.
When a wrong answer is tapped, it fades and your child tries again. Nothing is taken away and there is no clock. Three stars are given for getting at least seven of the eight right first time.
Like the other HTML5 games on StarSlate, it runs in the browser and takes two or three minutes. After a round, Adding Up and Take Away use the same small numbers in a different way.