Making ten

The ten frame shows you

A ten frame is two rows of five. Put counters in and the empty spaces tell you what is missing, without any counting at all.

Six counters in. Look at the gaps: four. So six and four make ten.

The pairs that make ten

There are only six pairs to learn. Six.

Once you know them, a great deal of adding becomes easy, because you can always look for a ten first.

Bridging to ten

Nine and three is hard to see. Ten and two is easy. So turn the first one into the second.

Move one counter across. The nine becomes ten, and the three becomes two. Nothing has been added or taken away — the counters were only shuffled — so the answer is the same.

Ten and two is twelve.

Why ten and not some other number

Ten is worth this trouble because of how we write numbers. Twelve is ten and two. Thirty-four is three tens and four.

Every time you make a ten, you have made a piece that the number system already knows how to hold. That is why looking for tens is the first thing to try.

Bridging, shown on the frame

Eight plus five is hard to see all at once. Ten plus three is not.

So move two of the five across to finish the ten. The five splits into two and three: the two completes the frame, and the three is left over. Ten and three is thirteen.

Nothing has been added or taken away. The same thirteen counters are sitting in a shape that is easier to read.

It works for taking away too

Thirteen take away five is the same trick run backwards. Take three first to get back to ten, then take the remaining two from the ten, which leaves eight.

Going down through ten is easier than counting back five times, and much easier than trying to hold the whole thing in your head.

The pairs that make ten do the work in both directions, which is why they are worth knowing by heart rather than working out each time.