7 Principles of an Abaku Example / Number – What Abaku Is

The core of Abaku is the Abaku number / example. What is an Abaku example?

An Abaku example is a number that represents an arithmetic equality written without visible mathematical signs.

Classic notation: 1 + 2 = 3
Abaku notation: 123

1. An Abaku example always consists of exactly two numbers (operands) and one result

Yes:
123 → 1 + 2 = 3
1234 → 12 : 3 = 4

No:
1236 → 1 + 2 + 3 = 6
12324 → 12 : 3 (= 6) and then 6 × 4 = 24, etc.

2. We always write and read an Abaku example only from left to right or from top to bottom

Yes:

1
2
3

or 123

3. An Abaku example first expresses the operation and only then the result – never the other way round

Yes:
1234 → 12 : 3 = 4

No:
1234 → 12 = 3 × 4

4. An Abaku example never contains a standalone zero

A single zero may not be one of the operands. A single zero may not be the result.

Yes:
6530 → 6 × 5 = 30
38240 → 38 + 2 = 40
250100 → 2 × 50 = 100

No:
101 → 1 + 0 = 1
110 → 1 − 1 = 0

5. An Abaku example can usually be written in several different ways

1234 → 12 : 3 = 4
1243 → 12 : 4 = 3
3412 → 3 × 4 = 12
4312 → 4 × 3 = 12

6. An Abaku example can also contain further “Abaku sub-examples”

1234 contains:
12 : 3 = 4
and at the same time 1 + 2 = 3

7. The ideal Abaku example is the one that contains the largest number of Abaku sub-examples

For the digits 1, 2, 3, 4 it is enough to change their order to get an Abaku example with more embedded equations:

4312 contains:
4 × 3 = 12
4 − 3 = 1
3 − 1 = 2

At the end of the chapter

What do you see (read) in this word?
Which missing sign (letter) do you automatically fill in?

S L _ V O

What do you see (read) in this example?
Which missing sign (digit) do you automatically fill in?

2 4 _ 3 2

Filling in the missing letter probably cost you almost no effort – your brain already does this automatically.
Filling in the missing digit likely took more effort – your brain does not yet do this automatically, even though it is, in principle, an analogous activity.

Do you see the point?
Numbers can also be read “automatically”. After a short period of practice, the brain starts to recognise equations in numbers on its own. If you bring Abaku into every maths lesson, you will see this in your pupils sooner than you think – because they already know this way of working with symbols from learning to read and write in their mother tongue.

Note – beginners are, on average and regardless of their formal level of maths education, initially able to recognise only three-digit Abaku equalities.