This is very near the abstract operation. It generally comes after the stamp game.The child must have worked very thoroughly with the golden bead material. He is acquiring the concept of addition, and the practice with the ‘Dot’ game furthers this ability. Elaborate apparatus is not required.

Material

• Paper, blank on the left side with columns on the right for thousands, hundreds, tens and units.

Presentation 1

1. Give the child a simple explanation about the sheet-the blank space at the side is for writing the problems: the first column on the right is for the units, the second for the tens, the third for the hundreds and so on.
2. For the first presentation, a simple addition is used:      
3. e.g.   1273
4. +3413

   4686

3. For every unit we are going to put a dot in the ‘units’ column, a dot for every ten in the ‘tens’ column but we must make sure we have the dots in the correct column. ‘There, we have all the dots placed-let’s count them – 6 Units, ‘6’ goes down at the bottom of the sheet in the ‘units’ column. 8 tens, the ‘8’ goes down at the bottom of the sheet, in the ‘tens’ column. 6 hundreds, the ‘6’ is put in the ‘hundreds’ column – and 4 thousands, and we put the ‘4’ in the ‘thousands’ column. So we have 4686, and we write the answer under the problem’
4. Summarize the problem with the child. He does only simple sums at first. Either write them for him or give him prepared slips. He uses a fresh sheet for each sum.Small sheets may be used for short problems.

Presentation 2

1. When the child is ready, give the presentation of the more complex addition.      2765

+1084

   2976

   6825

2. As before, put in the requisite number of dots; start counting the dots and when you reach 10 you say ‘What happens to ten units? They become-? one ten, right, so we will put a cross through these 10 units here and put a dot down here near the bottom in green. Now how many unit dots have we left?’ ‘5’ As before we put the 5 down at the bottom. For every 10 ‘tens’ we cross them out and put a dot near the bottom in (green) and carry these special dots over to the next column, because they represent ‘A hundred’.
3. This process is repeated until all the dots have been counted.

The dots in different colors are to focus the child’s attention on carrying. Any colors can be used. Some people like to use the various colors for the different categories, but an ordinary pencil will do.

Direct Aim

a) To illustrate the mechanism of the decimal system, i.e. that 10 of each category make one of the categories immediately above.

b) To focus the attention of the child on the mechanism of ‘carrying’.

c) To familiarize the child with the relations among the different categories, i.e.converting 100 units into tens.

Indirect Aim

To prepare the child for abstract addition.

Age of great interest 

About 4^1/2 years.