The Dot Game (Addition)
This work helps the child to move into abstraction operations. Usually it is introduced after the stamp game. Prior to this work, the child has worked thoroughly with the golden bead material. Thus far, he is acquiring the concept of addition, and the practice with the ‘Dot game’ furthers this ability. As a note, elaborate apparatus are 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 far 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:
e.g. 1273
+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, a dot for every hundren in the ‘hundreds’ column, and a dot for every ‘thousand’ in the thousands column. 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 green dot down here (in the first and smaller blank rectangular box near the bottom). Then carry these “green” dots over to the 10s column. Now how many unit dots have we left?’ ‘5’ As before we put the 5 down at the bottom. Likewise, 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’. ‘How many tens do we have left? Right, 2. And so on.
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
- To illustrate the mechanism of the decimal system, i.e. that 10 of each decimal category make one of the categories immediately to the left.
- To focus the attention of the child on the process of ‘carrying’.
- 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 4½ years.