Dot Game
Materials:
A board or paper which is divided into 6 columns
Five of these are headed 1, 10, 100, 1000, 10,000 written in the hierarchical colors. These columns are divided into small squares so that there are ten in each horizontal row. At the foot of each column are two spaces, the upper one for carrying figures and the lower one for the result.
There is a blank column at one side in which the equation to be done is written
A colored pencil or felt pen
A pencil or black felt pen
Tissue and damp sponge in a container to clean the board
Purposes:
To reinforce the relationships from one category to another
To illustrate the mechanism of carrying
To offer a further step toward abstract addition
Age: 4 ½ to 5 ½
Preparation: Dynamic addition with the stamp game and had good control with a pencil
Presentation 1: Horizontal
Invite the child, they will bring the board and the guide will bring the tray.
Indicate to each of the numbers at the top and have the child identify them. Introduce the 10,000.
Explain you will do addition. Write several four digit addends on the right side of the paper in a column. Alternate back and forth between you both writing addends. Try to get a minimum of six.
Explain you will make dots to represent quantities in the columns. Show the child the dark edges of the category.
Record the units, tens, hundreds and thousands of the first addend. Place the dots from left to right. Place a checkmark to the right of the number you just recorded or cross out the digits.
Continue for the next few numbers placing the corresponding dots in each category, dotting left to right and continuing to dot where you left off for each category, for all the numbers.
Let the child do the rest of the plotting
Once all are recorded, count what you have. Begin with units. Count the first row of 10 and remind the child what happens with 10 units. Line out the row and make a hash mark in the box above the answer box. Explain the hash mark tells us we will exchange. Encourage the child to count for the first few rows.
Explain that the number of dots left over is the answer and is written in the answer box.
Count the hash marks, and with a color write the number symbol for them in the tens box above the answer box.
Record the number of exchanges as dots into the next category, dotting where you left off.
Continue for the rest.
Show the child the answer and how to read it.
Record the number below the problem.
Presentation 2: Vertical
Setup as before including writing a column of addends.
Explain that you will record all the units first. Record the dots for the first two addends and then turn it over to the child.
When the units are all recorded, proceed with the counting, recording, and exchanging as before. Now the dots you carry will be the first dots in the next category.
Repeat for the rest in this manner but totally turned over to the child.
Control of Error: None, the accuracy of the answer is not the purpose.
Pedagogical Notes:
This is a preparation to work in columns abstractly with addition.
Notice now the level of abstraction- the golden beads offered concrete handling of materials, walking to the shelf to exchange, then to the same sized stamps of the stamp game all at the table, and now to no manipulatives. How is the child able to make these leaps? Concrete experiences!