Addition on a Counting Board
|
Using Dot Cards in Early Grades In early grades, even when children are exposed to many uses of numbers, they learn arithmetic as the skill of answering the questions, "How many?" and "Which one?" But using collections of small objects that can be counted and manipulated is difficult, because even a small jar of beans can make a big mess. A partial solution to this problem is to use dot cards. Click here to download printable dot cards. 
The cards shown above are example dot cards.
First Task Each child works alone. She (or he) has a counting board and only two tokens. Each child is given a dot card with the number of dots smaller than or equal to fifteen, and is asked to show the number on the counting board and say its name. Example 
Because the dot card shows the number 9, children should represent 9 on the counting board and say the number out loud. In this example, 9 is represented with
one token on the 4 square, and one token on the 5 square.
Second Task Children work in groups of two or three. Each child has a board and only three tokens. Each group is given three or four cards, with the total number of dots smaller than sixty-six. Each child is asked to put the total number of dots on the board by working with one card at a time. They work simultaneously, but each child adds numbers in a different order. Children should help each other, and ask the teacher for help when it is needed. Example  A group of children are presented with the three dot cards shown above. The following images show the process one child should take while working on the task. 
When given the first card, the child will represent the number on the board using tokens. In this example, the first card has 8 dots, so the child
may represent the number 8 using tokens on the 5, 2, and 1 squares.
When given the next card, the child will add the number of dots to the board. In this example, the newest card has 5 dots. The child will recognize that 8+5=13,
and represent the number 13 on the board. In this case, the number 13 is represented by tokens on the 10, 2, and 1 squares.
When given the last card, the child will add the number of dots to the board. In this example, the newest card has 14 dots. The child will recognize that 13+14=27,
and represent the number 27 on the board. In this case, the number 27 is represented by tokens on the 20, 5, and 2 squares.
All children in the group work simultaneously and add the cards in a different order. In the same group, a different child may add the cards as follows.
When given the first card, the child will represent the number on the board using tokens. In this example, the first card has 5 dots, so the child
may represent the number 5 using one token on the 5 square. The child does not yet use the other two tokens because they are not necessary for this representation.
When given the next card, the child will add the number of dots to the board. In this example, the newest card has 14 dots. The child will recognize that 5+14=19,
and represent the number 19 on the board. In this case, the number 19 is represented by tokens on the 10, 5, and 4 squares.
When given the last card, the child will add the number of dots to the board. In this example, the newest card has 8 dots. The child will recognize that 19+8=27,
and represent the number 27 on the board. In this case, the number 27 is represented by tokens on the 20, 4, and 3 squares. Note that although the cards were added in a different
order, both children in the group reached the same answer.
This task should be repeated many times until most children can do it without errors. In this task the teacher should work as a helper, promptly giving all help that is needed, and correcting students' errors. The teacher should also observe how children do the task, give advice, and deal with any misunderstanding that may lead to systematic errors. Third Task This task is an extension of the previous one. Children may work in bigger groups, or individually. Each child may use four (or even more) tokens. And sums are only limited by the capacity of the board. General Remark A restriction on the number of tokens students use in the first two tasks is very important. It prevents students from developing easy but very inefficient strategies for doing addition, such as piling tokens on one location and using regrouping rules to simplify the resulting configurations. Number Board index |