Creativity Module 16:
Counting Boards Computation
Addition and Subtraction on the Counting/Computation Boards
The place value or counting boards can be used for learning about computation. The teacher might have students make their own set of counting boards out of heavy construction paper.
Counting boards (also referred to as place value or computation boards) may be used for either teaching place value or for providing a concrete activity in computation from simple addition and subtraction through operations with decimals and signed numbers.
An individual counting board has nine spaces with increasing values from 1 through 9. An empty board has a value of zero. A value of one is obtained by “jumping” a chip onto the board, to land on space one (see Figure 9.4).
The boards can be a hands-on activity for computation as in addition without renaming for the example 25 +13 =38. Then have students’ problem solve to show only one chip on a space that involves making 2 for 1 exchanges on each board to show that the sum remains 38.
Exchange the single chip on the Units Board 5-space for 5 individual chips placed on the 1-space. Overloading a board space is a special instance to allow for regrouping. Now there are a chip on the 9-space of the Units Board and 5 chips on the Units Board 1-space. Make a 2-for-one exchange of the chip on the 9-space with a chip from the five chips on the Units Board 1-space, leaving a value of 4 on the Units Board 1-space and a value of 10 (9 + 1 exchange) for the other chip that now sits atop the Units Board.
Now place the Tens Board to the upper left of the Units Board. Make a horizontal move of the chip on the top of the Units Board to its equivalent value to the bottom space on the Tens Board. There now is a chip on the Tens Board 1-space that is valued at ten and a chip on the Tens Board 3-space with a value of 30. Exchange the 4 chips on the Units Board to 1 chip on the Units Board 4-space. Thus, the value of the boards is 3 + 1chips on the Tens Board, valued at 4 tens and 4 chips on the 1-space of the Units Board, yielding a sum of 4 tens and 4 ones, or 44. For learners with dyscalculia who have challenges with visualizing operations on numbers, the computation boards provide a hands-on vehicle for making addition and subtraction concrete.
First, have students investigate addition on the boards using a count-on approach. This means starting with a number that represents an addend. Then count up the number of spaces representing the second addend.
For the example, 2 + 3, place a chip on the 2 space and then count three spaces by moving the original chip up to the 5 space. To show the commutative property for addition, reverse the activity to 3 + 2 and the chip will again end on the 5 space; the sum will still be five, thus showing that the order of addends does not affect the sum.
To show that subtraction is the inverse operation of addition, for the example 5 minus 3, place a chip on the 5 space, and count down three spaces to land on the 2 space or for 5 minus 2, count down two spaces from the 5 space to land on the 3 space.
Allow practicing with many examples with the maximum sum of nine.
Counting Boards Computation Assessment
Teacher provides students with counting boards addition and subtracting problems involving whole numbers.
Teacher provides students with counting boards and asks them to work in teams of 2 or 3 to show addition and subtraction with renaming on the counting boards.
Teacher provides students with counting boards and asks them to work in teams of 2 or 3 to show addition and subtraction computations with decimal numbers.
Teacher provides students with counting boards and asks them to work in teams of 2 or 3 to show multiplication computations with whole numbers.
Teacher provides students with counting boards and asks them to work in teams of 2 or 3 to show whole number multiplication with renaming.