Napier’s Local Arithmetic Board is a tool that can be used to teach multiplication to elementary learners (ages 10-12) in your Montessori classroom. It is a hands-on way to practice mathematical skills, and it can help students develop a better understanding of how multiplication works, and provide a deeper insight into the base 2 system.
Short Introduction
The board is made up of a grid of 9 rows and 17 columns, with each square representing one of the following numbers: 32,768, 16,384, 8,192, 2,048, 1,024, 512, 256,128, 64, 32, 16, 8, 4, 2, and 1.
To use the board, learners place pegs in the squares that contain no printed numbers (the last row at the bottom, and the last column to the right). To represent the numbers being multiplied (the factors), learners add numbers together to form the factors. For example, to multiply 5 x 7, learners would place two pegs in the first row at 4 and 1 (to form 5), and three pegs on the far right column at 4, 2, and 1 (to form 7). Additional pegs will be added where all pegs intercept going vertically and horizontally (see pictures below). Finally, learners move the pegs (at the intercepting points) diagonally going downwards, all the way to the last row at the bottom. The product of equation 5 x 7 is found by adding all the partial products 32, 2, and 1 (32+2+1 = 35).
Materials
- 9-3/4 in. x 7 in. wooden board with a printed grid with pegs
- Instructional Guide printed in color
- 52 task cards with a visual control for errors on the back
Demonstration
When using Napier’s Local Arithmetic Board for calculation, the choice of the equation is important as the board has limitations. That is why we suggest using our set of task cards, which ensures that children are working within a reasonable range of equations.
Let’s use 25 x 5. To find the product, we must build the factors (25 & 5) on the board. The first factor (25) will be built on the last row, while the second factor (5) will be built on the last column to the right. Because the board only contains base 2 numbers, to build a factor such as 25, we must look for a number less than 25, which is 16. Now, we look for more numbers to add to 16 until we reach 25, which leads to adding 16 to 8 and 1 (16+8+1 = 25).
Next, we build the second factor the same way, but on the far right column. To make 5, we place pegs at 4 and 1.
(For demonstration purposes, we colored the pegs yellow)
Next, to find the partial products, we place pegs wherever the horizontal pegs intercept the vertical pegs. These same pegs are moved diagonally to the last row at the bottom to be added.
In our example, the partial products appear to be 64, 32, 16, 8, 4, and 1 which totaled 125.
25 x 5 = 125
Children can use a piece of paper or a whiteboard to record the partial products and find the final product.
They will find on the back of each task card a visual control for errors as well as a written answer at the bottom of the card.
In conclusion, Napier’s Local Arithmetic Board will make a useful addition to your Montessori classroom for advanced upper elementary learners, as it enhances the mathematical mind flexibility using multiplication and other basic mathematical concepts! For more innovative Montessori materials, visit our website at www.alisonsmontessori.com.
