Decimal Fraction Board - File 1
Decimal Fraction Board - File 2
To make the Decimal Fraction Board, print both files onto card. Cut the right hand margin from the first file. Glue the files together so that the right hand edge of the first file lines up with the left hand border of the table on the second file. Laminate.
There is a photo of my Decimal Fraction Board, made by the above method, at:
http://community.webshots.com/user/lisialil
Grid paper in Montessori hierarchical colours
This is a grid, colour-coded in the Montessori hierarchical colours, useful for recording addition, multiplication, subtraction and division problems.
A variation on the Montessori decimal checker board
This is a miniature, more abstract version of the Montessori decimal checker board. By the time I introduced multiplication of decimals to my son, he was moving very quickly from the concrete to the abstract on new maths concepts. I did not want to spend a lot of time making a decimal checker board for him to use maybe twice, so I made this quicker variation.
How to use:
Please note: These instructions will only make sense to people familiar
with the Montessori decimal checker board. For book
recommendations and links to websites with information on the
Montessori decimal checkerboard and other Montessori materials, please
see my Montessori Home Education
page.
Write the multiplicand horizontally along the centre of the checker board and write the multiplier vertically down the centre of the checker board (or vice versa).
Work out the product in each square of the checker board as you do when using the basic checker board - one row at a time always starting at the right and moving to the left - and write each product in its square.
Just as with the basic checker board, any product greater than nine needs to be rearranged: the tens removed and one unit for every ten placed in the square to the left. Obviously digits written in pencil can't be “removed” and “placed” as straightforwardly as bead bars can. The best way to get around this will depend on the individual child. The rearranged forms of the products could be worked out on a fresh copy of the decimal checker board, with the child referring back to the initial copy each step of the way, as shown here:
Or the products could be erased one at a time and rewritten in their rearranged forms. Or, as my son chose to, the products could be written in their rearranged forms initially.
Finally, just as with the basic checker board, all the tens need to be swept together and added up, all the ones swept together and added up, likewise all the tenths swept together and added up, etc. In my decimal checker board, the row above the centre line is the base row. Squares above that row should be swept diagonally down and to the left; squares below the base line should be swept diagonally up and to the right. Of course once again figures written in pencil cannot be “swept” as easily as bead bars can. My son did the addition in his head, writing the result at the bottom of the page one digit at a time. Some children may wish to write the addition problem out on a sheet of grid paper to work out. Or the decimal checker board could be cut into rows, the rows realligned and then added together.
The prerequisites for this work are the same as for the Montessori decimal checker board: the child needs to be comfortable with addition and subtraction of decimal numbers and multiplication of decimal numbers by whole numbers and needs to have had an introduction to multiplication of decimal numbers by decimal numbers to the extent that they have worked out:
0.1 x 0.1
0.1 x 0.01
0.1 x 0.001
0.1 x 0.0001
0.01 x 0.1
0.01 x 0.01
0.01 x 0.001
0.01 x 0.0001
0.001 x 0.1
0.001 x 0.01
0.001 x 0.001
0.001 x 0.0001
In fact, some children may enjoy filling out a blank copy of my decimal checker board before beginning work with it.
A blank copy of my variation on the decimal checker board
Some children may appreciate the extra cues that would be provided
by a colour-coded decimal checker board in Montessori hierarchical
colours. If anyone would like an editable form of my decimal
checker board so they can make a new colour-coded checker board, that
would be great: please contact
me .
Montessori
Material Makers in the Files and in the Subgroups' Files.
Copyright © 2006 Lisia Grocott: Verbatim copying and distribution of each entire article or file is permitted in any medium, provided this notice is preserved.
