Websites with Montessori printables for downloadMontessori Materials
Montessori Material Makers
My Montessori printables
Fraction circlesFraction circles: whole to sixths
Fraction circles: sevenths to twelfths
Print onto coloured card and cut out.
Grid paper in Montessori hierarchical coloursGrid paper in Montessori hierarchical colours
This is a grid, colour-coded in the Montessori hierarchical colours, for children to record addition, multiplication, subtraction and division calculations on.
Montessori decimal fraction boardDecimal 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.
A variation on the Montessori decimal checker boardA 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 usePlease note: these instructions will only make sense to people familiar with the Montessori decimal checker board. To learn about how decimal numbers are taught in the Montessori curriculum, see a Montessori manual such as Montessori Research and Development's Decimal Manual.
- 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. 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.
Or the products could be erased one at a time and rewritten in their rearranged forms. Or, as my son chose, 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, all the tenths swept together and added up, and so on. 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 realigned 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 variation of the decimal checker board before beginning work with it.
Some children may appreciate the extra cues that would be provided by a colour-coded decimal checker board in Montessori hierarchical colours. An editable version of my decimal checker board is available for anyone who would like to add colours. If you make a coloured version and would like to share it with others, please leave a comment; I am happy to host or link to a coloured version.