Thursday, March 19, 2009

Montessori Printables

Websites with Montessori printables for download

Montessori Materials

Livable Learning

Montessori Material Makers

My Montessori printables

Fraction circles

Fraction circles: whole to sixths

Fraction circles: sevenths to twelfths

Print onto coloured card and cut out.

Grid paper in Montessori hierarchical colours

Grid 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 board

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.

A variation on the Montessori decimal checker board

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. 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.

  1. 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).

  2. 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.

  3. 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.

  4. 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.

Montessori Manuals

Manuals for ages 3-6

Discovery of the Child - Maria Montessori.

The Montessori Method - Maria Montessori.

Teaching Montessori in the Home: the Preschool Years - Elizabeth Hainstock.

Basic Montessori: Learning Activities for Under-fives - David Gettman.

Shu-Chen Jenny Yen's online Montessori albums.

Don Jenning's online Montessori albums at the Montessori Teachers Collective.

Montessori World Educational Institute online Montessori albums.

InfoMontessori's online Montessori albums.

Manuals for ages 6-12

The Advanced Montessori Method volume II (also called The Elementary Materials) - Maria Montessori.

Teaching Montessori in the Home: the School Years - Elizabeth Hainstock.

Don Jenning's online Montessori albums at the Montessori Teachers Collective.

Division by a 2-or-3-Digit Divisor: a Montessori-Style Teaching Manual - Lisia Grocott.

Montessori Research and Development Montessori manuals available for purchase. I recommend the Montessori Research and Development manuals reservedly. Montessori homeschooling with my children, I have used the Decimals, Fractions, Maths, Geometry and Language manuals for 9-12. Both children have thoroughly enjoyed the maths and geometry activities. I do not believe there is a better programme available, Montessori or other, for teaching elementary maths. However, the Montessori Research and Development manuals I purchased in about 2003 are riddled with errors. Many of the activities are explained poorly and required modifying before I could present them to my children.

What is Montessori?

The prepared environment and the role of the teacher

In my opinion, the prepared environment is the base of a Montessori education. It is through the environment that the adult helper attempts to meet each child's individual, changing needs. The environment is clean, orderly and attractive. To begin with, the adult entices the child to work, through presenting and re-presenting a variety of activities, waiting patiently for the day when one of the activities will “call” to the child, and the child's concentration will be caught.

When that happens, the adult must quietly step back. The adult's role now is to protect that fragile concentration from interruption, for in the early stages, if it is broken, days or even one or two weeks might pass before the child's concentration is caught again. Even a friendly “How are things going?” or an awareness of being observed might be enough to shatter the child's concentration.

The child begins to make choices based not on surface appeal and whatever catches their eye but based on a deep inner desire to explore certain activities. The adult's role is to observe and consider, changing the environment and making new presentations and re-presentations based on the child's needs. The child will not be in this perfect state of knowing his or her own needs all the time; sometimes children will be slaves to whims. The adult must learn to distinguish between indiscriminate choices and the choices that stem from a genuine inner need.

Trust the child

I think the hardest task of a Montessori teacher or parent is to trust that children will educate themselves if allowed to follow their own interests as described above. According to Maria Montessori, there should be no compulsion. Children are invited and enticed to work, not coerced.


Closely tied to trust in the child is a great respect for the child. Not only are children treated with respect in all interactions, but their concentration is also respected. Adults do not interrupt a child who is absorbed in work, and children are taught to avoid doing so too.

Children's ability to care for themselves and the environment is respected. It has been observed that children derive enjoyment and a sense of pride and self worth from being able to look after themselves and their environment. To that end, presentations of practical life activities are made and children are premitted to do as much for themselves as they are capable of and as they want to.

The principle of respect encompasses every aspect of a Montessori environment. As well as respect between people, there is also respect for the things in the environment and for everything in the wider environment of the world. The Montessori materials are treated with care.

"Help me to help myself"

It is acknowledged that help can be a hindrance: when a child is capable, but only just, of doing up the buttons on a jacket and is trying hard to do so, it would be quickest to take over and do the task oneself, but that is not what the child wants, nor is it actually helpful to the child.

If a child completes a task or activity, ignorant of some sort of error, the child is not corrected. Instead the adult makes a note to re-present that activity at a later time.

The materials

Maria Montessori created a set of apparatus from which children can discover for themselves, and then practise, many different concepts. Even complicated mathematical concepts such as calculating cube roots are presented concretely with physical apparatus so that through seeing and building for themselves, children can reach their own understanding of each concept.