The Montessori math materials cover a significant number of areas - the range gives an opportunity for working with money and fractions and time and geometry...all still at the CASA/Junior level.

As we grow and learn and explore and reinforce, so do Montessori's amazing materials. Abstraction becomes a natural progression as the student moves through the Montessori Elementary curriculum.  While materials are still available for taking fractions into decimals and percentages and for working measurement through new levels, the materials become more detailed and complex allowing for easier abstraction as the foundational functional activities are, by now, well retained.

The decimal checker board while colourful and large and appealing to use, nows draws on earlier lessons - the coloured beads from CASA, the bank and stamp game.  The colours are lighter as numbers become percentages of numbers and as such really, really small numbers.  Squaring and square roots with the algebraic pegboard helps the student realize that squares of numbers are actually "squares".  Enjoyable, engaging manipulation of materials still draws and holds the interest of these pre-teens.  Replicating these numbers on graph paper with their representative numbers make for worthwhile documentation.

Math made - not only easy but - interesting, engaging and logical.  As reiterated over and over, Maria Montessori has the mind of a genius and a love of educating the young mind that has yet to be duplicated.  Copied yes - watered down yes - but Montessori's materials - the math in particular - are a scientific journey that is as exciting to take as it is to share.

With foundational groundwork in place the world of mathematics explodes.  Bead stairs - numbers represented by colour coded quantities - allow addition, multiplication, division and subtraction to become visually obvious exercises - teen boards and ten boards develop a real recognition and understanding of tens and units and of groups of tens and units..and then...the core of Montessori's math program the Bank Game.

The Bank Game is undoubtedly one of Montessori's absolute masterpieces.  Through specifically created bead combinations and colour coded quantity cards - students as young as 4 and 5 can combine calculations to 9,999.  A child can easily hold 1000 beads in cube format in the palm of a hand and compare that with jaw dropping interest to the golden unit bead held in the other.  There are 10 bars and 100 squares and thousand cubes to manipulate, combine, match and calculate.  This inquisitive young mind can began adding, historically thought "larger numbers", with ease.  From here multiplication - an extension of addition is logically next introduced.  Division is the "opposite" of multiplication...and so it goes.  

Even with this outstanding piece of material able to reinforce so many concepts - Montessori created parallel exercises to fortify already simmering abstraction.  The bead frames, strip boards, the finger charts and racks and tubes are but a few of the mathematical function material available for exploration.  Repetition breeds retention!

The wonderfully logical sequential world of numbers!  Montessori's analytical mind brought reality and common sense to this world of symbols creating exciting, colourful and - oh so appealing - materials to work through.  Recognize the symbol, understand the quantity and then bring those things together.  So simple, so logical, so easy to retain.  By breaking every concept and theory into steps and developing each piece of materials to address the stages of the development Montessori created - as with her Language Program - a pretty fail safe curriculum.

The youngest students enjoy the raised sandpaper symbols through 3 period lessons, counting and recognizing growing quantities through the red rods and the starting acknowledgement that putting symbol and quantity together give abstract understanding to numbers that are greater or smaller than others.  Parallel materials reinforce this discovery - the spindle boxes allow counting and sorting, numbers and counters give space to understanding odd numbers and even numbers...all this at Montessori's introduction level in a Casa class!

​The magical excitement of putting sounds together to make actual words is an experience to be envied.  While Montessori teachers experience it regularly it is never a feeling taken for granted.  Instilling word attack skills in children so young – Montessori creates the opportunity to bring the entire world to a child through the written word. 
 
Once the basic 26 sounds are absorbed and practiced and blended and created the child begins experimenting with phonograms – who knew that sh together made the sound “sh” or that if we see “ee” together that makes its own single sound. 
 
Phonograms matching and blending begins – my vocabulary now grows from fun or stag or fantastic to words like shout and enjoy and quest.  There is an explosion of word building and vocabulary which grow into burgeoning comprehension skills.  My literary skills can now be questioned and identified through grammar symbols and sentence structure.  Whole reams of cultural materials become more appealing on the advanced level of documented research. 
 
The joy of reading opens avenues that last a lifetime – Montessori support enables and excites the child on this journey in realizing the world through the written word.

​As with everything Montessori created, logic, simplicity and control of error combine to make learning engaging and fun.  The Sandpaper Tablets allow the students, through raised sandpaper representations, to isolate, recognize and reproduce the phonetic sound of each letter.  Presented in groups of 3 – each with a completely different sound – sounds are introduced individually or in very small groups.  The teacher traces one sound at a time and carefully introduces the sound and the formation of the letter through her demonstration.  The child is then able to repeat her actions and sound.  The famous Three Period Lesson – used in many Montessori presentations works its magic.
 

1. The sound is repeated and traced several times
2. The child is asked to identify each sound with the tablets in full view
3. Can you tell me what this is?

 
This versatile and engaging lesson is used so many ways, with so many different materials, that it remains testament to her methodology and scientifically, systematic educational journey.
 
Once the 26 basic sounds have been phonetically introduced it becomes very easy for students to begin to blend sounds into words.

The Nomenclature Cards present to the youngest students groups of realistic images helping then to expand their spoken vocabulary and recognize and experience the world outside of their immediate realm. 

Images of vehicles or food groups or furniture or types of weather – the groupings are unending.  Even at these young ages matching object to object, then object to picture, then picture to picture and eventually picture to word allow a logical progression into abstract thought and understanding.  Younger students love the objects and representation of things they can handle and match – the fascination of words spoken and phrases developed never fail to engage. 

​As always top to bottom and left to right subconsciously lay the foundations for reading, writing and organizational skills all so important moving forward.

​The Montessori Language Program has fascinated me from the day of my first introduction.  The Math materials are incredible – without question – but the language activities are so intelligently created, so logically sequenced and so beautiful to work with that it deems it almost impossible for a child not to be able to learn to read.  If one has strong reading skills everything we learn becomes so much easier.  Montessori promoted the use of realistic renditions for her materials, exciting the young mind with recognizable, identifiable objects or cards to manipulate.  While grammar has become a mere thought in traditional schools the Montessori student is alive and well in the realm of words and phrases and subjects and predicates.  Students are encouraged to question and manipulate - English is, after all, a seriously strange language. Words have more than one meaning, spelling rules change, two words can become one word, we can leave letters out, add an apostrophe and the word is the same even though it isn’t?  Punctuation can change the meaning of the same group of words – the changes and possibilities seem endless.

​The materials flow seamlessly and logically from Pre-Casa through to the end of Grade 6.  The Montessori student develops a strong understanding of the nuances of the English language – as with all Montessori areas – not simply learning but UNDERSTANDING and creating a foundation for all that lies ahead as they grow into solidly contributing members of society.  As is always possible moving forward in KNOWLEDGE with UNDERSTANDING.

​Today I get to do the Colour Tablet Box Number III.  I have already learned my primary and secondary colours – I have matched tablets to each other, to things in my classroom and to coloured pencils – I even finished a whole colouring sheet – it looked like a rainbow of colours.  I need a big rug for this.  I think I’m going to do the sun today instead of just the rows on a rug. 

​I marvel at the feel of the piece of felt I will use as my centre point – some people use the pretty pot of flowers…or nothing…but I like this round colourful piece of felt.  This box has many tablets so I must lift and carry it carefully to my rug. Look at this!  There are different yellows and greens and purples…all the colours!  I’m going to start with blues…hmmm…which is the darkest one…the darkest one left…the darkest one left. 

​The knobbed cylinders…every Montessori child’s favourite at some point.  Rectangular blocks housing knobbed cylinders that vary, by block, in height, width, weight and shape.  In the initial lesson each cylinder is removed from its housing, is examined visually and tactically and placed on the working mat in front of the space from which it came.  All cylinders are removed.  One by one, slowly, with much thought, they are returned to their correct space.  Each cylinder only fits properly into its own space – no student needs an adult “correcting” their work - Montessori’s marvelous materials show the way.  After all four cylinder blocks have been explored at different times – I challenge myself by mixing the order of the cylinders once removed.

​Can I through sight and/or touch find the perfect space for each one.  Further challenge could involve combining the cylinders of 2/3/4 blocks and returning them to each of the specially created spaces.
 
Think of it – gradation, sequencing, comparison, independent work all through only one piece of Montessori material!