This is the rough order of the Maths presentations for Montessori 3-6, I say rough because you will always get a slightly different take depeding on which album you follow. This post was prompted by a chance conversation with a friend who was not sure how to proceed with Montessori Maths, I remember this all too clearly at the start of my Home Ed journey as Montessori is not like anything I had ever come across before. Matters are also complicated if you cannot set out a full range of materials through lack of space or for any other reason. To understand Montessori maths you need to know that the Maths materials are grouped into categories some sequential and some paralell. The reason for the paralell or spiralling nature of Montessori Maths is that there is some obvious overlap of concepts and some concepts and exercises need knowledge from another group in order to progress.
Group 1: Numbers 1 - 10
The first section of Montessori Maths in my Album, deals exclusively with numbers 1 - 10. It starts out with the number rods, this includes the concept of one more and one less. Next you would present the number symbols and use them with the rods. After that you would progresses to using counters or objects with symbols this is mainly one to one correspondance work and you can use virtually anything for counting. Finally in this work you would complete the making of 10, 9, 8, 7, 6 etc... you would also complete subtraction of the numbers 1 - 10.
In summary this section involves one to one correspondence, sequencing the symbols 1 to 10 correctly, recognising and learning the symbols for numbers 1 - 10 and adding and subtracting numbers 1 through 10. Basically knowing the number facts 1 -10 this is the foundation of the decimal system. This group is sequential and the child must have totally mastered the concepts before proceeding to the next group.
This is the only time that you would focus soley on one area of maths, all throughout the rest of the album you would normally work on two or three different concepts like the Decimal system, linear counting and addition. However there is a caveat with the next group.
Materials used in this group are: Number rods, sandpaper numerals, counters and numbers, spindle box,
Group 2 : The decimal system
As the decimal system is based on 10 all the knowledge accquired in group 1 will now be used to understand the hierachy and system functions of the decimal system. Simple computations will also be covered in this section. When the learning of the decimal system is well underway you will introduce the Third Group, so you will begin giving paralell exercises.
Materials used in this group are the Golden Bead Material, large number cards, stamp game, dot board
Group 3:Linear counting
Linear counting involves learning the number and values 1 -1000 it also covers skip counting. Learning values up to a thousand will greatly assist with the childs understanding of the larger numbers involved in the decimal system.
Materials used in this group are: short bead stair, teen boards, snake game, 100 chain, 1000 chain, 100 board, squaring chains 1 - 10, cubing chains 1 -10
Group 4: Arithmetic Tables
The fourth group teaches the child to memorize the arithmetic tables, this again is a paralell group and can start to be introduced in the later stages of the decimal system and linear counting.
Materials used in this group are: dot board, addition strip board, subtraction strip board, addition snake, addition charts, subtraction charts, multiplication bead, mulitplication board, multiplication charts, unit division board, division charts.
Group 5 - Abstraction
This group again is paralell and overlaps with the other groups and is often referred to as the 'passage to abstraction'. In this group the child will start to recognise that they can complete the calculations more efficiently without the materials, however in order for this to be accomplished they need to understand the process of each form of arithmetic and know the tables of each operation. So they know the number facts for 1 -20 inside out and can quickly subtract or add any number 1 -20, similarly they must know their times tables. It is important to note that at the start of this work they may only know the addition tables as they may still be working on the subtraction tables from group 4.
Materials used in this group are: Small bead frame, Wooden heirarchial Material, Large bead frame, Racks and Tubes.
Group 6: Fractions
Typically this group is started when the passage to abstraction has begun
Materials used in this group are: Red fraction circles, fraction lables.
I hope that this helps.xx
