Montessori Nuggets

Montessori Painted Materials - NOT All-Natural

More on why we don't prefer natural materials all of the time.

Key Sounds in the English Language

The English language has 40-44 key sounds varying with dialect.

This video shows the key 42 sounds as learned in an AMI training center in the midwest.

Related Montessori Nuggets:

Sandpaper Letters - Single and Double (Phonogram)

Phonogram Key Sounds

Geography Charts - Protractor

Elementary Montessori utilizes many charts to express key concepts for the children to explore.

Geography has the largest collection of charts, with 3 subsets: normally numbered, a set for typically upper elementary numbered with an "a" following as well as a set of work charts.

One of the work charts is called the Protractor Chart.

The chart comes in two parts. The background piece and the protractor.
There are two protractor pieces so there is a back-up when the first wears out.

Cut out one piece, hole punch and use a brad.

Assembled

Naming the parts:

Yellow arrow = sun rays
Protractor piece = earth
Colored background = climate of the time
Degrees = lines of latitudes
dashed lines = tropics and lines of latitude on either side of the equator
red line = equator

Working with the chart:

Review previous work/knowledge (dates of the equinoxes and solstices in relation to the sun's rays).
Identify the parts.
Suggest that as we move the earth so that the sun's rays fall perpendicular to each line of latitude, the seasons change.
Select particular locations according to their latitude and explore the seasons accordingly.
Select locations from the opposite hemisphere and see where the city falls as the protractor is tipped accordingly.

This is one lesson (not provided in full detail here) that shows a key experience laying a foundation for further study. It invites explorations and potential questions. If this is as far as the child goes with the information, it is enough to have the basic information without wasting their time and energies for many days covering the same information; it fits within a grander set of other key experiences that includes much more already. Every child has their area of in-depth study, whether this one or another.

Botany Cabinet: Focus on the Essentials

An excerpt from the elementary biology album that reminds us why we use generic shapes in the botany cabinet, as opposed to leaf names specific to a particular region:

Once the child gathers a large body of knowledge from sensorial exploration, she can then begin to order and classify it.

An example of how this happens is by giving the child the name of the new shape rather than just giving the name of the plant from which the leaf comes. For example, the child can see that this plant has obovate leaves and so does this plant. That plant over there has sagittate leaves. When you give the name of the leaf shape, you give the children a tool to classify leaves and plants alike. Just giving the names of the plants, does not provide a basis for ordering and classification. This base of information is also built up through the use of nomenclature material in the primary. The nomenclature material is used by children who are reading and also those children who are not yet reading. Through the use of the nomenclature material, children learn the names of plants, parts of plants, names of animals and names of parts of animals. Eventually, all of this information can be ordered and classified. Another source for building up the child’s store of information comes from the stories, the poems and the songs that the teacher introduces about plants and animals.

All of this work becomes a foundation from which the children will launch with her work in the elementary.

Key Montessori Principles

There are only 2 key Montessori principles that apply to all people of every time, every age and every place.

All the other longer lists you see online and in other places? Fall under these two main headings.

Fulfilling human needs and tendencies

1) Meeting human needs
2) Fulfilling the human tendencies

That's it!

Many people think of the Montessori Method as a different type of education when indeed it is truly a vision for life – education as an aid to life. This concept is the over-riding principle through all Montessori work. The Montessori Method is not just about different materials and different presentation styles for the learning; the essence of the Montessori work is to help each child develop his potential even as adults continue the same striving. One’s *attitude* (state of mind) is a way of life – not just something thought of before entering the environment – but always. The process of Montessori training is a transformation of the adult – whether formal or informal – and it is an ongoing process, never entirely complete. It continues even afterward as more is learned, more is experienced and perhaps further training is taken; as time passes and experiences build upon experiences, the whys and hows of implementing this method are internalized deeper and stronger.

The adult must keep this idea of ongoing transformation alive while going working with children who are also constructing themselves.

Human Needs and Tendencies 1: Needs
Human Needs and Tendencies 2: Tendencies
Human Needs and Tendencies 3: Role of the Adult and the Environment
Human Needs and Tendencies 4: Montessori Method
Human Needs and Tendencies 5: Background and Definition
Human Needs and Tendencies 6: Above Instincts
Human Tendencies as Verbs

Respect for the particular developmental age of the person - aids us in meeting the needs and tendencies of the human person at each stage.

Four Planes of Development: Overview
Keys to Provide at Each Plane of Development

How do we know something is working or needs adjustment?

We need to understand child development and Montessori principles in order to apply our love of children towards assisting in their self-construction.

Observation is key to the Montessori method. We approach our observations of the child and the environment in a scientific way, which we are constantly perfecting, in order that our biases will remain out of the way and only the full truth will be revealed. In turn, our observations will help free us from prejudices and preconceived notions. Observation includes many mechanical skills, yes, but there is also a spiritual aspect which also must be cultivated.

Education must be inspired by a deep reverence for life. The adult must continue to study other areas of personal interest – be a lifelong learner, always interested in learning and exploring new areas; meanwhile strengthening and deepening learning in the Montessori – both of these areas through workshops, conferences, refresher courses or others. Within the Montessori field, mentorship developed with colleagues and others serve to provide support and ongoing self-checking.

Sandpaper Letters

Sandpaper Letters - Single and Double

See an AMI Montessori resource for further details not included here.

Materials

Box containing the letters of the alphabet, lower case and cursive, made of sandpaper cut out and mounted on thick cards or wood; consonants on pink, vowels on blue.

11 small letters – 4.25x7.5 inches: a e i o u x r v n c s

11 medium letters – 6x7.5 inches: t l g h d k y q b z j

2 large letters – 4.25x9.25: m w

2 extra large letters – 8x7.5 inches: p f

The letters are placed on the right side to hold the card with the left hand; or place them centered on the lower section of the card for use by both hands.

Lines are not necessary, providing only an unnecessary crutch for the child.

Sensitizing tray and a tray to carry the letters.

Display: Most letters are in the box but a few should be displayed on a reclining stand and rotated frequently.

Prerequisite

touch boards and tablets; geometry cabinet; sound games

(add in phonogram sandpaper letters after about the 5^th individual letter)

Guidelines to Follow

¨ The interest of the children (i.e. first letter of child’s name)

¨ Use three letters: one vowel and two consonants.

¨ Have a few letters on display and rotate them frequently (or child can do so).

Direct Aim(s)

To help the child become conscious of sounds in spoken language and to associate the sounds with the symbols through visual, auditory, tactile and kinesthetic senses.

Introduce the letter combinations in English that change their phonetic sounds.

Indirect Aim(s)

Preparation for writing and reading.

Age

3-3.5 (after much work with the geometry cabinet)

Endnote(s)

*Color backing should coordinate with the movable alphabet.

*Show a left-handed child how to hold the card with his right hand and trace with his left.

*Cursive is chosen over print because it has a more natural movement and is easier to form the continuous flow of each letter. It helps eliminate the reversal of letters such as b and d. Since most children know the names of the print letters, it is easier to give the sound of the cursive letters as a new experience rather than change the child’s current matrix of knowledge.

*The sandpaper letters are always presented at a table for correct writing posture.

*The sandpaper letters are the key to the whole world of written language. When Montessori was asked how the children in the first casa learned to write and read she said, “I gave them the alphabet.”

*The letters should be given in a lively and interesting manner.

*They should be presented early and fairly quickly (within three months). It is therefore critical that we keep track of the letters we have presented. Children who enter at the age of four and older many not have the same interest in tracing, so it is helpful to say to them, “Tracing will help your hands know how to write.” You can use the sandpaper letters and chalkboard together, or in games that involve fetching letters. Anything to help instill interest. The moveable alphabet may be used for sound consciousness as well, although this does not give the muscular experience that leads to understanding.

Phonogram or Double Sandpaper Letters:
Size: 4x9.5 inches; 6.5x9.5 inches

Sandpaper Cyphers

Materials

A set of figures 0-9 cut out of sandpaper and mounted on separate green boards (zero is placed at the back of the box); sensitizing tray.

Size: about 3x6 - no specific dimensions

Age

Approximately 4, after work with the number rods.

Language

cipher, numeral

New Information

Association of names of numbers with their corresponding symbols.

Endnote(s)

Present ciphers only when the child knows the names of the number rods. This presentation is always done at a table or chowki due to its preparation for writing numbers. The presentation is similar to the sandpaper letters, noting that the letters correspond to a single sound while the cyphers correspond to a whole word signifying a specific quantity. Present 1-9 after working with the number rods, returning to 0 after work with the spindle box. Other continuing with the sandpaper letters (tracing on chalkboard and paper, etc) should incorporate the cyphers.

Organizing a Montessori Day

Let's highlight a previous Nugget: Montessori Keys: Montessori as an Approach to Life

When we are teachers in Montessori schools, we strive to educate the parents on the fullness of Montessori, so they can have a Montessori-inspired home. This is best for the child, to be in a variety of environments where his needs and tendencies are respected and addressed while also tending to the needs and tendencies of the other people in that social structure (family, school, etc.).

When we are homeschool parents (whether trained Montessori teachers or not), we find that our work cycle naturally extends beyond the 3+ hour work cycle in the morning and (for 5 year olds and older) any second work cycles of the day. It becomes a 24/7 work cycle.

In our homes, or in Montessori schools that have the blessing of having children longer, we find that our work cycles become entirely natural.

We adults provide key presentations, that don't take just too much of the child's time; and we find we have time to be outside, to do art, to just sit and have a natural conversation, to plan that trip to the library, better yet for the older child to plan the errands needed. The children may choose to work with a Montessori material or apply a concept learned through Montessori experiences at any time of the day or night. I recall a 4 year old young man who awoke in the middle of the night to use the toilet, then proceeded to work on the puzzle map of Africa - the hardest of the set - he found it relaxing and found that he was indeed capable of working on it by himself. Why the middle of the night? Who knows! His mind was more relaxed; no distractions of noise and people and lights; no pressure from the adults around him (since they were allegedly sleeping, not (ahem) videotaping from around the corner).

In a home environment, the keys can be presented at any time. Maybe there is a dedicated school time - that is fine too - just remember what all happens at schools: snack, bathroom breaks, chatting with friends, watching the class fish, caring for the other animals, watering plants, gardening, working outside AND inside, food preparation, and more! The children do not have their hands on the materials every moment! So it is ok at home to have a variety of things happening - just provide the keys. The keys lay a foundation and a structure - and enjoy the freedom of time for exploration!

Snake Game post update!

The snake games have come up in conversation quite a bit lately. I updated this previous post with more detailed photographs and descriptions:
Motnessori Nuggets: Snake Games Part 1

All Montessori Nuggets on Snake Games

Peace Education in Montessori

Peace Education does not have to be a separate curriculum from the rest of the Montessori experience.

When we do separate it out, we minimize the value of the work Montessori did in observing human nature and providing for specific needs at specific planes of development, fulfilling those needs in a way that causes a child to reach his greatest possible potential, which will feed those needs and tendencies towards generosity and community.

Montessori's Own Writings:

Reconstruction in Education
Peace in Education
Education and Peace - Montessori Nugget quote here

Other Authors:

Lena Gitter: Montessori's Legacy to Children
Edwin Mortimer Standing: Maria Montessori - Her Life and Work
Montessori Nugget on Peace Education

Culture in Montessori

The Montessori approach to education and life really holds the corner on authentic culture!

We provide the children with keys to the world (primarily through the sensorial materials) in the first plane of development: 0-6 years old (infant, toddler, preschool, kindergarten) --- and keys to the universe at elementary (cosmic education), with the adolescent really finding his place in the history of the world by participating with society and working with the earth itself.

Through providing these key experiences, the child's time is freed up to explore his own personal interests, fully and thoroughly construct himself and, varying at the different ages, to explore the culture around him: first the culture of his own family, then that of the immediate community and/or school, then that of the entire world. By elementary, we are delving into the cultures of civilizations past and present.

How?

Through Exercises of Practical Life: first from the child's own culture, then expanding out to include experiences from other cultures.

Through Sensorial experiences: first explore consistent key materials on weight, length, volume, smell, sight, color, etc. And then through the child's work with the sensorial aspects of the world: the sandpaper, continent/painted, climatic, and oceans globes; the puzzle maps for the world, each continent, and the child's own country; exploring the flags of various countries, their meanings and histories.

Through the Language experiences: cultural folders for exploring by continent, then by theme within a continent - striking about conversations about what we see in the photographs. Studying biomes and climates of each area, how that affects the local people's choices of lifestyle.

And that is just for the 3-6 year old!!!
A Montessori Nugget with a brief description of where to find cultural aspects in the AMI-style 3-6 albums.

At elementary, we study civilizations of the past, use history question charts to guide our research into past cultures, as well as present cultures.

In geography, we look at economic geography in an interesting format - looking at trade products and usages; we look at the lifestyle of people in various regions of the globe, based on climate. We learn about the rays of the sun, the tilt of the earth - and the affect on climate - and the ensuing affect on the people. Indeed, everything we do in geography (earth studies) leads to the affect on the local people in each region.

In biology, we look even further into biomes and how those affect all the living creatures, including the people.

In language, we explore a variety of literature, learning about peoples of other areas and times, with dramatic performances and other experiences to highlight the beauties of a variety of cultures.

Music should be listened to that comes from a varietoy of cultures. Art experiences are keys-based, so that a child can read about an art form and have the basic skills already in place to follow their interests and explore the art of all cultures and all times.

We look at the history of mathematics and the contributions of a variety of people to our understanding of math and geometry....

and even language history and development - how cultures have affected one another's languages.

There is so much more I am not including! Children really do come out of a Montessori education with a strong sense of culture; a strong sense of being part of something bigger than themselves, where they play an important role; and a strong sense of *culture.*

Other Montessori Nuggets mentioning Culture - a non-inclusive list:
Elementary Geography Table of Contents - with notes of where to find Geography in Primary albums
Broadcasting Seeds
Art Presentations at all ages
Fifth Great Lesson - Story of Numbers
Benefits of the Prepared Environment
Great Lessons and Keys Lessons - Some Thoughts (Cosmic Education)
What Do We Provide Our Children?
Spiritual Preparation of the Adult - Who Owns the Learning?
Peace Education in Montessori
A portion of the Primary Biology Introduction
Cursive or Print Part 3
Handwork in Montessori

Special Needs and Montessori - Can it be done?

Montessori for Special Needs

Can it be done?

Um. Yes. Montessori started with special needs and found the experiences were applicable to the universal child. Even with "typically developing" children, there are always slight modifications to be made to suit personal interest, time of day, personality quirks and more. So we Montessorians just look to the individual child's needs in how to present the key experiences for their plane of development.

Previous Montessori Nuggets - not an all-inclusive list:

General thoughts on Special Needs
A link to the book Montessori and the Special Child by Reginald C Orem
Special Needs Identification and Treatment with Montessori Methods

A foundation to understanding that Montessori is useful for all children - the universal child, regardless of personal interests, personalities or learning needs:

Some Sources of the Montessori Method and Facets of Its Founder (this link allows the resource to be read online; only downloaded if you are part of one of their affiliates)

Montessori Books about Special Needs:

Didacticism: Montessori and the Disadvantaged Student (affiliate link to Amazon)

Additional Resources for Special Needs as related to Montessori:

Montessori 4 Autism: Releasing the Inner Child
Living Montessori Now - always has some excellent lists of resources
Montessori and Special Needs/Early Intervention - extensive list of related articles
Montessori Education for Autism

NOTE: The word "disadvantaged" has changed in meaning over the years. Previously, it was used to describe socio-economic factors with perhaps some inclusion of special needs. Currently, the word disadvantaged is more often applied to children with special needs, but can still be used in other ways. There is a book by Reginald C Orem about Montessori and the Disadvantaged - it is more focused on the socio-economic factors, more-so than special needs factors.

Walking on the Line - Control of Movement

Walking on the line in the Montessori Environment - not an readily understood area of the Montessori experience.

There is a good deal of information and photographs online for the walking on the line activity that are mis-leading at best and downright inaccurate at worst.

Some points that are the most readily confused:

The line can be an ellipse or a wandering line with gentle curves - we do not want corners or sharp curves. When long enough, it provides some "straight" lengths without the need for corners.
The line is a silent individual activity, but many children can do it at the same time. In a classroom, a group of children would be given the presentation.
The width of the line should be about half the width of the child's foot, in the ideal situation. Otherwise, three-quarter of an inch should be the narrowest.
The line should be a different texture from the floor itself, so the children can feel the difference (tying in the practice of wearing socks or being barefoot when doing this activity) - being barefoot helps in self-awareness and self-presence as well. ;)
It should be noticable in color when looking at it, but not distracting when looking at objects close to it. A different shade of the same color as the flooring is highly recommended.

An observation of the benefits of walking on the line: Walking on the Line Thoughts

Montessori's own writings on this topic - I am not including what others have written:

Discovery of the Child: depending on your edition, look around pages 89-126, in various places; some editions include walking on the line in the illustrations as well.
Absorbent Mind: depending on your edition, look around 195-224
Montessori Method (good for historical reading, was updated and renamed Discovery of the Child): 140-141, 339, 342-343
Montessori's Own Handbook (good for historical reading, this book was never updated): 26-28, 63, 64; illustrations 60, 62. In the Schocken edition: 63.
Advanced Montessori Method, Volume 2 - Montessori Elementary Material: 251-352, illustration 352
The Secret of Childhood: depending on your edition, 75-98
Education for a New World: 34, 59
The Montessori Index also suggests I cross-reference Gymnastics and the Silence Game - so any portions of Montessori's books that mention those two are likely to include Walking on the Line as well - or at least relate.

Some links for more information on Walking on the Line:

A section of this introduction to the Exercises of Practical Life by Ginny Sacket, AMI trainer
An article by Joan Bettman on Grace and Courtesy

There are more accurate resources available I am sure, but these were the ones I found the most quickly.

More recent scientific findings on the benefits of walking on the line?

Do a web search for "proprioception and walking on the line". Note all the exercises which utilize walking on a line as therapy for a variety of concerns. Then compare those exercises to the stages of the walking on the line activity in a Montessori resource that includes *all* the stages.

Amazing stuff!

Just another area that modern research is corroborating everything Montessori observed over 100 years ago.

Montessori Elementary Mathematics - Multiplication Checkerboard

Montessori Elementary Mathematics: Multiplication Checkerboard

Materials: white number tiles 0-9, gray numbers tiles 0-9, checkerboard[1], checkerboard bead bar box (only has bead bars 1-9)

Introduction:

This is the checkerboard. We are going to learn how to do multiplication on the checkerboard.

· Numbers: We have these numbers across the bottom (read and point to each number).

· Multiplicand and Multiplier: This ridge is where we place our multiplicand and multiplier (indicate the ridge at the bottom and to the right, respectively). We also have some numbers along the right side (read and point to each one). We will put the multiplier here.

· Squares – color and value: Then we have all of these colored squares. Here are the units (point to the lower left corner – green). Tens are here and here (point to each of the blue squares touching the unit square – 2). All of these are hundreds (indicate the diagonal 3 reds). Here we have thousands (indicate these 4). Here are the ten-thousands (indicate these 4). Continue with each category.

· Squares – value of beads: What is interesting about the checkerboard is that the value of the bead bar is determined by which square upon which it is placed. I have a 3-bar; if I put it here (place on the units square), it is three units. If I put it here (place on a hundred square), it is three hundred; if I put it here (another hundred), it is still 300. What if I put it here (place on a 100,000 square). We don’t have to stick with one bead bar. If I have a 3-bar here (on tens) and a 5-bar here (on hundreds), we have 530. What if I put it here? (slide each over one to show 5,300). What if I put it here (slide up and right one place – diagonally)? It is still 5,300. Repeat until the concept is clear and the children can readily read the numbers on the board – invite them to place beads and you read the number; and to place beads to read the numbers themselves.

Exercise 1: representing each multiplication with the bead bars

Prerequisites: knowledge of the process of multiplication; Introduction to the checker-board; Ability to read hierarchical numbers; (technically the children can do the 1^st exercise without knowing the multiplication facts); Can precede work on the large bead frame (this exercise only)

Notes: If the children choose very large digits, they will have a ton of bead bars in each square that will overflow into other squares. In that situation, after they have done the multiplications, exchange within each row before sliding diagonally; then finish the exchanging to reach the final answer.

This work can help the children learn their multiplication because they are represented by the quantities they are putting down each time. If they do know their facts and they’ve caught on to the procedure of exercise 1, move them right on to exercise 2 on another day.

Exercise 2: Using the Multiplication Facts

Purpose: Further experience in long multiplication. Indirect preparation for category multiplication.

[1] Boards: current manufacturing only go to units of millions; felt version and the presentation in AMI training goes to hundred-millions on the horizontal

why does the checkerboard have more than 3 spaces per grouping? e.g. multiples of thousands beyond hundred thousand?

Each square on the checkerboard represents the multiplication of the bottom and right-hand values. So a board that is 9 squares along the bottom and 4 squares along the side - that last upper left hand square will represent 100,000,000 taken 1,000 times.
The checkerboard does a few things for the children - it helps them work with VERY large numbers (now we can go into billions! - and it helps them see the "why" behind shifting the numbers one over when we multiply on paper (which the large bead frame starts to do) as well as the combinations of the quantities (so goes beyond the large bead frame in these concepts). I start the children with small numbers and they challenge themselves when they are ready to do the larger numbers.

Not to be confused with the Decimal Checkerboard (some tidbits found at Montessori Trails - a Montessori Nugget will be posted soon).

Elementary Montessori Materials Continue into Adolescence

Montessori materials truly go DEEP. Perhaps Montessori didn't have time to develop every detail from birth to college, but she left us an outline and some people have been able to follow Dr. Montessori's trailblazing style.

Looking at the Elementary and/or Primary Materials used into Montessori Adolescent Algebra

Geometry Sticks
Fraction Circles (metal works fine, but the plastic materials with the multiplies of each fraction family from 1 to 1/10 – you do NOT need or want the children to use fraction segments beyond 1/10)
Bead bars, squares and cubes from the bead cabinet (“complete bead material”)
Wooden cubing material
Power of 2 (Power of 3 if you purchased that too – or just make one)
Pythagorean Insets
Binomial Cube
Multiplication Checkerboard
Pegboard (ensure it is sized to your geometry sticks – so they all align properly – this generally means holes that are 1 cm apart from one another)
Yellow Area Material
Large and small geometric solids
Number/operations tiles – with some additions, including adding in the fraction labels as well (called Special Math Symbols on the adolescent album)
Set of 12 blue right-angled triangles

For review purposes:

Decanomial bead bar box (called “large bead bar box” in the album)
Constructive triangles

Montessori Phonograms - Key Sounds

In the English language, there are 16 "key" phonograms:

ai, er, ie, ee, or, ue, oo, qu, th, ch, oy, sh, ou, oa, ar, au

All others are variations on these ;)

The sandpaper letter phonograms

The sandpaper letters phonograms should be introduced at the same time as the individual sandpaper letters - learn 3-5 individuals, then introduce a phonogram; continue introducing one new one at a time with individuals in between such that all sandpaper letters, individual and phonogram, are finished up at about the same time - typically 3 weeks after beginning the first sandpaper letters ;)

In this way, the children can immediately write anything with the movable alphabet, without needing prompts or guides as to what they can write versus what they have not yet learned - they'll have learned it all!

Longevity of Montessori: Mathematics

The Montessori approach meets the needs of children where they are at - both collectively and individually. Therefore, it is an approach that meets the needs of ALL children. The only limitation is the preparedness of the adult to meet those needs ;)

A recent post at MariaMontessori.com introduces this concept as it applies to primary (3-6) and elementary (6-12). Montessori is Developmental

Even in our material,

Let's look at math specifically - just some highlights:

With infants and toddlers, we do a lot of natural one-to-one correspondence. Few toys, each that belongs in a particular place. Matching activities in sizes, shapes, colors. Helping to set the meal-table using a diagram of what goes where.

We can also give the language of numbers (counting), and children love language at this age, so most do pick up on counting numbers, although they typically skip a few numbers or repeat a few sequences ;)

Primary Mathematics:
While we don't typically start math in primary until around age 4, we begin with a few materials that extend into primary mathematics as well as into use at elementary and adolescence. Sensorial and Mathematics materials are both noted here:

Red rods - extend into the number rods
All the groups of ten we have extend into the decimal system
Pink Tower and Brown Stair can be used in geometry at elementary
Binomial Cube and Trinomial Cube (elementary and adolescence)
Geometry Cabinet and Solids (elementary)
Golden beads (elementary and adolescence)
Bead Cabinet and contents (elementary and portions in adolescence)
Snake games (if you purchase the negative snake game, it includes all you need for primary as well as elementary and adolescence)
Decanomial bead bar box (elementary and adolescence)
Stamp game (elementary and adolescence)
Short Division with Racks and Tubes becomes Long Division with Racks and Tubes (elementary)

Common Threads:

Place value color-coding remains consistent throughout all levels - into the checkerboards that are the visualization of the multiplication process, the bank game (just numbered cards, no beads), and more.
The bead cabinet colors also remain consistent through all levels - even into the solid wood blocks of the cubing material that is used in elementary and adolescence.