Multi Base Material - Upper Elementary Mathematics

(UPDATED! For clarity and to add search results at the end)


We strive to be keys-based around here. I provide the keys and the opportunities, my son uses them to their fullest potential at the right times.

Great.

Until I won a giveaway through Alison's Montessori for a beautiful, non-essential, non-keys Power of 3 Cube. This is an *abstract* presentation in my album - it is not intended to utilize a material because at that point, the material becomes a crutch to the child. If the child needs a material at this point, the child *creates* the material himself.

So. We're using that one for sensorial exploration for now - as a puzzle - in lower elementary; then I will pull it from the available materials for upper elementary. It's a neat little "puzzle" so I'm ok with that.


But then I placed an order for our remaining Montessori materials several weeks ago. Received everything; then realized I still have a couple of small purchases to make. Oops. That company doesn't have those things anyway, so it's fine. I get my list ready and figure out how much money we'll need to save and I have it ready for the right time. Ok :)

But then I went and pulled this out of storage (given to us a while back - I'd tucked it away without thoroughly checking it beforehand). I thought it was the Non-Decimal Base Board, but I never thought to wonder what was in the BOX (non-decimal base board does not require a box).

This is the one sold at Alison's' - ours is identical, but I don't know where we got it.
It's pretty - it looks neat - but it is definitely NOT an essential material.
Why do companies sell the non-essentials and LEAVE OUT so many of the essentials? 

I am now the keys-based, flummoxed owner of TWO non-keys-based materials that I didn't know I was getting! ;)


I *thought* it was the board for Non-Decimal Bases. But it's not. And I have *nothing* in my albums for this Multi-Base material. Thus it could be a great work to do! But it is not keys-based - it is an extra. I am "ok" with that to an extent, but if I can't figure it out in under 30 seconds, with my experience and training, then is it really going to be necessary for the child?
NO.

But my son MIGHT be interested in it and it might make a FANTASTIC follow-up if that is where his interests go (no, the local educational requirements in our area will not require what this board teaches, so I can't even pull it in for that purpose!).

Wish I'd double-checked first! Because now I don't have the Non-Decimal Bases board - but that should be easy enough to just draw out on posterboard. And anyone else who needs Non-Decimal Bases Board and you've already made a chart for primary use of organizing the golden beads into their categories (that chart being another non-essential material that could be useful and even necessary in some cases - it is 4 columns, with a row at the top to designate that units, bars, squares or cubes go in a particular column)... Just use that! Fine. I'm good with that. Easy and cheap!


But what do I do with this Multi-Base material? I am flummoxed and, frankly, borderline annoyed - both at myself for not checking a long time ago and at companies for making this stuff. I am looking for an album page, a set of album pages - or someone to just tell me which company sells an album that has it - just to save me time figuring it out and making up the album page(s) myself.

Any ideas?


I have contacted 5 companies who sell it, of the 3 who have responded thus far, they have no idea either! So my next question is where did they get the instructions on how to make the material? Many of the discount places get their materials from the same place in China I am sure, but not everyone gets their stuff from there; so where did the original pattern come from?

It is very sad and very disheartening that the gray line between "essential" and "extra" (but could still be good) is so blurred, that there are sometimes "extras" that just aren't even good, but are still being called Montessori - but that is for other posts!


Downer post - sorry! It gets better tomorrow!


(UPDATE 12/29/12: All but two companies have responded back to me; I contacted 3 others who all responded. Not a one of them has any clue how to use this material, or even where the pattern actually came from. Wow.

This pdf document makes ONE reference to it:
Workshop
“How Mathematics forms the brain–Montessori and
Multi-base Material” by Ms Han Kamphuis, pedagogical
consultant at Nienhuis.

Thus it appears to be AMI, and it appears to be relatively new.

Not one AMI elementary training center has responded to my messages, to date. Not even the one I attended.)

Will update further as anything new comes up.

Dot Game Fun!

I love the dot game - I don't know what it is - all the dots maybe? Nah - it's the organization of it - the beauty of it - the essential teaching of it!

And it is the one time that markers are typically used in a Montessori class - if the dot game is kept in a glass frame or laminated and mounted - the children can use a dry erase marker and eraser and use it again and again!


Legoboy did it at school, and wanted it to do it at home (that year I alternated subbing at Montessori schools and working at home - and homeschooling - it was a crazy, but wonderful year!) --- well, I just printed it out and he filled it in. We downloaded this version from Montessori Materials - a great place for some of the printable materials.

Then I had to print more - because he just ate it up!

Here is his first one... It's so pretty! I wrote the first set of numbers and everything else was on him.

The children check off as they do a row, so they can track where they are. They connect up the dots to create a "bead-bar of ten"; then carrying over is noted in red the first several times they do it, to really reinforce the extra work that goes into carrying. But these are all concepts that are actually KNOWN - the child has been doing this work throughout use of the golden bead material - for Legoboy, it had been almost two years with the golden beads, probably a year and a half with carrying, before he actually did the dot game. 

Montessori works in baby steps - so there are only two new things here: 

1. doing the work ALL on paper, in typical addition format (on the right side) --- but connecting it back to their previous work of no more than 9 in any category! 
2. introduction of the comma. Until this time they have not really been using the comma. There are many adults (ahem, me) who try to sneak that comma in there sooner - before the child is ready (too many new things at once if it is introduced sooner!) and most of the time the adult doesn't even realize he or she is doing it! It's so instinctive! But we want the children to focus on place value, so we don't worry about the comma until around this time - this is close to the time they will also learn about millions with the wooden hierarchical material - so the next step is to be introduced to the repetition of the categories (unit, ten, hundred; unit of thousand, ten of thousand, hundred of thousand, etc.). 

This material is only used for addition although multiplication could be done on it. There is more other work for the child to do and the point here is the two points listed above. So further operations are not necessary. 

By the 3rd sheet of this work, the Dot Game turned into a balloon popping game - pop 1, pop 2, pop 3, etc. until number 10 was the biggest POP of them all! 

oh the days when it wasn't about battles and weapons.... it just balloons popping! How I miss those days ;) 

Mathematics Materials: A Photo Journey

I started two separate posts, but there is so much overlap here! The materials can be pricey or tricky to make at first, but, as noted, most of it goes for several years!


A photo journey of our primary mathematics materials:

Numbers 1-10 (the candle is for decoration, polishing,
and it makes a neat representative of the number 1 ;)
Basket underneath for golden bead collections.
Most of this material is JUST for primary.
(except the small bead frame!)

There is also a small bead frame- but if you know you are going to do elementary as well, get the large bead frame and use for both (that is what we did). The dot game is downloadable. Teens and tens boards can be made of paper and cardstock (that was ours!). The memorization charts can be downloaded.



A photo journey of both primary and elementary Montessori materials:

At-home multi-purpose use ;)
This material is used FOREVER in Montessori!
It is WORTH it to have every piece of it - do NOT skimp here. 

Mathematics mats - especially for primary

Circle fractions are for both primary AND elementary

Division with Racks and Tubes
Test Tube Division
Can be used in primary for short division
Elementary for short and long division
and the materials can be used SEVERAL other places as well

Golden bead material - 45 of each, 9 thousands
(only one non-AMI primary presentations needs
more than 9 thousands - and you can make those)

Decanomial bead bar box - we get away with one box
by adding a few bars of pony beads on colored pipe cleaners.
Primary and Elementary
AND you can use this material for SO MUCH - just pull from it what you need!

The stamp game, large bead frame - belong here. Also, get a negative snake game and you'll have all you need for all the snake games.




A photo journey of JUST elementary Montessori materials:

flat bead from for elementary only

Elementary: power of 2 cube
(power of 3 cube is NOT necessary)

Montessori Protractor - this one is 0 - 360
Another one goes 0 - 100
Both are necessary in some form. 

Fraction skittles for division.
Some albums have them in primary for another purpose.
They are intended for dividing fractions by fractions
at the elementary level. 

sample of squaring and cubing in elementary
all material comes from the bead cabinet

too pretty of a picture not to share!
all material comes from the bead cabinet

Decimal Checkerboard for multiplying decimal fractions (decimals)

There is more I have not yet pictured: the squaring and cubing material; the pegboards.

Mathematics is huge! The nice thing is that primary materials DO carry over; and there is a good deal of the elementary material that can be consolidated, or made of paper, cardstock, or other items around the house, along with a few basic purchases. Or is multi-purpose for both primary and elementary with slight modification.

While this area is the most intense, materials-wise, it is also the most efficacious of all the Montessori materials. It is worth every second and every penny! 

:) 

Multiplying Sum by a Sum

Legoboy loved this work intensely - for about 3 weeks. Then he's done. He found the shortcut of adding up the quantities within parentheses and then multiplying, so we had to move on to unknown quantities to keep him practicing the proper procedure!

The idea is to start with lower numbers, with bead bars within one set of parentheses and number cards in a second set of parentheses; then show proper procedure for multiplying each bead bar by each "command card", finding partial answers and later putting them all together into the final product. We turn over the multipliers (commands) not being used, so that we isolate just the one individual being used at the moment.

Talk about good habit-forming right from the beginning and before EVER doing the abstractly!

So. He LOVED the work. And he loves drawing. But for some reason, he always rushed through the few drawings he made of his work onto graph paper. Go figure! Here is a sample - he started off well except for parentheses ;) As Grandma says: Funny boy!
(ordinarily the partial answers are placed underneath their corresponding bead work - not to the right as he shows it here - but he likes to have all of his work of this sort fit onto one piece of paper when possible). He still had the final product on a different piece of paper which he then tucked away somewhere I can't find to show you all! He does that with his favorite work until he is ready to share. I can't complain! At least he wrote the numerical answer at the bottom :)

Sample of 2-sum by 3-sum

1 unit by a sum of 2 addends, then switch it around. 

sum by a sum - basic presentation :) 

Primary Language Materials: Photo Journey

In no particular order, language-related photos I have - some with materials we've made - some with materials we've purchased or borrowed or were gifted:

Zoology and Botany classification cards
with definitions
A few samples of these are nice to have in the classroom or homeschool
focus on keys, then add an interest or two
Thereafter, find outline pictures online and invite the child to
"do research" to find the names of the parts
(so books on the subject would be great!)

small movable alphabet -
punctuation marks are missing from these boxes
the backsides of each letter should have the capital as well
perhaps if I'd made them with the capitals,
Legoboy wouldn't have struggled with them as much ;)
****This material carries over into elementary -
have blue, red, and black on hand for sure*****

wooden grammar symbols - genius!
****Carries over to elementary!*****

Our original handmade metal insets
Not so metal - they are foamboard
do it again? I would either buy them or cut from wood
or from mat board (picture frame backing)
***ALTERNATIVE: just get the geometry cabinet and use
the shapes from those drawers!****

Now, we also had beautiful living books, focused on reality - with a variety of beautiful artwork (nothing cartoon-like).

We read from the Bible - not from Bible storybooks.

We did a lot of artwork, which helps with handwriting and strengthening those muscles, thus the fraction insets (circles, squares and triangles) were utilized in various setting (we did not have these at home at the time, but I wish we had!). The circle fractions begin in primary and continue into elementary mathematics, with the squares and triangles presented in elementary geography.

We spoke whole-language - real words, full sentences. Yes, we played silly word games at times, but our usual conversations were imbued with respect for the child's intelligence - something hard to fight against in our culture that uses the wrong verb tense and pronouns for the youngest children. Mother-ese is WONDERFUL - but it shouldn't be used on a 2 year old except briefly in silly-snuggle time for just a moment. ;) "Him so beautifuls" being not quite right for a child over a few months old who is absorbing the rules of language. hehe.


These things (pretend stories, awful artwork, poor language) won't destroy a child, but they sure won't build him up and they could certainly slow him down. Everyone who asks my advice because they have been doing these things and have older children - just adjust now. Slowly purge the old books by adding in or emphasizing the good ones; remove the least loved of the others first, and faze out the usual favorites. But save the good literature for elementary! (Beatrix Potter, Wind in the Willows, Fairy Tales --- these are all moral tales and have a profound place in elementary!) Speak in whole, rich language, with a large vocabulary - provide very simple and short explanations only when obviously needed (child asks). If the child says the wrong thing, such as "pretty kitty" instead of cat or kitten, you say, "Yes, this is a lovely cat (or kitten depending on the age of the cat!). So you are giving another name for pretty, teaching its meaning in context without needing a definition, AND providing the accurate word for the age of the creature. No correction necessary :)