Decimal Fraction Board - when to start

Here's a question I am asked a LOT - whether this particular material or others. And most particularly those material that in reality bridge lower and upper elementary, making that "break" between the two ages within some albums cumbersome at best.

(this particular material has been asked about 5 times in the last month alone, hence I pick on this one ;) )

First "years" - definition: my numbering of "years" assumes the child will have the opportunity for a full 6 years' worth of elementary Montessori. If this is not going to be the case, then it can very roughly be considered as equivalent grade levels - in the US, a 6 year old is 1st grade; 7 year old is 2nd grade; etc. as of the beginning of the year.

When should a child start the Decimal Fraction Board?
It's really whenever the child is ready and depends on how strong was their primary and earliest lower elementary experiences. My albums have them noted as beginning between years 2 and 3 - so definitely starting in lower elementary. Year 2 if they have a very solid foundation or catch on quick; and year 3 to begin if if they needed a lot of remedial work or have teachers using albums that don't have the same foundation OR just plain don't have interest in fractions enough to get them there until year 3.
Anecdote: my son was voracious about fractions and I thought he would get to this work early - NOT SO. He took a seriously long break from all things fractions, but applied what he knew to real life, and only recently (year 3!) has come back around to fractions-study in general - and now he is starting this decimal fractions work. He had a bit of an intro to it because of a strong interest in money in years 1 and 2, but this material just wasn't cutting it for him. I backed off and now he's going at it full-force. 

With the extensions, it definitely lasts a year or a year and a half, so for most children would start in lower elementary and finish up in upper elementary (some children won't need it in upper elementary if they started in year 2 and "get it").

This is one of those works that shows how difficult it can be to delineate between lower and upper elementary ;)


Here is what my album page has for pre-requisites (the most important thing than actual age) -

Prerequisites: 

• concept of parts of numbers (fraction work); 
• knowledge of multiplication facts (esp. multiplying by ten – large bead frame, bank game); 
• familiarity with decimal system categories (golden bead, wooden hierarchical); 
• hierarchically colored beads/pegs (stamp game, pegboard, decimal system number cards, multiplication checkerboard, racks and tubes, etc. - enough of this work that the colors are intuitive to them now)

Shortly after working on this material, a few months, a year, maybe even days if you have a child for whom this material truly connects, you'll move the child on, at the right time, to the decimal fraction checkerboard:

By the time, they have the decimal fraction board, they have typically had the regular multplication checkerboard, and it is now just a matter of merging a few concepts. Wait until the child has each of the concepts down pat - or if there is a struggle, the particular type of struggle would be addressed with a synthesis - and go for it. The introductory lesson itself (just laying out the individual square of felt) will be enough to tell you if the child is ready or not. 

Thus the Decimal Fraction Checkerboard is potentially a lower elementary work as well - indeed, upper elementary prefer to use fewer beads, so introduce this work as early as is appropriate for the child in question. 

Above all else - have FUN with it! 

Geography Album and Potassium Chromate

Oh wow. Am I scared. We almost made a HUGE blunder.
(ok maybe not that huge, but it sure made me sick to my stomach)

We have these chemicals we use according to album pages in the geography album (forms of matter, chemical interactions) and the biology album (needs of the plant).

I have had supplies on hand to use with my son and have had the *correct* items. Tiny amounts purchased from a Montessori school that also used the same chemicals. We labeled each smaller container very carefully and everything was FULLY accurate. Still is. I'm just running low.

To do the presentations, I reviewed the album pages beforehand, used all proper safety procedures, and all has been *wonderful.* We don't use chemicals with similar names, so it is easy to keep them organized; and we only get out the chemicals we need when we need them.

The problem showed itself when I went to replace these chemicals the other night. I used the supply lists I created for my geography and biology albums, added stuff to my cart, but came up with two items that were not available at the top-notch science supply company I have come to love the absolute most because they are so homeschool-focused: Home Science Tools.

I e-mailed a Montessori comrade to ask where she got her supplies for potassium dichromate (geography album) and calcium nitrate (biology album).

Did you catch what I just wrote? 


Some background: 
In AMI training, the presentation is given to the trainees. The trainees furiously take notes by hand or on their laptops, while also trying to watch what is going on. Monday of each week of elementary training (primary was a bit different), all album pages from Monday through Friday of the past week are printed out, page-numbered, tucked into a large envelope and handed in. Album readers stop by the training center after-hours (so we can't know who they are and follow them home! ;) ), to drop off what they reviewed from last week and pick up the new week's set. The envelopes are THICK - anywhere from 80-200 pages each week.

A "lucky" few were then read by the trainers as well, before being returned sometime later in the week.

Changes are made based on the comments. Album pages can be required for re-submission or not, based on the trainer's thoughts; then final album-checks/reads are done at the end of the course.

But SO many typos slip through, grammatical errors... but the accuracy of the album page is supposed to be there.


I was one of those lucky ones that always had my album pages double-checked (probably to make sure I wasn't inserting Catholicism and homeschooling into a Catholic woman's work).


Yes, I just said that, and yes you probably read my voice tone accurately. I am extremely disappointed and disillusioned with AMI elementary training as it is - as far as the personalities and agendas of the people involved today (the content is fantastic!) - but through that many readers (and even my own use! but then, I had the material on hand and skimmed the page, there isn't another chemical with a similar name, and we're not supposed to be reading from the album pages as it is - they are supposed to be used for skimming/reviewing - I was using them properly! They were supposed to be error-free!).... and well, I just don't know what the chemical reaction would have been.


The fact is potassium dichromate is a vivid red-orange color; potassium chromate is yellow-gold. And I know that you are supposed to use just enough to make a brilliant gold color in the water - when a bit of lead nitrate is mixed in, a sediment precipitates down (you'll have to research that one to find out what is happening ;) ). So I would NOT have actually used the orange-red material, had I purchased it, opened it and saw a different color like that.

But the fact that it COULD have happened... scares me.


I am SO glad that Home Science Tools doesn't carry it.

Potassium chromate is a yellow chemical 

indicator used for identifying concentrations

of chloride ions in a salt solution with 

silver nitrate. It is a class two carcinogen 

and can cause cancer on inhalation. 

Wikipedia

Density: 2.73g/cm³

Density: 2.73g/cm³

Potassium dichromate, K2Cr2O7, 

is a common inorganic chemical reagent, 

most commonly used as an oxidizing agent

in various laboratory and industrial applications. 

Wikipedia

Formula: K2Cr2O7 Molar mass: 294.185 g/mol IUPAC ID: Potassium dichromate(VI) Boiling point: 932°F (500°C) Density: 2.68 g/cm³ Soluble in: Water

Formula: K2Cr2O7

Molar mass: 294.185 g/mol

IUPAC ID: Potassium dichromate(VI)

Boiling point: 932°F (500°C)

Density: 2.68 g/cm³

Soluble in: Water

I spent the next 4 hours combing through my albums to make sure every other indication was absolutely correct. That is the only such potential safety error. Whew. A few more grammatical errors; a few missing commas or periods. Ok.

Home Science Tools does carry the potassium chromate, so in the cart it went. Geography - CHECK.


Now for Biology: 

But in doing further research on the calcium nitrate, I wonder if I should be adapting that presentation to use a more natural substance. This one is man-made and people going for organic don't typically use it from what I read.
****Does anyone have a suggestion for replacement? The Biology presentation here is to set up an experiment with plants growing in several different glass jars of water - one is just water; one is calcium nitrate in water; one is magnesium sulfate in water; one is potassium phosphate in water; one is ferric chloride in water; the last jar is all those items in the water for a fully healthy plant.
(NOTE: magnesium sulfate can be bought very cheap in the pharmacy section - it is simply "Epsom Salts")
Ideas for the calcium nitrate?


UPDATE: I am still looking for a replacement for the calcium nitrate - something natural, organic....

Homeschooling Mistakes and Montessori

I found this link for Landry Academy recently with many homeschool articles. One in particular caught my eye and I thought, "Let's fit this in with Montessori homeschooling".

The original article in its entirety:

Top 10 Homeschooling Mistakes

copyright by Greg Landry - written in 2012

Through 15 years of working with thousands of homeschooling families, teaching 4th-12th grade homeschooled students, and teaching university pre-med students who were homeschooled, I have unique insight into what we're doing right and what we need to work on as homeschoolers. This article is particularly geared towards college-bound students but much of it would apply to all students. Since science is my area of expertise, the article is also slanted toward students interested in science.

1. Not doing enough testing and not doing timed tests.
2. Schooling year round or schooling too far into the summer. Students need to know that they can work hard for a prescribed period of time and then have a complete break from classes for a while. I believe it's actually counterproductive to school year round or with very little break.
3. Being squeamish on the science of Creation. Science is on our side - God created it. We need to boldly teach our students all the ways that science and the world around us support biblical creation.
4. Not starting to prepare for college early by beginning to take the ACT and SAT early - in 7th or 8th grade, along with other preparations.
5. Not starting serious high school sciences early enough.. especially if a student may be a college science major. Critical decisions should be made going into 8th grade.
6. For younger students, call the sciences what they are (chemistry, physics, biology, anatomy & physiology) rather than "physical science" and "general science" and teach them that way. This makes high school science more familiar and far less intimidating.
7. Not giving students a structured academic environment early. Beginning in 6th or 7th grade, provide a structured academic environment for students that includes deadlines that have to be met. Inability to meet deadlines is a critical deficiency in most homeschooled students.
8. Not looking for colleges early - most families end up doing this in a last minute frantic rush - not good for many reasons.
9. Not allowing students to take some of their classes as "outside" classes in the middle and high school years. Students need to begin the process of taking classes from others / being accountable to other teachers as they prepare for collage.
10. Losing our focus - all we do should glorify God. Press on! :)

Greg Landry is a 15 year veteran homeschool dad and former college professor. He is founder and director of www.LandryAcademy.com

Now again, with Montessori connections: 

Top 10 Homeschooling Mistakes

copyright by Greg Landry - written in 2012

1. Not doing enough testing and not doing timed tests.

      Montessori does not encourage timed tests to be used very much as we would ordinarily think of them. But it is great to play games with timers, introduce the time challenge when the child is ready and wanting, in order to build a foundation of success. In latest elementary is the time to introduce timed tests as we ordinarily think of them, with some practice runs - low-stress. If you anticipate your child going to college, yes, it is VERY good to get used to the stress of such tests, but a little at a time ;) The author of this article advocates starting in 7th/8th grade, even with plenty of time to finish the test, but just with that time limit; as a Montessorian, I personally advocate introducing little bits of it at a time - baby steps. So a game with a timer - totally non-pressure. Learning to do mental activities with lots of noise and distraction (as well as complete silence) - just do those things throughout your normal day. Once in a while have the child sit at a table with a hard chair and do a bit of work there (if they usually work on a low table on the floor, or snuggled on the couch). It doesn't have to be every day or even every week; just enough to be familiar and functional. 
     EDITED TO ADD - another thought: We have work-plans and work-journals. So there is a sense of responsibility in-built already. Sure, those time requirements are more of "sometime today" or "sometime this week", but there is also scheduling of times to meet for a presentation, and giving specific deadlines along the way. These skills contribute to "timed tests" skills because they lay a foundation early on. 

2. Schooling year round or schooling too far into the summer. Students need to know that they can work hard for a prescribed period of time and then have a complete break from classes for a while. I believe it's actually counterproductive to school year round or with very little break. 

     Montessori says YES! Part of a childhood is having "endless time" - time to become BORED! LET YOUR CHILDREN BECOME BORED! Boredom begets creativity, problem-solving, tests a person's character, provides fodder for fantastic grace/courtesy lessons! Avoiding boredom throughout all of childhood creates in children an internal sense of "gimme" and "gotta have" and absolutely no sense whatsoever of delayed gratification. There are times and places for fulfilling "needs" in the moment; but we *need* to differentiate wants from needs and also develop a sense of how to wait or work appropriately even for needs. The elementary years are the place to hone in on these skills - NOT the emotionally roller coaster adolescent years, when they NEED those skills in place already. 

     We can have school year-round, but take decent breaks that are clearly labeled - BREAK. VACATION. Some children will choose to work anyway - and that is *their choice*. 

     As elementary children get older, there comes a time we also have to say, "We are on vacation and while we know that the subjects we study are directly related to our lives and our world, we are not going to take any of our Montessori materials with us. 

     It is tough as Montessorians not to count everything our children do as school - because of the cosmic education nature of life and our Montessori-styled studies. But let's put it this way: there should be built-in times of the year, with NO work-plan, NO work-journal, NO major academic responsibilities. Just USING what has already been learned and just exploring the world. 
     EDITED TO ADD an additional thought: in some places, summer IS when we homeschool because it is SO HOT! Snow days are days that everyone else is at school and the weather is perfect for building snow men and making snow forts all day long! As homeschoolers, we have that flexibility to work on school as well as enjoy life according to the weather. Use these opportunities while they last :) 

3. Being squeamish on the science of Creation. Science is on our side - God created it. We need to boldly teach our students all the ways that science and the world around us support biblical creation.

     Within Montessori, it is very important that the family address their beliefs in lower elementary (and primary). Lay a strong foundation. Introduce other belief systems in upper elementary. Do not be afraid to address these emotionally-filled topics in all directions, *at* the appropriate time. 

     Intelligent discussions; RESPECTFUL discussions and sharing; and at some point, the ability to agree to disagree until we are all standing before God and can ask Him face-to-face. 

4. Not starting to prepare for college early by beginning to take the ACT and SAT early - in 7th or 8th grade, along with other preparations. 

     If college is the goal, then yes, you must be preparing for those requirements. See number 1 above. 

5. Not starting serious high school sciences early enough.. especially if a student may be a college science major. Critical decisions should be made going into 8th grade.

     Within Montessori, they should have a very strong foundation in the sciences by the end of elementary; with lots of time for personal research and exploration. Thus even by 6th grade (age 12), the child typically knows where their interests lie. By age 15 (end of adolescence), they should be ready to embark on their high school journey, with firm footing. 

6. For younger students, call the sciences what they are (chemistry, physics, biology, anatomy & physiology) rather than "physical science" and "general science" and teach them that way. This makes high school science more familiar and far less intimidating.

     YES! Montessori has the albums divided into geography (study of the earth sciences) and biology (study of life sciences). However, within the presentations and when doing their own research and projects, they should be learning the terminology appropriate to what they are studying, including what the study is called, be it physics or chemistry or taxonomy. 

7. Not giving students a structured academic environment early. Beginning in 6th or 7th grade, provide a structured academic environment for students that includes deadlines that have to be met. Inability to meet deadlines is a critical deficiency in most homeschooled students.

     While Montessori shares many characteristics with un-schooling and can be utilized with minor modification by un-schoolers. the fact remains that children must learn responsibility. Thus we utilize a work-plan/work-journal system that evolves over time to address the changing needs of the children and the family situation. 

8. Not looking for colleges early - most families end up doing this in a last minute frantic rush - not good for many reasons.

     This is a personal family matter. Not Montessori related, other than, for the most part, the Montessori model emphasizes

9. Not allowing students to take some of their classes as "outside" classes in the middle and high school years. Students need to begin the process of taking classes from others / being accountable to other teachers as they prepare for collage.

     This could begin in elementary as well. Online or co-ops. Or at first, simply anything with another adult in charge. This is one of the many reasons I do NOT join my son's tae-kwon-do class, despite his strong invitation. 

10. Losing our focus - all we do should glorify God. Press on! :)
    Yes! No particular Montessori response here ;) 

Infants, Toddlers and Toothpicks

I have mentioned this activity a few times - about an older infant or toddler sitting at their little table with a set of toothpicks and a jar of varying kinds.

Not everyone has baby food jars - some of us make/made our own ;) So an alternative?

NOT this (awesome spice jar from IKEA - lots of uses - this one ain't it)

Toothpicks go in, but don't all come out.
FRUSTRATING.
Does not encourage independence or skills. 

Ball jam jar
these glass jars come in a variety of sizes, including very short!
Get the wide mouth ones. You'll use them for everything!
Get the types that one-size lid fits all you get.
The child can even insert his hand to
remove the toothpicks without dumping. ;)