School Days - Botany, EPL, Language, Geography/History

We have been so way-laid from our plans these last few months as you will see with our botany studies... but I feel like we have utilized this season of Lent to really freshen up and clear out. So now, we can focus on things we love to do :)


Practical Life: 
Legoboy got right onto his morning chores, clearing up corners that he'd not quite done just properly the last few days. He even vacuumed (an extra). He must think it's almost time for his birthday ;) Actually, he has really begun to appreciate having a clean home where he can spread out his Lego projects and still find everything.

He arranged the prayer table a new way - with only a week to go until the start of Holy Week, he wants to be ready for some planning he has been doing for the Triduum. He lit the candles for prayer time and replace the old with new.


Botany: 
I wanted to replant our herbs in October or November, start the seedlings then, so that they could benefit from our south-facing balcony window through the winter and be strong hardy plants by now.
All of our herbs except marshmallow did NOT make the full cycle of life from our last planting. :(

Yeah. Um. Or not. Here it is April - we finally got them in.

According to our plans from last time, we made some changes:

• use a seed starter within the egg cartons
• make holes in the bottom of the cartons for the roots to not have to through so much thickness of cardboard (even soaked, many of the roots worked their way between the layers of cardboard, but not all the way OUT --- even after watering only the soil to attract the roots to the soil. 
• place the egg cartons in the seedling planters immediately (well, they now have holes in them after all)
• place directly in a warm window (we don't get as much direct sunlight right now, but a friend has a sun-lamp to loan us if needed)
• use this blue rack that has been making the rounds (we've used it for home stuff, Montessori stuff, in an atrium, in a Montessori co-op, in Legoboy's bedroom, and now into the living room stacked tall and narrow) --- it really helps all the plants reach the light, uses vertical space and not our entire floor space or play area. 

After getting this all squared away, Legoboy wanted to listen to some of the Herb Fairy stories again (Herb Fairies is currently offering a free herb cookbook and will soon open up their yearly Herb Fairy adventures ---- we are SO NOT into "fairies" and the like in our home, but we love this learning adventure!). We chose the one about roses today. Oh! All the things that a rose plant can help with! And the candy from the fruit! (actually you can make candy from the petals too, but the story didn't share that part - which means there is SO much more to learn about all the herbs we've been studying!). So we listened while I worked on tracing figures for a Garden of Francis order and Legoboy built some Lego structures. 

Practical Life Moment (as if herbs aren't practical ;) ) --- he went down to check the mail....
And we got our package from a Mountain Rose Herbs giveaway - I love winning giveaways!!! In this giveaway, we received a package of dried herbs: marshmallow root, chicory root, astragalus root powder, milk thistle seed, and burdock root --- all of which go along quite nicely with this month's Herbal Roots Zine which is on chicory. Many times, we can't do all of the recipes because we don't have the ingredients on hand. No excuse this time ;) So when we get to actually reading the Zine next week, we'll have what we need. Yay!

Our herbal studies have really gone deep. I blame Montessori on that. I can't imagine having time or energy to explore the options and make any basic herb-learning selection if we used any other curriculum. Using Montessori, this IS our botany studies (after the basic lessons). I know I gush about that freedom of time we have - but it is SO true! We worked out a plan today to choose one day a week to be our herb day - it could be reading the Zine and doing some of the activities, doing activities or watching videos from the various newsletters we are signed up for (Learning Herbs, Herbal Roots Zine, are the two that come to mind right away), doing or creating something from the kids herbal books he has, doing a recipe from the Mountain Rose Herbs catalogs (because they have recipes in there --- teas, foods, medicines, candies, you name it!).


Mathematics: 
We are taking a short break from the Montessori lessons while I create the follow-up cards for the upper elementary portions - I want him to work on these sections from the beginning, rather than what he's been doing (reviewing the lower elementary follow-up cards for typos and logic).

We played Act Your Wage again today and discussed some variations to try out next time. I'll post how all that goes ;)

I then assigned him some real life word problems of a sort, using our home finances as the foundation. It is amazing the insights he comes up with by "handing over" the finances to him. Not that he is really doing our home finances, but allowing him real life participation in real numbers and real situations, he sometimes comes up with ideas or asks just the right question to get me thinking of something better. And he finds the applicable Scripture passages when it comes to certain situations as well. He is the one to coin the phrase I have used a lot frequently: "the wife is to increase what the husband provides for the family". Well, that is perhaps a topic for our Catholic Hearts blog, but it ties in so well with our Montessori studies of real life, real experiences, inter-connecting all areas of school and life.

With these word problems, he has been looking at basic interest rates, savings rates, expenses, ways to expand our budget, etc. Utilizing both math skills, as well as logic, problem solving and ethics.


Geography/History: 
As an upper elementary student he is really delving into exploring the various beliefs about the origins of the earth and the early history of humankind. Last year, he explored various creation myths from around the world; he wants to get that book again from the library - I will post about when we do because it is recommended in the elementary Montessori albums and he wants to create some sort of analysis of the similarities amongst each one, as well as the differences - then see what those differences have to do with the culture the story came from.

Today he read a chapter from a book he has on Creation vs. Evolution.


Language: 
We finally had our discussion on what a debate is, how it works, no winners/losers yet how we can analyze a person's evidence as well as the presentation of that evidence. Look at the questions still unanswered and how many debates prompt people to do their own research.
All of this ties into his earth origins studies, because of the recent Nye/Ham debate (the link is creation perspective but I am short on time and can't find a link without a "bias") - we own the DVD - I watched part of it online but didn't have time to finish. We'll be watching the debate soon, tracking the evidence each one puts forth and see how well each one does in responding to the other.

Happy Birthday Legoboy!

The Goof ;)

Decorating his door for his party

Birthday Strawberry Angel Food Cake
(instead of shortcake - and it's whole wheat flour)

His favorite gift - no surprise ;) 

Personal Finances and Montessori

It is never too early for a child to experience the reality of finances - indeed, the sooner they experience this very real aspect of most modern cultures, the more comfortable they are maintaining their value systems with it and the more likely they are to be creative throughout life in various economic situations.

Montessori does not specifically address "here is an album page about personal finances" - what DO we have in primary Montessori and elementary Montessori?

• decimal fractions - with extensions to include local currency
• language nomenclature - on monetary units
• economic geography - studying the trades and interactions of current times (can be extended to historical and imaginative cultures as well)
• story problems/word problems using money and goods exchanges
• Goings Out - using real money and real exchanges in real every-day life. Planning purchases, planning errands, looking at gas prices and driving routes, reality of putting too many miles on the car needlessly, shopping around for the best balance of price and quality for services needed or desired, etc. Just living real life - and involving all family members. 

Doesn't sound like much, but it lays a strong foundation for each family to take those skills and experiences and proceed forward with their own value system in their own family unit. 

What have we incorporated into our Montessori experience to get into finances? 

Financial Peace Jr. - just the kit; we did not use the storybooks ourselves, but did borrow a couple from a friend. They are good for very young children; they did not go over very well with Legoboy at age 7 and 8. He said, "Yeah, I got that already." I felt it was pretty simplistic for Legoboy personally, because he'd been doing the envelope system of give/spend/save using upcycled parmesan cheese containers, since he was about 3. However, I do think the stories were good reinforcement of the lessons we'd been naturally experiencing his whole life. Ages 3-12 - I like it, but wish it had "more" for the 7-12 children who have had these lessons earlier on. I looked into the high school program he has, but it is more than what we need for a 10 year old boy. 

Your Business Math (Charlotte Mason style) - We wrote about the start of Legoboy's pet store here. This has been a great use of percentages, taxes, etc. We've been taking it slowly - and have a few months to go yet. Taking it slower than anticipated has actually benefited us because he can go back to his Montessori lessons, go deeper, then come back to this with new insight. He's even gone back and reviewed a couple of past months to see, "What could I have done different?" or "Oh! Now I see how that part works!"

Just living it - I have involved Legoboy on some level or another in our family finances from the beginning. Frankly, if this step is all a homeschool family does, GREAT! And it is entirely Montessori: real life, real experiences, real discussions, sharing of the family value system. Perfect! In infancy and toddlerhood, the child sees the transactions happening and the parent can verbalize what is happening - "we need $15 to give to the cashier to purchase this food" or whatever it is. In preschool, children can receive a small allowance (Legoboy started with 3 dimes each week: save, spend, give (church)). It is AMAZING how quickly he caught on. He saw a coloring book he wanted at Target. It was 99 cents plus tax. I told him he had his own money now and he could save up for it. When we got home that day, he asked me to write down how many dimes he would need to buy it. I told him "10" (I'd pay the sales tax to keep things simple for him). He TRACED 10 dimes on a piece of paper; then placed a dime on each circle as he got it (only the spend/save ones - he still gave a dime each week to church). When he had 10 filled in, he asked if we could go back. He talked about it off and on during that time of saving up, but he didn't harp on it, and he didn't ask if we could go back until he had them all. 

When we got there, that particular coloring book was gone, but he found another one at the same price that was suitable and he purchased that one instead. With his own money. I won't say he was "proud of himself" because I didn't get that impression; but he definitely seemed confident in himself, patient (he didn't stare at the chart he'd made for hours on end - just looked once in a while), and he definitely cared for that coloring book. 

At 5, he moved up to 3 quarters a week .Later, I introduced the idea of doing extra work for money. By 7, he didn't get a routine allowance, but he did have opportunities to earn money. Recently, approaching age 10, we discussed the idea that all that he does helps Mom earn money for the household, and yes he should have a share in that, in addition to having his clothing, food and educational needs met. He has always earned his own money for Legos, tae-kwon-do belt tests (I cover the uniforms since this is required "clothing") and tournaments, extra books (though it is interesting to see how much I include under "homeschooling" ;) ), and some other entertainment. Now, we have worked out a daily system with his daily chores and expectations where he doesn't get paid to DO them, but he does have to pay me from that money each day when I have to remind him or the tasks weren't accomplished (thus taking my time away from earning household income, or contributing to the amount of work I have to do to keep the household running - so he's "paying me" for my time spent). 

He really takes true appropriate pride in his work. He even said to me one evening, "I am really happy I have to work for the things I purchase. I like gifts, but if everything was given to me I wouldn't be happy - I'd be lazy and not satisfied with anything. But I know how much work I put into having the things I have. They are really mine because I worked for them." 

Our most recent addition to the personal finances education experiences: 

Act Your Wage - We purchased ours through Homeschool Buyers Co-op (a great place to be if you can control what you purchase - only buy what you would have anyway, just at a discount price!). 

This game is great for the 8+ crowd who have some solid basic financial foundation. There is not a lot of math involved - adding and subtracting - comparing greater than versus less than; doubling the emergency fund size. I have read some reviews that suggest it would be boring for adults; and maybe I see that. For our Montessori elementary and adolescent children though? I recommend it quite strongly! 

This was a slightly early birthday gift for my big 10 year old young man (ack - I did NOT just type that!!! he is getting too old!) - and of course we had to cancel our plans for a couple of hours and play the game, then discuss/critique it and now write this post. 

Indeed, as I think about the parts that others have written low reviews on - and ways to make it more satisfying for adults --- there are so many ways to utilize house rules for easier or harder (use fewer debt cards for younger children; more for older; have some choices built-in; etc.). Modify! 

As I look over the few state standards that contain information on personal finances, look over the college level courses I took in accounting, business management and personal finances.... I truly feel that we have really followed a good path. This game is an excellent step along the way; with a high school level course in basic business management or personal finances (both of which fit right in with the Montessori adolescent model!), I am truly satisfied that my son will leave his adolescent years with a solid foundation. The choices he makes will be his own, but I will have given him all that I can. 

Yay! Some satisfaction as we hit the double digits! 

;) 

Work Journals as Homeschool Proof

UPDATE 2:
The Real Question:
If the only requirements are "equivalent subjects to the local schools" (the state will not define the word "equivalent" - to give homeschoolers more rights) and "attendance of 180 days per school year" (the state, for the same reason above, will not define "attendance" or "school year" - each private school and homeschool can define their own school year, their own attendance, and their own equivalency to local school subjects) starting at age 7 until the child graduates (the state fully supports a parent-issued diploma based on the parent's own graduation requirements) ---- what is the best way to document those requirements while only providing the minimum. Each of these things must be shown upon request.

Solution 1: a list of numbers 1-180 - checked for each day of attendance, noting the "school year" only
(because even a marked calendar actually gives the days/dates of attendance - as the work journal idea presented below --- too much information)
It is pretty obvious if a child can have a generic conversation on the same topics the local kids would study - so that one is a verbal proof.

Solution 2:  same as above, but not even noting the school year other than the child's grade level? Or is that too much too?

How can we document attendance without giving more than "attendance"?

I am seriously looking for ideas here! I appreciate the 3 private e-mails I received, but the question wasn't really addressed, which is why I post this second update ;)





UPDATE:
I am pondering my post below. But I am keeping it up - for the sake of conversation - of working out the best plan for those who Montessori homeschool - or even unschool.

Clarification --- Three families in my state that I know of have been visited by DCS in the last 2 months. Each family uses some form of Montessori - and all had a work journal of the basic type that has the date and the name of the work done (not necessarily *what* that work is - such as "bead chain 9" - no description of what it is). With lawyers in place, meetings in their homes with the DCS person, the one thing they each shared with me that they appreciated having (so they didn't have to do anything else) was having that work journal to show *that* schoolwork was done on that day. No way could the DCS person know what the work done even was (and legally couldn't even ask). Apparently one of the lawyers involved also homeschools - and they were ok with the sharing of the basic work journal.

MBT has fantastic comments below - regarding NOT giving more than requested. The trouble in our state is, "what shows what is requested?" Yes, I appreciate the lack of definition of attendance, but how do you show proof of something that has no definition? Each family has to figure out how to do that and NOT provide more than necessary. These families made a particular choice and it worked well for them. Some families just print out a calendar and write the letter "S" on each day school was done. In our family, we school every single day of the week. Pick up any calendar and those are our school days. I wonder if a DCS agent would believe me. But there's my son's attendance record. Every - single - day - of - the - year.

Maybe I am putting this out there so someone else can answer the question for me. What evidence is the bare minimum for showing attendance in a state that doesn't define attendance, but requires 180 days of it - and no other legislation on homeschooling? Is a basic work journal too much? Certainly can be questioned less. How much does this depend on the definition of attendance? A calendar marking school days isn't in the definition either. And that is where the real conundrum lies - for me.



The original post: 


Let's pretend you live in a state that only requires attendance in school for 180 days - but the state won't define attendance for private school (and considers homeschools to be private schools).

Portfolios are great; community testimonial that your child is brilliant is great.

But you know what makes life SO MUCH EASIER when someone knocks on the door to question your child's absence from school (presence at home during school hours) ?

Hand them the child's DATED work journal. The contents (style, lay-out) don't matter, but the dates do.

Let me say - it is SO much easier to SAVE those, keep them in ONE place (not hidden somewhere in the piles of papers and boxes of papers that a certain Lego-loving Fiend likes to collect) - then it is to go back and use a calendar to note that school was done on enough days to count for 180.

Do you realize how questionable that looks!? But a work journal, obviously written in different handwriting styles on different days with different writing utensils - so much more believable.

Reality-check: 180 days is half the calendar year. We have school on some level or another every, single, day. 365 days a year. Even Sundays are music (Traditional Latin Mass choir or Novus Ordo chants); Latin with a bit of Greek thrown in; community service (altar serving); history (personal Bible study looking at the historical development); logic (the games we play together later in the day) and literature (Once Upon a Time lovers in this household - and we are always going back and discussing the original tales included in the series as well as the Disney versions - and many times other versions - compare/contrast, discuss the moral implications, changes through time according to culture, what components are the same in all versions because of universal truths, etc.).

Yeah, even Sundays count as school ;) And that's just what we do every Sunday - let alone what we do on only some Sundays (cooking to take food to others in need; art projects of a wide variety).


So, we have 180 days covered in less than the first 6 months of each year.

Of late, I have NOT been as adamant about the work journal as I should be; he does keep a notebook with study ideas, project ideas, he does have his work plan (his organization of the ideas in his head, the requirements he has to meet to attain the goals he has set for himself, and our family projects) and he works from that to move forward with his own work. He does not track dates these days. He should.

So there you have it. Bad idea on my part to not track anything (I don't even have a calendar printed out with "s" on it for every day). We'd need credible proof of 180 days of schooling this school year and last - and a not-quite-10-year-old reading and holding intellectual conversations on high school level literature, doing typical middle school math, pseudo-expert on Ancient Egypt, Ancient Greece and Ancient Israel, running his own small business on Etsy ---- not proof enough of adequate homeschooling.

Not when it is only attendance that counts.


Sigh.

Upper Elementary in AMI

Upper Elementary in AMI

Every once in a while I hear that AMI does not "seem to have much for the 9-12 year old." I have to admit I am perplexed by that statement. As a mother of an almost 10 year old boy who is in the middle of upper elementary right now and "started" elementary a bit "early"... well, he's still pretty busy. On the one hand, I am entirely amazed at what we have accomplished, but we also started elementary at 5 1/2 (giving us more time) and he's an only child of a single mom who runs two businesses from her home and off/on has part-time work outside the home (read that as: lots of free time to avoid school work and play with Legos instead). On the other hand, now the DEEP work is part and parcel of our everyday lives, I can't imagine adding anything MORE to what we do ;)


Here is what I see when I look at AMI albums compared to other albums, in no particular order:

• AMI albums have a general presumption that a child has done all or most of the work in the primary albums. 
• A child not coming primary IS given remediation sections in mathematics and language to "bridge" into elementary without that previous background. These DO NOT repeat the primary albums, nor do they take as long. A normally developing 6 year old starting elementary Montessori can anticipate being less than a "year behind" his peers by the 3rd year of elementary, and likely not even that much. I say "behind" in quotes, because no child is truly behind - he is where he is and we work with the child in that place (this is what following the child means - following his NEEDS).
  
• I personally strongly encourage use of the sensorial album with new elementary children; utilizing the presentations as "challenges" rather than presented work. It generally takes less than a month of daily sensorial activities to lay a strong foundation (while doing other subject areas of interest/need). But that is just my personal experience speaking.
• In general, AMI has fewer materials, with more use of the same material in a variety of ways, going deeper with the one material rather than spreading out to more materials.
  
• AMI lays the foundation and expectation for a child to go deeper with his work, ask his own questions, seek out answers and collaborate with others. There are cues along the way, begun in primary and continued throughout elementary - we do not provide all the child's math problems for example, but provide prompts of the sort of math problems to create on his own - we can monitor his work and prompt areas that need attention.
  
• Upper elementary (ages 9-12) does not entirely repeat 6-9 - but all concepts are reviewed. Since personal research is encouraged from the get-go, by the time a child is in upper elementary, he should really be going much deeper with his work. Review concepts in history, for example, and most if not all upper elementary students should be delving into their own personal study of local national history, state/province history, and another area of choice (generally children have an area of history they flourish in - GO with it).
  
• AMI does NOT bog a child down or remove his imagination, creativity, or passion for learning by dictating every single study he does. AMI provides keys - a foundation and a framework - then provides guides for following particular interests (Goings Outs, history question charts, reading great literature and delving into the language used, music experiences with the tone bars, economic geography, etc.). If a particular child or family has a particular interest or value, there is now time to follow that particular pursuit because you do not have 6 hours of schoolwork dictated to you for every day of upper elementary.
  
• AMI does not utilize some materials in lower elementary that WERE used in primary, that some other albums say are still necessary at lower elementary (some of these items, such as the small bead frame, are not even used in AMI remedial mathematics at the elementary level - yet it is a "crucial" material in other elementary albums --- all those concepts can be covered with the large bead frame and NOT slow a child down) ---- thus beginning to go deeper, sooner and freeing up time/effort at the upper end of the age spectrum, when children in the well-run AMI schools DO get into algebra in 6th grade (not ALL children do! even at the best top-notch schools - again, we follow the child --- but here is another point: many children do NOT get to all the presentations in the math album and have more to do as they enter the adolescent plane of development.... so how can there not be enough in math?)
• I can ALMOST see the concern in language - there is less "dictated" - there are less "direct lessons". This is a benefit to the child if they have done most or all of the official lessons in the language album before getting to upper elementary. Now they can explore IDEAS, delve into speech, debate, drama, writing papers in one style, then re-writing in another style for comparison ---- hitting on all those extensions of the early album pages that they weren't ready for in lower elementary or didn't have time for (because of all the personal research they were doing).
  

In summary, AMI is so RICH with the actual keys and with the individual paths of the children, that the only thing I can fathom in trying to understand "there's just not much there for an upper elementary child" is that "there is just not much there for an upper elementary child's parent to directly teach (if all the "lower elementary" work is done)". If all the lower elementary isn't done - well, there is what an upper elementary child can jump into, have fun and explore!



If a child has done ALL of the suggested work for the lower elementary child, here is a generic (not near as detailed as it could be) run-down of the work for an upper elementary child:
(please keep in mind that most children will not get to all suggested topics in lower elementary, because their interests and needs are elsewhere; some will delve into upper elementary topics earlier, but will need to get the other topics later)
(music is not included here - follow the child entirely on this one)

Geography

Chapter I: Creation of the Earth/Idea of the Universe

God with No Hands - experiments - follow-ups

Additional Creation stories

Composition of the Earth

Further Details of the Composition of the Earth (stages)

Formation of the Mountains

Chapter II: Nature of the Elements

Further States of Matter

Different Ways of Combining

Separation, Saturation, Super-saturation

Attraction and Gravity

Extensions of all of the above

Chapter III: The Sun and the Earth

Time Zone Chart

Tilt of the Axis: Solstice, etc

Seasons and the Two Tropics: terminology from tilt

Chapter IV: The Work of Air

Review entire chapter; cover anything missed; select follow-ups to research

Chapter V: The Work of Water

The River

The Rains - Erosion

Ocean Waves

Ice

Spread of Vegetation

People in Different Zones

Chapter VI: Human Geography

Human Geography (Economy)

Overview of Local Government

Follow-Ups

Study of Natural Resources - Introductions

What is Produced and Where

Study of Consumption

Study of Consumption - Follow-Up (extensive)

Comparison of Production and Consumption

Imports and Exports:

Volume of World Trade

World Commerce

FINAL NOTES: Children should be studying in areas of interest (astronomy, physics, geology, etc.) Topics of less interest will be covered in middle/high school.

Biology

Biology – Botany and Zoology

Botany Experiments and Exploration

Story Material

Dissection of Animals

Biology: Classification

Kingdom Vegetalia: Classification

Genera

Familes: Continuing Classification

Geneaology of the Plant

Tree of Classification:

Kingdom Animalia: Classification

Biology: Ecology

Ecosystems - variety

Language

Chapter I: History of Language

The Story of Communication in Signs

The History of Written Language

The History of Spoken Language

Chapter II: Grammar and Syntax

Compound Words - Conversations

Additional Grammar Symbols

Verbs - Simple Tense: Present

Verbs - Simple Tense: Past

Verbs - Auxiliary Verbs

Verbs - Simple Tense: Future

Verbs - The Perfect Tenses

Verbs - The Infinitive and Moods

Verbs - Negative Form of the Verb

LA: Simple Sent w Extensions - box 2

LA: Simple Sent w Extensions - on paper

LA: Verbal & Nominal Predicates (linking verbs)

Elliptical Sentences

Order of Sentences

Voice of the Verb

Voice of the Verb - Dictation

Transitive and Intransitive Verbs

Compound Sentences

Complex Sentences - Adjective Clauses

Complex Sentences - Adverbial Clauses

Complex Sentences - Noun Clauses - Direct

Complex Sentences - Noun Clauses - Indirect

Complex Sentences - Noun Clauses - Subject

Complex Sentences: Degrees of Dependence

Chapter III: Written Language

Written Language Part I & 2

Historical Investigation

Heraldry

Runes

Calligraphy

Decoration

Illustration

Illumination

Variety of paper

Exploration of grammar books

The Content of Children’s Work

Factual Writing - Various forms

Imaginative Writing - Various forms

Research and Note-Taking

Chapter IV: Spoken Language

Discussion

Reports

Speeches

Debates

Poetry Reading

Dialogue

Dialogue 2: Interviews

Chapter V: Literature

Introduction to Literature

Linguistic writing research

History of English Literature - research

Book of Kells

Chaucer

Etymology

Songs and Verse

Beowulf

Hymn of Caedman

Anglo-Saxon Chronicle

American Literature

include selections in the classroom

studies of authors and lives

Children’s Literature

older literature selections (pre 1900s)

1900s literature selections

Children’s Literature in the United States

Read and listen to books

Timelines

Biographies of authors

Goings Out related to literature

Other explorations

Chapter VI: Style

Style

Mathematics

Operations

Group Division

Group Division & Word Problems

Decimal Fractions

Relative Size of Terms/Numbers

Division of a Decimal Fraction by a Decimal Fraction

Leading to Abstraction of Multiplication of Decimal Fractions

Division of a Decimal Fraction on Paper

Squaring and Cubing

Squaring with a Hierarchical Value: stages

Pass From One Cube to Another

Cubing a Binomial

Cubing a Trinomial

Cubing a Quadrinomial

Cubing a Trinomial having Numerical Value

The Story of the Three Kings

Cubing a Number with Decimal Value

Square Roots

Square Roots - Abstraction stages

Special Cases - stages

Square Roots: review process and rules

Cube Roots

Cube Roots: Review concept and rule

Other Topics

Signed Numbers: Negative Snake Game

Signed Numbers: Operations (stages)

Powers of 2

Powers of 3: Full work

Powers of 2 and 3: Combined

Powers of 10

Operations Using Exponential Notation

Expanded Power Notation - Intro and Operations

Word Problems

Distance/Velocity/Time

Principal/Interest/Rate/Time

Non-Decimal Bases: Intro and Operations

Conversion of Number Bases

Balancing an Equation using operations

Solve for Unknown: Operations

Algebra Word Problems

Solve for Two Unknowns

All stages in upper elementary typically

Geometry

I. Introduction to Geometry

Various Geometry Stories from History

II. Congruency, Similarity, Equivalency I

Review all concepts in Upper Elementary

IX. Equivalency III

Equivalency with Iron Material: stages

Euclid’s Plate

X. Area

Concept of Area

Deriving Formulae with the Yellow Material: stages

Deriving Formulae with the Iron Material: stages

XI. Circle I

The Circle Nomenclature

Relationship Between Lines and Circumferences

Relationships Between Two Circumferences

XII. Circle II

Area of a Circle (stages)

Relationship Between the Apothem and Side of a Plane Figure

XIII. Solid Geometry

Concept of Volume

Equivalence as Related to Solid Figures

Three Important Dimensions

Equivalence Between Prisms with Various Bases

Derivation of the Formula

Solids of Rotation

Volume of the Pyramid

Volume of the Cylinder and Cone

Polyhedrons

Lateral and Total Surface Area of Solids

FINAL NOTES: Use 6th year to review and consolidate all concepts

History

The Coming of Life Story with Timeline

The Black Strip

Fundamental Needs of Human Beings – Charts --- some portions start in year 4

History Question Charts

Three Phases of History

Second Timeline of Human Beings

Migration Charts

Four River Civilizations

New World Civilizations

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BC-AD Timeline