I'm not fighting. I was simply participating in the discussion.

That's very cool. Unfortunately, it's behind a pay-wall, but congrats to your daughter.

You're right and I did make a mistake that I need to correct. A ratio is a comparison of different quantities or units. But you're right that one can take a ratio of quantities, in which case there is not additional units attached.

1/9 mph is a rate. Unless you're meaning 1/9 of a mile is traveled in an hour [iow, it would take 9 hours to travel 1 mile.] Then the 1/9 is a quantity (the amount of a mile traveled) and it's still a part of the rate. Again, your home school, your rules. You can teach whatever you want and how you like. What we decide to do in our home schools isn't anything more than what we do. That doesn't make what we're doing Best Practice. This is just saying that you can write a ratio using a colon, or a fraction bar. (I'll ignore the proportion for now) I have already said that Fraction Notation can be used to express ratios. I have already said that Fractions =\= ratios. The meaning and correct way to pronounce this word: OBJECT depends entirely on the context. The meaning and correct way to pronounce this word: ESTIMATE depends entirely on the context. The meaning and correct way to read and use a/b depends entirely on the context.

Fractions, being numbers, can be operated on. You can perform exponentiation, multiplication or addition on a fraction. In math, "equality" has 3 conditions. When we say that ratios are the same thing as fractions, we're saying that ratios = fractions. That's simply not true. Ratios ALWAYS have a unit attached and so 1/9 the ratio can't be universally substituted into an equation for 1/9 the fraction. 1/9 the ratio doesn't satisfy the Reflexive property either. 1A/9B =/= 1/9 the number etc. It's your homeschool so you can do whatever you want. But it doesn't change mathematical reality, nor does it mean that what you do is Best Practice. There is a long-established tradition of telling lies*to students in math class to help them do well on topic D or to just because the lie seems to hold as they progress from A-F, without concern for what comes after. *conditional-truths, without ever making the conditions known are as good as lies.

No they aren't. The same notation that is used for fractions can be used for ratios, but ratios are not fractions. Fractions are numbers. A fraction stands for a quantity. You can eat 1/2 of an apple or you can sell 3/4 of a herd of cows or have to refund tickets to 1/9 of a crowd of people. You can plot a fraction on the number line. Take the unit between 4 and 5, divide into into 7ths and you can plot the mixed number 4 and 2/7 or 30/7. A ratio is a comparison of different units. (such as dogs to cats, or yellow flowers to pink flowers or a persons height to foot size). You can observe that someone owns 1 dog for every 2 cats(1/2) , or that there are 3 yellow flowers to 4 pink flowers(3/4) , or a persons height is 9 times greater than the length of their foot. (9/1). The context of 1/9 determines if it's a fraction or a ratio.

One says it should be "Gil's" again and the other says it shouldn't be Gil's so that it sounds "more official" down the line.

Oh, what if I open up that first G and A? Gentleman's Academy for Dynamic, General & Elective Training

Heading in to Highschool, I have to say that Japanese is a bit of a worry for me. The goal is to become fluent in Japanese Conversation and Literacy by the time that they graduate. They'll be aiming to take and obtain Bilingual Professional Certification from the ACTFL in all domains by the time that they graduate so that they can add a professional certification to their resumes. Their tutor and I are planning to have them take the JLPT a few times during highschool to have something concrete to aim towards and plan from. Japanese is worrisome because it's something that I can't quality check very easily and I do not trust other peoples educational standards by default. But by the end of Highschool, I want them to read and write like educated young adults.

So, it comes from the definition of a negative exponent. A negative exponent is defined as the reciprocal of a positive exponent. n^3 is the reciprocal of n^(-3) and n^(-3) is the reciprocal of n^(3). n/n = 1. It doesn't matter how many times n/n is a factor, each factor becomes 1. As for when the base is negative, remember that (-7) / (-7) is also 1. so (-7 * -7 * -7 * -7) / (-7 * -7 * -7 * -7) is just another form of 1 * 1 * 1 * 1 , which is still just 1.

😃At Gil schools, we're all about the Unexpected.

When does he turn 18?

Bear in mind that it's much easier for an inexperienced teacher to create a poor quality, reading program than it is for an inexperienced teacher to create an high quality, well-designed reading program. It's ok to use a well designed program properly and get your jollies elsewhere. However, once you have a well designed program, you can expand on it, but be wary of getting too far off "the path" that a well designed program has you walking with your budding reader. I used a scope and sequence, but did my own thing. I made lessons a little more engaging than stare at this page and read, but we also had plenty of "stare at this page and read" days as well. Ultimately, a book isn't going to be jumping around the room for them.

Our home school runs with the calendar, so we'll be starting 9th grade in January. It just occurred to me last night that I don't know the name of their high school. They've gone to Gils Elementary Academy for Ruffians (GEAR) and are finishing up their 8th grade at Gils Intermediary for Zealous Mathematicians pursuing Other Studies (GIZMOS), and I really need to come up with...something. I'm 90% sure that I'm keeping the theme of GEARs, GIZMOs, so I have kept GADGET High in the back of my mind for a long time. Gils Advanced D_____ G____ E____ Technology? I don't want to use our Last Name or Street Name in the title. I absolutely hate the part of the state that I currently live in, so I don't want to pay homage to it with a name. I don't want to name it after the part of the state that I do like because I don't want my kids education associated with its reputation. (The Boys aren't from that part of the the state, I am) They really loved their previous schools, and they like telling people that they went to GEAR for elementary or are currently enrolled in GIZMOs, etc. I remember years ago, saying "well, I've got a few years to come up with the Highschool name" and now I've got a couple of months. I need a nifty acronym.... They want a "fun" school name for High School too.

Seriously? If you're that strict about language use in science, then you wouldn't even be using miles per hour in a science lesson since the official SI unit for speed is meters per second. Its' perfectly fine that you don't like the program or its authors or a poster on the forum, but I think you're going too far and trying to be arbitrarily rigid with this particular issue. Your comments in this thread are full of logical fallacies and poor reasoning and I think that you know it.

Very interesting. I have long noticed that students struggle with D=RT in math because they don't understand the concept in English, there are a lot of components to the D=RT relationship that are misunderstood.

One of mine was considering learning Russian. The first step was going to be to hire a native tutor to help him through a little textbook for Native Russian speakers to help him learn to read with good pronunciation and build up a basic vocabulary. We'd found a series of Russian school books at a used book store, but you can order one of these books off of Amazon. Teach Yourself Russian has some good reviews on Amazon and is available through the library system.

For my family learning Spanish* was a priority. I took a lot of things off of our plate so that it could get done. I was perfectly ok with them learning (Intensive) Spanish and Math for a few years. In the USA, "learning a language" usually results in people knowing a few hundred words that they can't really combine into meaningful sentences or converse with. I wanted my children to be able to converse with native speakers and to read and write in Spanish at the level of an educated person. So allowing the practice, study and development of their Spanish skills to be pushed to the side wasn't an option. I would not waste time with teaching them numbers and colors. As a matter of fact, a couple of years ago, at 10.5ish there were still some colors that they didn't recognize by name. They had a conversation in Spanish with a Spanish speaking teenager about how funny it was that they could straight up speak Spanish but didn't know certain colors. After that, they knew the names of whichever colors were missing from their vocabulary. Teach them functional language. Your kids don't need to know how to introduce themselves or say who is in their family. They need to tell you what the want or don't want, that they "didn't do it" and to discusss the pictures and illustrations in books with you. I would start a Morning Time ritual that is bilingual for a couple of weeks, then 100% in Spanish after that.

Thanks. This is a good point. So, for example, we've done US History extensively throughout elementary and middle school. In 6th grade they used my college textbooks as a spine, we read over a hundred books on US History from the library or used book shops. Most days, they wrote short responses to questions from the college textbook. I gave them practice assignments based on an APUSH Study Guide book that I got out of the bargain bin. They wrote essays, gave speeches, watched documentaries and read source documents. They memorized notable speeches and documents (for example, they can recite the Declaration of Independence and Emancipation Proclamation verbatim.) during elementary, but they analyzed them in more depth in middle school. They have studied the US Constitution with me and though they can't recite the whole thing, they can quote/cite the document extensively. They listen to the audio of Supreme Court Cases and can explain the structure of the US Government at a fairly detailed level. They don't know who holds every position in Government, or who each senator is/was, but they know key figures. In addition to the US History textbook, they've worked just as extensively from 2-volume college text for African American history and we've done a text on US Womens History as well. They are well-versed in but sick of US History. There isn't really a good reason to keep doing US History--even though colleges want them to study it between 9th-12th grade, they've already become quite familiar and well versed with far more detail of US History than most registered voters have learned. For highschool, their plan is to do African History, A Survey of Asian History, Japanese History and Latin American History. They're hopefully becoming global citizens--they know their countries history and quite well. We've done a lot of World History (en espanol) and they'll continue to read (en Spanish) on World History.. Likewise, our planned Highschool Math courses were going to be Single Variable Calculus Differential Equations Multivariable Calculus Numerical Analysis Linear Algebra Mathematical Statistics But our state "requires" that they take Algebra 1 and Geometry during highschool. They mastered Algebra 1 (and 2) and Geometry years ago. We're just going to list Calculus and above on the transcript with a footnote that the prerequsite material was covered before 9th grade. I'm confused. You get the sense that I'm not in favor of what exactly?

Admissions to our state colleges seems fairly test-based. I definitely didn't have a wonderful transcript or anything like that. But I got into college based on tests. After the first semester it really didn't matter how I'd gotten in. Once in college, whether or not I stayed in was again based on tests in each class--and of course ethical behavior. MANY US Universities want you to "have a solid transcript" (aka dictate your highschool experience) but that's an awful lot of time and energy to devote and sacrifice just for it to not wind up mattering after 1 semester. [Yes, I know that the foundation you bring from highschool helps you to keep up in college level courses, in theory, but I found that to be true in only a couple of classes. You can ace Gen Ed courses (ie the first 2 years of college) with great study and test taking skills alone. So long as we're earnestly preparing for their future goals, I'm not sure how/why it matters which "expected" courses we don't do. US College admission requirements are very limiting too. The Boys want to continue to study languages, mathematics, computers and they're going to continue reading and writing broadly. They want to continue to have sufficient time to build their business, volunteer and play sports.

Myself and my kids.

So, I'm confident that they'll have the test scores, though they'll be prepping to be sure that we hit the score mark. The current default, in so far as I have one, is that they'll do home-courses for subjects that they want to do and that I think are important for them, and continue doing DE until they max it out at the CC. @Miguelsmom Thank you for chiming in! Buddy, my eldest, has no desire to be in school during his 20s. He much prefers to get as much education as possible under his belt by 18 or 19.5 at the latest and go about his life. He's got a lot of ideas about how he wants to spend his 20s and "school" is not on the list. He isn't the type to choose to start college at 18 either. He's willing to finish with College around that age, but not start it. Pal, on the other hand, wants to get a PhD. He plans to accelerate through and get his Masters, take some time off and then start work on a PhD in either Mathematics or possibly a Computer Science. He wants to pause after his Masters to get married, Work FT, travel, have kids and start a business while working on his PhD. The Boys want to be in/go into business together when they're in their mid20s. @Farrar They're ready to start in January. Taking a gap semester doesn't appeal to them at all. As for graduating to college, our universities can be began in Spring or Summer, not just in the Fall. @Lori D. Thanks for the pointers about the credits. We won't be doing English. We home school bilingually and so they'll have Communication and Composition, or something of the sort because they read, write and discuss across the curriculum in 2 languages. They'll earn about 2 credits a year in Foreign Language, because they have an Intensive Conversation and Intensive Literacy course for Japanese each. I know that they aren't typically split this way, but it's not typical for people to actually converse and read/write the language that they study during highschool. One of them might continue with German, so if he does, he'll earn 3 language credits a year. They plan to earn about 6 math credits, starting with Calculus. Neither are particularly passionate about the natural sciences, so they plan to take Bio, Chem and Physics via DE and get the credit for it once and be done. Ditto for US Government and Economics courses via DE as well. At home, The Boys do Computer Programming as a part of their school. They've completed a couple of texts often used for 2 (or 3) semesters of programming at many of our states colleges/universities and several coding projects (dozens have been scrapped as well). They're still learning computer programming and I'm planning to give them credit for their abilities. They'll be learning more hardware skills as well-- Repairing Phones, laptops and tablets. I can't find schools (highschools or colleges) that offer hardware classes so I don't know what to call it just yet, but it's going on their transcript. The other things that they learn and study at the house? Well some of it will be converted into a course and put on the transcript. Communication and Composition is cross curricular, so I'll spin history and civics out of that so that it fits a transcript.

You could just put the missed exercises on a white board and have him re-do the problem for you like he's teaching it to you. Then, if he got it correct, point out that he missed it on the paper and let him fix it. If he got it wrong, go ahead and fix it with him and have him fix it on the paper.

We school Jan-Dec so The Boys will be starting "9th grade" in a couple of months. However, neither is particularly interested in a traditional highschool curriculum. We're in Florida. The colleges that they're considering are in-state. If we just continue to do our own thing, how much will that hurt them? We've been talking a lot about post highschool and for now they are pretty adamant about what they want to do and where they want to be in 1-year, 3-years and 5 years. I'm interested to hear what you veterans think? What might I be over looking? Cons and Pros of doing a Nontraditional High School in our homeschool I'm not worried about them being college-ready per-se, so much as I am in helping them be able to choose between different paths in young adult hood.