Kind of off-topic but I'm curious when you start having your kids take notes. That's something I haven't really done yet.

This thread brought back a lot of memories for me : ) I remember watching my grandmother write letters to her sister and feeling awed that she could write so evenly without lines. I am not as sure about my parents.

You know, I had never thought about the literal meaning of "guidelines" before! I guess if people practiced enough, they could write evenly and in straight lines on their own. My grandmother could, and I think my parents too. I guess it's one of those neglected skills. I only use it now when I write postcards.

I remember my grandmother used to make pencil lines for me when I was supposed to be writing neatly (like, for the final copy of a letter to a distant relative). She'd have me write in pen so that she could then erase the lines. I feel like I would never have the patience for that myself. But it did work nicely!

I think there's always going to be some variation in how fascism and communism present themselves -- but either system, taken to its logical extreme, ends up in a totalitarian disaster. I remember reading somewhere that the chief difference is not in how fascist and communist states operate, but in how leaders convince their followers to agree on these systems in the first place. Fascists tend to rally their followers around some sense of nostalgia for a forgotten past, or the sense that their culture is being threatened. Communists tend to rally followers around the idea that the current system is not serving the people equally. That's why it makes sense to see fascism as an extreme extension of right-wing conservatism and communism as an extreme extension of left-wing progressivism. I find the idea that both sides meet in the same place fascinating. Reminds me of the neo-conservatives who went so far left that they came around the other side.

Same here -- we never make those projects part of schoolwork. They are just a fun thing to do on the side. But I'm wondering whether I could use some of the format (index cards / lists) for actual school projects. I wonder. I mean, I've tried (and failed) to turn his interests into school, but I've never tried to use his formatting. Maybe worth experimenting with. Your daughters' meow language sounds amazing!

That kind of topic sounds like something my kid would LOVE. I mean, he doesnt know Dungeons and Dragons but that kind of analyzing and categorizing sounds so familiar 🙂 Last year he read Lord of the Rings and the Narnia books. It was great for me because I lived and breathed those books when I was little, so we talked about the characters a lot. He ended up using a set up index cards to make one card for each character. They were super primitive cards because he mostly just wanted to rate their evil/good quotient 🙂 but he had a lot of fun with it. Anyway this is reminding me that lists and index cards can be a part of writing projects, I want to think about this more!

I generally agree with the article you linked. But I think writing also has a lot to do with organization and mental clarity. It's not just about learning language patterns and having experiences; it's also about being able to communicate effectively. I used to tutor adults who were failing their college writing courses. Some of them were recent immigrants who had trouble with the language itself. But others were people who didn't have major mechanical problems, but who had just never learned how to organize their ideas. They weren't able to provide details, give explanations, or create arguments. They also weren't used to thinking about their audience. As a result, they were weak writers. I don't know what that has to do with kids, of course -- I guess I'm just thinking about writing in general, and how it works. My oldest kid is just in the third grade now, and I don't have him do a lot of compositions. I do have him do oral narrations every day, because I think that's a great way to practice organizing and communicating ideas. And he does copy work, and he reads a ton of good books. He does little compositions now and then. He also writes stories. They come out (in my opinion) really great. My goal for next year is to get him more comfortable with writing. Right now, if anything all the examples of great writing that he takes in have played on his perfectionist tendencies and he is always fretting over his word choice or about which order to put his sentences : ) I think in his case, having him do something slightly more formal (not every day) might help, because he is an analytical kid and it might be liberating for him to be able to break down how writing works. But we'll see -- I could be wrong.

I mean your expectations clearly weren't way off -- if anything it sounds like you were right on track. Did you feel like you were constantly re-evaluating? Was it an intuitive process, or did you use outside measures? Curious because I do struggle sometimes with my kids to know how much they're capable of. And I feel like for me it's a constant process of feeling them out (mixed with some outside touchpoints).

I'm starting to think about what I'd like my 8 year old to do for writing next year. He'll be in the 4th grade. Right now, it's like pulling teeth to get him to write. His mechanics are great-- spelling and grammar are excellent, sentences are complex and varied. The trouble is that he is a perfectionist and agonizes over every word. I've been thinking he'd actually benefit from a more formal approach to writing, so I'm planning to look at little essays with him and study their structure. I think that might demystify writing for him. I'd also like to teach him to make a simple outline. I'd like to have him work on descriptive writing as well. My husband has sometimes had him write a little sports "editorial" which has always gone well, so I think I'd like to have him do more of that. Still turning ideas over in my mind, of course and it'll depend how he responds. I love that you started this thread!

I am not very good at planning ahead and I mostly get away with it, because my kids are little. But whenever I start to feel anxious, I look at one of those "what your third grader should know" books. I don't necessarily go by the book, but it feels reassuring to have some kind of reference. Can you look at what kind of work local high school kids are doing, for a rough measure of how much you should be requiring? Or maybe college courses?

What would happen if you added an additional step for now? So for your example, if she first rewrote 194+153 as 200 + 153 - 6 ? and then 200 + 147 ? It might help her to really spell out what she's doing.

I do this, roughly, although in a notebook rather than a spreadsheet. I don't really instruct my kids much -- instead I have topics which I want to study, and lists of books / resources to go with those topics. I tend to update and revise the list pretty often though. Some of the books get used during our formal school hours; others are for random read-alouds. I use a mix of levels. I love the idea of purposefully finding books for myself too -- I'm going to start doing that!

I get it!! Thank you so much. That was really really helpful!!

You're a great teacher. Would it be fair to say that when we multiply fractions, we are not actually working with two different fractions? We are just working with one fraction which is being scaled by a factor? I mean, in multiplying, we are operating on one fraction by a factor which is expressed by the other fractio ? I don't know whether I put that clearly 🙂 While with addition or subtraction, we are working with two fractions which need to be put into the same form (common denominator) so that we can find their sun or difference?

Let me try : ) I want to get two fifths of three quarters. I'll divide each of the quarters into fifths. Each fifth is equal to a twentieth of the original whole. So that'll give me 15 twentieths. One fifth of that would be three twentieths. Two fifths would be six twentieths, or three tenths.

: ) Two fifths of a fourth. I divide my fourth into five parts this time. Each of those parts is equal to one twentieth of the original whole. I take two of those pieces. Two twentieths, or, one tenth.

This is so helpful : ) Okay. So I am trying to find two thirds of one quarter. I divide my quarter into three parts. Each of those parts is equal to a twelfth of the original whole. This time, I take two of those parts. Two twelfths, or one sixth.

To get a third of one fourth, I'll need to divide the fourth into three pieces. Each of those pieces represents one twelfth of the original whole. So one third of one fourth is a twelfth.

Okay. So when I multiply the denominators, I am basically saying I had already split my unit into three pieces, hence the 1/3. Now I'm splitting each of those thirds into two more pieces. And when I multiply the numerators, I'm saying, I'm going to scale the number of pieces by (in this case) one.

One sixth

Six.

Ooh I'd love that. Conceptually...does this answer the question? I'd expect 1/2 * 1/3 to be smaller than 1/3. Two times smaller. I usually think of 1/2 * 1/3 as "one half of one third". Or, half as much as one third of one.

Okay, I like that. And I can visualize it, too, which is nice. I feel a little more solid already but not 100 percent yet. I guess...maybe I am overthinking things. I am still trying to understand why it is that multiplying fractions is so much easier than adding fractions. Is that because of some fundamental quality of multiplication? Why don't we have to find a common denominator BEFORE we multiply fractions? Is it just that the method of multiplying numerators and the denominators is a shortcut to finding the lowest common denominator? or is there something conceptual that I'm missing? Ugh if anyone has a suggestion of books I can use to get a better understanding of this, I'd love that.

Okay. I feel like I do understand this. So in terms of why the algorithm works... we multiply the two denominators to determine the size of the fractional parts (since we are further subdividing the original whole) and we multiply the two numerators to determine how many of the new fractional parts we're talking about.