Math- just using a bunch of resources

[lulalu]

Ds is almost 9. He loves math, it comes easily to him. We have mostly used Miquon and Gattegno. He loved Minion. I really wish it would encompass all elementary math. 

Anyways ds does not need a lot of review, and he needs a challenge. 

I have been making a lot of problems and work on my own. Using a few resources (Gattegno, Graded Arithmetic, Miquon, RS games, games, etc.) He is doing well with math. But I keep wanting something easier for me. 

I have tried a lot of different curriculum for math. I just haven't found one I like. We've tried: Singapore 1 (just didn't fit right), RightStart (jumped around from topics too much), MEP 1 (moved too slow for us, and I couldn't easily do the lessons each day with just one child), Rod and Staff 3 ( way way too slow and not challenging enough), CLE 3 (too much review and not challenging enough). Whew what a list! We didn't stick to any of these for the reasons I listed. So I just keep making my own stuff and using Miquon. 

This year I also got Hands on Equations and he has loved that. 

Anyways, I keep trying to find the one right program to meet all my needs. But I am thinking maybe I am best just using a bunch of resources and creating my own scope and sequence for the rest of elementary math. Then just get books to fit what I want to cover. Next year I want to spend time on fractions, decimals, percentage and long division for sure. Then add in a lot of challenging word problems. I really do like Gattegno for introducing concepts. 

Who creates their own s&s for math? Is this just a sure way to burn out? Last summer I spent a lot of time making my own sheets and problems. But I do spend a lot of time second guessing myself if I am offering enough challenge. 

Thoughts? Resources? Encouragement from anyone who does this too? 

[lulalu]

@Not_a_Number I know you make your own math. Maybe you could help me with a scope and sequence to be sure I am hitting all the things we need to. 

[Not_a_Number]

1 minute ago, lulalu said:

@Not_a_Number I know you make your own math. Maybe you could help me with a scope and sequence to be sure I am hitting all the things we need to. 

I was just about to reply, lol!! 

As for scope and sequence, we've used Math Kangaroos, AMC 8s, and tests for AoPS classes like Intro to Algebra to make sure we're roughly covering all the bases. But I also have a very good idea of where we're going, so that helps -- I know what kids need to know for math contests and also to take calculus. (I also happen to know they often don't learn it from the actual programs they take, so I honestly don't worry that much about missing little pieces.) 

[Not_a_Number]

As for burning out, I'm currently doing it for 2 kids instead of 1, and I've had to take the radical step of writing their lessons one day ahead of time instead of the morning of 😉 . I write their work for next day the night before. We buy big Clairefontaine notebooks and fill them with written questions. I can give an example of a "worksheet", if you like! 

[Shoes+Ships+SealingWax]

We used MEP, Miquon, RightStart, LivingMath (history-aligned projects), Singapore Intensive Practice, & Beast Academy. The only thing that has ever quenched DS’ thirst is Beast Academy. He loves it enough that he is willing to struggle through hard problems / sections for the thrill of defeating them, which is a mentality I really wanted him to develop!

We play a ton of games in our homeschool (30-60min daily) & I create my own resources when DS needs extra practice with a topic & for a change of pace between books, but I like having a spine that takes over the day-to-day, week-to-week progression so that I can focus on adding in fun extras. 

We’ve done a unit study on graphing, created a city (lots of area & perimeter), & a few other things. This summer we’ll be working through Didax Pentominoes while reading Chasing Vermeer. I’m sketching out a “gap year” between completing BA & beginning AOPS, just in case he isn’t ready for the jump to a formal textbook style.

I’m not afraid of building something myself if I’m not content with what I can find pre-assembled. I’ve done so at various times for history, science, language arts, mathematics, & other subjects. I don’t prefer to do it all the time, though. It gets tiring & I find I’m not left the mental energy to add in anything additional. 

Edited March 2, 2021 by Shoes+Ships+SealingWax

[Not_a_Number]

5 minutes ago, Shoes+Ships+SealingWax said:

We used MEP, Miquon, RightStart, LivingMath (history-aligned projects), Singapore Intensive Practice, & Beast Academy. The only thing that has ever quenched DS’ thirst is Beast Academy. He loves it enough that he is willing to struggle through hard problems / sections for the thrill of defeating them, which is a mentality I really wanted him to develop!

I was actually going to recommend Beast Academy but forgot! Thanks for mentioning it.

That being said, we tried that route and didn’t like it as much as writing our own lessons. I feel like I do a better job communicating concepts than Beast does and I like things in a different order.

[lulalu]

We tried the free month trial of Beast this past spring. Ds did love it. I prefer paper so I would buy the books. I guess I just wasn't all that impressed. And he really likes the c-rods. I know I could add them in. 

Maybe we should try a book and see how it goes. 

[Not_a_Number]

Just now, lulalu said:

We tried the free month trial of Beast this past spring. Ds did love it. I prefer paper so I would buy the books. I guess I just wasn't all that impressed. And he really likes the c-rods. I know I could add them in. 

Maybe we should try a book and see how it goes. 

Why weren't you that impressed? For what it's worth, I'm also not that impressed. I did borrow some of their puzzle ideas for my Zoom class, but I didn't think it was conceptually awesome. (Although I'm not a C-rod fan, so that wouldn't be my issue.) 

[lulalu]

1 minute ago, Not_a_Number said:

Why weren't you that impressed? For what it's worth, I'm also not that impressed. I did borrow some of their puzzle ideas for my Zoom class, but I didn't think it was conceptually awesome. (Although I'm not a C-rod fan, so that wouldn't be my issue.) 

We did the chapter on place value. Which is something we worked on a lot already. And I don't think it did a great job with it. It was using Pirate money (if I remember correctly). I just found what we had done more deep and a better way to really nail place value. We used money, and Roman Numerals to do place value, and ds has a very strong understanding of it. 

Maybe it was just that chapter and only having a month to get into it. 

It is always on my mind to try. But I feel like I would also need to add the hands on aspect too. And then I might as well be the one explaining and teaching it all. 

[Not_a_Number]

1 minute ago, lulalu said:

We did the chapter on place value. Which is something we worked on a lot already. And I don't think it did a great job with it. It was using Pirate money (if I remember correctly). I just found what we had done more deep and a better way to really nail place value. We used money, and Roman Numerals to do place value, and ds has a very strong understanding of it. 

Maybe it was just that chapter and only having a month to get into it. 

No, you're right. They do a perfunctory job on place value, and then they jump to other stuff. I like using money (or poker chips, which is what I do) for place value MUCH better than what they do. 

My experience is that they do a perfunctory job on conceptual stuff, but they are good at puzzles/hard problems. That's why I don't use them. And place value is a good example. 

[Not_a_Number]

To be fair, we didn't get that far into Beast Academy. I started assigning occasional pages from their books when I was tired, and then all the REALLY long expressions made DD8 write wrong equations like 

45 + 10 + 5 + 8 + 9  = 55 = 55 + 23 = 78

and I freaked OUT and stopped assigning anything but the puzzles. And then I started running my own classes and made my own puzzle randomizers (want any puzzles? I have a thread on that!) so then we stopped using them entirely. 

DD8 loves the comics, though, so we have those around. But we haven't used the actual books since the grade 2 books, which she did a while ago. 

Edited March 2, 2021 by Not_a_Number

[Lori D.]

Possibly: Life of Fred as the spine + supplement of selected problems from one of the more traditional programs (like MEP)

Just doing a handful of problems from each lesson in a traditional program allows you to move as quickly through it as he needs, and fills in any "gaps" or does any light review that might be missing from Life of Fred.

That would also allow you the ability to still use the math games and puzzles and other supplements that he's enjoying now.

Edited March 2, 2021 by Lori D.

[Not_a_Number]

1 minute ago, Lori D. said:

Possibly: Life of Fred as the spine + supplement of selected problems from one of the more traditional programs (like MEP)

Just doing a handful of problems from each lesson in a traditional program allows you to move as quickly through it as he needs, and fills in any "gaps" or does any light review that might be missing from Life of Fred.

I think if her concern is conceptual learning, then that won't fit the bill. LoF isn't all that conceptual, and neither are traditional programs. 

I've looked at Miquon, and it's really its own thing -- very conceptual, but also gentle and playful and puzzle-y. If I liked C-rods or number lines, I would have been tempted to use it. It's the closest thing to my own preference for how to teach math. 

[Lori D.]

8 minutes ago, Not_a_Number said:

I think if her concern is conceptual learning, then that won't fit the bill. LoF isn't all that conceptual, and neither are traditional programs. 

I've looked at Miquon, and it's really its own thing -- very conceptual, but also gentle and playful and puzzle-y. If I liked C-rods or number lines, I would have been tempted to use it. It's the closest thing to my own preference for how to teach math. 

That's why I suggested LoF in conjunction with a traditional program -- get the concepts and practice from the traditional program, and the actual working out and puzzle-like problem-solving from LoF. Also, I have seen with other families who have a very "right-brained" (visual-spatial) learner, that LoF often clicks when traditional programs don't, as LoF is more "whole to parts" brain processing, while traditional Western programs are more abstract/algorithm based, or more sequential and parts-to-whole in presentation and brain processing.

Miquon is very "discovery approach", which is a form of global thinking (whole-to-parts) -- intuiting the pattern or the connection. It's just that Miquon is also very tactile, with cuisenaire rods, while LoF is more verbal and story-based in it's discovery approach

Edited March 2, 2021 by Lori D.

[Not_a_Number]

5 minutes ago, Lori D. said:

Miquon is very "discovery approach", which is a form of global thinking (whole-to-parts) -- intuiting the pattern or the connection. It's just that Miquon is also very tactile, with cuisenaire rods, while LoF is more verbal and story-based in it's discovery approach.

I guess I don't usually find "whole-to-parts" or "parts-to-whole" to be very useful distinctions in math education. I could just as easily argue that intuiting patterns is "parts-to-whole" learning, since you start with lots of simple examples and build up from there. And I find that algorithmic programs almost don't teach the concepts at all, either in a whole-to-parts or parts-to-whole way. 

The thing I like about Miquon is that it seems to build up the concepts in a careful, thorough way. Also, it's tested -- a smart person actually used it in a classroom and observed the results. I always really respect that method. 

 

5 minutes ago, Lori D. said:

Also, I have seen with other families who have a very "right-brained" (visual-spatial) learner, that LoF often clicks when traditional programs don't, as LoF is more "whole to parts" brain processing, while traditional Western programs are more abstract/algorithm based, or more sequential and parts-to-whole in presentation and brain processing.

Hmmm. What does it mean to be more abstract/algorithm based? Are algorithms abstract because they are removed from the physical world? 

Can you give me an example what kind of thing might click in LoF that doesn't click normally? 

Edited March 2, 2021 by Not_a_Number

[UHP]

We are just moving on to "Beast Academy 2B" tomorrow, I'm interested to read these takes on it and on its alternatives. My experience with it so far (we finished 2A over the course of about 3 months) is that it's kind of hasty: a child is not likely to read carefully the explanations in the comic book, and the workbook seems to expect a lot of learning to have happened over the course of just 3 or 4 problems when I would have welcomed 30 or 40.

But going through the workbook I often appreciate the miniature skill they are trying to teach next (like, locate the number halfway between 43 and 65 on the number line, or whatever), and figure out how to stretch their 3 or 4 exercises about it into 30 or 40 on handmade worksheets over the course of a few days. To me it seems like a lot of creative thought went into selecting these skills and putting them in order. But I haven't looked closely at anything else, it could be that what I'm doing would work as well or better using another textbook.

Before beast academy, we went through Zig Engelmann's curriculum for 4-year olds (but my student was 5) from the 1960s. It was hard to track down but I thought it was wonderful. I wish it had a sequel.

 

[Not_a_Number]

2 minutes ago, UHP said:

We are just moving on to "Beast Academy 2B" tomorrow, I'm interested to read these takes on it and on its alternatives. My experience with it so far (we finished 2A over the course of about 3 months) is that it's kind of hasty: a child is not likely to read carefully the explanations in the comic book, and the workbook seems to expect a lot of learning to have happened over the course of just 3 or 4 problems when I would have welcomed 30 or 40.

But going through the workbook I often appreciate the miniature skill they are trying to teach next (like, locate the number halfway between 43 and 65 on the number line, or whatever), and figure out how to stretch their 3 or 4 exercises about it into 30 or 40 on handmade worksheets over the course of a few days. To me it seems like a lot of creative thought went into selecting these skills and putting them in order. But I haven't looked closely at anything else, it could be that what I'm doing would work as well or better using another textbook.

I wasn't thrilled about their ordering. But then I'm very, very picky. 

 

2 minutes ago, UHP said:

Before beast academy, we went through Zig Engelmann's curriculum for 4-year olds (but my student was 5) from the 1960s. It was hard to track down but I thought it was wonderful. I wish it had a sequel.

What made it so good? 

[Lori D.]

49 minutes ago, Not_a_Number said:

I guess I don't usually find "whole-to-parts" or "parts-to-whole" to be very useful distinctions in math education. I could just as easily argue that intuiting patterns is "parts-to-whole" learning, since you start with lots of simple examples and build up from there. And I find that algorithmic programs almost don't teach the concepts at all, either in a whole-to-parts or parts-to-whole way. 

Hmmm. What does it mean to be more abstract/algorithm based? Are algorithms abstract because they are removed from the physical world? 

Can you give me an example what kind of thing might click in LoF that doesn't click normally? 

Abstract = non-tangible/concrete in presentation of concepts; in math, symbol (numbers/variables/etc)-based.
Algorithmic-based = equations; set of steps in a process; algorithmic-based math is abstract by its nature.

Saxon is very abstract in presentation (non-visual and non-concrete), and it is very algorithmic based, esp. in the higher maths -- memorize formulas, here's the set of steps for performing the formula, now plug and chug. [MUS is very non-abstract (concrete/tangible) in presentation, using physical manipulatives to demonstrate concepts.]

Yes, you are a math whiz and a natural at math so distinction between "whole-to-parts" and "parts-to-whole" probably is meaningless.

All I can tell you is that my experience is RADICALLY different. I have a VERY VSL DS#2. Abstract, algorithm-based, and parts-to-whole were all MASSIVE melt-down failures here, all the way through high school. He absolutely needed big picture first for context and meaning, coupled with concrete (non-abstract), to have ANY hope of it sticking and being able to internalize the concept.

Whole-to-parts or parts-to-whole probably does NOT matter a lot for the majority of people. But for those at the two ends of the bell curve, it absolutely DOES matter. That has just been my experience.

Extreme Visual Spatial Learners need context and meaning. Those provide connection to the VSL --  the "why should I care" or "what does this have to do with anything" is very important to VSL. Since they already struggle with that which is abstract (non concrete/tangible), they are lost right out of the gate if there is also no context and meaning. Whole to parts does that for VSL -- it gives them context and meaning from "big picture" to then work down into the parts. -- starting with parts and trying to get them to build up  

For VSL that context and meaning comes through:
- tangibleness; physical demonstration and/or hands-on (MUS) -- ability to actually SEE context
- story (LoF) -- provides context (real-world application) AND a "reason to care" (we all want to know how stories turn out)
- real-world context/application (Jacobs Algebra) -- provides context ("this concept really is used and is useful in the real world: here's how")

__________________________

@lulalu: LoF is just a suggestion. I was thinking it was available as an e-book or pdf file, which would make it more accessible to you, but alas, I'm not seeing it in that format anywhere. I do see a few random web links where you can either download the first book, or see samples of one or two of the other elementary levels. Looking at samples will most likely help you decide if LoF is a fit or not.

Wishing you all the BEST in your elementary math adventures overseas! Warmest regards, Lori D.

Edited March 3, 2021 by Lori D.

[Not_a_Number]

9 minutes ago, Lori D. said:

Yes, you are a math whiz and a natural at math so distinction between "whole-to-parts" and "parts-to-whole" probably is meaningless.

No, that's not really what I mean. I've taught a lot of people over the years. 

[Not_a_Number]

10 minutes ago, Lori D. said:

Extreme Visual Spatial Learners need context and meaning. Those provide connection to the VSL --  the "why should I care" or "what does this have to do with anything" is very important to VSL. Since they already struggle with that which is abstract (non concrete/tangible), they are lost right out of the gate if there is also no context and meaning. Whole to parts does that for VSL -- it gives them context and meaning from "big picture" to then work down into the parts. -- starting with parts and trying to get them to build up  

What I'm really saying is that I find that most kids do best with context and concreteness. 

[lulalu]

I will look at some samples of LOF. 

Ds really does love to figure things out by trial and error. And he loves puzzles to figure out. We have done some from MEP because they are well done and free. 

I am a very visual learner and need the big picture first. But ds is not as much as I am. He likes to struggle and figure things out, and then it is learned and stays there. I can always tell if he isn't understanding something easily. Then I just need to provide more time for him to play around and figure it out. 

[smfmommy]

If you don't care for Beast Academy but like their puzzles, they have separate puzzle books for levels 2 and 3 (and eventually the others).  You could add those to your arsenal for variety.

 

[UHP]

21 minutes ago, Not_a_Number said:

I wasn't thrilled about their ordering. But then I'm very, very picky.

We will be going through their treatment of "expressions" before long, if you remember anything you did to improve it I would be grateful. Is that where your warning about "45 + 10 + 5 + 8 + 9  = 55 = 55 + 23 = 78" comes from?

45 minutes ago, Not_a_Number said:

What made it so good? 

I wrote a little bit about it on a blog, if I paste a link here is it possible for me to remove it later? It's not actually sensitive but I've been hesitating for a few minutes in a row now to press send.

[Not_a_Number]

17 minutes ago, UHP said:

We will be going through their treatment of "expressions" before long, if you remember anything you did to improve it I would be grateful. Is that where your warning about "45 + 10 + 5 + 8 + 9  = 55 = 55 + 23 = 78" comes from?

I can't quite remember. It was in some place with really long additions. 

17 minutes ago, UHP said:

I wrote a little bit about it on a blog, if I paste a link here is it possible for me to remove it later? It's not actually sensitive but I've been hesitating for a few minutes in a row now to press send.

Oh yeah, you can edit posts. 

[UHP]

1 hour ago, Not_a_Number said:

What made it so good? 

The author of "Teach your child to read in 100 easy lessons" wrote a book a while earlier called "Give your child a superior mind." Towards the end he gives instructions for how to teach math to 4-year-olds. They are a little more dense than the hundred easy lessons but still detailed, and I tried them out with my 5-year-old. I typed up an excerpt of how it starts here.

[Not_a_Number]

13 minutes ago, UHP said:

The author of "Teach your child to read in 100 easy lessons" wrote a book a while earlier called "Give your child a superior mind." Towards the end he gives instructions for how to teach math to 4-year-olds. They are a little more dense than the hundred easy lessons but still detailed, and I tried them out with my 5-year-old. I typed up an excerpt of how it starts here.

Ooh, I do like 100 EZ Lessons... used it for both kids. 

I like the looks of that lesson 🙂 . I also start with "adding 1" as an early lesson, although I do a range of small numbers and not just 1. 

[Lori D.]

@Not_a_Number -- just want to apologize -- I was just rereading my post for errors and clarity, and one sentence sounded snarky in my response to your questions upthread. I don't "do snark" (lol) -- hopefully others who have been on these boards for a long time will verify that for me 😄 -- and I also don't want any of my posts to sound snarky. Just wanted to make sure there were no hurt feelings from my poor wording. Thank you!

[Not_a_Number]

9 minutes ago, Lori D. said:

@Not_a_Number -- just want to apologize -- I was just rereading my post for errors and clarity, and one sentence sounded snarky in my response to your questions upthread. I don't "do snark" (lol) -- hopefully others who have been on these boards for a long time will verify that for me 😄 -- and I also don't want any of my posts to sound snarky. Just wanted to make sure there were no hurt feelings from my poor wording. Thank you!

Oh, Lori, I didn't think you were being snarky!! I'm the snarky one. You're the kind one. I've been on here for a long time!! 

[lulalu]

2 hours ago, smfmommy said:

If you don't care for Beast Academy but like their puzzles, they have separate puzzle books for levels 2 and 3 (and eventually the others).  You could add those to your arsenal for variety.

 

That sounds more like what I would like. Thanks, I will look into these. 

[Lori D.]

1 hour ago, Not_a_Number said:

Oh, Lori, I didn't think you were being snarky!! I'm the snarky one. You're the kind one. I've been on here for a long time!! 

lol. How about we agree that neither of us is snarky. 😉 

But, I think we'll have to agree to disagree on one thing: the definition of "a long time."  I've been continuously active on these boards for 19 years -- now THAT is what I call "a long time". 😂 (Or, maybe that's just ancient... 😉 )

[Not_a_Number]

31 minutes ago, Lori D. said:

lol. How about we agree that neither of us is snarky. 😉 

But, I think we'll have to agree to disagree on one thing: the definition of "a long time."  I've been continuously active on these boards for 19 years -- now THAT is what I call "a long time". 😂 (Or, maybe that's just ancient... 😉 )

You're right that you're ahead of me there! Let's just say I've been on here enough to know the people who are never snarky 🙂 . 

[Shoes+Ships+SealingWax]

I find it very interesting that nearly every content-related complaint I’ve seen about BA has to do with Pirate Numbers. We were living overseas when 2nd grade was released & couldn’t get our hands on them, so we started with 3A. 

I will say the online platform was a complete flop here.  ADHD + a million possible directions to go in + no requirement (or even prompting, really) to read the Guides + SO MANY BRIGHT COLORS = 🤯

[Not_a_Number]

6 hours ago, Shoes+Ships+SealingWax said:

I find it very interesting that nearly every content-related complaint I’ve seen about BA has to do with Pirate Numbers. We were living overseas when 2nd grade was released & couldn’t get our hands on them, so we started with 3A. 

I will say the online platform was a complete flop here.  ADHD + a million possible directions to go in + no requirement (or even prompting, really) to read the Guides + SO MANY BRIGHT COLORS = 🤯

Maybe because many people only did the 2nd grade program? 😉 

I think it’s silly they never get to long division, for what it’s worth. I haven’t examined the rest of their stuff, though... do you have any complaints about any of it?

Personally, having flipped through it, I also like much more variable exposure than they do. They do some, but it’s not consistent. 

They also don’t do nonstandard equations, which was also important to me — that is, equations with an equals sign not right before an answer.

[Eilonwy]

We’ve used both BA (books, main) and LoF (supplement). With BA, my oldest started at 3C (now in 5C)  and my middle started at 2A (now in 3C).  I thought the level 3 books were better than the level 2, on the whole, and there was definitely not enough coverage of place value, which we had to work on more outside of the program.      I really like how they approach the micro-skills that @UHP referred to, and the puzzles.  It is odd that they don’t do “standard” long division. 

With LoF, the author tries hard to connect math to Fred’s life, but I didn’t find it had particularly clear explanations of math concepts. It seemed a bit scattered, the author’s firm opinions on some subjects bled though, and the story that connected it all together got kind of dull for my kids. Some kids probably love it, though. Fred’s life is rather odd, so I’m not sure the goal of connecting math to real life is entirely achieved. It is also not particularly puzzle-y, in my opinion. We can get it at our library, maybe that’s an option to have a look at a whole book.

Edited March 4, 2021 by Eilonwy

[Not_a_Number]

10 minutes ago, Eilonwy said:

I really like how they approach the micro-skills that @UHP referred to, and the puzzles.

What micro-skills did they address? I’m now curious!

[LauraClark]

To your original post (I can't speak to any of the suggested maths-we use R&S for our base): we took a couple month break from curriculum last year and did our own thing. It was somewhat challenging just because I like to tinker and do my own thing with a lot of our curriculum so adding in one more thing was a bit much. I still do that some-if ds9 or 7 are struggling with some concept I'll just make my own stuff until they figure it out. It is very helpful to have a curriculum just to have a direction: I feel very confident I would leave holes if I just totally did my own thing.  Making your own math might be a path to burnout, but if you're loosely following a curriculum and you suddenly feel like it's too much you can just switch to the curriculum for a break. In my non-professional opinion if you do that then the curriculum you use for a guide doesn't even matter that much because you're doing your own thing. I've run into what you describe with a lot of different subjects (it's like they're always rotating around to be a problem subject...) and I've made my own curriculum for various subjects at various times. I've gotten lots of encouragement here from others who have done the same thing. 

[Not_a_Number]

3 minutes ago, LauraClark said:

It is very helpful to have a curriculum just to have a direction: I feel very confident I would leave holes if I just totally did my own thing. 

I think that's a pretty reasonable concern! It really depends how much of a handle you have on what ought to be covered. I don't think I'd feel confident doing this for anything other than writing and math... well, I don't mind unschooling the content subjects somewhat, but that's because they are much less sequential and I'm not really worried about leaving holes per se. 

For what it's worth, though, I knew what key concepts I wanted to communicate, and I didn't really mind if I left minor holes if they weren't in essential subjects. Right now, we've started focusing on the AMC8, and there are things she hasn't seen (we've been practicing mean, median and mode, for example), but they are practically all of the form "here's a definition, now you know it." In my opinion, as long as you get the important basics down, you can always fill stuff in around the edges as needed. 

[Shoes+Ships+SealingWax]

1 hour ago, Not_a_Number said:

I haven’t examined the rest of their stuff, though... do you have any complaints about any of it?

Not particularly. We’ve needed more practice on a section or two, but I expect that to happen with any curriculum. It suits us far better than anything else we’ve come across, DS is excited to tackle it, & it means I don’t have to reinvent the wheel - I’m content. 

[kirstenhill]

1 hour ago, Not_a_Number said:

 

Personally, having flipped through it, I also like much more variable exposure than they do. They do some, but it’s not consistent. 

They also don’t do nonstandard equations, which was also important to me — that is, equations with an equals sign not right before an answer.

The 3rd chapter of 5A is completely dedicated to variables. I just did that one with DS9.  Is this photo like what you were talking about with non standard equations? There are definitely a few like this, plus word problems that would result in this style equation. 

 

[Not_a_Number]

2 minutes ago, Shoes+Ships+SealingWax said:

Not particularly. We’ve needed more practice on a section or two, but I expect that to happen with any curriculum. It suits us far better than anything else we’ve come across, DS is excited to tackle it, & it means I don’t have to reinvent the wheel - I’m content. 

I'm sure that the difference is that I like reinventing this specific wheel, lol. 

Also, I've seen far too many kids who couldn't do algebra in one way or another when I taught college calculus, so I had all these ideas how to make sure that kids could do algebra well eventually 😄. And then I couldn't find anything else that did what I wanted. Plus, I learned all sorts of weird things about mental models when I was messing with AoPS precalc... 

[Not_a_Number]

1 minute ago, kirstenhill said:

The 3rd chapter of 5A is completely dedicated to variables. I just did that one with DS9.  Is this photo like what you were talking about with non standard equations? There are definitely a few like this, plus word problems that would result in this style equation. 

 

Yeah, I've seen it, but I really like more of a slow burn with variables 🙂 . Starting them as "shapes to fill in" and interspersing them throughout the curriculum. I really love using them throughout elementary education to get a really robust variable intuition. 

Edited March 3, 2021 by Not_a_Number

[UHP]

You might be interested in looking at how Engelmann treats variables. My 5-year old, and his 4-year-olds, learned to interpret and solve 6+B = 7 before they learned about the subtraction sign. One tip for teaching variables to small children, is to not use the letters X or Y or Z or S or T, they look too much like numerals. Whether or not this will make anything much easier down the road, well I only hope.

 

[Not_a_Number]

1 minute ago, UHP said:

You might be interested in looking at how Engelmann treats variables. My 5-year old, and his 4-year-olds, learned to interpret and solve 6+B = 7 before they learned about the subtraction sign. One tip for teaching variables to small children, is to not use the letters X or Y or Z or S or T, they look too much like numerals. Whether or not this will make anything much easier down the road, well I only hope.

We use shapes! We fill in squares and triangles and pentagons and occasionally circles (they are much bigger than 0s, or they wouldn't work.) 

[Not_a_Number]

2 minutes ago, UHP said:

You might be interested in looking at how Engelmann treats variables. My 5-year old, and his 4-year-olds, learned to interpret and solve 6+B = 7 before they learned about the subtraction sign. One tip for teaching variables to small children, is to not use the letters X or Y or Z or S or T, they look too much like numerals. Whether or not this will make anything much easier down the road, well I only hope.

DD8 is now far enough into math that I can tell for sure that doing variables early was useful. She's obviously very accelerated, but she also has VERY good variable intuitions in a way that lots of bright kids I knew didn't. 

[UHP]

4 hours ago, Eilonwy said:

 I really like how they approach the micro-skills that @UHP referred to, and the puzzles.

NotANo. asked for examples. Here are three that are fresh for me, from the last few pages of workbook 2A.

1. Add a little, then take away. "Adding 19 to a number is the same as adding __, then taking away 1."

2. Ones digit. "Circle the two numbers from (243, 244, 245, 246, 247, 248) that have a sum with ones digit 4."

3. Adding numbers in a clever order, "What is the sum of five 16s and five 34s?"

I worry there's no advantage in having the kid solve just one of these problems and then move on, especially if she needs a lot of help to get through it. I've been improvising a lot of tiny variations on them, that I spread out over a few days.

[Not_a_Number]

6 minutes ago, UHP said:

NotANo. asked for examples. Here are three that are fresh for me, from the last few pages of workbook 2A.

1. Add a little, then take away. "Adding 19 to a number is the same as adding __, then taking away 1."

2. Ones digit. "Circle the two numbers from (243, 244, 245, 246, 247, 248) that have a sum with ones digit 4."

3. Adding numbers in a clever order, "What is the sum of five 16s and five 34s?"

I worry there's no advantage in having the kid solve just one of these problems and then move on, especially if she needs a lot of help to get through it. I've been improvising a lot of tiny variations on them, that I spread out over a few days.

Thank you! That explains it. 

Our homeschooling has always been VERY conversational, so I do take a very different tack from what they do. I mention these ideas, and if they seem intuitive enough for the kid to catch on, I keep coming back to them over and over, until they are internalized. 

I'd also worry about seeing it once and moving on! I like more of a spiral 🙂 . 

[R828]

 

15 hours ago, lulalu said:

That sounds more like what I would like. Thanks, I will look into these. 

As someone who has only used BA 2A take what I say with a grain of salt....I think BA is great for review, because it really encourages thinking about and playing with ideas. But there is no way I would want to use it as a primary curriculum. It moves way to fast and doesn’t seem to lay as strong a foundation as I would like. It’s great for review though. 

I’m also considering using only the BA puzzle books and not the entire curriculum. From the samples I’ve seen, I think the puzzle books would work great for what you are wanting. 

[Not_a_Number]

1 minute ago, R828 said:

As someone who has only used BA 2A take what I say with a grain of salt....I think BA is great for review, because it really encourages thinking about and playing with ideas. But there is no way I would want to use it as a primary curriculum. It moves way to fast and doesn’t seem to lay as strong a foundation as I would like. It’s great for review though. 

I’m also considering using only the BA puzzle books and not the entire curriculum. From the samples I’ve seen, I think the puzzle books would work great for what you are wanting. 

I’ve heard people say it gets better. I do think they are extra perfunctory with place value.

[Shoes+Ships+SealingWax]

4 hours ago, UHP said:

You might be interested in looking at how Engelmann treats variables. My 5-year old, and his 4-year-olds, learned to interpret and solve 6+B = 7 before they learned about the subtraction sign. One tip for teaching variables to small children, is to not use the letters X or Y or Z or S or T, they look too much like numerals. Whether or not this will make anything much easier down the road, well I only hope.

 

Yeah, I introduced DS to the idea of variables around the same time. He was working through Singapore 2 & getting frustrated with drawing out bar models for everything. We’re both very algebraic thinkers so he grasped it immediately. 

[Not_a_Number]

1 minute ago, Shoes+Ships+SealingWax said:

Yeah, I introduced DS to the idea of variables around the same time. He was working through Singapore 2 & getting frustrated with drawing out bar models for everything. We’re both very algebraic thinkers so he grasped it immediately. 

I do wonder if bar models are actually useful or not. I mean, I’m absolutely sure they can help kids solve things, but I wonder if it’s the best model for long-term retention of the strategies.