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NEM? Dolciani? What to do with my youngest... (long - sorry)


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This is long. Sorry.

 

After a few confusing years of ps Everyday Math and a year of Saxon 56 during which he did fine solving the problems and memorized the standard algorithms but still couldn't apply his math, my older son did PM3B-6, then the first maybe five? chapters of NEM. Then he paused to do Keys to Algebra 1-3 to cement "all those little rules" (his words), then we continued on in NEM. He did NEM1, NEM2, NEM3, and then he went off and did pre-calculus at the community college with Blitzer. Now he is doing technical calculus at college and he says he "rocks" at the algebra part compared to the other students. He is struggling with the calculus. This doesn't surprise us. He has always struggled mightily with math.

 

I kept him in Singapore because I had a strong feeling that he just wouldn't understand how to apply his math if he used a different book. Sometimes I wish that I had done Dociani with him, but then I remember my own high school's math classes. We used Dolciani. Only about 20 of us out 200 did calculus in 12th grade, so I think perhaps it isn't a magic bullet. I remember that I struggled with word problems that my son solved easily, even though I was several years ahead of him in math and doing that Dolciani. I also have trouble judging the Dolciani because my father did my math with me and taught me what he called the engineering way of doing things. This definately wasn't like I was being taught at school. It was more like Singapore than Dolciani.

 

Now I have to make the same decisions for my youngest. He is in 9th now and doing NEM3. I am wondering if I should switch him to Dolciani because I remember doing lots of things in 9th grade that he isn't going to get in NEM3 or even NEM4, like logs and matrices and series. I know my son could go straight into CC pre-calc next year after completing NEM3 (and we'd probably get to bits of 4) but he might want to peacewalk, which doesn't mix well with CC classes. Or he might not. Would those missing bits come back to haunt him later on in engineering school? I remember having a whole extra computer science math class that covered many of those bits. It was a waste of time for me because I had had all that in high school, but the fact that it was required might mean that my son would be fine if he doesn't do it in high school. Is there any advantage to getting through all of the CC's two semesters of pre-calc and their three semesters of calc before going to college?

 

Do I switch him to Dolciani algebra 2? I bought an old used one. (That is how I know we used it in high school. When I unwrapped it, my husband and I groaned. It brought back all sorts of memories.) It does indeed have those missing things. Then what happens to geometry? I figured out where those missing bits are in Singapore - NAM, which the more advance math students take concurrently with NEM3 and 4. We, however, are already spending between two and three hours a day on math. I can't imagine adding in NAM. We might have time to get to a few chapters of NAM at the end of this year if my son doesn't go walking for too long. I spent less than two hours on math in high school. I don't think this son is any less mathy than I was, so... so what? Is NEM particularly arduous? Is it worth it? Can we jump into Dolciani midstream? Do I suppliment with Dolciani? If he waits another year and doesn't do pre-calc until 11th, then he could do Dolciani Algebra 2 and/or NAM in 10th, but what would I call it on his transcript? Integrated Math 4? Questions, questions...

 

So the issues are:

Time spent each day

Time available each year (with peacewalking)

Peacewalking not mixing with community college (he would vanish mid-semester)

Missing bits

Geometry (included in NEM but not in Dolciani)

I like the applied-ness of NEM

Advantage of getting two semesters of precalc and three of calc at CC before going to college

 

My son himself wants to just keep doing NEM and add in NAM.

The community college says they will look at everything and offer advice.

Before I go talk to them, though, I'd like to know what the hive thinks.

 

-Nan

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Hi Nan,

My oldest followed a sequence similar to the one your 9th grader is walking now. He did NEM 1, 2, and 3 in 7th - 9th grade. He also did Key to Algebra and somewhere between NEM 1 and 2 he also fit in Dolciani Alg 1. He didn't do all of Dolciani Alg 1, just the word problems and just cause he had time between when he completed NEM and the end of the school year.

 

From NEM 3 I moved him into Dolciani Algebra 2 with Trig. We skipped many of the early chapters since the material was well covered in NEM. He did spend time on complex numbers, logs, matrices. He worked through the Algebra 2 book toward the end of 9th grade and some of the fall of 10th grade.

 

Sometime when I was planning his high school math series I sat with the NEM books and several Geometry books comparing topics covered and decided that he really had covered geometry in NEM 1 - 3 so he could skip a formal geometry course.

 

Then I made a HUGE mistake. I placed him into Pre-Calc using a Foerster book for 10th grade when he was really ready to go into Calculus. The Pre-Calc was such a repeat of Dolciani 2 w/ trig and I just did not get that early enough to move him into Calculus (I was also dealing with the death of my Dad that year and handling the estate...) Life goes on and DS will some day forgive me for messing up his high school math sequence. I have told him though that he did learn to use a graphing calculator that year :)

 

My point is that after Dolciani Algebra 2 a child could move directly into Calculus. And much of the Algebra 2 was a repeat of NEM 3!

 

Planning, ahhh, never ends.

 

Carole

Edited by Blue Hen
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Can't help with the specific math programs, Nan, but here are a few questions that might help you back up a little and get a "bigger picture", which then might help in figuring out a math progression, FWIW. ;) BEST of luck in figuring out what your math -- and overall homeschooling -- journey should look like for this DS. Warmest regards, Lori D.

 

- What are your overall homeschool goals for this DS?

- What do YOU most want to instill in him (and hence, spend most time with him)?

- What field is DS interested in, or leaning towards? How much math would be required for that? Is the amount of math you're doing now overkill for that?

- How interested is he in math now? Several hours worth a day?

- What about other interests? Could the math be spread out over the 4 years of high school to allow more time for other interests / coursework?

- What do YOU want to teach him? The math? Or if something else, can you leave off after NEM2 or NEM3 and let CC take care of the rest of his math?

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He's headed for engineering, as far as we can tell at this point, so no amount of math that we can cover will be overkill. He isn't really objecting to the amount of math, just to the amount of homework. I don't think he's noticed how much he's been doing. He doesn't dislike NEM, and when I've inquired about video programs or something else more self-teaching, he hasn't been interested. He likes having me teach him math. I feel like all I'm doing is reading the textbook aloud, but apparently that is important to him. I'd rather do it this way, too, because this way I'm reminded of what I'm doing. I don't remember any of it until I read about it. I want to teach up to pre-calc, but I'd rather the CC took over at that point, mostly because of transitioning into classroom learning. I feel like I wouldn't have any trouble teaching through calc - I've had it even if I don't remember any of it, but the transition is probably going to be tougher for this one, who only went to kindergarten, than for his brother, who had done through 4th grade. I want him to far enough in math to make him desirable to an interesting engineering school, not just something blah. The CC said they would help me take a guess at how far he should go. Off the top of their head, they said they thought he should peacewalk rather than take more calc. From the point of view of general educational goals, I agree. I just don't want to botch the college-prep part.

Thank you for the list. It all feels rather muddled and that helps.

-Nan

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Then I wonder what I did in 11th grade? I think it was called linear algebra? What is that? I seem to remember redoing all our algebra with the function sign, and that not making any sense to me at the time because since they seemed to follow all the same rules, I didn't see what the big deal was. It certainly wasn't called pre-calc. Maybe we did more trig? That is very useful information about the geometry. Thank you. Food for thought. My older one said some of the pre-calc was review. He tested into CC pre-calc after NEM1 and part of NEM2, but we didn't think he was ready so we waited another year. He said he did some guessing.

-Nan

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Then I wonder what I did in 11th grade? I think it was called linear algebra? What is that? I seem to remember redoing all our algebra with the function sign, and that not making any sense to me at the time because since they seemed to follow all the same rules, I didn't see what the big deal was. It certainly wasn't called pre-calc. Maybe we did more trig?

-Nan

 

Nan,

 

If you and your husband used Dociani in high school, as I did, you may have followed Algebra II/Trig with a course called Analysis. Dolciani's version of Precalculus is more theoretical than the modern precalc text. As Carole (Blue Hen) pointed out, an engineering oriented kid could jump from Dolciani's Algebra II/Trig text to Calculus. My son is not mathematically oriented, but I still had him work through the Analysis text. My kid likes physics so I will not be surprised if someday he pursues something there. Thus I wanted him to have a more theoretical background. If you think your youngest is more algorithmically oriented (which is usually the preferred path of most engineers), you could have him do Algebra II/Trig at home and then test at the CC to see what follows. Some CCs want all students to begin in a Precalculus class so he may repeat the material. Or he may be able to jump into a Calculus course.

 

Sorry that I can't comment on the NEM business since I do not own those books.

 

Jane

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Hmm... Now that you mention it, I think Analysis was in the title, too. I think it might have been Linear Algebra and Analysis? And it is funny - you are saying exactly what my middle son said when I asked him what he thought his younger brother should do. He said something like, "Why on earth would you want to switch away from NEM? I rock at algebra compared to the other kids in my class. NEM is engineering math and he's going to be an engineer." (I'm not surprised if he can do algebra better than the rest of his class- not because he's good at algebra but because all the mathy students are in a different calculus class.) Part of me is worried by youngest's fascination with physics though, and wonders if he is going to wind up being a physicist or something. I probably shouldn't worry. This one has mechanical engineer written all over him. The middle one has the more theoretical brain; he is finding his fundamentals of engineering class easy but boring. The youngest is more like the oldest; they like hands-on. Thank you very much for your input. Bit by bit this is unmuddling.

-Nan

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You're making me want to look at NEM.

 

When I was getting my master's degree, most of my classmates (all of whom obviously already had a bachelor's) could not do very basic algebra. It was .... scary.

 

By the way, I don't want to overwhelm you with info, but the Indian government has put all their texts online. It might at least be fun to look at. The easier site from which to download them is http://ncertbooks.prashanthellina.com/ .

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Oooh! Thank you! This is great! I would love to look at them. I've been curious about other countrys' math ever since someone posted that site about international competition. Something billion???? Was that you?

My son seems to be having an international year: math from Singapore, history and language arts from France, literature from the Med (TWTM great books ancients). Science is from our back yard, so I guess that evens it out LOL.

Thank you.

-Nan

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He's headed for engineering, as far as we can tell at this point, so no amount of math that we can cover will be overkill.

 

 

Knowing that then, should help a little in figuring out a math progression

 

 

 

He isn't really objecting to the amount of math, just to the amount of homework.

 

 

Can you just "pick and choose" your way through some of these additional texts you were asking about, rather than doing the ENTIRE textbook? That way you can hit the topics you're not getting through NEM, and you don't have to spend an entire year on a textbook when some of it is review. That does require you spending some time going through the text and highlighting what you want to cover and also making sure that you don't also have to do a quick review of something covered in a previous lesson necessary to the lessons you are interested in...

 

 

 

He likes having me teach him math. I feel like all I'm doing is reading the textbook aloud, but apparently that is important to him.

 

 

Our older DS is a very auditory learner and he really likes this too. :001_smile: This year (age 17, gr. 11) is the first year he has decided to go ahead and do it all himself.

 

 

 

The CC said they would help me take a guess at how far he should go. Off the top of their head, they said they thought he should peacewalk rather than take more calc.

 

 

Oh, that is very helpful! I really think that colleges are looking for well-rounded students -- not just straight academics from a student. And the older our students get, the less opportunity they have life experiences, try things outside the schooling, develop interests/leadership/character qualities, etc. So if the CC is even encouraging the peacewalk (or if it ends up being some other interest), I'd say, definitely do it!

 

 

 

From the point of view of general educational goals, I agree. I just don't want to botch the college-prep part.

 

 

Nan, I REALLY don't think at this point it would be *possible* to mess him up for college prep -- you're already way ahead in math, you're doing and enjoying science at home, you've got your foreign language just about finished... You've just about got all the required credits all done already. Now you can more focus on specific programs you want to cover, and use these last years to really pour into his heart. Warmest regards, Lori D.

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Can you just "pick and choose" your way through some of these additional texts you were asking about, rather than doing the ENTIRE textbook? That way you can hit the topics you're not getting through NEM, and you don't have to spend an entire year on a textbook when some of it is review. That does require you spending some time going through the text and highlighting what you want to cover and also making sure that you don't also have to do a quick review of something covered in a previous lesson necessary to the lessons you are interested in...

 

 

 

This is also how we've been attacking math for the past few years. One of my kids is interested in a science or engineering career. We've used a combination of Saxon Advanced Math and Blitzer for precalc, then Saxon for physics and calculus. The book we're using for a "spine" is Engineering Mathematics by Stroud.

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Well, that is comforting, I guess. You haven't seen his writing, though. And I sure wouldn't want to graduate him with the amount of science he's had so far. It probably isn't any worse than some bad high school, though. You are right. And he's even been through enough literature, albeit in a not very mature way. I guess you are right and he probably is about where a bad student from a bad high school is when he graduates. Considerably ahead in a few areas, even. I never looked at it that way. The only real comparison I have for him is his friends, whose schoolwork I don't see but who discuss things in the car when I drive them places and always worry me. Well, they worry me when they aren't chattering away about how if they had a black death dragon with a penitrating eyeball they could roll a 2d6 and wipe out their friend's hord of slathering creepers. The rest of the time they talk about what a cool play Waiting for Godot is or how cool it was to turn a penny silver or their latest debate.

-nan

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. The only real comparison I have for him is his friends, whose schoolwork I don't see but who discuss things in the car when I drive them places and always worry me. Well, they worry me when they aren't chattering away about how if they had a black death dragon with a penitrating eyeball they could roll a 2d6 and wipe out their friend's hord of slathering creepers. The rest of the time they talk about what a cool play Waiting for Godot is or how cool it was to turn a penny silver or their latest debate.

-nan

 

 

This evening one of my dd's classmates from gr 1 (she was in ps K-2) was talking about his honours Geometry class. Not only are they doing 2 column proofs, but they have to do written projects. One was on a number of mathematicians (Euclid, et al), and another had to do with triangles. The latter either had to be a 2-3 page written paper, or a poster with a number of specific triangles drawn on it with a one page paper. He also hates paragraph proofs (they're doing both) and I've just decided to switch dd's supplementary Geometry to one with paragraph proofs because they have the logic written in the answer key, and I can follow the logic. I can't grade the 2 column proofs in the old Dressler. Makes you think, doesn't it? I've been following this thread since you posted it and am chiming in on this tangent, but it gave my pause to wonder if my course is honours level or not. I don't plan to call it that, but want it to look like one. Perhaps I'd better pull the history of math book I have out and have her start reading it or something. She does want to pursue sciences/math.

 

Wai

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Yup. There is no way I can offer an academic education that is even close to the one our public school offers, to say nothing of better. We keep homeschooling because I think at home my children can learn some things the public school can't teach them, non-academic things that might be more valuable than the academic ones; and because we learned the hard way that our particular children don't learn well in school. The reason I keep periodically panicking over this third child is because I think that he actually could learn in school. His friends are definately getting a better academic education, and they are doing all sorts of cool extra things as well. I have done a much, much better job at getting him speaking and understanding a foreign language, although he'd write it better if he'd learned in school. The problem is that he isn't going into French; he's headed for engineering. As a future engineer, it is very nice for him to be able to do history and great books comfortably at home with me in a more engineering-suitable, accessible sort of way, but I feel I would be doing him a disservice as a future engineer if I provide good foreign language, a few interesting non-techinical projects, more suitable literature and history, but inferior math and science. If an interesting college accepts him, then I'm willing to settle for that and a bit of free time, but if they don't, then I am afraid that the advantages I can offer at home, many of which consist of inferior academics, either deliberately so or accidentally, won't balance the disadvantages. We're not even considering sending him to public school, but I am still trying to do the best I can, trying to offer him good non-academic learning outside his future field and non-academic learning inside his future field and good math and science and non-techinical academics since this is his last chance to learn that before focusing on technical subjects in engineering school. It is a lot to balance. So far I am managing to do half of that, the non-technical/math/science half, but I feel like I'm not doing a good job at the technical stuff. My other problem is that we delayed sending him to public kindergarten (the only grade he did in school) because at 5 I was still carrying him around all the time (very little and light, and youngest). So now he is a 15yo 9th grader. So part of what I compare him to his where I was academically at 15: he's ahead in the French, a little in the writing/literature, about equal in the science, and behind in the math.

I don't know. I go round and round. Thank you for posting. Everyone here is always saying how superior their homeschooling is to their local public school. Maybe I wouldn't worry so much if I lived some place else. At least our CC offers good science and math.

-Nan

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You've brought up many key questions about education...

At least our CC offers good science and math.

I think, though, that if your son has a very good foundation, it can be built upon, and by calling upon the community colleges, you are setting up a way for this to occur. You also are perceiving your son as a whole person, instead of only evaluating his academic progress/prowess in math, and that is a valuable perspective. There are plenty of lopsidedly educated people in all fields, including in engineering, who lack other skills, such as social, and if your children don't do well at school (academically or otherwise), then it's not much good to compare to what they could have done, because what could have happened might have been negative, after all. You don't want a young Galois on your hands.

 

I think your interest in involving the community college, and any other outside tutor or supplementary activities, will help fill the gap, but your humbleness is probably helpful in staying realistic and opening yourself up to additional opportunities instead of staying content.

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The problem is that he isn't going into French; he's headed for engineering. -Nan

 

 

Having a second language could really open up doors for him once he gets a degree in engineering. The other things you're teaching will help him to be more well-rounded. But, since I've been worrying lately and my first is a freshman, I don't have any sage advice to offer.

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I think, though, that if your son has a very good foundation, it can be built upon, and by calling upon the community colleges, you are setting up a way for this to occur. You also are perceiving your son as a whole person, instead of only evaluating his academic progress/prowess in math, and that is a valuable perspective. There are plenty of lopsidedly educated people in all fields.

 

This is so true.

 

And realistically, there just isn't enough time in the day to do each subject with the same degree of focus, so in most cases, something's got to give. :)

 

My eldest is a freshman in college. He was well-prepared in math, but one of the areas we skimped on was literary analysis. (My fault entirely, because I like to read for pleasure, rather than dissect the books.) :tongue_smilie: He's now taking a required freshman course in literary analysis, and he's had to make a huge leap along the learning curve in a short time in that particular subject. So it would have been better had we done more of it, and now I'm making a bit of a course correction in that regard with my younger kids. But the truth is, no one can be a specialist in everything, so all we can do is strive for balance within the big picture (eg. a student whose bent is in liberal arts should take some math, but can get by without calculus, and a kid who wants to be an engineer should have adequate exposure to the liberal arts but is likely better off putting the lion's share of his time into math rather than multiple years of Latin). And as parents, it's not our responsibility to prepare them for every eventuality, but to attempt to imbue them with the skills necessary to pursue their interests, and more importantly, to teach them how to live well-balanced lives.

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What I've noticed also about engineering types is a sort of creative approach to problem solving. I don't know what exactly one does to encourage/develop this, but I think jumping around and trying different things, and playing with challenging problems (are these any good? Challenging Problems in Algebra pub by Dover), keeps the brain from sticking too closely to just answering the problems in the book. How much thought is really involved in figuring out that one needs to use the quadratic equation to solve the problems in Chapter 6, Section 2, titled "Solving Equations with the Quadratic Equation" ? Not much.

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LOL - My son is currently struggling through 2.4 Problems Leading to Quadratic Equations. It is taking him forever to set up the problems. The ones at the beginning are easy to set up: A lawn 46 m by 34 m has a path of uniform width around it. If the area of the path is 425 square meters, find its width. Then they get harder and he slows way, way down: A room can be paved with 1210 square tiles. If the side of each tile were to increase by 1 cm, it would only take 1000 tiles to pave the room. Find the dimensions of each tile. I'm not sure why he is so slow.

 

My husband excels at creative problem solving and it has stood him in good stead in his engineering jobs. I would love to teach it to my son, but I don't know how. My son loves those long involved strategy games involving lots of little models and dice, D+D or Warhammer types. As far as I can see, those involve manipulating complex systems. Perhaps that will help? NEM has a problem solving page after each chapter, but my son can seldom solve the problems. I keep hoping trying and then looking at the answer will help, but it doesn't seem to be.

 

Good old Dover. I have a Dover book on problem solving. I should look at it again. And I'll look at the look-inside pages of your Dover book and see how it differs from NEM. Gelfand (think I got the name right) Algebra is supposed to have good problems, ones that really require you to think.

 

More to do GRIN. Working on creative problem solving IS actually something I can do. At any rate, I can do it more easily than trying to find a way for him to learn robotics or something. And it is a sort of math that he won't find boring or tedious and be unhappy about doing. Thank you very much for the suggestion.

 

-Nan

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Well-balanced lives... I'm aiming for that. And my son is being fairly cooperative (unlike some technical children). It is hard, though, not to worry about college applications, especially having just done them two years in a row with his older brothers. As I said, left to my own devices, I'd concentrate on that balance and the thinngs he's not going to get in college (along with strong math), and let him learn the technical stuff once there, but it is sort of a can't win situation because if we do that, he might not get in. If you were a college, would you pick the student who had done lots of technical things, demonstrating interest and ability, or would you pick the student who just said they wanted to be an engineer, but hadn't actually done much technical stuff or gone all that far in science and math? I'd be inclined to pick the demonstrably technical-minded student.

-Nan

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left to my own devices, I'd concentrate on that balance and the thinngs he's not going to get in college (along with strong math), and let him learn the technical stuff once there, but it is sort of a can't win situation because if we do that, he might not get in.

 

 

Yes, I know what you mean - I struggle with that as well. So much to do, so little time... :tongue_smilie: And so I've had to let some things go in favor of more important things. And of course, each child is different than the one before him, so that makes for quite a juggling act. :)

 

I don't think you need worry about him not getting in since you're planning on CC for math, so his transcript will show outside validation in the subject area he's planning to pursue as a career. Ideally, if he can sign up for courses where he already knows the material from doing it at home with you first, he'll end up with a higher cumulative average for his transcript.

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"Ideally, if he can sign up for courses where he already knows the material from doing it at home with you first, he'll end up with a higher cumulative average for his transcript." That is another thing I am worried about. Sigh. We signed his brother up for a few easy courses first, so he could get used to going to school before he had to deal with pre-calc and chem. The youngest will have had Hewitt's Conceptual Physics (adapted a bit) in 7th, some of Conceptual Chemistry not done very well (I couldn't seem to manage this as well as the physics for some reason) in 8th, natural history (better than bio for our family) in 9th, and then will do chem and physics at the CC. At least that is the plan. I'm not at all sure this is enough preparation for college level chem and physics, and I'm not sure when to fit in the semester of easy classes. Maybe next fall and then have him not begin chem and physics until 11th... That would give us a year to do fun science, like perhaps that hands-on chem book, or some astronomy, or something. In theory, he'll be ready for pre-calc next year. If BlueHen is right, then perhaps his pre-calc will be easy for him. We'll see where he places. And who knows what my son himself will want to do, and he has a ton of say in all this. I'm trying to hit a moving target.

-Nan

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