My favorite is still the little yellow "Cliff's Notes Geometry" from Wal-Mart for $9.98. :) We kill off traditional Geometry in our house in a summer.

Heather--that is a PERFECT way to teach proofs! Love it! No proof needs to be "exactly like" the answer in an answer key. Frankly, that's why hs parents who aren't math people hate to teach Geometry...it's so much harder than Algebra to grade. I use that strategy with my students in Algebra, even..."Explain your answer." Once they realize that they can't just guess an answer, and that they have to understand what they did in order to get credit, then we can really get down the business of learning math. :)

My daughter always managed well in the 14-17 range of credit hours. I think she took 18 one summer, but not all of them concurrently. She finished her BA in four years, but that was probably 11 semesters (including summers). My younger dd completed 40 hours in high school, but will easily take another five years (LOL) to finish her BA. She's working on an AA in graphic design, and will follow it up at a university in an entirely different field. So it will be a separate, second degree. Anyway, she manages about 14-16 hours each semester well.

Geometry leads very well into PreCalculus as well, particularly the Trigonometric functions. :) Lots of schools are using the Algebra 1/Algebra 2 approach. Then Geometry is taught "algebraically" in the lead in, and developed more toward proof in the middle of the year, ending up with lots of work with trigonometry, and setting the stage for PreCalculus. Lori (who still hasn't decided what I will teach next year to my 9th graders! LOL!)

Honestly, if you get *how* to turn it from a repeating decimal into a fraction, you are doing better than 98% of the free world. I'd accept unsimplified forms of those fractions, particularly for crazy ones like Teachin' Mine's example of N = 10,021,512 / 9,990,000 which could certainly be simplified by dividing by 2 or 4 or maybe even 8 (LOL), but goodness, it's enough that the kid got the problem IMHO. LoriM (who has to look up that procedure EVERY YEAR I teach it! LOL!)

I just wanted to say I agree entirely with Nan. :) She's a genius, and you should listen to her. LoriM PS As far as the "grade" bit goes, I teach in a school. I allow corrections on daily homework to bring homework back up to 100%, but on tests only "halfway" to 100%. So, I'd let him fix it, and give him an 80%. And I'd probably include at least 5 problems from this test on the next one.

in a private classical Christian school (6-8th), and only my Algebra I students in 8th grade use a TI-83 or TI-84 (depending on which they buy). My younger students do have access to calculators in the classroom, but not graphing ones, just basic. Here are some advantages: (1) Kids can quickly generate a set of graphs to represent a function with a variety of y-intercepts. Then we can talk about what those graphs *mean* when the y-intercept changes. (2) Kids who are weak in math facts (and face it, at 14yo if they don't know what 8*7 is they aren't going to bother learning from a flash card) are now much more accurate with *arithmetic* calculations and can concentrate on higher math. (3) Before (2) makes you gasp in horror (LOL), realize that for some kids, seeing 1/8 = 0.125 on their calculator screen is the first time they've put that fact together, because they've *NEVER* learned how to convert a fraction into a decimal, and they haven't memorized the most basic facts about fractions/decimals/percents no matter how wonderful their teacher is and how long she has harped about the necessity of knowing these things...(whew, taking a deep breath...) (4) Calculations for statistics (and generating graphs to go with them) is much faster. Now, I say all that only to say that my dd who graduated with a BA in mathematics used her TI-84 Silver edition all the way from age 16 to age 20, which went from College Algebra to BA Mathematics. :) And yes, I made it through a MS in Statistics/Mathematics with a scientific calculator, and graphed everything by hand. When I didn't write a computer program to do it for me... But, I worried all summer about these 8th graders, and instead I have kids who were bombing arithmetic in the fall mastering it now with a calculator in their hands. It does free some tension, and allows us to move ahead with understanding number and space, without bogging down in the trivial operations. I don't know many companies that give cashiers a pencil and piece of paper to calculate a total of your purchases and apply tax (!), but it's really good if the cashier can estimate and make sure that the five things you purchased should be about $80. That's something that I can emphasize when they have a calculator in their hands. "Does your answer make sense?" is a question I ask about forty times a day. :)

Oh, and I forgot that Danica McKellar's new book Hot X: Algebra Exposed was just released...it's as good as the others. More Algebra I related, but great for giving some new paradigms to consider with integers and linear equations. :)

I think much depends on the nature of your student. If you have a student that loves to read, then I'd suggest you add some mathematical reading to her list for this year. One very readable book is The Lady Tasting Tea and then another that I think every high schooler should read is Flatland (which also has a cartoon movie version and great teacher tools at the Flatland website). I have several texts I use to spice up traditional math. We use logic problems to think "out of the box" (not extra LOGIC, but fun types of problems--grin!). We also use math history stories...Agnesi to Zeno is a good one as is Men of Mathematics by Bell. Don't forget some probability and statistics as a great break from traditional algebra. Or measurement--my students are often still grappling with measurement concepts, and can't keep straight which is bigger: 3K or 1 mile? So working on relationships and conversions gives them a respite from the abstract nature of algebra. Any pattern game--Mastermind was one of our kids' favorites. And OMSH posted about a great game on Ree's blog this week...I think the larger version of that game would be a hoot to play as a family. For Algebra II, there are so many great software packages out there that she can learn to use. Tinkerplots or Geometer's Sketchpad would be a great way to bring technology into the curriculum. HTH, LoriM

We use English I, II, III and IV. :)

In my high school biology course, I had to replicate lab sketches with precision and color them with colored pencil. Less art than copy work, but still...very challenging. My teacher was particular. Ratios had to be perfect in enlargements...extraordinarily neat lettering, etc. So, I had my dds do something similar. They are both more artistic than I am, so it wasn't as challenging for them, but they really enjoyed it. Full set of sketches to match the dissection series we did. I have a resource I use with my middle schoolers...http://www.amazon.com/Keeping-Nature-Journal-Discover-Seeing/dp/1580174930 Several of them really enjoy keeping a journal.

I have always added to any curriculum--literature, history, Spanish, Chemistry, you name it--and I didn't need a degree in each of those to konw that a book alone is insufficient for learning. Even a book and a solutions manual. Or a book, a solutions manual, and video lectures. It didn't mean that my Campbell Biology was a bad curriculum, or "didn't fit" my child's learning style. It simply meant that there are more ways to approach learning Biology than just reading the book and answering the questions in each chapter. Most curricula I bought for my children did not have a teacher's manual. I had to use my expertise in learning and teaching (and when I didn't have expertise, I got resources to *give* myself expertise), and more organization and planning than anything else, to ensure my children learned material. I had to talk with them about the subjects they were studying, and I had to assess their learning daily, weekly, and monthly, and make sure we were on track for their goals in each field. My rant of the day (LOL) is that math is NO DIFFERENT from literature, history, or any other classical subject. You need a plethora of materials--that bring in math history, allow for math projects, get to organize real data, and yes, practice the basic facts. One math textbook just won't cut it. Not if you are trying to have a classical education...which is why I think we are all still here at WTM. :) I don't know if you noticed, but my own children used Saxon, Lial's, Jacobs, BJU, MUS, and some traditional texts. I added history, projects, conversation, and real world math to *every* one of them. I also teach from PH science texts--and I add reams of stuff to them as well. I guess I just can't imagine teaching any "program" the way a teacher's manual tells me to. LOL. :) I don't teach programs. I teach children. If I have to stand on my head or recite poetry or sing really cheesy algebra songs to get them to learn math, that's what I do.

I have degrees in mathematics and statistics. My daughters came home for school in 3rd and 7th grades (respectively). My older daughter used: Saxon Algebra 1/2, Saxon Algebra 1, Jacobs Geometry, A Beka Algebra II, BJU PreCalculus, MUS Trigonometry, an old college textbook for Calculus I, an old college textbook for Statistics, and then entered the CC where she took College Algebra, PreCalculus, Calculus I, and Statistics before graduating from high school. (At the university, she completed the Calculus sequence, and moved on to complete a BA in mathematics, summa cum laude.) My younger daughter used: Saxon 54, Saxon 76, Jacobs Elementary Algebra, Jacobs Geometry, Lial Intermediate Algebra, Lial PreCalculus, her big sister's old PreCalculus with Calc I textbook, and has now taken Statistics at the CC, and is planning to take College Algebra next spring (her fall semester is full). She has NO intention of majoring in mathematics, but she is working on an associate's in graphic design, and will continue her BA in marketing or business, both of which will include accounting and finance courses. I say all that ONLY to show you that there is no "one" path, no "one" book and no "best" curriculum out there, other than the one you USE to practice mathematics until you understand it, and perform it accurately, and think about it logically. Some books are more self-teaching, some books require a teacher, and some kids need more explanation, while some kids require less. Personally, I teach Saxon Course 2, Saxon Course 3 and Saxon Algebra I to 6th, 7th and 8th graders again this year. I love the books. I love the new editions by Stephen Hake, and I find the way they are organized to be a brilliant way for students to learn math. Not just learn to do it, but learn to think about number, patterns, spaces, relationships and geometry. I will probably teach through the Saxon sequence at my school's new high school (we add 9th grade next year, and I will get to order Geometry!), since we use Saxon K-8 currently. I add A LOT to the books. We are a classical school, after all. My kids do hand-on investigations, demonstrate problems on the board and outside, work a lot of math in science lab, and usually create a portion of their assessments themselves. By mid-year, my walls are covered with data displays the students have created to organize surveys they've written. Anyway, the biggest mistake I've seen with any homeschooled math curriculum is that the parent-teacher buys the book and solutions manual, and assigns lesson one on Monday, lesson two on Tuesday, lesson three on Wednesday...and thinks that working a daily lesson set (right or wrong!) is "teaching" math. I'd have a riot in my classroom if my students worked 30 problems each day without time for instruction, discussion, modeling and graphing! Not to mention every single week we introduce some historical mathematician, or some bit of math history into their timelines... Anyway, there is more to math than Saxon, sets 1-120. Even Saxon needs a teacher.

I am grateful that although my daughter had completed Algebra 1, Algebra 2, Geometry, Trigonometry, Statistics, and Calculus at home with me, we chose to start at College Algebra when she entered the CC at 16. I've said it before and I'll say it again (grin), I think there is plenty of time for your child to move into higher math *even if* he regresses and repeats some concepts in Algebra at the college level. My daughter actually graduated with her BA (in mathematics!) before the age of 21, after having "started over" at College Algebra at 16. So don't worry about putting him behind, or making him "bored." It should help him firmly master algebra and give him a taste of the pace and demand of a college course on material he's already fairly familiar with.

My daughters could have attended large schools. They are small fish, but their species is piranha! :) Extraverted in every way, academically well-prepared, and happy, confident young women...I know they would have done well in the high school you describe. My older dd would have been in the chorus; my younger dd would have been in the band. But I am so thankful that they homeschooled through high school. I wouldn't trade that experience with them for any size classroom, or school setting. Now, that may sound hypocritical, since I teach fulltime in a small, classical school now (6-8th grade math and science), and I know that my students and I have a great relationship and they learn (usually) and I enjoy teaching them (usually!). But I also know that it in no way resembles the intimacy my daughters and I shared in our homeschool, nor do any of my students love to learn and speak my language as my own children do. It comes close, and quite often...often enough that I love that echo of feeling, and keep going. Even in a small school, you must continue to "homeschool" your child. Primary selection of curriculum and requirements goes to someone else, but only you can have individual conversations with your child about what he has read, and what he believes about it, and how that makes him feel...and how that meshes with your family, your values, his goals for his life, and his faith. Even a small school can suck up your evenings with hours of homework. Even a small school has a few kids you'd prefer your child didn't have to deal with each day in class. Even a small school occasionally hires incompetent teachers. If I had to choose it all over again, I'd do everything in my power to convince my child of the power and flexibility of home schooling through high school. I'm grateful every single day that I had those critical years with my children.

For courses like this, I wrote a contract (think "syllabus") with my child for weekly minutes of practice, and performances (open mic nights, recitals) for the year. She listed pieces of music she planned to master, and I asked her to make sure she knew the "context" of the piece (artist, when it was written, why) if asked. I had her keep a journal of her practice time, and then she gave herself a grade at the end of each quarter based on her own evaluation. (She is her own worst critic.) I asked her instructors for feedback on her diligence and courage, and incorporated that into my evaluation. Oh, and I also reminded her that if her effort fell, we'd stop paying for lessons. GRIN. So, that worked too. To me, it was obvious in advance she'd have an A. But she took it very seriously, and often struggled over the idea of "giving" herself an A when she could have practiced more, and tried harder pieces.

I agree with Elisabeth entirely. English I (or English 9, depending on how you designate), Algebra I, Biology (with Lab?), History (which unit? Ancients? Modern?), Personal Finance, CIVICS (which is what I'd call Model UN, if you spend 2 hrs per week all year in class), and PE. Finance, Civics and PE would be half-credits, others full credit. Order a full dissection series from Home Science Tools, or Carolina Biology...and anything else you need for life science labs. 5.5 or 6 credits, if you decide the literature component for English I is too time demanding, then you might give 1.5 credits for English.

I think that's why many WA hsers use Running Start. :)

I'm another one (like Jann) who has no problem at all with my students knowing the content of a test before they take the test. I don't offer written assessment in such a way that the "right answer" is going to give them the grade. I teach in a classical school, so a good third of each of my tests requires the student demonstrate comprehension of the concepts (often by writing their own problems, and "teaching" me how to solve the problem they've written). Knowing before the test that they'll be expected to write a problem or two enables my students to prepare more completely, and I challenge them to write non-trivial problems, and even give more credit for better written work. Even "simple" skill tests in my classes are clearly given to my students in advance...we drill fraction math, or percent/decimal conversions, and then they are given duplicate "blank" tests to fill in quickly. That's not cheating...that's mastery of memory work. Heck, even if it's only pattern recognition, well, that's an important math skill! :) Unless your grades are based 100% on test scores, I'd think that it's no big deal for a student to know the test questions before testing.

Since I'm here, I'll offer my standard advice...College Algebra/PreCalc (or College Algebra/Trig or whatever titles they use) at the CC would be my choice. You can give him dual enrollment credit on his transcript (if he needs it) for senior year, or not if he doesn't. But doing math at the college at the college pace on topics he already understands pretty well (particularly if he showed mastery with CD Precalc last year) will give him "easy A's" on his college transcript, and give him confidence should he choose to take more college math. Jumping into a college math classroom on new topics, no matter how well prepared you are, isn't always the best plan for a high school student. Even a CC teaches math at a pace and expectation very different from a high school teacher. I think it's wise to "warm up" at the college with material you know pretty well, and perfect your math solution practice, before moving on to the pace and challenge of new material at a college or university. It sure worked great for my DD, who graduated summa cum laude in mathematics...but only after she started at College Algebra when she was 16. She gained confidence, and made a bundle tutoring math all the way through college. :) Especially tutoring the College Algebra course...which was easier for her to tutor, having taken it there herself.

I'm glad to see you've gotten nothing but praise for CAP. DH was asked to speak at the CAP encampment in VA a couple of years ago before he retired, and I went with him to Ft. Pickett for the event. It's an outstanding program, and as a former Chief of Recruiting for USAF ROTC, he is a huge fan. It demystifies aviation for a lot of young people who might not have aviation opportunities without CAP, and it definitely is a leading contender for USAF recruits-in-training. :) I wish I'd been in CAP during high school (although how I'd have squeezed it in, I have no idea!). I think it's a great activity, and has taken up the slack where the Girl Scouts have fallen into political correctness. Leadership, responsibility, opportunity to serve...many, many kudos to CAP here in our house!

Here less than I once was, but still here. :) My younger dd graduated from our homeschool in May, and we paid her tuition to continue in her college program (she completed 40 hours while still in high school) at our local community college. My older dd graduated from the university last December (BA Mathematics, summa cum laude), and married in January. I teach fulltime now at a classical Christian school. I teach middle school math and science, and am the 8th grade homeroom teacher. This year, I'll have 17 8th graders, 11 7th graders and 22 6th graders. We use Saxon math (taught "up a year", so my 8th graders are in Algebra 1), and PH Science Explorer Life Science for 6th grade, and unit studies from Event-Based Science for 7th grade. (8th graders have Logic instead of formal science.) It's a very busy school year, and so I will be here far less for the next few months, until my next holiday. :) Feel free to PM me anytime. LoriM

That was a refreshing, lovely story! What a neat young woman.

Yes, if you are going to list "Algebra 2 with Geometry" and "Precalculus with Geometry" I'd include SAXON in the title of the course, and give 1.5 credits for each. Then any administrator familiar with the very popular Saxon method would know exactly what happened with your embedded Geometry program, and your student gets the four credits of math he/she has validly completed--Algebra 1, Algebra 2, Geometry, and PreCalculus. And Calculus makes FIVE credits of high school math.

Whether he'll "need" four credits of math for college admission is one thing. I'd encourage you to have your student study math every semester of high school, and expect your student to have at least two semesters of higher math in college, no matter what career field he plans to enter. Even if your student is still struggling to be a better Algebra student, it's a good fight, and one he should continue to have. There is no "absolute" time in life where one is too late to learn Algebra (or Geometry, if that's the harder thing), and the beauty of homeschooling is that you don't have to have a deadline for finishing a book. Just do the next lesson, and do more problems until you understand it well, and it's easy to do. Then do the next lesson. And the next. I love the quote that says, "Whenever a student tells me they are finished studying math, I tell them to listen carefully. They'll hear the doors closing." I had a daughter who was "not a math student." She changed dramatically in a five year span to meet my expectation that "every well-educated person completes the Calculus sequence." She ended up with a BA in mathematics because that was the "easy" major to get to graduate early. GRIN. I have another daughter who is "not a math student"...we'll see where she ends up, but right now she makes a bundle tutoring high school math. Not her favorite subject, but she sees the value in the skill. :)