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    Query About High School Calculus

    Hi, I'm hoping one of the mods or parents with experience can help me with this.

    My kids finished High School Algebra I last year, and are finishing Geometry this month, and will begin Algebra II next month.

    I don't have any experience with Calculus: I am confident that I can teach it, however, and am looking to start myself this autumn, so as to be ready for teaching the kids next year ...... But there seem to be a few options for HS Calculus? Pre-Calculus, Calculus, and AP .... Is Pre-Calc definitely necessary prior to a 'regular' Calculus course for High School students? Or, after successfully completing Algebra II are they generally ready for the regular course?

    I would greatly appreciate some feedback on this: textbooks are far too expensive for purchasing various levels to look through at home!
    homeschooling mother to a 16yo boy & 18yo girl, both learning at the high school level, and an adult son whom I homeschooled all the way through. You are welcome to read more about our homeschooling life at my blog: link via my username. Please forgive any typos in my comments here! I'm disabled and can't always type clearly.

    #2
    Re: Query About High School Calculus

    .... So I'm continuing my research and pondering .... It looks like PreCalculus covers Algebra and Trigonometry -- which is what Algebra II covers -- but going further than Algebra II, relating it to Calculus.

    I imagine that a student who is strong in Algebra II would be able to go directly into Calculus, and a student for whom Algebra II was really challenging, would be better off going on to PreCalculus.

    Since I'll be teaching myself Calculus concurrent with teaching my kids Algebra II, I'll be able to start incorporating Calculus concepts, after the fashion of a PreCalculus course, during the final third of their Algebra II year with the goal that they'll then do a full year of Calculus, without needing a full year of PreCalculus inbetween .... We'll see how it all goes!
    homeschooling mother to a 16yo boy & 18yo girl, both learning at the high school level, and an adult son whom I homeschooled all the way through. You are welcome to read more about our homeschooling life at my blog: link via my username. Please forgive any typos in my comments here! I'm disabled and can't always type clearly.

    Comment


      #3
      Re: Query About High School Calculus

      It really depends on your "algebra 2" book. Some are just algebra. Some include basic right angle trig and others include full blown trig with graphing and all. Before calculus you need full blown trig, logarithms, analystic geometry (graphing circles, hyperboles etc) and ideally matrices. There is no standard on what an algebra 2 book covers. In most series there is both an algebra2 and pre-calc book and both are needed. It really is a lot to try to fit algebra 2 and pre-calc into one book and I would say if they did it would only be for advanced honor students. If you are looking for a calculus option, Kolbe academy sells a Foerster book with lesson plans and tests.
      Debbie- mom of 7, civil engineering grad, married to mechanical engineer
      DD, 25, BFA '17 graphic design and illustration
      DS, 23, BS '18 mechanical engineering
      DS, 21, chemistry major
      DS, 18, Physics major
      DD, 15, dyslexic, 10th grade customizednMP plus co-op
      DS, 12, super squirmy, possible dysgraphia, MP 7A
      DD, 6 , K- finally one who seems to like drawing and writing- first one since my oldest!

      Comment


        #4
        Re: Query About High School Calculus

        Just "for fun" I looked at the table of contents of some popular math books. None of the following cover any trig at all (or just very basic right angle trig) in their algebra 2 books: Teaching Textbooks, Chalkdust, Abeka, Saxon
        Kolbe uses a Foerster book called Algebra and Trigonometry for algebra 2. If you use their honors plans which cover the whole book and get an A then you will be ready for calculus. If you use their "regular" plans which don't cover every chapter or if you get a low B or lower in the honors course then you go to pre-calculus before calculus. They use a Foerster book called Precalculus which covers more indepth than algebra/trig book.

        In general my opinion is that to try to cover everything after algebra 1 and before calculus (excepting geometry) in one year is a lot and only for very advanced students and only if you use the right book. At my boys high school they cover algebra 2 and precalc in two years even for the honors students. At their old school they offered an option of doing it all in 3 semesters and starting calculus mid junior year but only for the very advanced math students. In that case they did a semester of calculus junior year and then did AP BC level calc senior year (BC is the faster paced class that covers calculus 1 and calculus 2)

        IF you plan to take calculus at a college they will probably either make you take a placement test (so you will have to have totally mastered that functional trig) or base placement on ACT or SAT score and again in order to score high enough you have to have mastered advanced trig.

        If you plan to teach it yourself, you can always decide to slow down or back up if needed.
        Debbie- mom of 7, civil engineering grad, married to mechanical engineer
        DD, 25, BFA '17 graphic design and illustration
        DS, 23, BS '18 mechanical engineering
        DS, 21, chemistry major
        DS, 18, Physics major
        DD, 15, dyslexic, 10th grade customizednMP plus co-op
        DS, 12, super squirmy, possible dysgraphia, MP 7A
        DD, 6 , K- finally one who seems to like drawing and writing- first one since my oldest!

        Comment


          #5
          Re: Query About High School Calculus

          Oh, I am teaching them Trigonometry, no worries there. Thanks for chiming in!
          homeschooling mother to a 16yo boy & 18yo girl, both learning at the high school level, and an adult son whom I homeschooled all the way through. You are welcome to read more about our homeschooling life at my blog: link via my username. Please forgive any typos in my comments here! I'm disabled and can't always type clearly.

          Comment


            #6
            Re: Query About High School Calculus

            My point was simply that if you skip precalcus check your algebra 2 book because most do not teach trig or if they do they only teach right angle trig and not graphing, solving trig equations and trig identities. If your algebra 2 book does not teach trig you can teach it alone with a small trig book. I didn't want others reading this to think they could move from, say, Saxon algebra 2 directly to calculus. And enjoy learning calculus yourself. One of the aspects of homeschooling I like best is getting to relearn and master material I had been exposed to in school but later forgot. I had no idea how much trig and calc I had forgotten (and I'm an engineer) until I tried to teach my daughter. It was actually fun relearning it.
            Debbie- mom of 7, civil engineering grad, married to mechanical engineer
            DD, 25, BFA '17 graphic design and illustration
            DS, 23, BS '18 mechanical engineering
            DS, 21, chemistry major
            DS, 18, Physics major
            DD, 15, dyslexic, 10th grade customizednMP plus co-op
            DS, 12, super squirmy, possible dysgraphia, MP 7A
            DD, 6 , K- finally one who seems to like drawing and writing- first one since my oldest!

            Comment


              #7
              Re: Query About High School Calculus

              Originally posted by momgineer View Post
              It really depends on your "algebra 2" book. Some are just algebra. Some include basic right angle trig and others include full blown trig with graphing and all. Before calculus you need full blown trig, logarithms, analystic geometry (graphing circles, hyperboles etc) and ideally matrices. There is no standard on what an algebra 2 book covers. In most series there is both an algebra2 and pre-calc book and both are needed. It really is a lot to try to fit algebra 2 and pre-calc into one book and I would say if they did it would only be for advanced honor students. If you are looking for a calculus option, Kolbe academy sells a Foerster book with lesson plans and tests.
              Momgineer already gave excellent advice. I wanted to add that while algebra2 usually covers graphing logarithmic and exponential functions at a basic level, precalculus takes it deeper: translating, stretching, shifting. The extra depth is quite necessary before starting calculus. Similarly, algebra2 teaches how to graph conic sections (ellipses, hyperbolas, parabolas), but precalculus also teaches how to stretch, shift, and rotate them. Again, it's difficult to tackle calculus without these skills in hand. And to clarify, "trigonometry" is more than just the sin, cos, and tan ratios for right triangles. Students must learn how to use the trig identities, polar coordinates, and graphing of all trig functions (including secant, cosecant, cotangent), with stretching, translation, etc. These skills are thoroughly covered in a good precalculus course.

              MP Online Academy uses the Larson text for precalculus. I would look at that book and be sure to master that content before beginning calculus.

              Best wishes,
              Cindy
              Last edited by Cindy in Indy; 07-04-2015, 07:17 AM.
              Cindy Davis
              Science and Math teacher at Highlands Latin School - Indianapolis
              ds-26 college graduate: independent young adult
              ds-24 college graduate: 3rd year med school
              dd-22 college graduate: working as a registered nurse

              Comment


                #8
                Re: Query About High School Calculus

                Originally posted by momgineer View Post
                My point was simply that if you skip precalcus check your algebra 2 book because most do not teach trig or if they do they only teach right angle trig and not graphing, solving trig equations and trig identities. If your algebra 2 book does not teach trig you can teach it alone with a small trig book. I didn't want others reading this to think they could move from, say, Saxon algebra 2 directly to calculus. And enjoy learning calculus yourself. One of the aspects of homeschooling I like best is getting to relearn and master material I had been exposed to in school but later forgot. I had no idea how much trig and calc I had forgotten (and I'm an engineer) until I tried to teach my daughter. It was actually fun relearning it.
                Oh yes, you're absolutely right, it's a good thing to clarify. Sorry if I wasn't clear initially. Back when I was in high school (lo, a great many years ago!) the course was called Algebra-Trig. These days everyone is calling it Algebra II, so that's what I had taken to calling it. I didn't realize til recently that not all Algebra II courses/texts include proper Trigonometry. In any case, i have good books here that cover all the good stuff

                In terms of Calculus vs PreCalculus, as I say, we'll see how it all goes! I'll be able to tell next spring/summer which route would be most beneficial for my kids. Knowing them as I do I can say right now that it would be reasonable to guess that my son would be able to go directly into Calculus, while it is also reasonable to assume that my daughter would be better off with PreCalc, but in either case, I won't know for sure until next year ... They both need four years of high school maths, and either/or PreCalc or Calc would be number four for my daughter (who would be going on 18 when she finishes the year that inculdes it), and of course for my son too, but he is an entirely different kettle of fish. He's either going to end up homeschooling through the first couple of years' worth of college credits, or he'll go early. That wouldn't be my first choice. Academically, sure, he'll be 'ready' by 15/16 (they are at the same level, academically, in every subject) But socially? I don't know that that would be a sensible choice.
                homeschooling mother to a 16yo boy & 18yo girl, both learning at the high school level, and an adult son whom I homeschooled all the way through. You are welcome to read more about our homeschooling life at my blog: link via my username. Please forgive any typos in my comments here! I'm disabled and can't always type clearly.

                Comment


                  #9
                  Re: Query About High School Calculus

                  Have you ever looked at the Art of Problem solving website for your son? They have some really neat looking books covering topics like discreet math that aren't usually covered in high school.
                  Dorinda

                  For 2020-2021
                  DD 17-12th with MPOA(Classical Studies 3), CLRC (Latin 6, Greek 5), Thinkwell (Calculus and Chemistry), Vita Beata (Divine Comedy), American History
                  DS 15-9th with Lukeion(Latin 1 and Greek 1), Vita Beata (9th Literature)
                  DS 12-7th with Right Start Level H online class, Vita Beata (6th Literature)
                  DS 6 - 2nd blazing our own trail with Right Start D and a mix of MP materials

                  Comment


                    #10
                    Re: Query About High School Calculus

                    Originally posted by Mom2mthj View Post
                    Have you ever looked at the Art of Problem solving website for your son? They have some really neat looking books covering topics like discreet math that aren't usually covered in high school.
                    Thanks for the tip! It looks like they have some good books there!
                    homeschooling mother to a 16yo boy & 18yo girl, both learning at the high school level, and an adult son whom I homeschooled all the way through. You are welcome to read more about our homeschooling life at my blog: link via my username. Please forgive any typos in my comments here! I'm disabled and can't always type clearly.

                    Comment

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