notagoodfitafterall Posted March 25, 2023 Share Posted March 25, 2023 For K-6, we mostly used a math outline I found on here by @Hunter. We added a bit of hands-on geometry in elementary. For middle school, though, we did Wentworth's First Steps in Algebra and A First Step in Euclid by J.G. Bradshaw. I have a copy of Kiselev's I plan to have the kids work through for geometry, but I'm not sure of a good algebra course. Our internet will not support streaming, so online courses are not an option. I'm leaning towards Dolciani or Lial, but I'm not sure which I like better. I'm also not sure if Wentworth's was "enough" to be an algebra course or if it was more of a prealgebra course. Even though the programs are inexpensive, I would hate to spend money on a course we didn't need. Quote Link to comment Share on other sites More sharing options...
Malam Posted March 26, 2023 Share Posted March 26, 2023 (edited) Just curious, have you worked out some of the problems from Kiselev? (example exercise: "Construct a tangent to the arc of a given sector such that the segment of the tangent between the extensions of the radii bounding this sector is congruent to a given segment.") Dolciani and Lial are pretty different books: With Lial, you have a giant book divided into many sections each with many practice problems. It's intended for a professor to choose to assign some problems as homework, and for college students to continue to practice the sections they've decided they struggle with. There are some challenging problems in the mix (ex. factoring p^2(p+2)^2+p(p+2)^2-6(p+2)^2 ), but they aren't labelled as such (the teacher/professor is presumable expected to go through and find them when choosing which to assign for homework). The primary advantage of Lial over Dolciani is its use of graphics, which can be useful when studying functions. Dolciani is more manageable in size, it tends to include more formal math concepts like sets and defines functions more formally (Lial: "A function is a relation in which, for each distinct value of the first component of the ordered pairs, there is exactly one value of the second component." Dolcaini: "A function is a correspondence between two sets, D and R, that assigns to each member of D exactly one member of R"). It came from the "new math" of the 60s, when mathematicians had a large (some say too large) role in creating curriculum. Dolciani's challenge problems seem to be more interesting than Lial's (ex. simplifying (a+b)^6-(a-b)^6) If you're the type of person to like a book such as Kiselev, you'd probably like Dolciani more than Lial. I had a look at Wentworth, and I would suggest using Intermediate Algebra if you choose Lial or Algebra and Trigonometry Structure and Method by Dolciani P.S. If you choose Dolciani, note that while what I said above is for the 1996 edition, the older ones are alleged to be even more formal and new-math-y. I'm not sure if it got "watered down" given that it still has some good challenge problems, and even some (BASIC) programming exercises, which I doubt you'd find in the older editions Edited March 26, 2023 by Malam 2 Quote Link to comment Share on other sites More sharing options...
Malam Posted March 26, 2023 Share Posted March 26, 2023 By the way, have you hear of the Art of Problem Solving textbooks? They're very popular among math-enthusiastic families. I suggest you take a look at their algebra book if it's in your budget. https://artofproblemsolving.com/store/book/intro-algebra https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/intro-algebra/toc.pdf https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/intro-algebra/exc1.pdf https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/intro-algebra/exc2.pdf https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/intro-algebra/exc3.pdf https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/intro-algebra/index.pdf Quote Link to comment Share on other sites More sharing options...
notagoodfitafterall Posted March 26, 2023 Author Share Posted March 26, 2023 I am currently working through Kiselev. If it proves too much, I'll have the kids do Wentworth's First Steps in Geometry before trying Kiselev. The big appeal of Lial and Dolciani for us is that they're dirt cheap if bought used. I also like that Lial goes through precalculus. If we do Dolciani, we'll do Brown for precalculus, and I'll start looking for an inexpensive solutions manual (the textbook is about $3, but the teacher's manual is currently $72!). More digging is definitely required now. Thank you so much! You're a huge help! Quote Link to comment Share on other sites More sharing options...
Malam Posted March 26, 2023 Share Posted March 26, 2023 (edited) Check out https://www.bookfinder.com/ for used books, it's an aggregator of just about every used book site. You can get the introduction to algebra book and solutions manual for under $50. That's not super cheap but it's an alright deal. There are also plenty of free math texts: https://aimath.org/textbooks/approved-textbooks/ Edited March 26, 2023 by Malam 1 Quote Link to comment Share on other sites More sharing options...
notagoodfitafterall Posted March 26, 2023 Author Share Posted March 26, 2023 Just now, Malam said: By the way, have you hear of the Art of Problem Solving textbooks? They're very popular among math-enthusiastic families. I suggest you take a look at their algebra book if it's in your budget. https://artofproblemsolving.com/store/book/intro-algebra https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/intro-algebra/toc.pdf https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/intro-algebra/exc1.pdf https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/intro-algebra/exc2.pdf https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/intro-algebra/exc3.pdf https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/intro-algebra/index.pdf I've heard of it, and it was something I was considering. I've heard a lot of people say switching to it is difficult. And, frankly, it's just not really in our budget this year. My goal is to do math for less than $20 this year. Quote Link to comment Share on other sites More sharing options...
Malam Posted March 26, 2023 Share Posted March 26, 2023 23 minutes ago, shoestringsandducttape said: If we do Dolciani, we'll do Brown for precalculus Keep in mind there is a precalculus text for Dolciani, it's called "Modern Introductory Analysis, although the solutions seem nonexistent. 1 Quote Link to comment Share on other sites More sharing options...
notagoodfitafterall Posted March 26, 2023 Author Share Posted March 26, 2023 If I can find a solutions manual for it, it would be worth considering. I'm reading the link about "New Math" you sent. It's rather interesting, and it's probably going to send me on another late-night research session. My husband is going to cuss you under his breath while I'm in that mode, but he'll thank you for the results. 🙂 Quote Link to comment Share on other sites More sharing options...
notagoodfitafterall Posted March 26, 2023 Author Share Posted March 26, 2023 Answers to problems in Wentworth's higher algebra : George Albert Wentworth : Free Download, Borrow, and Streaming : Internet Archive A higher algebra : Wentworth, G. A. (George Albert), 1835-1906 : Free Download, Borrow, and Streaming : Internet Archive I'm not committed to Higher Algebra, but it's worth putting out here. Quote Link to comment Share on other sites More sharing options...
Guest Posted March 27, 2023 Share Posted March 27, 2023 Have you heard of MEP? It is free and I’ve heard it’s very good https://www.cimt.org.uk/projects/mepres/primary/index.htm Quote Link to comment Share on other sites More sharing options...
notagoodfitafterall Posted March 27, 2023 Author Share Posted March 27, 2023 1 hour ago, WTM said: Have you heard of MEP? It is free and I’ve heard it’s very good https://www.cimt.org.uk/projects/mepres/primary/index.htm I have. I'm hesitant to consider it because students in the UK specialize in the last two years. They only take three or four subjects, so I worry there's an expectation that they can handle more work in those few chosen subjects. I don't want to have to cut back on everything else in order to use it, if that makes sense. Thank you so much, though! I will definitely give it a second look. 🙂 1 Quote Link to comment Share on other sites More sharing options...
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