|3rd, 4th, 5th, 6th, 7th, 8th grades||KhanAcad|
|Arithmetic||KhanAcad book1-web book1-print book2-web book2-print|
|Basic geometry and measurement||KhanAcad|
|Algebra 1||KhanAcad book-web book-print|
|Geometry||KhanAcad book1-web book1-print book2-web|
|Statistics & Probability||KhanA-basic KhanA-adv|
|Precalculus||KhanAcad book-web book-print|
|Sudoku (logic puzzles)||easy medium hard very hard|
|KenKen (logic & arithmetic)||pdf web1 web2|
|SAT red book (Algebra 1 & Geometry)||t1s1 – t1s3 – t1s6 — and so on|
|NC Math Contest||Algebra 1 Geometry Algebra 2|
|UNCC Math Contest||Algebra Comprehensive|
Algebra 1 and High school geometry are the minimum for high school graduation, and then you’ll have to decide how much more math to study. Statistics is a mostly self-contained topic that has a lot of real-world value and is less difficult than the higher math track (Algebra 2, Trigonometry, Precal, Calculus). If you see yourself working in a science / technology / engineering field, or if you want to keep that option available without needing a lot of remedial work in the future, then you should definitely learn Algebra 2 and Precalculus. It’s nice to learn calculus in high school, but many people take it in college even if they’ve already taken it once in high school.
No matter your level, start Khan Academy with 3rd grade and finish every course up to Basic geometry and measurement. Do this by taking the Course Challenge repeatedly, without guessing on anything and without using a calculator unless it’s provided on-screen. This will uncover the topics you don’t already know, which you can then learn from the video lessons. If this is boring or is too easy, that’s fine; practice helps to solidify your skills. It’s a one-time task, it will be over in a few weeks, and it will find your place in the curriculum. That’s much better than jumping ahead of where you really belong and having holes in your knowledge that you’re not aware of.
The best part of Khan Academy is the instructional videos. You should take time to watch them and learn all you can from them. A lot of thought and many revisions have gone into making those videos; they pack a lot of information into a short time.
Aside from traditional live classes with a teacher, there are three ways to get math instruction: (1) from a video, (2) from a book, (3) from a tutor. Videos can be very effective; they allow you to pause, replay, and adjust the speed which is impossible in a live class. But if you study math from videos only, the downside is that you don’t develop the skill to learn math from a book. Watching a video is like being a passenger in a car; you can only go where the driver takes you, and the car has to stay on the road. To continue the analogy, learning from books is like riding a bicycle. It takes more effort and it goes more slowly, but it uses your own power, develops your own strength and endurance, and you can travel off-road where cars cannot go. Learning from books puts you in control of your studies and habituates you to think independently; learning from videos makes you passive and dependent in comparison.
Learning math from a book is difficult. I don’t recommend it to everyone or for every lesson. But if you’re good at math and you want to pursue it to a high level, you need to be able to learn math from books, and the only way to develop that skill is to practice it.
There is a huge amount of repetition of topics in math books with different titles, especially ones with Algebra in the title. Arithmetic and Prealgebra books can be nearly identical. Books titled Beginning Algebra, Algebra 1, Intermediate Algebra, and Algebra 2 have at least half of their material in common. The same is true of books titled Algebra 2 and Precalculus. When you move up to a new math book, usually there are several chapters you should skip because you’ve already learned them.
A tutor is a teacher who works with one or a few students at a time. Tutors are expensive because the cost that otherwise would be spread across many students is paid by one or a few. But tutoring is also very effective because it answers all your questions in real time, and the tutor can explain things that he sees you don’t know or have misunderstood. A major difficulty in the learning process is that you don’t know what you don’t know (a tautology but also an important insight), so without a guide you can waste enormous amounts of time and energy going down wrong paths without realizing it. Working with a live tutor eliminates all of that waste.
You can get a lot of the benefits of a tutor just by having someone on call to answer your questions, without needing to look over your shoulder all the time. You probably already have a relative or a friend who could do this. There are also tutors available online, perhaps for free; for example, my county public library provides access to tutor.com (a paid service offering text chat with live tutors) to library patrons, and the service can be accessed from any location. Also there are subject-specific public discord servers, but like society at large these are full of immoral people who are at war against most things good and holy. Such people are best avoided.
A good plan is to keep a running list of math questions to ask your tutor the next time it’s convenient, once every few days or every week. That way you can avoid wasting time searching for answers when you’re stumped.
Besides instruction, you need practice. Khan Academy has unlimited practice problems, but I prefer math problems on paper – from a book or a problem set. That helps reduce your screen time. Also you need to practice doing math work on paper, especially graphing and data analysis (box plots etc.), as opposed to always doing them by dragging things around on a screen. Likewise, you should use your own physical calculator rather than the on-screen calculator; the TI-83 Plus / TI-84 / TI-84 Plus are good and are available used on ebay for reasonable prices.
There is a large collection of math problem solving in this curriculum. You should spend at least 1/4 of your math study time working through problem sets.
If you struggled with math in grades 3 to 8, quite possibly it’s because you were presented with topics that were beyond your grasp at that age. For example, the Khan Academy third grade math course teaches number lines with fractional scaling, which is very challenging at that age. I believe it’s pointless to spend time and effort on math topics that are too hard during the elementary school years. Children are ready for a math topic when it makes sense rather easily, without a struggle or a resort to rote memorization without any understanding of how it works. There is a big leap forward in reasoning ability somewhere between ages 12 and 14 – psychologists call it the transition from the concrete operational stage to the formal operational stage – and after that it’s much easier to learn math. If you couldn’t do math before age 12, don’t think it must always be like that. Give yourself a fresh start.