Math is one subject where it pays to have a curriculum, either in print or online. Many providers offer both. For online systems, be sure to have your child try the free trial versions, in addition to your own research.
Placement Tests
If you don't know which level / grade to start with, several publishers provide a free placement test. These can be used even if you aren't going to use that specific curriculum, just as a guide for where to get started. Here are some links, or go to your specific publisher's site to search:
Math Mammoth Placement (1-7)
Teaching Textbooks Placement (3-12)
Singapore Math Placement (1-6)
Saxon Math Placement: Elementary K-3, Middle Grades 4-8, Upper grades 9-12
Popular, traditional math workbooks for grades K-8, mastery based and thorough. Plenty of examples and explanation. Free placement test online for deciding where to start. Generally aligned with public school grade levels. Free videos on their web site also.
Singapore Math (aka Primary Math, Dimensions Math)
Widely used K-6 math curriculum, focusing on a deep understanding of concepts. Generally moves quickly and includes topics sooner than a traditional grade level system. Mastery based, with some review, teacher's editions and textbooks available.
Recommended for visual learners, Math U See is focused on manipulatives to illustrate math concepts, from kindergarten through high school, although they are most often used for elementary grades. Workbook lessons with hands-on kits for each level. There is also a digital app version of the manipulatives, and DVD video instructions for teachers on how to use them. A bit more expensive than others due to the extra products. Levels are not by grade but by subject (addition, fractions, etc).
Grades 2 - 5, visual and fun math books and apps, taught with cartoon characters. Part of the complete curriculum by Art of Problem Solving, so students can continue into the upper grades available for AoPS. Books are comparatively expensive, online access is via monthly subscription. Generally for advanced learners, they focus on critical thinking.
A more rigorous math curriculum, designed for college bound or gifted learners who want a challenge, or to prep for math competitions. Focuses on putting math skills to use to solve complex problems. Books or live online classes available.
Right Start emphasizes learning math concepts in the early years (K-6) using an abacus and lots of hands-on games. The book bundles have lessons and explanations on how to use the games and manipulatives, which must be purchased to use the program. Not as many worksheets as other math programs. Fairly expensive, but sometimes available used, or through charter school stipends.
Just for early grades (K - 3), this set of books has lessons for basic arithmetic that make frequent use of base 10 blocks to practice concepts and do activities.
Holt Mathematics and Prentice-Hall Mathematics
Textbooks made for school, but with enough examples and lessons to use at home. The problems are keyed to the examples, with odd-numbered answers in the back so a teacher's edition is not necessary. Chapter reviews and tests are in the student edition. Especially helpful for 6th grade and up, but available in grades 1 through calculus. Search for "Holt Mathematics", or "Prentice Hall Mathematics" etc. on Amazon and buy used for best prices.
Very spiral based with lots of review in every lesson, follow up lessons spaced widely. Fyi, you will hear Saxon math mentioned occasionally but be aware many people strongly dislike it. The main criticisms are the lack of focus on one thing and it can be dry and drill based.
Online math curriculum for grades K-12, on a subscription basis. Known for its flexibility, you get access to all lessons, all grades, and can assign your own or have the student move through in order. Short video lessons get to the point (in an Australian accent :) ) with 10-15 problems per lesson. Parent determines what percentage equals "mastery". Light on review, so some supplementing may be necessary or just go back to earlier lessons for reviews.
Online math content by publisher McGraw-Hill, for grades K-12. Automated progression through the curriculum, once the student takes the placement test to see where to start. Student must master a subject before moving on (not adaptive). Subscription based. Feedback is graphic so the students can see how they are progressing through the material. Lesson instructions are reading / example, no voice or video, so some parent instruction may be necessary.
Computer-based lessons and practice with dynamic feedback, for grades 3 - 12. Formerly on CD's, now version 3.0 is available online, with an inexpensive monthly subscription. Spiral-based, with approximately 25% new content and 75% review content per lesson. Printable eBooks or hard copy books also available. Generally the pace is a little slower than traditional math curriculum.
Free, online video lessons on every math topic from kindergarten to college level math. Accessible by topic search or as "missions" (pre-selected lists of topics with practice problems and quizzes). Not an organized curriculum although all topics are covered. You'll mostly need to plan your own progress. Great for kids who learn by listening/watching a video and doing a few problems. Frequently Khan Academy is used as a supplement or as a quick way to get extra help on advanced subjects.
Entertaining video lessons on all elementary math subjects through pre-algebra. Free on their web site, with corresponding printable practice sheets for each lesson, for a $20 annual fee. More lively than Khan Academy for the younger ages. Not a curriculum but they cover all the topics, similar to Khan.
Online middle and high school math courses, from 6th grade through calculus. Videos and practice problems, automatically graded. Purchase a course and have access to it for one year. Also high school science.
Online monthly subscription to the Time4Learning platform includes math through the high school level (as well as their other core subjects).
Live video courses for 8th grade through pre-calculus. Choice of live with a teacher, 3 times/week, or part live / part video lessons.
Video courses do the teaching along with a textbook for the student's use. Algebra through Calculus. Videos are screen capture with voice-over, brighter than Khan and using more technology. Videos are on a flash drive, and you need to purchase the textbook elsewhere separately.
Keep in mind that the math goals of homeschooling high school may vary. If you are with a charter school, they will require the Oregon state standards for a diploma (three credits of math at the Algebra level or above). If you are doing it yourself, the amount of math needed depends on the student's educational goals. College, vocational school, or work life will require different amounts of math. You may decide that personal finance math is a better focus than geometry, for a non-college career path. Or you might decide to focus just on what is needed for the SAT/ACT tests your college requires.
If you do go on to advanced math, how to cover it? Parents may not be prepared to teach Algebra, Geometry, Trig, and Calculus. In that case, the focus can shift to a curriculum that contains enough lesson material for the student to work independently (written or video), or to an online class with a live teacher, or a tutor.
MathTV.com - Teacher / whiteboard videos explaining most math topics, from Basic math through Pre-Calculus.
GeoGebra - Visual tools online for doing algebra and geometry, graphing etc.
Great Courses - Made for adults, they do offer some high school level math courses online. tip: wait for one of their 70% off sales.
NextLevel Math - Online math tutoring one-on-one, via video chat, for middle, high school, and college levels. Pay by the hour.
Prodigy - Online games for grades 1-8. Made for schools to assign extra practice to students.
Dragon Box - Fun math apps, famous for their graphic algebra learning game.
Monster Math - Creative math games including logic and story problem techniques
Critical Thinking Co - Look up their app games such as Math Detective, Math Analogies, etc
ST Math - Visual math learning with NO numbers involved
Splash Math - Math games for grades K-5
GregTangMath - Elementary math games