What’s a parent to do after a child finishes Singapore Math 6B? After even the Challenging Word Problems 6 supplement? I’ve googled that question, asked other homeschooling moms on forums, and pondered it with friends each time a child neared that mathematical cliff. There is, of course, no perfect answer. If your child is mathematically talented and young, delaying the algebra, geometry, algebra II, precalculus, calculus chain should at least be explored. (The Art of Problem Solving folks explain why rather well.) My older decided to start that chain immediately just before turning ten (albeit taking it at a slower pace), and he’s been largely happy with that choice. My younger son, ten, more recently began life after Singapore 6B, so his path is still in its evolution.

So here are some possibilities. I’ve divided them up depending on whether we’ve made use of them at the pre-algebra/algebra level or not. Some are linked to my reviews while others remain on my ever-growing list of curriculum to review here. Hopefully, the lists will provide some options for the child that gets to that point several years before his or her teens as well as for kids who reach it later. If you have more ideas, add them (with any links) to the comments section.

# What We’ve Done

- Jacobs’ Elementary Algebra: When my older son was done with Singapore 6B at nine years old, he wanted to go right into algebra. Honestly, I didn’t know of any other path to offer, although his insistence was strong enough that I’d likely not have swayed him. Harold Jacob writes with humor, which appealed to my older son. Jacob quickly moves through the pre-algebra basics not covered in the Singapore series (negative numbers, exponents, absolute value, order of operations, and various mathematical properties) and onto a sound algebra program. (Review here.)
- Keys to Algebra: My younger used the first of these ten books while working on Singapore 5. The series is a consumable set of low-cost workbooks designed for a student to use alone. They are fairly dry but provide plenty of practice and start with pre-algebra concepts. I’ve known of families who have used these before a deeper study of algebra or along with the last books of Singapore.
- Algebra Survival Guide: This book breaks algebra down into bite-sized components, starting with a fair amount of pre-algebra (properties, exponents, negative numbers, radicals, etc.) Each page presents one concept, and many concepts are briefly proven along the way. For practice, there’s a consumable workbook with answers. While not a full algebra course in my opinion, it certainly does a fine job introducing many concepts that could make a more challenging algebra class more manageable. My younger is enjoying this book now.
- Penrose the Mathematical Cat: Theoni Pappas has a number of books for children and adults that introduce a variety of mathematical ideas that sit well beyond the traditional curriculum. My younger son and I started reading these together during the Singapore books and enjoyed discussions about fractals, mobius strips, infinity and more. These are definitely our antidote to math anxiety and traditional math blues.
- Life of Fred Prealgebra: Life of Fred has a growing body of followers. We’re not part of them. We tried the first book (reviewed here) and found it rather dull and lacking much math. If you’re looking for a light diversion for a few months, this may work for you. It didn’t hold interest here.
- Challenge Math: Edward Zaccaro presents an array of largely pre-algebra topics that are generally accessible before the end of Singapore 6B but could also be enjoyed after completion as a way of strengthening problem solving skills. His 19 chapters explore some pre-algebra basics (fractions, percents, volume, for example), trigonometry, algebra, and even a bit of calculus. With three levels of problems at the end of each chapter, there’s plenty to play with here. He has an algebra-specific title, Real Life Algebra, that sits on my Amazon wish list.
- The Number Devil: Fiction meets math in this playful trip through math topics that won’t be found in most math books. The author plays with combinatorics, fractals, Fibonacci numbers, roots and exponents, and more. A few folks on the web have created study guides and lesson plans for this book, which go a long way to flesh out this rather content-heavy book. Again, it could be appreciated before finishing Singapore 6B.
- Calculus By and For Young People: Here’s another book that takes meaty, real mathematical concepts and presents them in accessible ways for kids. While the author cites that kids as young as 7 could use it, it’s likely to be best appreciated with kids with a good understanding of fractions and decimals. It contains plenty of hands-on work with excellent explanations.
- Descartes Cove: Distributed by Johns Hopkins Center for Talented Youth, these six CDs make a quest out of math problems. The math is quite obvious and the pace is slow — it’s not a high-speed video game sort of experience. It’s aimed for middle schoolers and covers some algebra, geometry, measurement, probability, and more. The math demands higher-order thinking skills, putting it in a different league than the fast-twitch math fact games designed for the younger set. My older enjoyed this when he reached the last levels of Singapore.

## What We’ve Not Done — Yet

- More Singapore Math: Two options exist for families that want to carry the Singapore experience through Algebra II. Both mix geometry, algebra, and other topics throughout four levels covering four years of math. I’ve held back, not wanting to commit to a program that makes moving to another more traditional program more logistically challenging. Both programs are said to be quite challenging. It’s still on the list of possible next steps.
- Art of Problem Solving: This publisher is known for rigor and deep thinking and is aimed at those that not only excel at mathematics (mine do) but really love it (mine don’t). Their pre-algebra book would be a fine place to start the series, which largely covers ground that Singapore 6 does not. Online classes (for a fee) and online problems (for free) could complement the text, although these books stand alone quite well. It’s still on my short list as well. My older tried the online Introduction to Probability and Counting course and was overwhelmed and discouraged. Like I said, it’s best for those students who love math, have ability, and really want to work hard.
- Thinkwell: This company offers a host of math courses from middle school to college. Instruction is via video, and problems can be done and graded online. Dr. Burger is an engaging instructor who adds enough humor to make the lecture interesting. My older son used Thinkwell for College Algebra (before they offered Algebra II) and found it appealing. However, for the child who needs a live human for instruction (and my older son does), this may not be the best choice.
- ALEKS: ALEKS is another online learning system. Unlike Thinkwell, it contains no lectures. Like Thinkwell, it generates and grades problems. My older son used this for some of precalculus, but it has courses at the pre-algebra and beginning algebra level. Here’s my full review, but in summary, I recommend ALEKS as a supplement rather than a full curriculum.
- Khan Academy: This amazing free educational resource is a repository of chalkboard-style videos about math, science, economics, history, and more that’s growing by month. For many of the K-12 levels of math, practice problems follow lessons. We’ve used this for some cosmology, history, math, and chemistry over the years, largely as a supplement to other curriculum. He may not appeal to kids who need pizzaz to pay attention, but his methodical, clear presentation makes for fine watching for more patient viewers. Tracking a student’s watching and practicing progress is available. My younger son has watched largely non-math topics, while my older son has worked through much of the precalculus lectures. Like ALEKS and Thinkwell, we’ve not used this for the pre-algebra or algebra level.

I’m sure I’ve left many post-Singapore 6B avenues left unexplored. If you have paths you’ve taken and would be willing to share, please add them to the comment section. Links to the sources are appreciated. It seems my next step is to review the resources we’ve used. That’s a bit larger job than I imagined when I set to making this list, which grew far longer than I imagined. I best get started.

We’ve followed up with Singapore’s NEM 1 and 2. So far they’ve been very good for us here. I don’t really know why the rush to find something new after what has worked so far, but then, we’ve had nothing but success with the NEM program.

I’m glad they’ve served your family well. NEM and Discovering Mathematics are still on my short list, although I hesitate to commit to the integrated math model largely out of concerns that if, a year or so down the road, we don’t care for it, that we’re stuck starting algebra and geometry over. Simply put, they make a transition to a different program difficult and they could limit flexibility. When I was looking, some five years back, I didn’t know anyone who had used them but found plenty who’d used and liked Jacobs. So there we went. I’m delighted to hear positive feedback on that program, however. Thanks!

Transitioning to a traditional sequence after DM1 or NEM1 should be easy as it is mostly pre-algebra. Yes, the first book does get a bit into the easier parts of algebra 1 and geometry, but that would just allow the student to progress a bit more quickly through those courses.

We are doing DM1 now paired with Horizons Pre-Algebra. I accelerated DD after she finished Singapore 5A so the review in Horizons is perfect for quickly moving through the skipped topics of 5B-6B. Additionally, I like the spiral format of Horizons to make sure that DD really has everything totally rock solid before she moves on to algebra 1.

Forgot to mention that I’m considering getting the new Horizons Algebra 1 book when it is published next fall.

My older son, who thinks more along the lines of great literature and history, absolutely LOVES ALL of the Life of Fred books (we’re on Alg 2 and have done all from fractinos and decimals up – including both pre alg books with biology and economics). I am pleased to report that he has improved in math/algebra to the nth degree now that he is not looking into the eyes of Saxon, Teaching Textbooks or other similar programs. He is able to take the “story” of Life of Fred and use the math that is being taught withing it in a real life application in EVERY SINGLE lesson. I was cautioned not think of it as a whole course, or for a college-bound student, but believe solidly that those cautioners were WRONG! LOF has also introduced Home Companions for some of the books that give the students some extra practice when needed (we do all of it because I know my child is better for a little more practice). I highly recommend you look at it yourself instead of taking someone else’s word for it. Life of Fred is perfect for some kids!

Thanks for the enthusiastic review of LOF. We gave the Pre-Algebra I with Biology a try, but neither of us cared for it. (Here’s my review.) My older son tried his Advanced Algebra and had the same response. LOF certainly fits the needs of many homeschoolers, however, igniting an interest for math while thoroughly covering the material and used as a sole text through the high school level. It truly broadens the selections for math in a new direction. We ended up using Singapore’s Discovery Math, which we both really like. He appreciates its similarity to the previous Singapore materials, and I appreciate the depth and rigor of the program. This truly is the best benefit of homeschooling — the freedom to choose what works best for our children. Hurray for your son’s found pleasure in math!

We are enjoying “Mathematics, A Human Endeavor” by Jacobs. It is billed as a (college?) textbook for people who do not like math but I think that people who like math will enjoy it even more. It’s all the beautiful fun stuff that they never seem to get around to in school because there isn’t enough time. We aren’t through 6B, but we’ve started this book and are having fun with it. I think that if my daughter hadn’t been interested, I would have worked through the book on my own. I have a math degree, but this isn’t the sort of thing you normally get to study and I love it.

The current edition is expensive, but the older editions are more reasonably priced. Our library has several copies.

We have been using Singapore from 1a-7a (Discovery Math). My oldest is in 8th grade and after spending part of last year on Saxon Algebra, we switched back to Singapore. Math has been a favorite subject for all 5 of my children ( my kindergardener is in 1A). The curriculum we use recommended switching from Singapore in elementary to Saxon in Middle School, so we did. She had completed 6B and the curriculum suggested, if having completed 5B, to start in Saxon 8/7. I purchased the 8/7 and that lasted a week, she was bored stiff, seeing her losing interest in Math was heart breaking. I ordered Saxon Algebra and while we waited, she tried Singapore Discovery 7A for a month and was being challenged almost too challenged so we switched to Saxon Algebra and spent 2 months in this, again she was losing interest. We switched back to Singapore DM 7A, she is completing it next week in her 8th grade. My 6th grade son completed 6B and I am again at the crossroads of whether to switch to Saxon…My 5th grader is in 6A. As I look through Saxon Algebra and compare the two, I see benefits to both. At one point, I thought of doing Saxon Algebra and adding the story problems from Singapore for fun. The Saxon approach is how I learned Math so it is comfortable for me. My 8th grader has said the 2 months she spent in Saxon Algebra has helped her with Singapore 7A, so it was not a total loss. My 6th grader likes reading the text book for Saxon Algebra in his leisure. Looks like we are using both!

Thanks for writing up your approach and the potential options for a math-inclined student beyond Singapore. I really appreciate hearing some of the options you have considered. We have used RightStart from the beginning. My 7yo son and daughter are just finishing up Level E, the last level before starting on their intensive geometry course designed for middle school. We do plan to move forward with that, but RS suggests doing it over two years alongside algebraic work. I think we’re going to hit Singapore 5AB and 6AB quickly next (we have covered most of the topics already in the course of doing RS, but there are a few things I think it will be useful to pull from those books before moving forward), but then I’m considering a lot of the curricula on your list. I already have AoPS pre-algebra, so we’ll probably pull from that, and I like the look of Challenge Math here, which I hadn’t seen mentioned before. I’m kinda at a loss, and my kids aren’t even eight yet, so I feel like I have a lot of years of math to plan! Anyway, thanks for the suggestions! I’ll definitely be looking through them to see what might be a good fit for us.

I would add Jousting Armadillos pre-algebra/algebra series by Arbor Center for Teaching is a very interesting choice right now. This is relatively new to the homeschooling community since it only became available in 2012.

http://www.arborcenterforteaching.org/publications/books/

I saw that most of these posts were made 4 years ago, we are now at the dreaded “what to do after 6B” crossroads. Can anyone comment on what ended up working / not working for them? We’ve loved Singapore and don’t want to switch, but the info out there on Dimensions and New Elementary Math is sketchy. A hybrid school nearby uses Math-U-See (MUS) and since we plan on enrolling them there eventually (in 2 years), we’re thinking of starting with MUS pre-algebra. Any advice?

Unfortunately, Singapore Math has been slow to roll out the replacements for Discovering Mathematics. They appear to still be only done with two years of materials. We bought ahead and continue to use the older editions, but I’ve not seen copies available online for some time. MUS is a very different curriculum — far less focused on deep mathematical thinking. Art of Problem Solving is an excellent choice to consider. Jacobs Algebra and Geometry texts are also strong next choices. Good luck!

What would you recommend all through HS after Jacobs algebra? Thanks!

That’s a hard one, as there are so many more online options available now. For my older son, we used Jacob’s Geometry text, but that was so long ago, that I can’t tell you much about it.

My younger son stayed with Singapore, and that was excellent, but the books we used are now out of print, and we couldn’t access the series that came beyond that. He did some precalc with LIVE Online Math, as he’d had some trig. Well Trained Mind Academy has more math as time goes by, and that might be worth a look if AOPS isn’t for him. (It’s not a good fit for my guys.) Depending on his age and motivation, dual enrollment for math can be quite successful.

Good luck!

What would you recommend for algebra for someone that has a math mind but is probably not advanced. So something middle ground but that he could do independently through high school without much help from me? My son’s favorite subject was math in public school and now since homeschooling has done 2 modules of videotext in 6th and principles of mathematics 1 in 7th, and is getting more problems wrong than before, and doesn’t seem to enjoy it anymore.

It is likely worth a try moving to Algebra, as that may increase interest. We worked out of texts at this age, which allowed my sons to move at their own pace. If they had a skill down, we moved on without doing all the problems. Challenge can be everything when it comes to motivation.