What I Did After Singapore Math (& Other Math Fails)

Homeschool algebra options for high school and middle school

When I was a homeschool kid, there were really only handful of ways to handle algebra: Saxon, Abeka, the Christian university publisher which shall not be named, or the local community college. If you got stuck, you consulted Key to Math workbooks. Now, there are so many options for teaching homeschool algebra, it’s hard to narrow them all down! Yet if there’s one question I get asked more often than any other, it’s this —

Help! What comes after Singapore Math?

That’s the million dollar question, isn’t it? Let’s tackle it.

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This post is long. I wrote it myself. I’ll never, ever, use ChatGPT to generate any kind of content.

For years, math was the easiest subject for me to decide when planning my homeschool year, because the answer was always Singapore Math. (I prefer Primary Mathematics: Standards Edition. You can read all about why I love Singapore Math.) But when we finished up the primary K-6 sequence a couple years ago, we quickly discovered the options for middle school math in this country are pretty much a quagmire.

Singapore Math already has middle school math for grades 7 and 8.

In retrospect, after Singapore K-6 math, I should have simply moved on to Singapore Maths’ secondary 7-8 sequence, New Elementary Mathematics. I am not sure why I did not. Perhaps it was the confusing name: New _Elementary_ Mathematics. Perhaps I paid too much heed to the bitter advice of homeschool moms who were jealous of Aveline’s math prowess, and treated me poorly as result. (Okay, we don’t have to unpack that here, but if you’ve ever been in this situation, you know what I mean. I hope I have learned from this, and hope I will trust my gut more in future.)

In any case, if I had to do it all over again (::waves to Lochlan::) I would simply move from

• Singapore’s Earlybird Kindergarten Math Standards A–B, to
• Singapore’s Primary Math Standards Edition 1-6, to
• Singapore’s New Elementary Math 7-8, then to
• a provider of iGSCE Mathematics, such as Dr. Frost Maths’ FREE self-paced iGSCE Cambridge International math course, or a Cambridge Extended Mathematics for iGCSE text (I bought this one for $6, but there’s a newer edition as well)

So the first answer to “What math should I do after Singapore Primary Math?” is, more Singapore Math!

Save yourself! If you’re reading this in time, you still can do this sequence!

And if you’re like me and you didn’t, keep reading. I’ll tell you everything, including a list of more homeschool algebra curriculums you might want to consider.

But wait! Why are you talking about Standards Edition and New Elementary Math? I need information on Singapore’s Dimensions Math.

People always ask me why I didn’t do Dimensions Math, and chose Primary Math: Standards Edition instead. The answer is simple: because Dimensions for K, 1, 2, 3, 4, and 5 simply didn’t exist when Aveline started math. By the time the full series of Dimensions Math K-5 finished rolling off the presses, Aveline was already done with primary school math.

If you’re doing Dimensions, you can simply complete the recently released K-5 series, then move right into the older Dimensions 6-8 middle school math series. This is essentially the same as completing the Standards (or US Edition, or Common Core) editions, and then moving in to New Elementary Math. In both cases, you’ll finish Singapore Math in 8th grade already having Algebra I under your belt.

Ok, but what do you do after Singapore Math’s New Elementary Math? Does Singapore Math teach algebra?

Another super common conundrum: what to do after the last book in Singapore Math’s New Elementary Mathematics series, or, after the last book in the Dimensions 6-8 series? A mom in my online homeschool group — which is free to join, by the way — reports that she asked Singapore Math for advice on high school math. Singapore Math replied, “Singapore math programs do not continue beyond Grade 8. Students may move on to Geometry and Algebra II programs.”

So if you complete New Elementary Math 1-2, you’ll already be done with Algebra 1. If you complete Dimensions 6-8, you’ll already be done with Algebra I. That’s amazing.

If you’re reading this and you’re wrapping up Singapore middle school math and are looking for Algebra II and Geometry options, be sure to read all the way to the end. I’ll link to a bunch of high school math programs you might love.

See how much easier it would have been for me if I had just bought New Elementary Mathematics? Instead, I wandered about in the hinterlands of middle school mathematics. Woe is me.

Here’s what worked, and what didn’t. Learn from my mistakes. (In fact, my mistakes are why I didn’t write this blog post sooner. People don’t have the patience for listening to circuitous tales. Everyone wants a quick fix and an easy answer. But here’s my tale.)

Why Art of Problem Solving and MEP / CIMT didn’t work for us

After Singapore Math’s K-6 sequence, we tried — not at the same time — both Art of Problem Solving’s Pre-Algebra and Mathematics Enhancement Programme (MEP) from the Centre for Innovation in Mathematics Teaching (CIMT). Neither worked for us. I hope I won’t get a lot of emails about this, but remember, every student is different. I certainly am not going to keep you from Art of Problem Solving or MEP / CIMT, but if you are trying these and you’re discouraged, consider maybe they’re just not the right fit for your student.

Simply because a product is recommended over and over in homeschool subculture, doesn’t automatically mean you are going to thrive using it.

For us, the Art of Problem Solving’s Pre-Algebra didn’t provide enough instruction (although I understand that’s part of the learning philosophy). We gallantly plodded through, but it wasn’t engaging, and certainly didn’t make us want to continue on using the rest of AOPS secondary math series. Even Alcumus, AOPS’ free customized math program which will give the user progressively challenging problems, is easy for a student to “game” and only do the easiest problems. (Yes, my child did this.)

As far as MEP / CIMT, it was the plethora of errors in the secondary-level teacher’s materials which sent me screaming into the sunset. Ain’t nobody got time to argue with a kid over proofreading math texts. But it’s important to point out I do absolutely agree with the MEP philosophy of teaching math. I believe that the UK model (see also: the Hungarian model or the Singapore model) on which Mathematics Enhancement Programme is based is the right way to go. While the specific execution of the available MEP materials wasn’t a good match for the way my brain is organized, the scope and sequence is solid. (Later in this post, I’ll talk more about the positives of UK-style maths, and other options which might work for you.)

These years weren’t necessarily wasted, but after wandering in AOPS-ville and MEP-land for too long, we switched gears.

Which brings me to the next important point —

Here’s how you can prepare for high school math and bridge the gap between primary math and algebra by focusing on problem solving skills:

Even though AOPS and MEP were a fail for us, the rest of this blog post focuses on wins. Let’s talk about everything that has worked or us. At the end of this post, I’ll link to additional homeschool algebra options we haven’t tried, but might be a great match for you.

There’s still quite a bit to read, so grab the permalink and pin this or share this to come back to later if you need to!

Practice middle school mathematical thinking with Edward Zaccaro’s math challenge books.

Mathematical thinking is too often overlooked. It’s a skill that’s really taught well in Singapore Math, and I wanted to make sure we didn’t neglect it as we moved forward in math.

To hone those problem solving skills, I highly recommend Edward Zaccaro’s books. (Colleen Kessler of Raising Lifelong Learners originally recommended these to me at a conference where we met Mr. Zaccaro — so credit goes to her!)

These aren’t a full math curriculum, per se, but it’s absolutely worth pausing to work on these skills. I see no reason why they couldn’t be used as a semester or two while you bridge the gap between elementary school and middle school, or between middle school and more algebra. Of course, you can also use these alongside whatever math curriculum you’ve chosen.

Depending on where your child is in math, you’ll either want

• Upper Elementary Challenge Math (concepts from grade 3-5 standards),
• Challenge Math for the Elementary and Middle School Student (concepts from grade 5-8 standards), or
• Problem Solving Genius (problem-solving concepts from grade 4-12 standards)

Problem Solving Genius is an especially great book to jump in to after finishing Singapore Math’s K-5 or K-6 math sequence. The format will be familiar since the content is still conversational, the problems are fun, and the student will learn some new mathematical concepts, too. Aveline really likes it.

Browse all of Edward Zaccaro’s math books for gifted kids to see which titles might be the best match for you.

Brush up on computational skills with the Doodle Maths app.

Another fun option, especially to keep computation skills sharp: Doodle Learning’s Doodle Maths app. It’s not a full math program, but it’s a very effective enrichment and it’s a great way to check for gaps. This is a subscription-based product and is based on UK math standards for ages 4-14. It’ll differentiate instruction up to eighth grade math, based on your child’s baseline assessment. If you have a mathy kid who excels at thinking conceptually (AKA mathematics), but might need some more computation (AKA arithmetic) practice, this will be a great fit. We have certainly loved it! This programs works best if you only use it ten or so minutes each day.

Do note, if you’ve already finished New Elementary Mathematics or Dimensions 8, then Doodle Maths will be too easy for you. It covers skills through US 8th grade, or UK Year 9.

You can get a steep discount if you purchase Doodle Maths through the Homeschool Buyers Club. Note: believe there may also be a US version now, but the previous link appears to still be for the UK version. If you have questions, you can contact Doodle Learning directly.

Take advantage of the UK’s vast range of math resources to teach integrated mathematics.

Remember how I mentioned how kids who finish New Elementary Math 1-2 or Dimensions 6-8 will come out of those books having already done Algebra I? That’s an example of integrated math. For Americans, integrated math is still somewhat of an unknown, although it’s common pretty much everywhere else.

In districts which take the integrated mathematics approach, algebra isn’t an end unto itself. It’s simply one of the half dozen or so strands of math you learn as you go through your middle school and high school years. Integrated math sets a wide feast of mathematics, so kids learn more than just algebra, or just geometry.

I love the integrated mathematics approach. I love how all the various and sundry skills are presented in a connected and holistic way, interleaving amongst each other. In fact, most countries around the world take this path. And materials from the United Kingdom, already being in English, are a great resource.

This integrated approach is the main reason we have chosen to continue with a non-American approach to math, especially coming from the Singapore method.

How does Integrated Math compare to a standard Algebra and Geometry sequence?

Middle or high school students who complete courses in Integrated Math I, II, and III will earn the same number of credits as student who complete Algebra I, Geometry, and Algebra II. (Bonus: they’ll also get some instruction in trig, statistics, and more.) In the UK, you’ll see the term “GSCE Maths” or “iGSCE Maths” for the material that’s generally covered in Integrated Math I, II, and III or Algebra I, Geometry, and Algebra I.

(And at the end of this post, I’ll list even more algebra, geometry, and calculus options for homeschoolers, so hang in there.)

Help! I’m lost. What do you mean by GCSE? How can I match up US grades to UK Years and Key Stages?

Here’s a quick reference to the way age and stages work in the UK:

• Nursery is equivalent to US preschool, or ages before 4
• Reception is equivalent to US pre-kindergarten, or ages 4-5
• Year 1 is equivalent to US kindergarten, or ages 5-6
• Year 2 is equivalent to US Grade 1, or ages 6-7
• Year 3 is equivalent to US Grade 2, or ages 7-8
• Year 4 is equivalent to US Grade 3, or ages 8-9
• Year 5 is equivalent to US Grade 4, or ages 9-10
• Year 6 is equivalent to US Grade 5, or ages 10-11
• Year 7 is is equivalent to US Grade 6, or ages 11-12
• Year 8 is equivalent to US Grade 7, or ages 12-13
• Year 9 is equivalent to US Grade 8, or ages 13-14
• Year 10 is equivalent to US Grade 9, or ages 14-15
• Year 11 is equivalent to US Grade 10, or ages 15-16
• Year 12 is equivalent to US Grade 11, or ages 16-17
• Year 13 is equivalent to US Grade 12, or ages 17-18

You’ll most often see material identified by Key Stages, abbreviated KS. These work as follows:

• EYFS: Nursery and Reception
• KS1: Years 1-2
• KS2: Years 3-6
• KS3: Years 7-9
• KS4: Years 10-11 (You will also see this listed as GSCE)
• KS5: Years 12-13 (You will also see this listed as A Levels)

For middle school math, you’d look for KS3 (Years 7-9). For Integrated Math I, II, and III / Algebra I, Geometry, and Algebra II topics, you’d look for KS3 or GSCE (Years 10-11). For even higher math, you’d look for at KS5 or A Levels (Years 12-13).

The term GSCE stands for General Certificate of Secondary Education, and is usually connected with exit exams for various subjects, taken between Years 9-11 (ages 14 and 16) throughout the United Kingdom. When you see iGCSE, this is referring to the International General Certificate of Secondary Education. Of course, anyone can access and use the iGSCE curriculum for any subject even if they’re not going to take the exams. I’m using the iGSCE Maths framework as a guide for Aveline’s Integrated Math credits.

If you’re not in love with this option, keep reading. At the end, I’ll link a whole list of even more homeschool high school math options.

But first, what curriculum we’re using for algebra after Singapore math:

Here’s where my mistakes show up. If we had used Singapore middle school math — such as New Elementary Math 1-2 or Dimensions 6-8, we wouldn’t even need an Algebra I curriculum. But I didn’t, so I do.

We’re using Understanding Algebra I, part of the Mathematical Reasoning series from The Critical Thinking Co. It’s fantastic. I highly recommend it! Since Understanding Algebra I is a paperback worktext, it’s not intimidating. There’s no bulky teacher’s guide, and the solutions PDF is free (can you hear the angels singing?)

There’s some debate among homeschoolers about whether it’s a complete curriculum (perhaps because it isn’t stuffy enough, haha!) but both the Critical Thinking Co. and Cathy Duffy say it is.

And here’s the curriculum we’re using for iGSCE Maths: Dr. Frost Maths’ FREE self-paced high school math curriculum.

What math should I use after Singapore Math? We’re finally getting to the answer. After Singapore Math New Elementary Math 1-2 or Dimensions 6-8, you should be able to jump right in to iGSCE Maths.

Dr.Frost Maths is a FREE online math platform based in the UK. It’s a registered charity in England and Wales, named after its founder, mathematics aficionado Dr. Jamie Frost. This may be one of the most overlooked treasure troves on the math internet, actually.

We’re using Dr. Frost Maths as our main high school math curriculum next year. Dr. Frost Maths — or simply, DFM — is wonderfully systematic, with everything broken down into key skills. It is a self-paced high school math curriculum which includes instructional videos for most key skills. And it’s completely free.

Each time key skills are revisited in the curriculum, they’re taught in progressively more complex ways. I love that! Because of this, Dr. Frost Maths — and UK math in general — is both mastery (sequential) and spiral (scaffolded).

Here’s a quick guide to navigating the Dr. Frost Maths website.

To access a course, go to Dr. Frost Maths, then click on the Menu in the upper left hand corner. Under Tasks and Learning, click on Courses. From there, click on Exam Boards and Publishers. (Remember, this is all free!)

You have a lot of options in front of you. To see what I mean, click on Go underneath the Edexcel heading. Here are all the free Edexcel courses.

To brush up on grades 6-8 math, look at courses for Year 7, Year 8, and Year 9. To move on to Integrated Math I, II, and III (Algebra I, Geometry, Algebra II), go to Edexcel’s iGSCE Foundation or iGSCE Higher.

You can also access another version of iGSCE Maths by going back to Exam Boards and Publishers, and clicking Go underneath the Cambridge heading. This will give you the Cambridge Exam Board’s version of iGSCE Maths.

We are doing Cambridge iGCSE Mathematics next year.

You can easily see what a sample lesson will look like by clicking on any key skill in any of the courses above, and clicking practice. For example, here’s the first lesson of Cambridge International’s iGSCE Mathematics. Click the blue practice button to start the lesson, or tick specific subskills to isolate your practice session to only those topics.

Using FREE math videos for FREE math help when you’re stuck

We’ve used Dr. Frost Maths for quite a long time now for key skills practice. Whenever Aveline gets stuck on a concept, we go over to the Dr. Frost Maths website, look up the skill we need help with, watch a video, and complete some practice problems. It works so well for us. (Bonus tip: you can also do this with the Maths Genie YouTube channel, and with videos on the Corbett Maths website. The Maths Genie YouTube also has a GSCE Maths Full Course playlist. Do you know about the Chrome extension which blocks all YouTube ads?)

Using the exam feature to test out of review skills in Dr. Frost Maths

Next year, Aveline will officially begin Cambridge International’s iGSCE Mathematics

Since she’s already completed The Critical Thinking Company’s Understanding Algebra I, the first part of iGSCE Mathematics will be review. If you’ve already completed New Elementary Math 1-2 or Dimensions 6-8, you’ll also encounter some review. but here’s a huge perk about DFM: it doesn’t force you to go through lessons you’ve already mastered.

As you work through a course, you can attempt exams and test out of a whole bunch of already-mastered skills at once. Just tick the “exam practice” boxes rather than the “key skills practice” boxes, and proceed with the lesson. (Exam skills begin with E.) No more getting stuck in endless loops of review!

Aveline loves being able to focus her time on topics and key skills which are actually challenging (or which truly need review), and I love the online dashboard on my parent account which gives me visibility into all the skills attempted, mastered, and in progress. We can both see the linear progress, which is hugely motivating. The parent dashboard also gives me access to the complete markscheme, AKA the solutions — not just the answers! This is vital.

10+ homeschool curriculum options for Algebra, Geometry, Pre-Calculus, and Calculus

Maybe you’re completely uninterested in attempting the iGSCE framework. That’s ok! As I promised, here’s a helpful roundup of even more high school math curriculum options for your homeschool.

We haven’t used these, but you might find the perfect match here! Keep reading…

If you skipped down to this part, you may have missed that I recommend Dr. Frost Maths, a FREE self-paced integrated high school math curriculum based on the UK model.

If you’re looking for video or self-paced high school math curriculum options after Singapore Math, try these:

ALEKS

This is an adaptive self-paced online math program, which will differentiate based on the ability of the student using the curriculum. Individual (non-school) pricing for can be found here. You can choose a single algebra or single geometry strand, but ALEKS also offers Integrated Math I, II, and III. Pro tip: if you’re looking for Algebra II / College Algebra, then consider Arizona State University’s Universe Learner program, which also uses ALEKS.

Arizona State University

This unique program allows anyone, including high school students, to take first-year college classes for $25. After you take the final exam, if you’re happy with your score, you can pay an additional fee and choose to transcript the class for college credit. At the time of this post, the fee for transcripting the online College Algebra / Algebra II course was $400. College Algebra at ASU is a self-paced course which runs on ALEKS.

(Thanks to @marielhowsepian for all the info about College Algebra at ASU!)

CTCMath

This online math program combines videos and interactive “worksheets”. CTCMath a very flexible option, since one subscription gives you access to all math K-12 levels, right through Calculus I. It’s important to note that the questions are almost all multiple choice, which could be a significant deterrent to mastery if you have a student who is skilled at guessing multiple choice questions.

Mr. D Math

Highly popular among homeschoolers, these self-paced courses are the brainchild of Dennis DiNoia, and have expanded beyond math to other LIVE course offerings as well. For self-paced math, students can choose from pre-algebra through pre-calculus. One big thing which sets Mr D Math’s self-paced courses apart? Students can get help from a live teacher.

Shormann Math

Shormann Math offers self-paced math courses for pre-algebra through calculus. Although pre-recorded lessons for Saxon are also available, if you were scarred by Saxon as a homeschool child, fear not. The Shormann courses are separate from Saxon, and have been completely redesigned since the SAT math portion changed in 2016. The content in a Shormann course will prepare your student for standardized testing. Shormann uses a partially integrated approach, so Algebra I will give you the first half of a Geometry credit, and Algebra II will earn you the second. Placement tests are available.

Thinkwell Homeschool

These à la carte 6th grade through Calculus video math courses come to you from the same company as Rosetta Stone. Thinkwell also offers IB, AP, CLEP, and Honors options, as well as some non-math courses, such as science and economics. Placement tests are available.

VideoText Interactive

This video program groups credits uniquely: the Algebra course gives the student Algebra I, Algebra II and 0.5 pre-calculus credits, while the Geometry course gives the student one credit of geometry and a half credit of either pre-calculus or trigonometry. Read more about the VideoText math approach.

If you’re looking for physical pen-and-paper high school math curriculum options after Singapore Math, try these:

The Critical Thinking Co

These paperback worktexts, a part of the Mathematical Reasoning series, are accessible and approachable, yet thorough. I describe them in a little more detail above. Choose from Understanding Algebra I (we’re using this right now), Understanding Geometry and Essential Algebra for Advanced High School Math and SAT.

Jacob’s Elementary Algebra

This classic Algebra I textbook has been republished by Master Books. Why is that a big deal? Because now the solutions manual for Harold Jacobs’ elementary algebra is easy to obtain! Also available: Elementary Geometry. There are DVDs available for both.

Foerster’s Algebra II and Trigonometry

This is a highly-esteemed Algebra II text. The solutions manual for Foerster’s Algebra II and Trigonometry can be hard to find, but Veritas Press sells it in PDF form.

(Why isn’t Paul A. Foerster’s classic Prentice Hall Algebra I on this list? Because the solutions manual is out of print!)

Math-U-See

Known for their hands-on approach to elementary math, Math-U-See also offers pre-algebra, algebra I, geometry, algebra II, pre-calculus, and calculus. A huge plus of this curriculum — complete solutions manuals! And additional instructional DVDs are available.

Want to outsource high school math? Here are 7 options for LIVE online high school math classes.

I’m constantly amazed at how much more support there is for homeschool students now, compared to when I was homeschooled! This isn’t an exhaustive list, but here are a few of the places you can find online high school math classes:

• Mr D Math
• Memoria Academy
• The Potter’s School
• Scholé Academy
• Veritas Scholars Academy
• Well Trained Mind Academy
• Wilson Hill Academy

What do you think? What will you do after Singapore Math? Will you be trying Integrated Mathematics courses, or will you go the more traditional Algebra I & II and Geometry route?

Hopefully the resources here can help you bypass the pitfalls of my mistakes. I hope you found resources to help you as you continue your math journey after Singapore Math — or at least, found some new ideas to research.

Did I miss your favorite option for high school math? Have questions about iGSCE Maths? Leave a comment below!

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