Math 1: Commercial Curricula
Math 1: Commercial Curricula
Update: I’ll soon be adding comments on Math Mammoth. I’ve also summarized this information for quick reference. Please stop by! I will be adding interesting tidbits such as a video that looks at the drawbacks of curriculum reform in math.
If you are using an Old Fashioned Education (OFE) or Ambleside Online (AO) curriculum you will need to select a math program. Here are some ideas for you. I’ve grouped them under three main rubrics: 1) commercially available math curricula, 2) free math curricula and textbooks, 3) interactive math games and helpful printables. Except for the first category items, all the math resources on these pages are available free of charge. This may be helpful to you if you are starting out, even if not on a tight budget. Sometimes it may take a couple tries to find a curriculum that is a good fit for both you and your children!
As far as manipulatives are concerned, I suggest you look around your home and get creative! You can buy fancy sets of manipulatives but may find they are not much better than what you have already at home - or what you could have made or purchased at a garage sale or dollar store. Ideas for manipulatives include: bottle caps, bingo markers, poker chips, Lego, wooden blocks, coins, drinking straws, etc. These can all be turned into counters, but with a little imagination you can use them to teach operations, fractions, place value, etc. Or try virtual manipulatives! National Library of Virtual Manipulatives has a full range of interactive manipulatives for grades K-9. You can also find printable charts, graph paper, counters, and much more online at any of a hundred web sites. Just use your favourite search engine!
We do like our Cuisenaire™ rods (free printable version), and they are quite helpful if you are going to being using Miquon Math. At roughly $10-$15 for a starter set this is one manipulative that is worth investing in. If you are using a program that leans more on base-10 blocks look into these instead. Both the rods and the blocks are quite flexible in terms of what you can teach with them. Homeschool suppliers and teacher’s stores should be able to offer you a good selection of both.
Popular Homeschool Math Programs
Living Math is completely non-traditional, and uses living books to teach rather than textbooks or worksheets. The book lists can all be downloaded free, but Ms Brennan asks that parents consider purchasing books through her Amazon affiliate account if they use the lists without the pay lesson plans. Subscriptions that allow access to the lesson plans are very affordable, but do keep in mind that the books must then be obtained. If you are able to find them from the library, so much the better. But if you have to buy a lot of the books it will add to the cost of using this program.
Living Math is designed by a homeschooling parent, to be used with multi-age groups. Lesson plans & book lists are available for three levels: Beginner, Intermediate and Advanced/High School. Each level goes through the same subjects during the same time frame. There are 32 lessons, grouped into four historical periods from ancient to modern times (C1). A second set of 32 lessons examines math through the biographies of mathematicians (C2). While a complete list of books for C1 is available, the C2 books don’t appear to be on the site. There are also a great many books listed by subject, as well as books specifically recommended for beginning to use living books in math teaching. A great many other resources are also available on the site, so check it out!
Subscription rates for the lesson plans are $20 USD per quarter for one level, or $40 USD per quarter for access to all three levels. The program is self-paced and can be used as a complete curriculum or a supplement. If you have questions about how to teach math without the drills and memorizing and worksheets, articles are provided to help you learn more. There is a restricted access forum, and there are quizzes offered for those who feel they need these.
Developed by a (CM) homeschooling family, this math program is intended to make math preparation & teaching easier for homeschool parents. It is reasonably priced (around $40 - $45 USD per year) and works from the concrete to the abstract. Grades 1-4 include a parent guide, and after that the program seems to be self-teaching. They offer 1-6, plus a year of algebra. Geometry is covered in a new document, intended to tie algebra and geometry together as a foundation for trigonometry & calculus. A free PDF download of the draft version is currently available, so take advantage now if you are interested!
The parent guides cut down on planning time, by giving step-by-step instructions for demonstrating certain concepts. Mental computation and word problems seem to be a focus early in the program, although most of the pages in the earlier student books have very little writing. This makes them good for ESL students or children who are not yet reading. It seems the preparation for algebra begins very early in these books, and I wonder if perhaps it might be a little too much, too soon. Other than that concern, this looks like a good system. It’s affordable and doesn’t rely overly much on expensive manipulatives (moderately priced manipulatives packages can be purchased, but the items are all listed & you may already have what you need.) If you go on to use the earlier books with younger siblings you can get the student books separately, at under $20 US.
This is an extraordinarily popular program among homeschoolers. It uses videos to teach, and so it is a boon to parents who feel unsure of their own abilities to teach math. The web site is really well laid out and informative. At a glance (or a few quick clicks) you can figure out placement, manipulatives required, scope and sequence, etc. for any given level. The lessons begin at Primer level (children beginning to count and quantify) and proceed through levels Alpha to Zeta, then continue on up through pre-algebra, algebra, geometry, and pre-calculus. There is also Stewardship, a Christian approach to personal finance.
I had understood this to be a very expensive system to use, but was pleasantly surprised to find the Primer level materials cost $42 CDN without manipulatives. Levels Alpha through Zeta cost $57 per year. The $31 starter blocks set is re-used throughout the program, so you won’t be buying expensive manipulatives each and every year. High school levels can be almost $100 per year, but if you have a large family you will only need to buy teachers packs once per level. The student packs are fairly reasonably priced ($21 per year) and I think they may actually be reusable. You might want to consider getting a couple families together to reduce the cost, if yours is a small family or you only have some of your children homeschooling at the moment.
One neat feature of the program is a song book and CD that teaches skip counting and addition facts through music. I like the idea of including music with instruction (especially in math, as they are closely related skills!) This is an optional part of the program, but might be worth purchasing especially if you can get a few families together for a sing-along! There are two sets of songs on the CD: one with a Christian theme incorporated into the teaching, and the other drawing upon science for its lyrics.
Math-U-See offers a great deal of material through the web site, including blogs and FAQs, and a placement chart. There is also a Math-U-See users group that you can join to get support from folks who are using the curriculum. Further, if you are ever stuck on anything you can book an appointment for a support phone call from one of their helpers, or you might be able to ask your local representative’s advice.
If you are considering the Math-U-See method you can order a free DVD sample, which I did & immensely enjoyed! The demo package arrived quickly, and it was pleasant viewing. It answered my questions about kids getting dependent on the video. Actually, it’s not that much of an issue because a) the videos are intended for parent-teachers to view in preparation for teaching a lesson (although kids can watch too) and b) if the teaching videos are like the sample DVD, it’s not a passive experience to watch them. There is colour and movement and even humour, and the learning process is multi-sensory (a three step process involving building, labelling & then talking about a model.)
Math-U-See is a method that simplifies math as much as possible. It also has a highly visual approach to representing math problems. Steve Demme, who developed the program, is a former math teacher who taught at both the primary and secondary levels. The demo shows that he has a solid grasp not only of how to do math, but when and why. He also knows kids and teaching, and how to present things so kids will understand. One example he gives in the demo is how you can teach kids in primary school to factor a trinomial if you use a good visual to explain it. (Not that he’s suggesting we all go out & do that, it’s just to demonstrate that math isn’t so big & scary when you know how to put it into terms kids will understand!)
There are 30 lessons per level of Math-U-See, and each lesson is on the DVD or video. Viewing the videos takes about 10 minutes, roughly once a week. Then the student does practice with the blocks, and can do the worksheets. Each lesson includes a few sheets of practice and a few of systematic review that covers material already learned plus the new material. There is a test book, which gives one test per lesson plus four unit tests and a final exam. Tests are viewed mainly as diagnostic (so you can be sure your child has mastered the skill.) You can use them as extra exercise sheets, or give your kids practice writing tests.
Keep in mind that this system can be used starting at a very young age (as soon as your child is starting to count and quantify objects - some kids begin at age 4 or 5.) The lessons progress through four stages: 1) counting, 2) adding/subtracting, 3) multiplying/dividing, 4) exponents/roots. Preparation for algebra begins very early (in the add/subtract phase, I believe) but it is done very gently. Some skills are taught in a non-traditional sequence, for example the primer level introduces skip counting by 5’s and 10’s and even telling time! Other skills may be demonstrated first in a non-traditional fashion (e.g. regrouping, which most of us learned to call carrying & borrowing, is used to teach kids to do quick computations.)
Although slightly more expensive than some of the popular homeschool math curricula, Math-U-See is well thought out & provides a level of support that you won’t find in other programs. Unlike some others, it will carry you from pre-school right up to college level. It is creative, but its emphasis is definitely on teaching mastery. It is suitable for all types of learners due to its multi-sensory approach, and offers opportunities for both enrichment and remediation or review. It definitely deserves a look!
This is another program that is very popular among homeschoolers because of its non-traditional approach and cost. It is intended for grades 1-3, though it can be a good review for older students who need to strengthen their math skills. The program was created in collaboration with children, and teaches by presenting the student with problems that will lead them to discover patterns and draw their own conclusions. In other words, there is no lecturing or memorizing. Children learn at their own pace, and do not have to do all the worksheets in order to progress through the program. There is no busy work, and it is not even required to do the sheets in a particular sequence (students don’t even have to do all the work on a given sheet.) Some parents offer their children a selection of appropriate sheets to work on, and allow the children to choose.
It is a good idea to get the teacher’s book (Lab Sheet Annotations) in order to become more familiar with the teaching philosophy behind Miquon. Even if you are good at math, you may find that you learn a thing or two in reading it! All the “why’s” are explained for you, and Ms Rasmussen underlines that to be good teachers we have to be our own first students. It is possible to do Miquon without this book (skip the first few work sheets, though!) so if you are on a budget get it later. You can also download it as a PDF at a lower cost than buying the hard copy. The student workbooks can also be purchased as e-books, for a slightly lower price (advantageous for Canadian homeschoolers while the dollar is strong!) This is good for larger families, as it will likely cost less to print only the sheets you need than to order several hard copies of each book.
If your children do the full six books of Miquon (2 per year) they will learn math in a non-traditional sequence, but at a very gentle pace. All four basic arithmetic operations (+, -, x, ÷) are introduced by the end of grade one, and students learn a few other things by the end of grade 3 that are not normally covered until later. This non-traditional sequence was developed to respond to what average children in Ms Rasmussen’s math classes were able to do, and other programs similarly adopt a non-traditional sequence (e.g. the free Défi-Math program, which will be included on the Math 2 page.)
Educators who offer these programs sometimes say that traditional learning sequences actually hold children back. From my personal experience, this would seem to be true. Both my older girls were able to intuitively understand (and put into practice) concepts such as multiplication, division, fractions, etc. well before they were “supposed to.” With a traditional approach I was afraid to encourage these discoveries, lest they get confused attempting material that was too far beyond their level of instruction. With Miquon I have learned to respond to their discoveries without fear. We give them work that gently challenges them to go further, trusting that they will know where their own limits are.
Miquon uses the Cuisenaire™ rods. If you can’t get them right away, you can print up the free version from the link above. Other manipulatives may be helpful, but are not required. There is no text book at all for this program. The student workbooks are consumable, and cost $6.50 USD each in e-book format, or about $8 USD in hard copy. Begin with the Orange Book. For folks who would like to transition to Singapore Math, or to use the two programs concurrently, this comparison chart may be helpful.
This program is very non-traditional, and was designed to prevent children from becoming dependent on counting in order to do computations. NB: It is intended to be started at age 4 or 5, so don’t wait till grade 1 if you are wanting to use it! The system uses an abacus as one of its main teaching tools, and is very visual. The idea seems to be to teach children to visually recognize groupings of 5 and 10 so they won’t have to count. It makes use of tallies, as well as the abacus. Draw-backs are that the program relies on very expensive manipulatives and that it leaves off after fourth grade (there is a geometry program as well, but no directions about when it should be taught.)
You may find it very helpful that an evaluation grid is at the front of the teachers’ guides, with all the years skills listed and check boxes for mid- and end of year. The geometry lessons looked really beautifully done too. This looks like a well thought-out program but may not be the best option for those on a budget. Additionally, it may not be the best choice unless you can start it at the preschool level (there is a placement quiz for older children, if you want to give it a try.) You might be able to get the manipulatives together yourself at a lower cost. There is a virtual abacus that could substitute for the more expensive one, if you need it. The books themselves are $45 - $65 US for teaching guides, and $10 - $18 US for workbooks. Alternatively, the worksheets for the whole program can be had on CD for $100 US.
Saxon Math is reputed for being a rigorous program. There is a special homeschool edition that is quite popular (just follow the link, it will take you directly there.) The site will give you all the placement and scope & sequence information you need. There are even online activities to supplement the texts. Supplies for each year include the student workbook, the teaching guide and what is called a meeting book, which the student uses for practice. The books run about $80 - $100 USD a year, depending on the level (slightly discounted if you buy a package.)
The program covers K-12, with books being grouped by level: Primary (K-3,) Intermediate (4-8) and Upper (9-12.) The Upper Levels include algebra, geometry & trigonometry, and high school pre-calculus. The Primary Level of Saxon Math places emphasis both on hands-on work and mental computation. It uses a multisensory approach (hence the heavy reliance on manipulatives) and intended to build confidence through success. Course numbering in the Intermediate and Upper Levels may be a bit confusing, but essentially the first number is for the average student and the second is for the more advanced student. So Math 5/4 is for the average 5th grader or a more advanced 4th grader.
Keep in mind that Saxon is often more advanced than other programs, so if you are switching over use the placement tests. As far as the Upper Levels are concerned, the progression is from Algebra 1 to Algebra 2, then Advanced Mathematics. Afterwards the student is ready for Saxon Calculus or can enroll in a college calculus class.
One of the negatives with Saxon is that it requires an expensive manipulatives kit. The kit, however, contains all materials needed from K-3. The kit description lists all the items and tells when they will be needed. You might be able to get just some components and improvise others, or you could try to get a second-hand kit. If you are pretty sure you will do well with Saxon, though, it is not especially expensive when the cost is spread over just the four years one child would use it (under $10 USD per years.) It’s just a matter of the initial outlay.
Homeschoolers who enjoy a lot of structure may find Saxon reassuring, though others will find it restrictive and struggle with it. I have heard quite a few say their children absolutely bloomed using Saxon Math, but an equal number have said their children came to hate and dread their math lessons while using Saxon. This is one of those curricula you will either love or hate! Need more information? Check out the user forum.
Singapore is so called because it was developed following the instructional model used in Singapore, where students are known for their outstanding math skills. If you get Singapore for your younger ones, the books are actually called Primary Mathematics. The high school books are called New Elementary Math or New Syllabus Math (both grades 7-10) or New Math Counts (less challenging, grades 7-10) and College Math (grades 11-12.) Singapore schools have a different structure, so try not to get confused by the titles! A two-year (age 4 & 5) kindergarten math program is also available.
Singapore math is known for being rigorous, and some students do not much care for it. If you have a very keen math learner it may be for you - or you may want to do as a lot of homeschool families do, and transition into Singapore from the Miquon math. Singapore places emphasis on mental math and word problems. If either of these is difficult for your child, Singapore might be too much for them without a very slow and relaxed transition.
There are placement tests available on the site, if you need them. The kindergarten and 1-6 programs are split into two: an “A” book for the first half of each year, and a “B” for the second half (kindergarten consists of 1A & 1B for 4-yr-olds, and 2A & 2B for 5-yr-olds.) Some of the high school books are similarly split, but most are full-year texts and workbooks.
The program is taught using a text, a workbook, a teaching guide and a solutions manual (these last cover several years, whereas there is one guide per student text.) A homeschool version of the teaching guides is available, and is less expensive than the school version. You do not have to buy the answer books, as answers are supplied in either the student books or the teacher/homeschool instructor books.
Singapore books are reasonably priced, and some suppliers will offer them in packages at a slight discount. Texts at the elementary level are $8 USD each and workbooks are just under $4 USD each. The homeschool manuals are $12 each. The high school materials vary a bit more in price, but you should be able to get a year’s worth of texts for about $16 - $25 USD.
Workbooks run about $8 - $13 USD per year and are not consumables. They are intended for students wanting extra work and are completely optional. They come with answer keys. The question of teaching guides is a bit complex, but essentially they are not needed with the Math Counts books. If you are going to use Singapore be sure to do your research to avoid buying the wrong or unnecessary materials. Also check out the customer forum, which has areas both for prospective users & those who have purchased one of the books.
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Due to the sheer bulk of information to be shared in this subject, I am splitting it into three pages. Please look for Math 2: Free Curricula and Math 3: Interactives & Printables.
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