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Algebra 1 curriculum – recommendations for home schooling

This article lists some recommendations for an algebra 1 curriculum for home schooling – in particular for those of you who have used Math Mammoth during middle school years, and want to know where to continue after that.

(Please note: Math Mammoth users can go to an algebra 1 program directly after finishing Math Mammoth grade 7, since MM7 is a pre-algebra program.)

In a nutshell, I recommend for most homeschooling parents to use a textbook along with some video instruction.

Why a textbook? Because it is good for students to learn to use a regular algebra textbook at this stage of their studies. It helps prepare them for any further studies (whether college or vocational) where they need to learn on their own, reading a textbook.

Also, good textbooks include not only basic exercises but also challenging ones. If you decide to go with some online algebra curriculum or video instruction, a regular textbook can act as a reference and as an additional problem "bank" for those challenging problems. You can also use it to check that your student is really getting instruction in all the typical algebra 1 topics.

Why videos? Because those replace the component that is present in regular classroom: the teacher explaining concepts and ideas. Learning algebra from a textbook alone might be too difficult for some students. If the parent cannot explain the math, videos will help bridge the gap. In today's world, there exist MANY free websites with algebra videos that can be used. And, some companies provide videos tailored to a specific textbook.

In this article, I first explain some basic options for algebra 1 in a homeschool setting. Then, some textbooks are described in more detail. The article also lists free algebra video websites, algebra online curricula, and gives a link to algebra tutorial website list.

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Options for algebra 1 course in a nutshell

  1. Use a regular textbook, along with video instruction specifically tailored for that book. There exist several companies offering this, often with a steep price tag, considering that nowadays you can find even free algebra video courses online. Here are some options:
    • Math Without Borders (using Foerster's Algebra). Includes video lessons to match the textbook plus solutions to assigned problems on video. $79 + you need to purchase the textbook separately. Please see my review for more information.
    • Foerster's Algebra For an online class with this textbook, check out Liberty Tutorials.
    • Ask Dr. Callahan (using Jacob's Algebra). about $200.
    • VideoText Algebra — both algebra 1 and algebra 2. This one does not have a textbook but printed course notes and exercises (the videos are the "textbook"). I would consider purchasing some used textbook for a handy reference and for additional problems, especially for applications and word problems. $299 online version; $599 on DVDs.
    • Chalkdust (using Algebra by Ron Larson). $469. See also the site Algebrawithinreach.com mentioned further down on this page.
  2. An online class using a textbook. For example, Liberty Tutorials offers classes using Foerster's Algebra 1 book.
  3. Use a regular textbook, along with videos from various math websites that may not be exactly tailored to the book. This is probably one of the most affordable options, because there exist so many sites offering free math videos.
  4. Use a regular textbook, along with an online math curriculum or tutoring. Similar to the one above, but more expensive. However, you get more support and resources, such as online quizzes, worksheets, reporting, etc.
  5. An algebra course from one of the homeschooling companies. The drawback is that the authors of these products may not be math professors or even math teachers, and so the mathematics is often on a more "shallow" and superficial level than in textbooks authored by mathematics professors & teachers. Also, the explanations given for concepts may also be lacking in depth, and concentrate only on how to do the calculations, and not on the "why", or on the connections between concepts. Of course this varies from product to product, but I have seen some that judging from the samples were really "shallow".

    However, I'm not saying these can't be used. If your student does not need a strong math background for future studies, they can be fine. Some families may also prefer the "format", whether it be many workbooks, a computer-based curriculum, or some other format.
  6. Enroll your child in a community college basic algebra course.
  7. Hire a tutor, either a tutor that visits your home or an online math tutor.
  8. What about Saxon algebra 1? The problem with Saxon is not the content itself, but how the lessons are organized. Saxon mixes in the topics and does not have chapters on certain broad topics, like other algebra books. For example, one lesson is on range, mean, median, and mode. The next is on conjunctions, the next is on percents, and the next one on polynomials—and so on. I don't think that is the best way to learn. You can read more about my opinion on Saxon math here.
  9. What about Teaching Textbooks? This program is generally recognized as being quite easy and not challenging. The word problems I have seen in their samples are definitely too easy, for any grade I've looked at. Therefore, you cannot expect it to teach problem solving very well. This is actually unfortunate, because many parents and kids like its format. It would be a good program for low-performing students because it is so easy.

    This is verified for example by this review left for my other math site:
    We loved this curriculum until we looked at the Prentice Hall Algebra I book that the local high school was using. Then we realized that Teaching Textbooks Algebra I is way behind grade level! My son completed TT Algebra I and now is going through the Prentice Hall Algebra I book, to fill in the gaps, which are huge. This is taking him another 4-5 months! I had trusted Cathy Duffy's reviews of TT, and found I was wrong not to check it out more.
    However, the method of Teaching Textbook is great -- the kids enjoyed doing it on their own, with access to the CD's and textbook.

    If your student is college bound and plans to take the SAT and/or enter public high school, I would not recommend this curriculum.

  10. What about Singapore New Elementary Mathematic (NEM)? This series of books covers grades 7-10, and is considered to be quite challenging in its problems. Also, it may not have enough explanations of concepts, and the sequence of topics does not follow the traditional American way, but prealgebra, algebra, geometry, and statistics topics are mixed. If you feel comfortable with this, it will be fine, but I would only consider it for "mathy" kids because of the difficulty of the problem sets. Singapore Math also offers other series for grades 7-10 that are easier than NEM; please see a comparison here. Well-Trained Mind forum has lots of discussions about using NEM.
  11. Someone once asked my thoughts concerning Algebra 1 book by the Critical Thinking Company. This is a single textbook/workbook that contains the instruction and exercises all in one book. Based on what I read about it, it looks good! There are plenty of word problems and also challenging problems. However, based on user reviews, the explanations in this book may not be detailed enough for many students. Also, Cathy Duffy says it lacks tests and mixed reviews. I suggest supplementing this book with online videos that teach the concepts and with some source for review problems (maybe a textbook).

A regular algebra 1 textbook

If you go with the option #2 or #3 listed above, the textbooks that I recommend are:

  • Harold Jacobs Algebra
  • Foerster Algebra 1
  • Prentice Hall Mathematics Algebra 1
  • Art of Problem Solving Introduction to Algebra (for strong math students)

The choice between the top three might not be easy. In a nutshell, Jacob's book is lively, concentrates on concepts, well-admired by a lot of people for its entertaining style, and has very good and interesting exercise sets. However, it is also a bit "lite" in content.

Foerster's book is considered one of the best, if not the best, by some. It goes much deeper, perhaps too deep for some students. It has superior, detailed explanations, lots of basic exercises, and challenging word problems.

Prentice Hall book is a regular, colorful schoolbook that is comprehensive in the content covered, and has a free online video & other resources to go with it.

The boxes below describe these books in more detail.

Disclosure: I get commissions for purchases made through Amazon links on this page.

Harod Jacobs Elementary Algebra

Harold Jacobs Algebra 1

Jacobs' book is kind of a literary work in itself. The instruction for a new topic always starts out with an interesting example from history, a cartoon, or such like. This makes the text livelier and easier to read, and can make math "more fun" in a sense. The exercise sets also include some very interesting problems that tie in with history or are otherwise amusing or amazing! The interesting problems thrown in help build mathematical intuition AND the love for mathematics.

One of the main drawbacks though is that the author often gives minimal explanations in the text, and not many worked-out examples. This is because a lot of the learning is supposed to happen within the exercises, which often follow the "guided inquiry" method of instruction.

There are three exercise sets for each lesson, of which set 1 is always review. There are answers in the back of the book for each exercise set 2.

Jacobs' algebra is also on the easy side, as far as CONTENT goes. While it does have the same chapters as any regular algebra book, in several topics, it does not cover the same depth as Foerster's or other algebra books. I'll give you some examples.

In inequalities involving absolute value, Jacobs only teaches inequalities that have "x" without a coefficient, for example | x + 4 | < −5. He does not include inequalities of the type | 2x + 4 | < −5. Also, he does not cover inequalities with two variables at all (for example, y > x + 4). In radical equations, the problems are limited to such as have x under the radical sign, for example √x + 2 = 5. Problems that include both √x and x are not included (for example √x + 2 = 5 + x). Also, Pythagorean Theorem is not covered. Scientific notation is not covered. These lacks are not necessarily a problem, since any algebra 2 book will review all of algebra 1, and should cover those topics.

The book also seems to teach the math on an easier level than Foerster or the Prentice Hall book, often practicing visual models in detail, and using exercises that build student's conceptual understanding step by step. This can actually be of great benefit for students who are not ready for more "algebraic" or analytic reasoning. It also means Jacobs' book could easily be used with younger audiences—some proficient, "mathy" kids could even study it in 7th grade.

See this list to purchase this book and the supplements at Amazon:

Algebra I: Expressions, Equations, and Applications by Paul Foerster

Foerster Algebra 1

With Foerster, you can definitely "hear" a teacher speaking to you through the text. The book is written to the student, with excellent, sometimes even pedantic, explanations. The text often includes little tips like what a classroom teacher might say, such as "the vinculum is supposed to extend over here" or illustrations why something cannot be done.

Foerster's algebra goes fairly deep into the usual topics of algebra 1. The book includes both basic and challenging exercises, including lots of word problems. It is an excellent textbook when it comes to explaining mathematics. Foerster's approach is very analytical and logical, relying on mathematical thinking—which can be very good for students who are going into sciences.

The main difficulty I can see for homeschooling parents is that some of the exercises are quite challenging. Thus, Foerster's book may be too difficult for some students.

Answers to odd-numbered exercises are given in the back of the book.

David Chandler from Math Without Borders has created a Home Study Companion for Foerster's book, which can be incredibly helpful for homeschoolers. Please see my review on Foerster's algebra 1 and of the Home Study Companion for more information and example pages.

A costlier, but more personalized option, is an actual class using this textbook. Check out Liberty Tutorials for online classes with Foerster's Algebra 1.

To purchase this book on Amazon:

Prentice Hall Algebra 1

Note: the original publisher of this book was Prentice Hall, then for a few years it was Pearson, and now it is Savvas.

This is a basic, comprehensive textbook used in public schools. It is typical of modern textbooks in that it has quite a bit of color and multiple authors. The book is more "cut and dried", without the bits of humor that you find in both Jacobs' and Foerster's books. It seems to have sufficient amount of examples, and lots of varied exercises.

The newer editions of Prentice Hall Algebra 1 (2011, 2012 and 2015 editions) are fine products, also. The 2012 and 2015 editions are aligned to the Common Core Standards, and thus emphasize conceptual understanding and mathematical modeling more than the previous editions. For example, the publisher has added "Error Analysis" exercises, "Reasoning" exercises, and rich mathematical and real-world problems to the book.

In fact, the newer editions sound better to me than the earlier ones; however there are two drawbacks: 1) They are also more expensive on Amazon—even used copies—and 2) The companion website for the new editions requires an access code. The access code is supposed to be simply the ISBN of the teacher edition, but I did not get it to work. Update: The companion website for these editions apparently used Flash and is no longer functional.

The current publisher Savvas also sells their own algebra 1 curriculum called Envision Algebra 1. I do not know if it's based on Prentice Hall books or not. Rainbow Resource Center carries it nowadays in place of the older Prentice Hall books. The product includes a textbook and a 1-year license to an online platform called Savvas Realize.

The following links go to Amazon.com.

Art of Problem Solving Introduction to Algebra

Art of Problem Solving Introduction to Algebra
(for high-performing math students)

This book is written by the founder of Art of Problem Solving, Richard Rusczyk. For each topic, there are many example problems with detailed solutions and explanations, through which algebraic techniques are taught. The explanations often highlight ideas on best problem solving approaches, which is something you don't usually see in regular algebra textbooks. Exercises for the student follow.

Introduction to Algebra book goes through all the typical algebra 1 topics, plus present several topics that are usually part of Algebra 2 curriculum, such as exponents and logarithms, quadratic inequalities, functions, and complex numbers. The solutions manual includes full solutions, not just answers, which is a definite plus.

This book is indeed quite good for its intended purpose. It contains challenging problems, and is especially meant for "high-performing" math students, because it emphasizes problem solving, proof, and challenging problems. It is NOT for weak or average students or for those who do not like problem solving. Please check out the long excerpts (samples) on AOP website to see if the book would be a good fit for your student.

Links to Amazon:
Introduction to Algebra
Introduction to Algebra Solutions Manual

Free algebra video websites

You can use these FREE video websites to accompany any algebra textbook you might have. To use them, first check the topic of the lesson in your textbook. Then find matching videos on these sites. You can definitely also leave this task to your student: he/she can read the textbook text, find videos, and then watch one or several videos on the same topic, before attempting to do any of the exercises in the textbook.

Over 6,000 free, online video lessons for basic math, algebra, trigonometry, and calculus. Videos also available in Spanish. Also includes online textbooks. See also my review.

BrightStorm Math
Hundreds of free videos covering all high school math topics from algebra to calculus.

Algebra Within Reach
Free algebra videos presented by Dana Mosely, worked-out solutions for selected exercises, and other companion helps for Ron Larson's algebra textbooks.

Khan Academy algebra
Learn algebra 1 — linear equations, functions, polynomials, factoring, and more. Full curriculum of exercises and videos.

Free online interactive lessons for high school algebra, calculus, and AP calculus. Also for other subjects.

An online algebra curriculum

There exist several commercial online curricula offering algebra courses to homeschoolers. I cannot really say which ones would be the best since it's not possible for me to review and evaluate all of them, so that will be left to you.

These curricula are always based on either videos or animated tutorials. The exercise sets may be less comprehensive than those found in regular algebra textbooks, and often focus on the most basic types of exercises. You usually get access to simple online quizzes and a system that tracks student progress. You may even get one-on-one support from a tutor or teacher.

From what I've found, a lot of the online curricula don't have enough word problems, or the problems are not very good (too easy). Another typical lack is in challenging problems and applications. Consider supplementing — for example with the word problem lessons from Foerster's Algebra 1 textbook. His word problems are excellent!

Besides commercial algebra online curricula, in recent years some organizations have started offering FREE online courses. This is of course a fantastic opportunity. Just keep in mind that such courses may not provide enough exercises nor any support. This means the parent should know some algebra so as to be able to guide the student. For additional exercises and challenging problems, you can use some algebra textbook, online worksheets, or such.

Khan Academy algebra
Free videos and exercises for algebra topics.

Free algebra flexbook from CK-12
A complete algebra textbook (free) by CK-12 Foundation. You can also find lots of algebra videos, tutorials, animations, and exercises.

Derek Owens Algebra 1 course
An algebra course based on video instruction and a student workbook that the student fills in while watching the videos. Mr. Owens and his assistants are available for questions and can also provide extra practice problems. Based on what little I could see in the workbook sample and some of his videos on Youtube, this course looks good. (However, please don't take this as an absolute recommendation; check out actual user reviews etc. to learn more.)

EdX Introduction to Algebra
A free self-paced video course covering a standard curriculum in high school Algebra I. You may need to supplement this with an additional source of problems and exercises.

MA001: COLLEGE ALGEBRA from Saylor.org
A free course with videos, a PDF textbook, and lots of exercises. It begins with a review of some pre-algebra concepts. Topics include linear equations and inequalities, graphing, exponents, polynomials, and rational expressions.

Unlock Math
Unlock Math courses are based on engaging video instruction and interactive exercises. The courses are comprehensive and quite step-by-step. However, it doesn't have many word problems, and some that it has are quite easy, in my opionion. The course includes 1 challenging problem per lesson, which is a good thing; I just wish it had more of those!

A multimedia curriculum with activities, videos, interactivites, and assessment tools. Free trial available.

CTC Math
CTC Math offers math courses with video tutorials, interactive questions (mostly multiple-choice), and worksheets. It provides a good coverage of topics and plenty of practice. However (as is common with these video-based curricula), it lacks in word problems/problem solving.

Multimedia video lectures that take the place of a traditional textbook, plus automatically graded exercises & homework. Titles offered are from grade 6 through calculus. The teacher on the videos is Edward Burger, who has a unique and intuitive approach to learning math. Online access to any one course $125 a year.

A collection of lectures by college professors, including algebra, trigonometry, calculus, and statistics courses (for high school/college). Subscriptions $45 first month, $35 monthly thereafter; $300 a year; they give you access to all courses.

Tablet Class
An online curriculum and math learning system. Includes videos lessons, course materials, review notes, practice worksheets, tests and answer keys. Courses offered are prealgebra, algebra 1 & 2, intermediate and college algebra, and GED math.

Art of Problem Solving's online learning system for gifted students. Offers a customized learning experience, adjusting to student performance. It is specifically designed to provide high-performing students with a challenging curriculum. Alcumus is free.

While not supported by videos, this is a very good resource, since it provides a full online text for algebra 1 with interactive exercises. The full text is provided as PDF files (one for each section), and those include solutions to the exercises in the text. free.

An online maths tutoring system with 480 full audio/visual lessons presented by a real teacher, synchronised with animated graphics and backed up by tests and progress reports. For UK key stages 3 and 4 (11-16 year olds). 16 free trial lessons. Subscriptions £15.99 a month, £99.99 a year.

More algebra tutorials — free

There exist dozens of algebra websites, which usually have short tutorials on algebra topics. Some of them have short quizzes also. They wouldn't replace a textbook because of lack of exercises, but sometimes it's helpful to read several explanations for the same concept.

Please see a LONG list of these algebra websites here. The list also includes algebra worksheet sites, online calculators, and a few algebra games.

If you have suggestions or comments about this article, let me know.

By Maria Miller


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