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.
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 45 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.
Cindy
If you go with the option #2 or #3 listed above, the textbooks that I recommend are:
The choice between the top three might not be easy. In a nutshell, Jacob's book is lively, concentrates on concepts, welladmired 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.
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 workedout 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:
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 oddnumbered 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.
To purchase Foerster's book on Amazon:
To see this book for yourself, you can preview chapter 2 of the 2009 edition here. 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.
As a definite bonus, Prentice Hall Algebra 1 (2009) book has a free companion website. (If the link is broken, go to www.phschool.com and navigate to the algebra 1 book.) You will find narrated, interactive video tutorials for every lesson. Additionally, the site has lesson quizzes, chapter tests, vocabulary quizzes, and some realworld applications to supplement Prentice Hall Algebra 1.
The following links go to Amazon.com.
You can purchase Prentice Hall Algebra 1 homeschool bundle at Rainbow Resource. This bundle includes a teacher edition, student text, student workbook, teacher guide, and a parent guide pamphlet.
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 realworld 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.
The publisher's website has more information here. If that link doesn't work, go to www.pearsonschool.com → mathematics → algebra, and you should see Prentice Hall Mathematics Algebra 1 listed.
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 "highperforming" 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
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.
MathTV.com
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.
www.mathtv.com
BrightStorm Math
Hundreds of free videos covering all high school math topics from algebra to calculus.
https://www.brightstorm.com/samplevideolessons
Algebra Within Reach
Free algebra videos presented by Dana Mosely, workedout solutions for selected exercises, and other companion helps for Ron Larson's algebra textbooks.
www.algebrawithinreach.com/eia6e/content/instructionalvideos
HSTutorials.net
Free animated and narrated math tutorials  prealgebra, algebra 1, geometry.
www.hstutorials.net
Khan Academy algebra
Learn algebra 1 — linear equations, functions, polynomials, factoring, and more. Full curriculum of exercises and videos.
www.khanacademy.org/math/algebra
HippoCampus
Free online interactive lessons for high school algebra, calculus, and AP calculus. Also for other subjects.
www.hippocampus.org/HippoCampus/Algebra%20%26%20Geometry
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 oneonone 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.
www.khanacademy.org/math/algebra
Free algebra flexbook from CK12
A complete algebra textbook (free) by CK12 Foundation. You can also find lots of algebra videos, tutorials, animations, and exercises.
www.ck12.org/book/CK12AlgebraI/r5
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.)
www.derekowens.com/course_info_algebra1.php
EdX Introduction to Algebra
A free selfpaced 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.
www.edx.org/course/introductionalgebraschoolyourselfalgebrax1
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 prealgebra concepts. Topics include linear equations and inequalities, graphing, exponents, polynomials, and rational expressions.
learn.saylor.org/course/ma001
Unlock Math
Unlock Math courses are based on engaging video instruction and interactive exercises. The courses are comprehensive and quite stepbystep. 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!
www.unlockmath.com
Mathletics
A multimedia curriculum with activities, videos, interactivites, and assessment tools. Free trial available.
us.mathletics.com/secondary/
ThinkWell
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.
www.thinkwell.com
Educator
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.
www.educator.com
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.
www.tabletclass.com
Alcumus
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 highperforming students with a challenging curriculum. Alcumus is free.
artofproblemsolving.com/alcumus
ONE MATHEMATICAL CAT, PLEASE! A First Course in Algebra
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.
onemathematicalcat.org/algebra_book/online_problems/table_of_contents.htm
Conquermaths
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 (1116 year olds). 16 free trial lessons. Subscriptions £15.99 a month, £99.99 a year.
www.conquermaths.com
Mathematics.com.au
Animated maths lessons, worksheets, topic tests and worked solutions for years 712 in the Australian curriculum. 32 free lessons available to
trial online. Online membership $26.95 AUD month; $127 for six months; $197 AUD per year; family plans available. Also available on CDs.
www.mathematics.com.au
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.
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