Pre-algebra is sort of "in-between" course. It is bridging the world of numerical computations of elementary math, and the world of algebra where we manipulate variables. Pre-algebra courses typically cover these topics:
Most students take prealgebra in 8th grade, just prior to taking algebra 1. However, it is possible to study these topics in 7th grade as well, if the student has a good foundation from grades 1-6.
Of the typical topics, decimals, fractions, integers, exponents, and percent have already been studied in 5th and 6th (and 7th) grades. In fact, typical 7th grade and pre-algebra courses are very similar (that is why some students will be able to do pre-algebra in 7th grade.)
On the other hand, solving linear equations and inequalities, proportions, and graphing WILL again be studied in algebra 1. Geometry topics will be studied in high school geometry. So, for a student who has mastered 6th (and 7th) grade math, a lot of prealgebra is review and a lot of it will be studied again in high school.
The name "PRE-ALGEBRA" actually summarizes the course well. The idea is to let students become more familiar with the usage of variables instead of just numbers, and to make sure that fractions, decimals, and percent are solidly mastered before an actual algebra course.
As strange as this may sound, I would not recommend any of the common homeschool curricula for pre-algebra, but instead a normal textbook such as might be used in public schools. I don't mean just any textbook - I simply mean a good, regular textbook.
Why? First of all, The best math texts are written by people who have studied mathematics quite a bit in college level and who also have taught it. Of course, that's not sufficient for being a good author, but it's a good starting point. In contrast, homeschool companies who offer math books for high school do not typically enjoy the privilege of having as good authors for their books. The result is, their texts tend to emphasize rote memorization of techniques.
Secondly, it is beneficial for students to get used to a "regular" textbook feel as they move towards high school, because I would recommend regular textbooks by Jacobs or Foerster for high school math. They need to learn to read and use the math textbook themselves to some degree, and become more independent in their learning of math. I realize most students WILL need help, and maybe even lots of help, with prealgebra, algebra, geometry, and so on, but my point is just that they also need to get used to using a textbook as a source of help and study tool.
And, pre-algebra, being such an in-between course is a good time to do just that.
I also recommend that you get two or more different books. For example, get a book that you consider your main textbook for the course, and then get one or few others either from library, from friends, or buy as a cheap used copy. The purpose of this is so you can COMPARE the exposition of any particular concept. The student may "get" it better when he reads it explained in a few different ways. Also, having an additional book or books gives you additional practice problems if the need arises.
I have not personally seen most of these books but I've looked at the previews when available, or read other people's recommendations about them.
The links below to go to Amazon. You can often get a used copy for around $10 including shipping (consider buying 2 different ones).
The answer keys or solution manuals can be harder to find. They are typically sold by the publishers themselves, and it is not totally clear if homeschoolers can easily purchase them from the publishers, but I would try. I do know Prentice Hall has allowed homeschoolers to buy them for some another high school math books. Sometimes you can find used copies at Amazon or elsewhere. I've provided links to Amazon below if I found the answer key offered there.
Remember also that the answer to any equation and proportion can always be checked by plugging the answer into the equation, and all calculation problems could be checked with a calculator.
Prentice Hall (Hover over links to see more info from Amazon.)
Get access to preview a chapter of the 2007 student edition at the publisher's website. You might also enjoy the accompanying student web page that includes quizzes, assessments, projects, and real-world applications.
Teacher's editions, solutions, etc. should be available even for home educators from Prentice Hall , but you need to first register with the Oasis system and have your credit card pre-approved (let me know if you succeed). Here is the order page for 2007 teacher's edition and order page for earlier teacher's editions.
On the publisher's website you can see the table of contents and sample pages for the book. It says you can purchase the solution key, teacher's edition, etc. by contacting their customer service.
The companion website is called ClassZone.com. It contains examples, puzzles, games, and an interactive instructor with online lessons that can help you master the material. You actually get quite a bit of content on this website.
Prealgebra by Margaret Lial
Lial's texts have proven very popular over the years because of their clear and student-friendly exposition. You can see a preview at publisher's site (Take a Closer Look). This book covers the topics of:
Introduction to Algebra: Integers; Understanding Variables and Solving Equations; Solving Application Problems; Rational Numbers: Positive and Negative Fractions; Rational Numbers: Positive and Negative Decimals; Ratio, Proportion, and Line/Angle/Triangle Relationships; Percent; Measurement; Graphs; Exponents and Polynomials.
Answers are provided for the odd-numbered exercises. Chapter tests and cumulative review exercises have answers to all the problems.
Pre-algebra by Dolciani
Pre-Algebra: An Accelerated Course by Mary P. Dolciani
This text provides several problem sets that increase in difficulty, with great word problems. It is rigorous in an old-fashioned way. Not cluttered with images. It also has answers to selected exercises.
The publisher's website has teacher's editions, online editions, etc. It says you can purchase teacher's editions by contacting their customer service.
Holt, Rinehart, and Winston also has a website to go with the 2004-2005 edition of their pre-algebra book. This site has online movies for chapter openers, and homework help problems, and chapter projects.
MathTV.com contains hundreds of FREE video lessons for prealgebra (a.k.a. basic math) and high school courses. Besides the free videos, they also have a textbook that covers pre-algebra topics called Basic Mathematics by Charles P. MacKeague (XYZ Textbooks).
This textbook will be available during 2009 and it will be accompanied with video clips that show how to solve problems in the book.
Thinkwell courses are highly acclaimed and could work well for a child who likes video lectures and computers.
The Great Courses Mastering the Fundamentals of Mathematics (DVD or online video course)
Mastering the Fundamentals of Mathematics consists of 24 video lectures, covering "basic math", includign fractions, decimals, percent, ratios, exponents, integers, geometry, and more. You could perhaps combine the course with Math Mammoth grade 7 worksheet collection for more practice problems.
Math Mammoth Grade 7 Worksheets Collection
Math Mammoth Grade 7 Worksheets Collection is a supplemental material only. It contains worksheets for all typical pre-algebra concepts and topics. The problems on the sheets often test conceptual understanding, and include very varied problems from basic practice to challenges. These worksheets cannot replace a textbook as they do not contain the explanations of the concepts.
Shmoop.com Prealgebra consists of free learning guides (tutorials) for all prealgebra topics with interactive practice problems, step-by-step examples, graphs, and real-world applications. This can be used for an online pre-algebra textbook.
YourTeacher is a subscription service with video lessons and exercises. Many of the public school textbooks are also perfectly aligned with YourTeacher's curriculum.
YourTeacher subscription costs $49.50 a month, or $199.50 for a year. I have written a review of it in the past. It can work really well for a student who likes to view videos and work on the computer part of the time.
A large list of websites offering free algebra or prealgebra tutorials and/or videos can be found on my other site (HomeschoolMath.net).
Normally, a student completes all the grades up to and including 7th grade math, and then does pre-algebra in 8th. Some students may do pre-algebra after 6th grade, instead of a regular 7th grade math. Since 7th grade math and pre-algebra are so similar, you could also have child start pre-algebra in 7th grade, but spend 1 1/2 - 2 years with it, making sure things are not rushed.
If your child seems to struggle greatly with pre-algebra, he might not have sufficient foundation for it. It also may be that his brain just needs to develop a little bit more before going for prealgebra. These programs may be able to to fill in the gap:
Math Mammoth Grade 5 Complete Curriculum and Math Mammoth Grade 6 Complete Curriculum deal a lot with fractions, decimals, percent, integers, and other topics, starting from easy, visual models. A student who has studied Math Mammoth Grade 6 Complete Curriculum should be well prepared for pre-algebra without any 7th grade math course.
Hands-On Equations® is a program for learning beginning linear equations using a physical balance scale, pawns to represent the unknowns, and number cubes for the constants. It is also useful as a part of a prealgebra program. See my review.
This is a somewhat light-hearted, easy-to-read book about pre-algebra. It doesn't contain exercises; just examples and discussion on the student's level. See also my review.
Key to...® is a series of inexpensive workbooks on decimals, fractions, geometry, and percent.
See also: Algebra 1 recommendations
I hope these resource listings are helpful. If you have any comments or advise on purchasing solution manuals or teacher's editions directly from the publishers, please let me know.
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