Elementary Algebra, written by Harold Jacobs, is a splendid, informative introduction to algebra.
As I entered 9th grade, I was very apprehensive about taking algebra . Although math had heretofore been one of my favorite subjects, I had become so lost in the fog of x’s and equal signs presented in pre-algebra that algebra seemed to me some unknowable phenomenon of dismaying necessity . Even the basic simplifying rules persisted in stumping and mortifying me at every attempted application. Math was easy; two plus two was always four, always had been and always would be, but Algebra rules seemed impossible to pin down and set in concrete. To me, algebra was a confusing, but, as I was painfully aware of, necessary subject; one I longed to master, but couldn’t. Then, I delved into the clear-cut, voluminous pages of Elementary Algebra—and at last, everything made sense! This book’s rare and excellent presentation of beginners’ Algebra hinges on three main tenants: approach, lesson material, and good example problems.
Approach
Instead of the usual method of first hammering the simplifying rules into the student’s head, and then applying the the rules to progressively harder equations, Mr. Jacob introduces the student to “unknown” letters, ( x’s and y’s), and teaches the student to think in terms of these “unknowns.” In other words, the student is shown through number problems and other interesting examples, how much he can determine about a monomial containing an “unknown” without even knowing what number it represents! He also learns, through frequent practice, how to juggle x’s and y’s around with familiarity and confidence. That way, instead of the dreaded, ambiguous x and y, these “uncertains” become well-known friends, simply representatives of real, knowable numbers. Next, as the student begins to feels more comfortable working with representative letters, Mr. Jacobs introduces new concepts, always relating them back to the students’ understanding of unknowns. This strategy helped me immensely. Instead of memorizing a bunch of dry rules, I was, under Mr. Jacob’s instruction, actively discovering why they were true. I understood how to figure out these rules on my own, based on my understanding of the role x’s and y’s play in equations. After all, simplifying really is simple so long as the goal of simplifying doesn’t get lost in a fog of its own rules.
In addition, Harold Jacob’s approach also scored high with me on interest and readability. Nearly every lesson begins with a thought provoking quote or an interesting fact. Then, in the lesson write up, Mr. Jacobs expands on this tidbit, through it introducing the lesson topic. This added interest can make an otherwise dull or tedious lesson flavorful, memorable, and exciting! I definitely benefited from Elementary Algebra’s straightforward, enjoyable approach to algebra.
Lesson Write-Ups
Besides being enjoyable, the lesson write ups are concise and clear, often containing unique, affective explanations. For the most part, the lesson explanations stayed succinct , presenting all the necessary info without boring the reader. Also, although some concepts were difficult for me to get a grip on, with perseverance and occasional assistance from the algebra authority, Daddy, I was able to understand what I was learning. Clarity is definitely a strong point in Elementary Algebra; Harold Jacobs uses pithy writing, enlightening graphs, and even stories to get the facts across. For example, in chapter 16 on inequalities, Mr. Jacob includes a sketch made by a child who was asked the question, “If a zoo keeper wanted to weigh his elephant, how would he do so? The child responded with a detailed drawing of a elephant hanging in a sling attached to one side of a giant “scale,” with a basket of weights balancing it on the other side. Mr. Jacobs then went on to explain that, supposing that the elephant was somewhere in between six and seven tons, if a six ton weight were placed in the basket, the scale would slant toward the elephant, but if one more ton were added, the scale would slant toward the toward the basket of weights. Thus, x, the elephant’s weight is more than six and less than seven. This is expressed by the inequalities x>6 and 7>x. By interesting, helpful illustrations like these, Mr. Jacobs makes algebraic concepts clear and cemented in the reader’s mind.
Lesson Material
Finally, I really appreciated the use of helpful example problems in the lesson material. In my old math textbook, I was frustrated with the simplicity of the example problems, as in the actual lessons, the student was expected to answer much more difficult problems. While I realized that I needed the simpler examples to understand concepts that would be confusing if presentedin a more complex problem, I did wish that my math program included a few advanced examples as well. Enter in Harold Jacobs! Although there are plenty of mind-stretching problems in the problem sets that, though not particularly addressed, build on the principles the student knows, these are in proper proportion. Not too much, not too little. Basically, Elementary Algebra does a good job of maintaining the right balance between the two extremes of spoon-feeding each principle’s applications to the student or making him figure everything out on his own.
Special Plus
Harold Jacobs can be used with a teacher or independently! ( Let’s hear a round of applause.) With an average of an hour of assistance every two weeks , I was able to understand everything. It took plenty of hard work, (perseverance is a must!), but if you’re willing to put in the necessary time and energy, you can complete the textbook on your own.
Con
The only problem I had with the Harold Jacob math program was the way the answers to the problems were presented. They were closely squished together , which made it easy to lose my place as I checked my answers form the grading book.
Quick Facts
The lessons are meant to be done in a separate page.
The tests are no harder than the lessons and each has a special bonus question.
At the end of each chapter is a review lesson.
There is a midterm and final review.
There are seventeen chapters containing about six lessons each.
There are four sets of questions in each lesson but the reviews. (Reviews have only two sets.)
1. The first is short and has review questions from previous chapters or lessons.
2. The second and third contain basically the same amount of problems, the only difference between them being the different problems.
3. The fourth set is usually a brain teaser that focuses on some aspect of the
Not for the Complacent Student!
If you’re planning to tackle Elementary Algebra independently, make sure you have the impetus to get through it before you make the purchase. This course is tough! It expects you to work and thing hard. While some lessons are easy, I have spent hours on others. I’ve also filled out multiple notebook pages while working on just a couple difficult problems. (Don’t worry—they’re not all that tough; I’ve heard that there is usually only one really complex problem per lesson, although it often seemed more like two or three to me!) I often got pretty stuck on one lesson, but after the end of the chapter, everything fit together and made sense. All this to say, success is dependent upon devoting a good amount of time and energy to your math every day. (You don’t have to be an Einstein; all it takes is good old down-to-earth work!)
Elementary Algebra, written by Harold Jacobs, is a splendid, informative introduction to algebra.
As I entered 9th grade, I was very apprehensive about taking algebra . Although math had heretofore been one of my favorite subjects, I had become so lost in the fog of x’s and equal signs presented in pre-algebra that algebra seemed to me some unknowable phenomenon of dismaying necessity . Even the basic simplifying rules persisted in stumping and mortifying me at every attempted application. Math was easy; two plus two was always four, always had been and always would be, but Algebra rules seemed impossible to pin down and set in concrete. To me, algebra was a confusing, but, as I was painfully aware of, necessary subject; one I longed to master, but couldn’t. Then, I delved into the clear-cut, voluminous pages of Elementary Algebra—and at last, everything made sense! This book’s rare and excellent presentation of beginners’ Algebra hinges on three main tenants: approach, lesson material, and good example problems.
Approach
Instead of the usual method of first hammering the simplifying rules into the student’s head, and then applying the the rules to progressively harder equations, Mr. Jacob introduces the student to “unknown” letters, ( x’s and y’s), and teaches the student to think in terms of these “unknowns.” In other words, the student is shown through number problems and other interesting examples, how much he can determine about a monomial containing an “unknown” without even knowing what number it represents! He also learns, through frequent practice, how to juggle x’s and y’s around with familiarity and confidence. That way, instead of the dreaded, ambiguous x and y, these “uncertains” become well-known friends, simply representatives of real, knowable numbers. Next, as the student begins to feels more comfortable working with representative letters, Mr. Jacobs introduces new concepts, always relating them back to the students’ understanding of unknowns. This strategy helped me immensely. Instead of memorizing a bunch of dry rules, I was, under Mr. Jacob’s instruction, actively discovering why they were true. I understood how to figure out these rules on my own, based on my understanding of the role x’s and y’s play in equations. After all, simplifying really is simple so long as the goal of simplifying doesn’t get lost in a fog of its own rules.
In addition, Harold Jacob’s approach also scored high with me on interest and readability. Nearly every lesson begins with a thought provoking quote or an interesting fact. Then, in the lesson write up, Mr. Jacobs expands on this tidbit, through it introducing the lesson topic. This added interest can make an otherwise dull or tedious lesson flavorful, memorable, and exciting! I definitely benefited from Elementary Algebra’s straightforward, enjoyable approach to algebra.
Lesson write ups
Besides being enjoyable, the lesson write ups are concise and clear, often containing unique, affective explanations. For the most part, the lesson explanations stayed succinct , presenting all the necessary info without boring the reader. Also, although some concepts were difficult for me to get a grip on, with perseverance and occasional assistance from the algebra authority, Daddy, I was able to understand what I was learning. Clarity is definitely a strong point in Elementary Algebra; Harold Jacobs uses pithy writing, enlightening graphs, and even stories to get the facts across. For example, in chapter 16 on inequalities, Mr. Jacob includes a sketch made by a child who was asked the question, “If a zoo keeper wanted to weigh his elephant, how would he do so? The child responded with a detailed drawing of a elephant hanging in a sling attached to one side of a giant “scale,” with a basket of weights balancing it on the other side. Mr. Jacobs then went on to explain that, supposing that the elephant was somewhere in between six and seven tons, if a six ton weight were placed in the basket, the scale would slant toward the elephant, but if one more ton were added, the scale would slant toward the toward the basket of weights. Thus, x, the elephant’s weight is more than six and less than seven. This is expressed by the inequalities x>6 and 7>x. By interesting, helpful illustrations like these, Mr. Jacobs makes algebraic concepts clear and cemented in the reader’s mind.
Lesson Material
Finally, I really appreciated the use of helpful example problems in the lesson material. In my old math textbook, I was frustrated with the simplicity of the example problems, as in the actual lessons, the student was expected to answer much more difficult problems. While I realized that I needed the simpler examples to understand concepts that would be confusing if presentedin a more complex problem, I did wish that my math program included a few advanced examples as well. Enter in Harold Jacobs! Although there are plenty of mind-stretching problems in the problem sets that, though not particularly addressed, build on the principles the student knows, these are in proper proportion. Not too much, not too little. Basically, Elementary Algebra does a good job of maintaining the right balance between the two extremes of spoon-feeding each principle’s applications to the student or making him figure everything out on his own.
Special Plus
Harold Jacobs can be used with a teacher or independently! ( Let’s hear a round of applause.) With an average of an hour of assistance every two weeks , I was able to understand everything. It took plenty of hard work, (perseverance is a must!), but if you’re willing to put in the necessary time and energy, you can complete the textbook on your own.
Con
The only problem I had with the Harold Jacob math program was the way the answers to the problems were presented. They were closely squished together , which made it easy to lose my place as I checked my answers form the grading book.
Quick Facts
The lessons are meant to be done in a separate page.
The tests are no harder than the lessons and each has a special bonus question.
At the end of each chapter is a review lesson.
There is a midterm and final review.
There are seventeen chapters containing about six lessons each.
There are four sets of questions in each lesson but the reviews. (Reviews have only two sets.)
1. The first is short and has review questions from previous chapters or lessons.
2. The second and third contain basically the same amount of problems, the only difference between them being the different problems.
3. The fourth set is usually a brain teaser that focuses on some aspect of the
Not for the Complacent Student!
If you’re planning to tackle Elementary Algebra independently, make sure you have the impetus to get through it before you make the purchase. This course is tough! It expects you to work and thing hard. While some lessons are easy, I have spent hours on others. I’ve also filled out multiple notebook pages while working on just a couple difficult problems. (Don’t worry—they’re not all that tough; I’ve heard that there is usually only one really complex problem per lesson, although it often seemed more like two or three to me!) I often got pretty stuck on one lesson, but after the emd of the chapter, everything fit eogether and made sense. All this to say, success is dependent upon devoting a good amount of time and energy to your math every day. (You don’t have tp be an Einstein; all it takes is good old down-to-earth work!)