Blitzer precalc - how many and which type of problems

[Nan in Mass]

Does anyone have experience with this book?

 

Is my son way off in how long it takes him to do the problems?

 

I like its applied, function oriented approach but I am generally disliking the book. Too many words and it seems to be overcomplicating some things. Ug. For those of you who go over a section with their child and then assign problems, how much time do you spend going over a section? How much time do you expect your child to spend solving problems on their own? Doing all the odds for a section would take hours, so I can't simply assign odds. The person I had lined up to help me figure this out (good private high school math teacher whose kids all passed their AP calc test) just said to have him do all the odds. That would be about 75 problems/day. When I go through and assign what I think is important, I wind up assigning 30 or 40 problems and it takes my son 2 hours to do them all. I don't mind spending 2 hours a day on math (although 1 1/2 would fit into our schedule better) but I don't think we have time to spend 3 or 4. And if you are familiar with Blitzer, are there sections that we could skip? I have the syllabus for the CC precalc class he should be taking but can't because he is going to Japan. It hasn't been particularly helpful because we are going from NEM3 and a tiny bit of 4 to Blitzer and the syllabus skips some things that my son doesn't remember that I think are important. Anyway, if anyone has the book, would you be willing to tell me what you did?

-Nan

Edited November 7, 2010 by Nan in Mass

[Jann in TX]

Blitzer is a popular community college math text author (although I personally do not like his style--'overcomplicated' is a good description...). These texts--and most college math texts are written with a block format--2-3 lessons per week instead of 'daily' lessons like most high school texts.

 

Most likely working the 'odds' will end up being 15-30 problems per day (with each lesson taking an average of 2 days to complete).

 

If there is a chapter review then I would assign ALL problems.

[Nan in Mass]

I usually count up the lessons but this time, I thought my son was going to be gone for 3 months or so in the middle of the school year so we'd be doing it in summer anyway, so I didn't bother. Now I know he'll be gone for only a month. I have now counted and you are right - if we do a section every two days (with one for every review), we will only miss by 11 sections.

 

Do you have any suggestions for presenting the material in a less complicated way? My normal strategy for math is to read the textbook aloud, working all the example problems on paper (pointing doesn't seem to work for those), adding my own comments. That approach is not working well with the blasted Blitzer. Sigh. I am not an experienced enough teacher to feel confident about reading the section beforehand and then just reteaching it my own way. Some sections, things I remember well from my own math, I've done this way, but some of the things aren't familiar enough to me that I remember having developped my own way of thinking about them. Or I don't remember what it was, anyway.

 

-Nan

[Jann in TX]

I have a Blitzer text for College Algebra. I do not care for the layout or the order the concepts are taught--it is NOT a text I would choose. DD used the College Algebra text for about one week! (an adult friend I tutored last year gave it to me --current edition)

 

DD and I are very happy with Pre-Calc 3e by Lial. This text BUILDS on Algebra 2 concepts--and the text flows 'naturally' for lack of a better word. The layout is nice--even if it is a HUGE hard back text.

 

I usually go through the examples in the text with dd then send her on her way to work the problem set (most of the odds but I do pick and choose some). Sometimes I go over 1 or 2 examples then I have her go and work the related homework problems--if time permits that day we go over an additional example or 2...this breaks up longer lessons into manageable chunks--and since each example builds on the previous one it works out well.

 

I must say that while we were thrilled with Lial for Introductory and Intermediate Algebras (Algebra 1 and Algebra 2) I --for lack of better judgement-- had dd try Chalkdust Pre-Calc (it BOMBED big time with dd). I briefly had her try the Blitzer text while I was waiting for the Lial text to arrive-- we could not be happier with it. Lial is each to teach from and easy to work out of... it has challenge and rigor--but it is UNDERSTANDABLE for high school students (and their out of date math moms).

 

The BEST purchase of the year (besides the Lial text) has been the Graphing Calculator tutorial DVD by http://www.mathtutordvd.com/ This program is so NICE to have -it beats trying to figure out the paper manuals and is easy to follow.

[Nan in Mass]

Thank you. I have another question for you but I can't type it up right this sec (have to go do math : ) )

-Nan

[Nan in Mass]

Ok - next question. Maybe this is just the straw that broke the camel's back, or maybe it really is important - either way, it feels important to me, but I might be wrong. I guess I want to know if I am wrong. Either way, I am still going to find some other way of presenting the material to my son (switch books or make my own lectures or figure out the matching Khan videos or something). So here is the latest bit that worries me.

 

The book presents solving inequalities with absolute value this way (quoting Blitzer's Algebra and Trig: An Early Functions Approach, p. 287) (I am using ! for a vertical bar):

 

We know that !x! describes the distance of x from zero on a real number line. We can use this geometric interpretation to solve an inequality such as !x!<2. This means that the distance of x from 0 is less than 2, as shown in Figure 2.14 (number line). The interval shows values of x that lie less than 2 units from 0. Thus, x can lie between -2 and 2. That is, x is greater than -2 and less than 2. We write (-2,2) or {x ! -2<x<2}.

 

Some absolute value inequalities use the "greater than" symbol. For example, !x!>2 means that the distance of x from 0 is greater than 2, as shown in Fig 2.15 (number line). Thus, x can be less than -2 or greater than 2. We write x<-2 or x>2.

 

These observations suggest the following principles for solving inequalities with absolute value.

 

(Blue box)-------

Solving an Absolute Value Inequality

 

If X is an algebraic expression and c is a positive number,

1. The solutions of !X!<c are the numbers that satisfy -c<X<c.

2. The solutions of !X!>c are the numbers that satisfy X<-c or X>c.

These rules are valid if < is replaced by <= and > is replaced by >=.

----------

 

Example 5 Solving an Absolute Value Inequality

 

Solve and graph the solution set on a number line: !x-4!<3

 

Then the book goes on to give several examples, solving each by rewriting the the inequality with the absolute value bars using the rule in the blue box.

 

Ok. This works. But doing it this way suggests that one should memorize the blue box, which isn't necessary, really. Now I know why my older one, who used this book in CC precalc, spent so much time memorizing his precalc before the tests and I am kicking myself for not checking up on what he was doing. Is there any reason why you couldn't present the material like this? I know it is a bit slower, but it seems to me it would be better at making sure the student understood the material. Maybe it is less correct mathematically, though?

 

I would do the problem thus:

 

Rewrite !x-4!<3 without the absolute value sign:

 

x-4<3 -(x-4)<3

 

Solve the two inequalities:

 

x<7 x>1

 

Rewrite as compound inequality if possible:

 

1<x<7

 

Graph on the number line:

 

(number line)

 

Why doesn't the book teach it this way? Is there anything wrong with this way? It wouldn't require any memorization at all, this way, or at least, no memorization other than remembering what the absolute value sign means and the properties of inequalities. Am I being overly upset that the book doesn't teach it this way?

 

And:

Are you familiar with NEM? Do you think we would like Lial's coming from NEM?

 

-Nan

Edited November 10, 2010 by Nan in Mass

[Teachin'Mine]

That book sounds like it would do a better job roasting marshmallows than teaching math. :tongue_smilie:

[Nan in Mass]

Does that mean I can dump it in the woodstove to warm us up this stormy day and have marshmellos for lunch?

[Teachin'Mine]

Does that mean I can dump it in the woodstove to warm us up this stormy day and have marshmellos for lunch?

 

:lol:

 

Absolutely!!! :D

[Jann in TX]

There are many different ways to work advanced math problems...

 

This is where it (homeschooling) is nice to have the FREEDOM of choosing a text-- you can fit the text to the student instead of fitting the student to the text!

 

Your approach/suggestion is similar to the way Lial teaches--you might want to take a look (but only if you are willing to switch down the road!)

[Nan in Mass]

Jann, is the table of contents for Lial precalc online? I took a fast look and didn't turn it up. I can look again if you don't know off the top of your head.

And thank you for all your help.

-Nan

[Jann in TX]

Here is the link to the text at the publishers site

 

Lial Pre-Calc 3e