Help! Lial's Intermediate Alg. 8th ed Section 2.3, 2.4

[distancia]

Please, please help, anyone who uses Lial's Intermediate Alg 8th edition. This is dd's 3rd year with Algebra 2; she is now in college taking it and she just isn't getting it. I think it's in an early concept, and with your help I think I may isolate where her problems are originating!

 

She did fine in the first few pages of the book. The problems began in Section 2.3. Specifically:

 

#20 (page 86). She wrote the equation correctly, she has no problem there. She's great at translating word problems. However, her mistake began at the step .75n +6 = n - 3. She then tried to isolate the n by drawing a line under each expression and then putting a .75 under it, dividing each side by .75 (reducing to eliminate n), instead of the easier step of adding the n's to simplify. Where does this concept go back to, fractions or Algebra 1, and what is it called? This is where she is befuddled.

 

#53 (page 89) was similar. She did not multiply both sides by 10 to eliminate the decimal, which made the equation very cumbersome. Where is she supposeld to have learned this concept? So she writes

.10x + .50(40) = .40(40+x), then re-writes to: .10x + 20 = 16 + .40x , then she reduces to 4/.3 = .30x/.3 . The solution is far less complicated. What does the way she is solving indicate she is lacking in math skills?

 

I do see a few careless errors in her work, but those are not conceptual points she is missing. What she appears to be doing is haphazardly applying steps that she thinks (hopes?) will work without fully understanding why she is doing what she is doing. Problem #20, above, is where her weakness is.

Edited March 19, 2011 by distancia

[Jann in TX]

I looks like your dd has not learned or has forgotten basic rules of equation manipulation.

"Add, Subtract, Multiply or Divide--What you do to one side you do to the other". This is the main 'rule' and it is taught in Pre-Algebra and early in some Algebra 1 courses. When working with equations, all addition and subtraction must be completed (simplified as much as possible) BEFORE any division (or multiplication) can be done (if your goal is to find a solution). In your first example your dd did not complete the subtraction before she chose to multiply-- while she ended up with an EQUIVALENT equation it was not in simplified form and therefore incorrect. She should have subtracted the 'n' from both sides first THEN divided by .75

 

Clearing the decimal does help--but it is not necessary. Eventually she will come across equations where she will need to clear the 'fraction' (denominator) or she will NOT be able to go on.

 

As far as your second example goes-- it goes back to the rules of fractions-- possibly taught in Pre-Algebra but most likely brought to student's attention in Algebra 1 (I point this out to my Algebra 1 students). The denominator of a fraction must be a POSITIVE WHOLE NUMBER (non zero, non decimal, non radical...) Your daughter left her answer with a decimal in the denominator and that is NOT in correct simplified form.

Equivalent is not the same as correct! Think back to basic fractions-- 12/14 is not a correct 'simplified' answer because both numerator and denominator are divisible by 2... 6/7 is the 'correct' simplified answer--but both fractions ARE equivalent!

 

The word problems show similar lack of detail/focus. I have my students write the 'formula' into (or above) the chart (procedure signs +, -, x, / , = ) go on top of the vertical lines. In #22 it would be Rate X Time = Distance with the 'x' and the '=' just above the vertical lines.

 

Chapter 2 is a review of Algebra 1-- it does not contain Algebra 2 topics or concepts. Students moving forward in the text need to have a firm grasp of word problems as this foundation (chapter 2) is expanded throughout the text.

 

I've worked with other students who earned scholarships due to their high English scores (and they did NOT take Algebra 2 in high school)--BUT not having Algebra 2 has really hampered them in college--they have to take outside classes at a CC or they have to be disciplined enough to learn the material on their own (possibly hiring a private tutor).

 

It sounds like your daughters life-goals will require more math--through Algebra 2 at least and possibly beyond. Sure some English-based majors will not require additional Math--but any Science-based ones will.

[distancia]

Thank you, Jann. That gives me a great place to start.

 

DD continually insists that she "knows all this stuff" but it is clearly apparent that she hasn't learned how to manipulate the equations to solve them. I looked over some other materials and found that some of this is called (I believe) "linear equations in one variable". I spent a good portion of this afternoon re-teaching myself how to do this and proving--to myself--that each problem can be solved more than one way, ie. one can first add the constants, or one can first add the variables. One can move left, or one can move right. There is some flexibility in certain situations. The skill is knowing when to be flexible and when to remain consistent, aka, follow the rules.

 

I think DD is of the mindset that all problems are solved the identical way, i.e. formulaically, and if there is even the slightest deviation from one problem to the next--for example, a decimal instead of a whole number--she doesn't know what to do.

 

She keeps complaining that math seems so arbitrary, there are no hard and fast rules, but in fact, she hasn't grasped all the rules and used them as tools. To her they are changeable, like moods. This comes from not having learned on her own--through doing hundreds of problems--that the rules do work if applied correctly.

 

Now, if only I can get my dd to listen to me. That's another thread.

Edited March 20, 2011 by distancia