LOF Decimals/Percents question

[buddhabelly]

EDITED TO ADD: A few chapters later he uses my words when he reminds the students of the rule! Yay, me.

 

Is there anyone who is nearing the end of LOF Decimals/Percents, or who recently finished it? I wonder what your opinion is about the way something is presented. (I will check to see how Singapore teaches it, too.) It is about finding percents and what number is ______ percent of a number and that kind of thing. First, he teaches that if you know both sides of the "of," you multiply. We're good with that, because we know that "of" means multiply from our work with fractions. (1/4 of 9 means the same as 1/4 x 9). But then he said that if you don't know both sides of the "of", you divide the number closest to the "of" into the other number.

 

Example: 7 is what percent of 48? You would divide 48 "into" 7. This is correct, but see below.

 

I just don't like that rule. Two reasons: One, it is easy to get it backwards by remembering "divide the number closest to the "of" by the other number." Secondly, I just don't like the wording -- is that really something a mathematician would ever say?

 

So I proposed to my son that we change the rule to "the number closest to the word 'of' is your divisor." Then we reminded each other of the words divisor (it cuts, like an incisor) and dividend. There is no way to get my rule backwards (because it doesn't include the word "dividend", and it seems more, I dunno, professional.

 

Anybody else encounter this in LOF? Or if not, what do you think?

 

Julie

Edited March 9, 2010 by buddhabelly

[Capt_Uhura]

I don't like that either. That's just memorizing an algorithm w/out understanding what is really going on, IMHO. I'd like to know how Singapore handles this. I don't think RS E goes into this but I will take a look and report back if it does. The one thing that got my attention with VideoText was that they don't teach "invert and multiply" but rather why that works.

 

Capt_Uhura

[Cindyg]

I don't like it either. I don't understand it, and I can't remember it. DS, however, accepts it without argument. We're on our 3rd LOF book (pre-algebra), and it's still the rule. :( This in no way ruins LOF for us. And I assume he teaches a better method when he feels the children are old enough.

[nmoira]

Example: 7 is what percent of 48? You would divide 48 "into" 7. This is correct, but see below.

This type of question seems to intuitive to me, it would never occur to me it could be problematic. I don't know how Singapore handles it because we never got that far, but Mathematics 6 simply says:

 

In order to learn what percent one number is of another, we need to:

 

(1) divide the first number by the second

 

(2) express the resulting quotient as a percent

 

 

e.g.

A class has 25 students, 10 of whom are girls. What percent of the class is girls?

 

 

 

10/25 = 0.4 = 40%

-------------------------------

 

The other possibility is less intuitive, and Schmidt's way works when the questions formulated thus:

 

10 is 5% of what number?

But is a bit less intuitive with:

 

Find a number if we know that 5% of it is 10

 

 

Schmidt: 10/.05 = 200

 

 

Mathematics 6:

 

To find a number when a percent of it is known:

 

(1) Express the percent as a fraction or decimal

 

(2) Divide the given number by the fraction

Several examples are given in the preceding section (of Mathematics 6) showing that, generally speaking, to find a number when a fraction of it is known, divide this fraction into the corresponding number. Though it goes on to say in simple cases, use a two step procedure; i.e. divide by the numerator to find the unit fraction, then multiply by the denominator to find the whole:

 

e.g.

25 is 5/7 of what number?

 

25/5 = 5 so 1/7 of the number is 5

 

5*7 = 35 so 7/7 of the number is 35

You can do the same thing with percentages -- this is Zaccaro's "Think 1" approach -- also without the use of algebra. This is my preferred method because nothing need be memorized due to its simple logical flow.

 

Find a number if we know that 5% of it is 10

 

10/5 is 2 so 1% of the number is 2

 

2 * 100 = 200 so 100% of the number is 200

 

 

 

Edited March 6, 2010 by nmoira

[buddhabelly]

I am too tired to understand the responses, but I just wanted to thank you. Very busy right now moonlighting as president of a nonprofit and homeschooling by day. The highest level Singapore we have is 5, and they only do the simplest of the calculations: what is 5% of 500? So just the multiplication. We would have to look in higher Singapore books.

 

I suspect they do it somewhat like Zaccaro, if I had to guess.

 

I hope to look at nmoira's answer a bit more when I have some clarity.

 

THANK YOU!

 

Julie

[Capt_Uhura]

I believe this is covered in SM 6A. It's all done w/ bar diagrams and such so no confusing says to memorize. :001_smile:

 

lesson 2: one quantity as a percentage of another

lesson 3: solving percentage problems by unitary method

[buddhabelly]

Thanks, that's very helpful. Does anyone have Singapore 6A and 6B to sell me? Yes, my child is going to school in the fall but I'm still addicted to homeschooling materials. Must. Have. More. Michael Clay Thompson.

 

Julie