Triangle Diagram

It looks like it's a crutch for setting up the problem mechanically, without understanding what you're doing.

You're told to set things up this way:

               small-number
             -----------------
            percent | large-number 

                  small-number
       percent =  ------------
                  large-number
-or-
       small-number
       ------------ = large-number
         percent 
-or- 
     small-number = percent * large-number

 W-R-O-N-G                         1
          small-number = ---------------------- 
                         percent * large-number

And of course the small-number large-number placement in the setup fails when the percentage is >100.

-- CatherineJohnson - 06 Mar 2006

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Comments

LOL... burn that book!

Never in my life have I seen an equation with percents in it. I've only seen a final answer converted into percent, or a percent converted into a fraction or decimal for use in an equation.

Maybe I just don't get around much.

Chris

-- ChrisAdams - 06 Mar 2006

you know, you're right!

I've never seen an equation with a percent in it, either!

-- CatherineJohnson - 06 Mar 2006

Pardon my French, but WTF? "12 is 50% of 24" translates directly into "12 = 50% x 24", which is much more straightforward than "12/50% = 24".

"is" --> "equals"

"of" --> "times"

"to" or "for" --> ratio, so "divided by", e.g. "there are 3 boys for every 4 girls" or "2 dogs to every cat".

Oh, okay, I see they did show the multiplication, but not as the first choice.

Oh, hey, just saw your comment re Saxon and is/of/equals/times. There's an echo in here. Those triangles make my head hurt.

-- GoogleMaster - 06 Mar 2006

Hey, I see they get to Explore and Apply math, but when do they get to Learn it?

-- GoogleMaster - 06 Mar 2006

Well, I'm glad you had the same reaction.

I was completely befuddled by the triangles, and so was Ed.

The teacher didn't even bother to try to teach them; she told the kids to skip over them.

-- CatherineJohnson - 06 Mar 2006

This is actually an interesting question, because I've noticed that other countries teach finding the whole number when you know part in arithmetic.

Russian Math gives kids a HUGE amount of practice doing equations like 12 ÷ .5 = 24, and Liping Ma talks about it in her section on partitive & quotitive division.

I'm pretty sure that it's customary, in the U.S., to delay teaching this until kids can set up equations with variables....

-- CatherineJohnson - 07 Mar 2006

I've never seen an equation with a percent in it, either!

I have, when I was working on tax.

But that was with people who convert percentages to decimals at a subconscious level.

-- TracyW - 07 Mar 2006

Tracy

Were you taught finding the whole number when you know part of the number?

-- CatherineJohnson - 07 Mar 2006

Beats me. I can't remember having any problems with it.

I sincerely doubt that there was any consistent policy about teaching the skill in NZ though when I was at school. As far as I understand, there was no national curriculum then outside the national exams in high school.

-- TracyW - 07 Mar 2006

They do HUGE amounts of these problems in RUSSIAN MATH and, obviously, in China, too. The Chinese teachers all instantly produced story problems requiring kids to find the whole number when a part is known.

That was the section that threw everyone I knew reading the book.

Teachers were supposed to produce word problems for 1 3/4 ÷ by 1/2.

If American teachers could figure this out (most couldn't) they only gave problems for a 'unit' of 1 3/4 being divided into pieces each measuring 1/2.

The Chinese teachers all produced these amazing word problems about "The mom bought a box of candy. She gave 1/2 of it which weighed 1 3/4 kg to the grandma. How much did the box of the candy originally weight?"

I had NO idea what these problems meant when I first read them, and I mean ZERO idea of why this problem called for division.

Of course if I wrote it out as an equation with an unknown, then I divided.

KUMON does exactly the same thing. They have tons of quite difficult fraction division problems where you divide the part in order to find the whole.

-- CatherineJohnson - 07 Mar 2006

I still have no clue what the hell partitive division is.

When it's whole numbers it's "finding the value of a unit when the value of several units is known."

When it's fractions it's finding the whle when ou know the value of a part of the whole.

-- CatherineJohnson - 07 Mar 2006

Triangle Diagram

It looks like it's a crutch for setting up the problem mechanically, without understanding what you're doing.

You're told to set things up this way:

               small-number
             -----------------
            percent | large-number 

                  small-number
       percent =  ------------
                  large-number
-or-
       small-number
       ------------ = large-number
         percent 
-or- 
     small-number = percent * large-number

 W-R-O-N-G                         1
          small-number = ---------------------- 
                         percent * large-number

And of course the small-number large-number placement in the setup fails when the percentage is >100.

-- OldGrouch - 07 Mar 2006

Those percent triangles are wretchedly pointless. It looks as though their inventor looked at the 'fact family' triangles and missed the point, but tried to copy them anyway.

-- CarolynJohnston - 07 Mar 2006

Those percent triangles are wretchedly pointless. It looks as though their inventor looked at the 'fact family' triangles and missed the point, but tried to copy them anyway.

You know, you're right.

I just realized that tonight.

They were trying to do a percent version of the number family triangles.

-- CatherineJohnson - 07 Mar 2006

Old Grouch

I'm going to print this out and POUR OVER IT.

-- CatherineJohnson - 07 Mar 2006

Whatever works. But then, equations work too. I don't suppose they move quickly from triangles to equations. It reminds me of the multiplication and division triangles used in Everyday Math. Different just to be different. The same doesn't sell.

But I don't understand why EM doesn't use these percent triangles. Maybe I haven't seen them yet. I have seen this for my 4th grade EM son.

"What is the One?"

15 is 50 percent of?

or

10 is 2/3 of?

Of course, the numbers are all nice and they never explain how to calculate the answer for:

7 is 15/17 of?

When I saw him bring home a "What is the One?" worksheet, I didn't know whether to laugh or cry. What if the "One" is 30? What if the "One" is 3.21467? They could have at least used the word "whole", but then how could they explain why 3.21467 could be a "whole" or "the One"?

Discovery? No. Constructivism? No. Conceptual Understanding? No. Different? Yes.

-- SteveH - 07 Mar 2006

When I saw him bring home a "What is the One?" worksheet

what is the one?????

they were using one to mean 'unit'

was that it?

in the case of 15 is 50 percent of, 30 would be 'the one'??????

-- CatherineJohnson - 09 Mar 2006

"in the case of 15 is 50 percent of, 30 would be 'the one'??????"

Yup. Good old Everyday Math. The reference book has more pages about the calculator than about fractions.

-- SteveH - 10 Mar 2006

The student reference book in EM does talk about fractions of a clock face and adding/subtracting fractions using pattern blocks. I started to look at it because I did not understand the point of Megan's homework (eg, covering double hexagon figures with various shaped pattern blocks and then figuring out the fraction each block covered. They also have differently shaded portions of a clock face to figure out adding/subtracting fractions, stating the Babylonians did it, or something).

Then the reference book said "a method that ALWAYS works, however, is finding the common denominator." So that's why you don't see anyone walking around with bags of pattern blocks or sundials!

Megan is very confused. The common denominator is mentioned in passing. There also is a chart of equivalent fractions provided, I guess to discourage a student from finding the common denominator themselves.

-- KathyIggy - 10 Mar 2006

I found the reference books in Everyday Math utterly useless. The information in there is laid out without any reference back to the 'Student Math Journals' that they actually work from. No child is going to be able to find what they need in there without the help of a parent or a teacher.

-- CarolynJohnston - 10 Mar 2006

"I found the reference books in Everyday Math utterly useless. The information in there is laid out without any reference back to the 'Student Math Journals' that they actually work from. No child is going to be able to find what they need in there without the help of a parent or a teacher."

I agree. My son never looks at it. I look at it to try and figure out what on earth they were thinking. Also, there is no indication in the reference book about what grade it is for. My son is in 4th grade, but there is a section in the book on algebra that talks (very briefly) about basic algebraic properties. Then again, they talk mostly about "What's My Rule" and "Frames-and-Arrows Diagrams". However, I can't believe that this book is for fifth graders too.

I just checked and found that there is no reference to their "Fraction of" and "What is the One?" problems. It even fails as a reference book.

All of this talk of discovery and conceptual understanding is just false. Everyday math is just slow (his teacher told me yesterday that the homework is only meant to take 15 minutes - my son does the 4/5 problems in 5 minutes, and that is slow), poorly done, and jumps around way too much. I find it incredible that it has enjoyed so much success.

It just dawned on me that the reference book might be THE ONLY reference book (ISBN 1-57039-911-5; item No. 39911)for EM. Does anyone know? Mine has a picture of a small sailboat on the cover with dimension variables that are meaningless, a butterfly, a really bad compass, a couple of paper clips, and bowline knot that isn't around anything. Like EM, all fluff and no substance. Play math. Low expectations.

As one of the authors says: EM is not for the elite. I assume that the elite mean those who expect to take college prep math in high school. Of course, schools know who is who in grade school, right?

-- SteveH - 10 Mar 2006

Steve, no, the reference books change from year to year.

Are you KIDDING? The AUTHOR says that EM is not for the elite?

-- CarolynJohnston - 10 Mar 2006