46.
China has a population of 1.24 billion in 1997, with a projected increase in population of 22.6% for 2050.
What is the population of China projected to be in 2050?
India has a population of 0.97 billion in 1997, with a projected increase in population of 57.8% for 2050.
What is the population of China projected to be in 2050?
The US has a population of 0.27 billion in 1997, with a projected increase in population of 44.4% for 2050.
What is the population of US projected to be in 2050?
47. Which of these three countries is projected to be the most populous in 2050?
I assume that I know how to do these problems, but I'd appreciate an answer check if anyone has the time or inclination. Seeing as how I don't have the answer key.
The fact that I am asking this question on a blog is further evidence of the ineffective pedagogical practices employed by my school district (per pupil funding: $22,000/yr).
C. worked this problem in a homework set a couple of days ago.
Or, rather, he attempted to work this problem.
The next day, the teacher sent around a student monitor to mark down whether the kids had or had not done their homework. I assume everyone got credit for having done the homework, since the kids who haven't done it just write a different date on an old assignment and the student monitor gives them credit.
Then the teacher went over the homework in class.
So.
My child has attempted to do this problem.
He has seen the problem "gone over" in class.
He still can't do the problem -- and until last night, when I had him attempt to do the problem in front of me, he didn't know that he couldn't do the problem. He followed the demonstration in class, or thought he did, and thus felt no need to "seek extra help."
The fact that he was not "proactive in seeking extra help" is viewed by our teachers and administrators alike as a character flaw, a sign of immaturity or both.
It is not viewed as a sign of ineffective teaching.
Where is Galen Alessi when we need him?
This is a weird problem since you pretty much need to use a calculator because of the numbers. It also requires either knowing what a billion is and being able to deal with scientific notation or realizing you can just leave everything in billions.
ReplyDeleteCan you guys do this problem which just has the per cent part?
John has 50 dollars in the bank with a projected increase of 20% by next year. What is the projected (total) amount of money John will have next year?
46. 1.52 billion, 1.53 billion, 0.39 billion. (Procedure: 1.24 * 1.226 = 1.52, etc.)
ReplyDelete47. India, although technically it's too close to call, due to rounding.
THANK YOU SO MUCH!
ReplyDeleteThose were the answers I got, but....
I think it's worth describing briefly what happened last night.
I was tired & stressed (horrific deadline pressures with the book; not-getting-the-reading-done-fast-enough; etc.)
C. has a ZILLION massive, huge projects, tests, etc. due this week.
He can't manage all this stuff. Period. He's a good kid; he's a smart kid; he's a responsible kid.
None of that matters. The tasks he must complete this week are beyond his capacity to manage. (Seeing as how I've missed my book deadline, and seeing as how I personally don't know a single writer who has ever met a book deadline, I GET the problem.)
So.
In my exhausted & frayed state, I sat C. down to re-do the population problem because I knew he'd missed it on his homework. I also assumed, correctly, that seeing the teacher "go over it in class" hadn't cleared up the difficulties.
Looking at this problem, trying to figure out how to reteach it to C., I decided to use a chart like the charts his teacher taught him to use for distance problems.
otoh, I had used the Saxon method of "bubble drawing" to make sure I was doing it right....
AND: being exhausted and frayed, I started to get "balled up" between these two methods. I had also simply set up an equation to solve the problem, so that was a third approach.
I finally settled on the chart.
C. understood the chart approach quickly. He generalized at once from the charts he'd been taught earlier in the year.
He also saw, immediately (though he hadn't noticed it before) that this problem was DIFFERENT from the percent increase and decrease problems he'd been doing.
This problem didn't ask for the percent increase; this problem GAVE him the percent increase & asked him to find the actual number of people by which the population was projected to increase.
The chart.
let x = increase in population.
Chart labels:
orig pop .. proj. inc .. final pop
Chart line 1:
1.24 bil ... x ... (1.24 + x)
Chart line 2:
100% ... 22.6% ... 122.6%
As soon as C. had this set up he decided he could solve the problem as a proportion.
I hadn't even thought of that.
I'm sorry to say that this new twist threw me for a loop. I'm still not "fluent" enough in algebra or arithmetic to be able to see, instantly, that of course a proportion would work.
(Or maybe I'm not fluent enough when I'm tired...)
So at this point I was feeling anxious that I didn't know what I was doing & was sending C. off on a wild goose chase.
C. set up a proportion, solved it, and the answer was wrong.
I semi-lost it.
Why didn't the proportion work???
What was wrong???
Why didn't I get it???
My bewilderment quickly turned to fury over the fact that the district has refuses to correct homework AND refuses to supply an answer key to parents so we can correct homework -- not to mention the fact that I knew that if I had hired a department teacher to tutor I would have that teacher's home phone number (presumably) and would be able simply to pick up the phone and ask him or her what the answer was.
So at that point, stressed, frayed, bewildered, AND furious, I was having one he** of a time troubleshooting C's answer.
Yet another episode in the life of a parent trying to reteach a course in a school district that outsources core teaching responsibilities to parents while refusing to share any of the school's taxpayer-funded teaching materials with us.
As it turned out Chris' answer wasn't wrong.
It was right.
I had simply failed to remember that the value for "x" wasn't the total projected population.
We needed to add "x" to 1.24.
It took way too much time to arrive at this realization.
Outsourcing homework correction to parents is wrong.
The school needs to collect and correct homework; the SCHOOL needs to assume responsibility for knowing what the kids do and do not know.
Not the students, and not the parents.
The students don't know what they do and do not know; the parents are paying the school to teach.
"Percent Increase" problems can be set up like this:
ReplyDeleteLet C = current value.
Let F = future value.
Percent = n/100
F = 1 * C + (increase * C)
F = C * (1 + increase)
[distributive property]
For a 22.6% increase:
increase = 22.6/100
[Remember that percent means "per 100" or "n/100".]
F = C * (1 + 22.6/100)
F = C * (1 + .226)
F = C * 1.226
Oooh! Ooooh!
ReplyDeleteThis one looks hard. Even for "guess and check"...
"INDIA has a population of 0.97 billion in 1997, with a projected increase in population of 57.8% for 2050.
What is the population of CHINA projected to be in 2050?"
Yes, I'm a smartass this morning.
-Mark Roulo
You have to be able to easily switch between percent and decimal and you have to know which number the percent is based on.
ReplyDeleteBack when I taught, I used to use the idea of the store owner and customer. The store owner always uses the wholesale price as the number to base percents on, and the customer always uses the retail price. The store owner talks about markup (going up), and the customer talks about discount (going down). Then again, the store owner is a customer to the wholesaler. It can get quite confusing, but you just have to know which number is the 100% number.
"China has a population of 1.24 billion in 1997, with a projected increase in population of 22.6% [of the 1.24 billion number] for 2050."
The 100% number is 1.24 billion, so you have to multiply by 0.226 to get the increase. The fast way is just to multiply by 1.226.
Another thing to look for is whether you are going up or down. In this case, they talk of an "increase", which means that the lower number is the 100% number. You are increasing from the base (100%) lower number.
You could say that the polulation of China is currently 1.3 billion. In 1997, it was 4% less. What was the population in 1997?
We are going to a "less" number, so the 100% number is the larger number. You have to subtract 4% (.04) of 1.3 billion. Since I use the word "of", you know you have to multiply.
For the store owner, they talk of mark(up), so the 100% number is the lower number. They might markup a product by 100%, but they can't give a discount of more than 50% or else they will lose money. The percents are different going up and down because they are based on different numbers.
What if you aren't given the 100% number? Then that number is the unknown 'X'.
If you buy a product for $35 that was marked 30% off the retail price, what was the original retail price?
You're going down from the retail price, so the original price is the 100% number.
X - .3*X = 35
.7*X = 35
X = 35/.7
X = $50
I don't like charts or any other diagrams for these problems. You need to be able to write down the equations, if necessary.
Also, If you talk of an increase of 22.6%, This means that you multiply the 100% number by 100% + 22.6% = 122.6%, or 1.226 to get the new number.
If you talk of a decrease of 4%, then this means that you multiply the 100% number by 100%-4% = 96%, or .96 to get the new number.
[X - .3*X = 35
ReplyDelete.7*X = 35]
What's the mathematical language to describe .7 as it relates to .3?
I think all percent problems are solved easiest by proportion. Like Steve, I don't like charts unless they are necessary.
ReplyDeleteEx. China
1.24 x
____ = ___
100 122.6
(sorry - I can't get this to look right no matter how many times I correct it. So resorting to the slash 1.24/100 = x/122.6 )
If you change the percents to decimals, it's even easier. It really is just multiplying 1.24 times 1.226 to solve for x.
The real question is, aren't students expected to keep notebooks in class that contain class notes covering exactly what the teacher covered in class and solved examples? The students then have guided practice for doing their homework. Any problems they did in class should also be in the notebook. Those notebooks should be checked regularly by the teacher with feedback. Learning to take good notes should be an objective of any course. For seveth grade, I say if it's on the board, it's in your notes.
I think all percent problems are solved easiest by proportion.
ReplyDeleteI have a study saying exactly that!
The chart essentially maps out all the possible proportions one can use.
Saxon uses these charts.
I'd say they're a terrific teaching tool; at least the charts were for me.
The charts helped me "detach" from whatever ONE PROPORTION I thought would solve the problem. (I know that's not the clearest sentence I've ever written.)
The charts also establish the part/part/whole relationship amongst the 3 terms.
The real question is, aren't students expected to keep notebooks in class that contain class notes covering exactly what the teacher covered in class and solved examples?
ReplyDeleteBasically, the answer is 'no.'
I'm sure that if I complained I would be told C. was supposed to have written all this stuff down.
But none of the kids write all this stuff down, and the material is apparently put on the SMART Board (or wherever it's put) too fast to write it down AND follow the demonstration, etc.
The SMART Board, of course, makes it possible for the teacher to save his notes from the classroom presentation and post them to edline from which all the students (and parents) could download them.
Rudbeckia Hirta posts all of her in-class board notes online for her students to download.
But no one does that.
Our teachers put stuff on the board, assign homework, give tests.
The rest is up to us.
If the student doesn't get something he is to "be proactive and seek extra help."
Those notebooks should be checked regularly by the teacher with feedback.
ReplyDeletenope
Learning to take good notes should be an objective of any course.
ReplyDeleteNot in our school.
Not ever.
Here, learning is largely a matter of character.
If you learn the material presented in class, you have good character.
If you don't learn, you need character education or your folks need to pay one of the teachers $120/hr to tutor.
OR you're just not up to it because you can't think inferentially or the course is "conceptual" or you didn't score that well on the CTBS.
etc.
There's one other explanation: if your kid can't or won't or doesn't take good notes, that is a sign of immaturity.
ReplyDeleteWhen he's mature, he will take good notes.
Something like that.
However, no math teacher has ever mentioned "notes" to me or to any kid I know.
They're expected to observe what occurs on the board and be able to do it on the homework.
As far as I can tell.
I immediately saw this as a Singapore style bar model, forgetting how easy it would have been to simply multiply. My 7th grader solved the problem with proportions.
ReplyDeleteI MUST find the proportion article.
ReplyDeleteI found it utterly convincing, since I was taught to solve percent as a proportion - and it's the one aspect of arithmetic I really "got" and used constantly throughout my entire adult life.
I was slightly horrified when I found out about inverse variation this year, working my way through Saxon Algebra 2!