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Wrong answer. This was for elementary school graduation in Singapore. A very famous one a few years back when my kids were still in middle and high schools. They could not do it. Can you do bar drawing?? I will post a video link when I find it.
Dagnaggit. I had the bar graphs set up right, I had the problem set up right, and then when solving for x and y, I somehow managed to divide 66 by 3 and come out with 33. When I fixed that error, I got it right:
7x = 18 + 4y (7x is Jim's half of the chocolates, and 18+4y is Ken's half of the chocolates)
y = 12 + x (y is Ken's half of the sweets, and 12+x is Jim's half of the sweets)
Common Core puts this in 6th grade proportional reasoning standards and uses scaling of ratios. ex. 40/100 X 3/3 = 120/w. w= 300 -120 = 180. It is also covered in that same grade in writing and solving equations standards ex. 0.4x = 120 with inverse operations x= 120/0.4. X= 300. 300-120 = 180.
Dagnaggit. I had the bar graphs set up right, I had the problem set up right, and then when solving for x and y, I somehow managed to divide 66 by 3 and come out with 33. When I fixed that error, I got it right:
7x = 18 + 4y (7x is Jim's half of the chocolates, and 18+4y is Ken's half of the chocolates)
y = 12 + x (y is Ken's half of the sweets, and 12+x is Jim's half of the sweets)
That's always been my problem in math, I get the complicated part just fine, and then mess up on the easy arithmetic because I'm going too fast. Lol.
I did like the "no algebra required" version of the bar graphs too. It's a little harder to follow though without having moving pieces like he had.
That one was a well known HARD math problem that outraged many Singapore parents in 2009. It circled among my kids Asian friends first, then spread to more kids. No one in her high school, including all teachers, can solve it by using only elementary math. Fast forward to 2016, I guess Singapore parents' math skills improve along with their kids. This type of problems become less significant.
I did read it. I didn't expect to be graded on that one I am pretty sure the main "issue" for many was to find out how many pages that book actually has and then you can answer whatever is being asked.
In the example above where you say that's how you teach 4th grader - How about if the question says 45% instead of 40%. How do you teach your 4th grader then?
You may have read it, but did you understand it?
Steps to solve a word problem:
1. Read the problem (reread the problem)
2. Understand the problem (what are you solving?)-This is where you messed up. You solved the total number of pages, not the number of pages left.
3. Develop a plan (What do you know? what do you need to know?)
4. Execute the plan (solve the problem)
5. Check Your Self
Realistically, a 4th grader wouldn't be expected to solve this type of problem, especially using the 45% unless it was to challenge the student (more advanced).
4th grade you want to work with friendly numbers to build the concept strength (think powers of ten, benchmark fractions and percents).
I'd propose the question just like you and let them apply what they know to try and solve. You'd be surprised how many kids will arrive at the right answer by drawing models (singapore math strategy).
What I would expect a kid to do is apply what they know. Percent is per 100...so your whole is 100.
120=45%
They know that 45% (which they know) + p (we do use variables) = 100%
Next:
45 + 55 = 100
45 + (45 + 10) = 100
Now they are replacing percentage with page numbers.
120 + (120 + n) = Total pages
240 + (n) = total pages
Now I would guide them to understanding that 240 pages=90%
They would hopefully know that if 240 is 90% then they would divide 240 by 9 since there is an equal parts. 240 is 9 equal parts. Which is 26 4/9 (we haven't learned to convert remainder into decimals yet, but I have taught them that the remainder is a fraction).
So the remaining 10% is 26 with a remainder. You add the 90% to the 10%
240 + 26 4/9 = 266 4/9, which really isn't possible b/c a page can't be a partial page unless it was ripped...so they have to decide what to do with the remainder. Do we round up, or round down? I would expect them to add another page, since there is a partial page.
Answer would be 267 pages.
As noted, a great many people with a high level of math proficiency and interest choose career paths other than teaching.
Especially other than elementary ed!
Quote:
Originally Posted by Good at Math
True. But that example is very simple basic math. It shows up only on primary school exams in Asia.
You know this how?
Quote:
Originally Posted by eok
Before people had calculators and cash registers, it was more important to be able to add a column of figures quickly and accurately than it is today. Therefore, that was the focus of math teaching in the lowest grades. Speed and accuracy. It was called cyphering. It's now spelled ciphering, and is no longer used with that meaning. The good students were the ones who could quickly and accurately add a column of numerals, without ever making any mistakes.
Teaching modern students to notice patterns and use them for shortcuts probably helps develop their brains for all kinds of mental activities. That they notice 60% is 1.5 times 40%, is more important than knowing how to figure the answer the hard way. Because, knowing the hard way doesn't exercise their intelligence as much. The key issue is what they notice, more than what they know. Pattern recognition. Seeing the pattern and taking advantage of it. But how do you teach that? The only way I know is by giving them tons of work to do, and letting them find shortcuts, to reduce their workload. But is that abusive to those who don't have talent at finding patterns?
Why is a teacher who doesn't even know what a remainder is teaching math at all? Hire a teacher, or two or three, who are really *good* at math and *love* math, and have them teach *ALL* the math courses.
Oh, wait, to attract that unique skillset, you might have to start their pay above many of the other teachers with more *seniority*, and that's certainly not going to fly with the Union. And so it goes on and on with the kids really the losers in the end..
True. But that example is very simple basic math. It shows up only on primary school exams in Asia.
You know this how?
I have seen plenty of exam papers from Asia. This kind of questions only belong to primary schools. Their secondary school exams are never that easy. SAT often have simple problems like that. Doing well on SAT doesn't mean "college math ready".
Common Core puts this in 6th grade proportional reasoning standards and uses scaling of ratios. ex. 40/100 X 3/3 = 120/w. w= 300 -120 = 180. It is also covered in that same grade in writing and solving equations standards ex. 0.4x = 120 with inverse operations x= 120/0.4. X= 300. 300-120 = 180.
If Common Core puts it in 6th grade, we are a good distance behind East Asians.
B. Even if they are good have zero incentive to become teachers
Exactly
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I am pretty sure the main "issue" for many was to find out how many pages that book actually has and then you can answer whatever is being asked.
