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Public Zone 公開區 => General Topics 綜合題目 => Topic started by: kido on 08 May 2011, 23:54:02
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Last year I (my son in fact) encountered the following maths problem, he couldn't solved it and asked me. It's in the photo. It's quite interesting as it's like an IQ question rather than an ordinary maths question.
It worthed quite a while(really quite some time, haha ) for me to understand what it was trying to teach me.
Also I'm just wondering how a P3 student could solve this problem.
To translate:
Given: 21 - 12 = (2-1) * 9 = 9
and 710 - 170 = (7-1) * 90 = 540
calculate
Q5. 630 - 360
Q6. 2729 - 2279
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630 - 360 = (6 - 3) * 90 = 270
2729 - 2279 = (7 - 2) * 90 = 450
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tell me....why is it??
nobody (in school) teachs me this kind of maths before.....
pls explain...
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My guess is that this type of question is more about problem solving technique, and demonstrating some cool number tricks, rather than the arithmetic.
So, if we look at the examples we see:
21 - 12 = (2 - 1) * 9 = 9
710 - 170 = (7 - 1) * 90 = 540
So, the first part of the pattern is that for the flipped digits a subtraction is performed: i.e. given ab - ba then the first operation is (a - b).
The second part of the pattern is that the result of (a - b) is multiplied by 9 * 10^n where n is determined by the number of digits after ab.
So, in the trickiest case:
2729 - 2279
we would solve as:
2ab9 - 2ba9 (where a = 7, b = 2)
1 digit (the number 9) after ab so n = 1
which gives:
2ab9 - 2ba9 = (a - b) * 9 * 10^n = (7 - 2) * 90 = 450
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My guess is that this type of question is more about problem solving technique, and demonstrating some cool number tricks, rather than the arithmetic.
So, if we look at the examples we see:
21 - 12 = (2 - 1) * 9 = 9
710 - 170 = (7 - 1) * 90 = 540
So, the first part of the pattern is that for the flipped digits a subtraction is performed: i.e. given ab - ba then the first operation is (a - b).
The second part of the pattern is that the result of (a - b) is multiplied by 9 * 10^n where n is determined by the number of digits after ab.
So, in the trickiest case:
2729 - 2279
we would solve as:
2ab9 - 2ba9 (where a = 7, b = 2)
1 digit (the number 9) after ab so n = 1
which gives:
2ab9 - 2ba9 = (a - b) * 9 * 10^n = (7 - 2) * 90 = 450
so this is a kind of primary 3 level maths?????
what a wonderful world...
I wonder this is a superhero primary 3 level.....not for my son....sorry...
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I wonder this is a superhero primary 3 level.....not for my son....sorry...
This is no superhero P3 Maths, just copied from an ordinary text book...
I think what Primary school learn now has undergone radical changes, and also they seemed removed (or tuned down the importance of) some 'mechanical' things like practicing addition/subtraction in 3 or 4 digits. Maybe this is due to advance in computer and we no more needed to accurately practice algebra.
I don't know whether this is good or bad.
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I see the examples like q's comment - that it's more of an IQ test on pattern recognition and math curiosities rather than hard core mathematics principles.
This little trick reminds me of our little poem:
3 guys walking 70 miles
5 horses riden by 21 people
7 brothers came home for 15 days
take out 105 is the answer
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This is no superhero P3 Maths, just copied from an ordinary text book...
I think what Primary school learn now has undergone radical changes, and also they seemed removed (or tuned down the importance of) some 'mechanical' things like practicing addition/subtraction in 3 or 4 digits. Maybe this is due to advance in computer and we no more needed to accurately practice algebra.
I don't know whether this is good or bad.
I personally think this is wrong. Sometimes things worthwhile doing are boring but necessary.
I have repeatedly told me kids the story of a full grown adult who couldn't add or estimate distance by converting km to mile. Unfortunately this kind of adult is more and more common these days.
Yes nowadays we have computers and calculators everywhere. But most of the smart and successful (business & job wise) people I know almost always have a good sense of numbers. They can visualize numbers in their heads. This is a good indicator of how well you can understand abstract concepts, and see the big pictures.
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I have repeatedly told me kids the story of a full grown adult who couldn't add or estimate distance by converting km to mile. Unfortunately this kind of adult is more and more common these days.
Oh, shoot! I can't convert mile to km and vice versa ;D ;D ;D ;D
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I personally think this is wrong. Sometimes things worthwhile doing are boring but necessary.
I have repeatedly told me kids the story of a full grown adult who couldn't add or estimate distance by converting km to mile. Unfortunately this kind of adult is more and more common these days.
Yes nowadays we have computers and calculators everywhere. But most of the smart and successful (business & job wise) people I know almost always have a good sense of numbers. They can visualize numbers in their heads. This is a good indicator of how well you can understand abstract concepts, and see the big pictures.
Time really changes....
I feel sympathy ....
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Oh, shoot! I can't convert mile to km and vice versa ;D ;D ;D ;D
Well, the story was like this. We were hiking in Sai Kong. There was a sign that says something like 3.5 km to somewhere, and she asked how many miles is 3.5 km. I told her 1 mile is about 1.6km, and she couldn't estimate in her head how many miles is 3.5 km given the 1.6 ratio. I think for an adult, this is unacceptable.