Teaching your kids right math

I found 此地无银's math question yesterday and tested my son (also in 5th grade) last night. Let me put back the question here:

I have pennies, nickels, dimes, quarters, one dollar bills, and five dollar bills.  There are twice as many nickels as pennies, twice as many dimes as nickels, three fewer quarters than dimes and the same number of one dollar bills and five dollar bills as there are nickels. The total value of the money I have is $93.82.  How many dimes do I have.

As soon as he read the question, he figured out the number of pennies had to be 2, or 7, when he started verified, he realized the 2 was too small, then he verified 7 using calculator (I hate this, but well this is american), then he told me the answer was 28.

At least he got some points and found the right answer quite quickly. However he missed some key points the question was looking for. So I taught him the right math behind this question.

1) There are even number of nickels and odd number of quarters, so only quarters and pennies contribute to cents, so to end up with 2 cents, the number of pennies have to be 7, 17, etc.

2) The total amount is less than $100, so number of 5 dollar bills is less than 20, thus number of nickels is less than 20 and number of pennies is less than 10.

The right anwser is 7 pennies and 28 dimes.

If you tell this solution, a 5th grader should understand completely. But not all of them can figure out themselves, because they are not taught. This is actually good math question, but since it "provides" back door solutions, it easily misleads kids to forget logic thinking.

 

所有跟帖： 

• 经验是通过实践总结出来的。 -trivial- ♀ (571 bytes) () 06/12/2012 postreply 06:08:34

• 回复：经验是通过实践总结出来的。 -flagsix- ♀ (411 bytes) () 06/12/2012 postreply 06:29:20

• Yes, that would be a well-trained student. -trivial- ♀ (110 bytes) () 06/12/2012 postreply 07:03:49

• 回复：Yes, that would be a well-trained student. -flagsix- ♀ (323 bytes) () 06/12/2012 postreply 07:24:53

• I fully understand your points. -trivial- ♀ (233 bytes) () 06/12/2012 postreply 07:54:25

• 试和积累感性认识很重要，解决实际问题也得靠尝试，哪能保证有现成套路啊？ -calligraphy- ♂ (0 bytes) () 06/12/2012 postreply 07:25:48

• Thanks! This is exactly my point. -trivial- ♀ (0 bytes) () 06/12/2012 postreply 07:55:37