4th grade word problem...please help

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amy21

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My daughter has a math problem that I cannot figure out how to get her started, much less get the right answer. Any help is appreciated.

The problem.....

A factory packages 4250 boxes of cereal. The number of oat cereal boxes is 715 more than the number of wheat cereal boxes. The number of fruit cereal boxes is 5 times the number of wheat cereal boxes. How many fruit cereal boxes does the factory package?
 
amy21 said:
My daughter has a math problem that I cannot figure out how to get her started, much less get the right answer. Any help is appreciated.

The problem.....

A factory packages 4250 boxes of cereal. The number of oat cereal boxes is 715 more than the number of wheat cereal boxes. The number of fruit cereal boxes is 5 times the number of wheat cereal boxes. How many fruit cereal boxes does the factory package?
Click to expand...
It is hard to know how to answer you because we do not know what your daughter is expected to know. This is a simple algebra problem, but I doubt your daughter is expected to know any algebra.

Does your daughter know the guess and check method?
 
amy21 said:
A factory packages 4250 boxes of cereal. The number of oat cereal boxes is 715 more than the number of wheat cereal boxes. The number of fruit cereal boxes is 5 times the number of wheat cereal boxes. How many fruit cereal boxes does the factory package?
Click to expand...
Since we're dealing with a fourth-grader, variables and systems of equations are likely out of the question. So:

Oat boxes and fruit boxes are defined in terms of the wheat boxes, so start with wheat boxes. Draw a square for "the number of wheat boxes". Then how many squares should you draw for the number of fruit boxes? For the oat boxes, draw a square and a rectangle, with the rectangle labelled as "715".

The overage (the part that isn't squares) is 715 of the 4250. So how much of the 4250 is represented by the squares? How many squares are there? So how much does each square represent?

...and so forth. ;)
 
amy21 said:
My daughter has a math problem that I cannot figure out how to get her started, much less get the right answer. Any help is appreciated.

The problem.....

A factory packages 4250 boxes of cereal. The number of oat cereal boxes is 715 more than the number of wheat cereal boxes. The number of fruit cereal boxes is 5 times the number of wheat cereal boxes. How many fruit cereal boxes does the factory package?
Click to expand...

I have a granddaughter who is in the fourth grade right now. Her class has been working on "problem solving" techniques, and one that seems to be stressed is the guess and check method.

Since the numbers of boxes of fruit and oat cereals are given in terms of the number of boxes of wheat cereals, let's take a GUESS at how many boxes of wheat cereal there are. Since I know that there were 4250 boxes in all, I know that the number of boxes of wheat cereal must certainly be less than 4250. I'm going to try 2000 boxes of wheat cereal as my first guess.

The number of boxes of oat cereal is 715 more than the number of boxes of wheat cereal; that means the number of boxes of oat cereal would be 2000 + 715, or 2715.

And the number of boxes of fruit cereal is FIVE TIMES the number of boxes of wheat cereal. That means there must be 5 * 2000 or 10000 boxes of fruit cereal.

Now, we need to check. Remember that the total number of boxes must be 4250. And we have 2000 wheat, 2715 oat, and 10000 fruit. Wow....that is WAY bigger than what we want. And that tells us our guess of 2000 boxes of wheat must be way too big.

So, let's make a smaller guess for the number of boxes of wheat cereal. I know we need a guess that is quite a bit smaller than 2000 (our first BAD guess!). so I will guess that there are 500 boxes of wheat cereal this time.

Now, use this guess to determine how many boxes of oat cereal and fruit cereal there would be. And check the answer you get. If your guess is incorrect, and it may very well be, you should be able get some useful information about how to ADJUST your guess. If your total number of boxes is too large, you know you need to try a smaller number of boxes of wheat cereal. If your total number of boxes is smaller than 4250, you know your guess at the number of boxes of wheat cereal is too small and you need to make your next guess a bit larger.

Obviously this is not as efficient a method as using a system of equations, but it is "doable" without any algebra at all.
 
But it is certainly something everyone should know- if you have no idea how to solve a problem try something, then check to see if it helped. We get plenty of people here who need to learn that!
 
Romsek said:
I don't have a ton of experience teaching children but this sounds like more trouble than just teaching them algebra.
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I am currently tutoring a 12-year-old who skipped a grade and is finding algebra a challenge. This is a very bright, very conscientious kid although math is not her strong suit. I think trying to teach algebra to 10-year-olds is likely to be a failure for the huge majority. Of course some could grasp it, but most likely will not. All failure does is to persuade people that they can't do math at all. I know in my case that algebra was introduced in the 8th grade, not the 4th, and that many of my classmates found the subject difficult even at that age.

I am, however, very uncertain about the utility of problems that require guess-and-check.
 
Iterative solutions - like Newton-Raphson algorithm for finding roots of non-linear equations - are "guess-and-check" (albeit educated) methods.
 
Subhotosh Khan said:
Iterative solutions - like Newton-Raphson algorithm for finding roots of non-linear equations - are "guess-and-check" (albeit educated) methods.
Click to expand...

Thank you for that observation...it validates my thinking that "guess and check" is indeed a worthwhile tactic. Khan strikes again! :)
 
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