Strange problems

[Steven G]

Attached is an assignment that I daughter did in her 4th grade class. Am I missing something or are these solutions all wrong. I would think that in all the problems the answer would be from up to the smallest of the given numbers.

 

[Ishuda]

OK, Problem 1 (assuming I did it right):
1. Grace is preparing grab bags for her store's open house. She has 24 candles, 16 pens, and 40 figurines. Each grab bag will have the same number of items, and all the items in a bag will be the same. How many items can Grace put in each bag.

The way the question is asked there isn't a unique solution. There can be 1 of each item in each grab bag for a total of 16 grab bags with 8 candles and 24 figurines left over. There can be 2 of each item for a total of 8 grab bags with some left over or 6 candles, 4 pens, and 10 figurines in each grab with 4 grab bags and nothing remaining or ...

 

[Steven G]

OK, Problem 1 (assuming I did it right):
1. Grace is preparing grab bags for her store's open house. She has 24 candles, 16 pens, and 40 figurines. Each grab bag will have the same number of items, and all the items in a bag will be the same. How many items can Grace put in each bag.

The way the question is asked there isn't a unique solution. There can be 1 of each item in each grab bag for a total of 16 grab bags with 8 candles and 24 figurines left over. There can be 2 of each item for a total of 8 grab bags with some left over or 6 candles, 4 pens, and 10 figurines in each grab with 4 grab bags and nothing remaining or ...

Ishuda, so the answer can be any integer from 1 to 16 for the pens? My daughter's teacher is saying that the answer is the common factors of 24, 16 and 40 so 1,2,4 and 8. How can one think of the problem so that is the correct answer?

 

[Ishuda]

Ishuda, so the answer can be any integer from 1 to 16 for the pens? My daughter's teacher is saying that the answer is the common factors of 24, 16 and 40 so 1,2,4 and 8. How can one think of the problem so that is the correct answer?

Well you can narrow the field of answers by requiring that no items be left over. In that case you can only make
1 grab bag with 24 candles, 16 pens, and 40 figurines.
2 grab bags with 12, 8, and 20
4 grab bags with 6, 4, and 10
8 grab bags with 3, 2, and 5
and finally come to a unique solution with the 8 grab bags (for this case) if you want the maximum number of grab bags and no items left over.

 

[Steven G]

Well you can narrow the field of answers by requiring that no items be left over. In that case you can only make
1 grab bag with 24 candles, 16 pens, and 40 figurines.
2 grab bags with 12, 8, and 20
4 grab bags with 6, 4, and 10
8 grab bags with 3, 2, and 5
and finally come to a unique solution with the 8 grab bags (for this case) if you want the maximum number of grab bags and no items left over.

Yes, a few minutes ago I concluded just what you said. But there is still a problem as they are asking how many items can be put into a bag NOT how many bags there are. These problems came directly out of the textbook. Amazing. I have always felt that PhD mathematicians (I do not think one is a mathematician w/o a PhD) should be writing these books for the younger grades but it would be hard, if not impossible, to get them to write 4th grade books.

 

[Ishuda]

Yes, a few minutes ago I concluded just what you said. But there is still a problem as they are asking how many items can be put into a bag NOT how many bags there are. These problems came directly out of the textbook. Amazing. I have always felt that PhD mathematicians (I do not think one is a mathematician w/o a PhD) should be writing these books for the younger grades but it would be hard, if not impossible, to get them to write 4th grade books.

The problem with writing problems is that you need to be clear about the conditions. This is generally done by having an independent person do the exercises with all due diligence. However, sometimes that is not done or the due diligence is still due on publication of the book.

BTW: I have been called many things in my life and held many titles. Among those things I have been called and had a title as is a mathematician [not that I would necessarily agree but I did accept the money]. I've never had a PhD and refused to get one although I have taught PhD's in other disciplines including both hard and soft sciences.

EDIT: In this case, I think there should have been a statement with the "Solve each problem" to indicate no items were to be left over for any of the problems.