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Hey guys,

I'm doing the final (open-book) test for my Teaching Elementary Math. I've got my father with and we're both stumped on how to do this particular question. Let me cut/paste it over:

Based on the meaning of fraction to reason: if 9 hamsters are 3/5 of the total number of hamsters in a pet store, how many hamsters are there?

Explain your reasoning process in the way students in middle elementary school can understand (pictures are optional, but not required).

We know the answer is 15, but trying to figure out how we actually arrive at it (which is part of the reasoning process). I would assume "middle elementary" would be around Grade 4 (ish), so we likely wouldn't be introducing algebra into this particular problem.

The thing is, Dad is really good with math, but he does it all in his head. So he can't explain to me how he came to the conclusion of 15.
Help?

15.

...yeah, I said that. The problem is trying to figure out how to get to that answer and how to show a Grade 4 class how to reason out that answer.

Sorry for partly reading

Heh, no worries. I thought you were just being a dick.

You could change it into a semi-word problem: 9 hamsters is 3 fifths of the total. Therefore, divide 9 hamsters by 3 to get 3 hamsters is 1/5 of the total. Then you multiply by 5 to get 15 total hamsters. This assumes Grade 4 has learned basic division, I forget when I learned that during grade school.

Can you just show them how 9 and 3 are related? If 3 groups of 3 hamsters equals 9 hamsters, then two more groups of 3 (to reach 5/5) is 15.

"Kids, based on the explanation, you know 9 makes up for 3 parts of the whole. That means one part is 9/3=3. Looking at the explanation, you see the whole consists of 5 parts, and therefore, the total number of hamsters is 5*3=15. Isn't math fun?"

Lurker said:

You could change it into a semi-word problem: 9 hamsters is 3 fifths of the total. Therefore, divide 9 hamsters by 3 to get 3 hamsters is 1/5 of the total. Then you multiply by 5 to get 15 total hamsters. This assumes Grade 4 has learned basic division, I forget when I learned that during grade school.

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"That's your answer. That's your answer!" - My Dad.

Use a pepperoni pizza as your diagram.

--Patrick

So class we can write this equation as the following

9/X = 3/5 just look at those fractions, aren't they annoying? Let's get rid of them!

Start by multiplying each side by X to get

9 = 3X/5 now we have a nice clean number on one side, let's make the other side neat and tidy too

By multiplying by 5 to get

45 = 3X

So all we have to do now is clean up the one side by dividing by 3 to get

15 = X

So 9/15 is the same as 3/5!

Now shut the fuck up you little shits!

There are five cages. There are nine hamsters in three of them. All the cages have the same number of hamsters. How many hamsters are there total?

You should find a website called Exemplars. They're a Mary website where teachers find problems of the week for students. They provide the teacher with models of real student work for explaining why an answer is correct. Very handy. Don't know if it costs anything; my school uses it.

A python has gotten into the hamster cages. By the time we noticed it, there were only 9 hamsters left, which is 3/5 of the total amount of hamsters we started with. How many hamsters did the snake eat?

I always hated the old word questions that used the term "take away." It normally lead to the wrong answer.

5 apples on the desk and you take away 3, how many apples do you have? -they were looking for 2 but the correct answer would be 3. because you are holding the apples.

stienman said:

There are five cages. There are nine hamsters in three of them. All the cages have the same number of hamsters. How many hamsters are there total?

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I'd have said something like this, too.

All of the hamsters in the shop are kept in cages. Every cage has the same amount of hamsters. Three of these cages hold 9 hamsters, in all. That means there are three hamsters in each cage. There are five cages, all told. So, if there are five cages with three hamsters each, we have 16 hamsters total (hamsters breed almost as fast as rabbits, after all )