Can someone please help with this Alg. problem?

[stephanie]

I feel like such an idiot about this. I understand independent/dependent variables and domain and range. My ds seems to as well. However, he keeps getting this math paper back to correct this problem and I'm just not understanding what is wrong with it. And no making fun of the mom  :001_tt2: ..lol. Here goes...

 

The weight of each kitten in the litter of 5 is between 10-12 ounces. Jill chooses a basket that can support the total weight of the litter. Identify Independent/dependent and reasonable domain range..

 

Here's what ds put..Independent variable=litter  dependent=weight domain=5 range=50-60 oz. 

 

I'm sure it's some very simple solution that I'm completely looking over. 

 

Help, please!

[Kendall]

Does each kitten weigh the same?

 

independent=weight of one kitten=x

dependent=total weight of the litter=y

 

y=5x

 

 

domain is 10-12 inclusive   (most likely)

range is 50-60 inclusive  (most likely)

 

Usually in real life when we say between we mean it could be 10 or 12.

 

If each kitten weighs a different amount then you would have too many variables and then I'm not sure what they are asking for.  Maybe I'm missing something.  

 

[stephanie]

Does each kitten weigh the same?

 

independent=weight of one kitten=x

dependent=total weight of the litter=y

 

y=5x

 

 

domain is 10-12 inclusive (most likely)

range is 50-60 inclusive (most likely)

 

Usually in real life when we say between we mean it could be 10 or 12.

 

If each kitten weighs a different amount then you would have too many variables and then I'm not sure what they are asking for. Maybe I'm missing something.

It doesnt say each kitten weighs the same- just that there are 5 that weigh between 10-12 oz. The teacher has marked that the domain is the only thing wrong?

[kiana]

If she says that that's the only thing wrong then domain should be 10-12. Why? Because your input will be the weight of each kitten, not the number of kittens.

[Kendall]

If the domain is wrong then the independent variable is also.  If 10-12 is the correct domain, then the independent variable should be the weight of a kitten.

 

 Still, I can see why you would be confused because it doesn't make sense to me for the independent variable to be the weight of each kitten since the weights are all different and the total weight is dependent on all of them.  I don't see how this could be a two variable function or relation.

 

I'm not convinced this is a great problem nor am I convinced that it is truly assessing what the author of the problem wanted it to.  Maybe if I could see the lesson and all of the problems around it I might think differently. 

 

If you really are going to input each weight individually then there are really 5 independent variables and one dependent variable, assuming that you are trying to get the total weight (which is the only thing that makes sense given the wording of the problem).  

 

so

a=weight of first kitten

b= weight of second kitten

etc.

 

W=weight of the litter

W=a+b+c+d+e

domain of each variable a,b,c,d,e is 10-12

range of W is 50-60

 

Someone correct me.  Am I way off base on this?

 

Can you ask the teacher about this problem?

[stephanie]

If the domain is wrong then the independent variable is also. If 10-12 is the correct domain, then the independent variable should be the weight of a kitten.

 

Still, I can see why you would be confused because it doesn't make sense to me for the independent variable to be the weight of each kitten since the weights are all different and the total weight is dependent on all of them. I don't see how this could be a two variable function or relation.

 

I'm not convinced this is a great problem nor am I convinced that it is truly assessing what the author of the problem wanted it to. Maybe if I could see the lesson and all of the problems around it I might think differently.

 

If you really are going to input each weight individually then there are really 5 independent variables and one dependent variable, assuming that you are trying to get the total weight (which is the only thing that makes sense given the wording of the problem).

 

so

a=weight of first kitten

b= weight of second kitten

etc.

 

W=weight of the litter

W=a+b+c+d+e

domain of each variable a,b,c,d,e is 10-12

range of W is 50-60

 

Someone correct me. Am I way off base on this?

 

Can you ask the teacher about this problem?

I've already emailed her...lol. I'm stumped bc the weight IS different for each one. The only independent I thought was the # in the litter? I will get back when I hearfrom her..

 

Thank yall!

[kiana]

I agree with everything Kendall said.

 

But -- if the teacher says that the variables and range he gave before are correct, the only possible choice for domain is the weight per kitten.

 

This is not a good problem to help students understand independent and dependent variables.

[mathwonk]

Forgive me, this sort of thing sets off my mathematical nonsense detector.

 

I am a college math professor and this problem makes little sense to me. I am tempted to say it is primarily asking for jargon. I would say this is an estimation problem - the total weight of 5 kittens weighing 10-12 ounces each is between 50 and 60 ounces, so the basket needs to support at least 60 ounces, unless you hold it from the bottom of course.

 

I don't see a need for any variables independent or otherwise. I suppose you could say the desired output is the total weight, so maybe that would be called a dependent variable, but why do that? I mean of course it helps to ask what you are looking for, what quantity you need to estimate, but why give it an odd name?

 

So hopefully the word "range" applies to the key quantity, the total weight, so it would run from 50 to 60.

 

But is it looked at as a function of 5 variables? each kitten's weight counting as one? and each having range (i.e. domain) 10-12? What a needlessly confusing way to look at this.

 

 

Maybe I can play that game if I say W = K1 + K2 +...K5, where Ki is the weight of the ith kitten, and W is the total weight.

 

Then there are 5 independent variables, the Ki, and one dependent variable W, and the range (domain) of each Ki is 10-12, and the possible range of W is 50-60. But I would never ask it in an uninformative way like this.

 

 

By the way mathematicians do not always use these terms "domain" and "range" so much any more.

 

Of course we know what the books say they should mean, but actually there is a no complete agreement on what "range" should mean. I.e. is it the interval within which the output values are allowed to lie, or is it the actual set of output values that occur in the given problem.

 

In this problem however only the first possibility is plausible, since the second interpretation would be a single number, the unknown total weight.

 

But for this reason we geometers tend to use more often the more geometric terms, "source", "target", and "image", for these three concepts, at least for geometric problems.

 

Even in analysis the term "codomain" is sometimes preferred (for the possible range of output values) to alleviate the possibility of two meanings of the term "range". Unfortunately it sounds artificial.

 

I would try to find a better math course/book/teacher. Or maybe teach them more suggestive terms like "inputs" and "output". then these correspond to independent and dependent variables, and "possible (values of the) inputs" and "possible (values of the) outputs" should presumably correspond to domain and range.

 

 

It may help your child to remind that the desired domain and range are probably supposed to be intervals of numbers, and the "variables" are letters corresponding to the actual kittens, but should represent not an actual kitten, but a number for each kitten.

 

So although in a philosophical sense the domain is the litter, they really want us to use the variables to pass from the kittens in the litter, to numbers in the domain, i.e. their weights.

 

 

so really there are three relevant sets in this problem, and two functions, two domains, and two ranges.

"

the first domain is as your child said, the litter of kittens. then the "independent variables" K1,...,K5, are themselves functions from that domain to the range of possible individual weights, namely the interval [10,12]. However in this first function these variables actually represent values, hence are the "dependent variables" in this case. I.e. the Ki take their values in the "range" interval, which characterizes "dependent variables".

 

(Confused yet?, I am. But remember, since here the values Ki are the outputs, they are the dependent variables. I.e. here the kitten is the input and its weight is the output.)

 

Then the second function is given by the addition formula W = K1+...+K5.

 

Now in this formula the Ki are inputs, hence independent variables, and the total W is the output, or dependent variable.

 

The domain of this function of 5 variables is the product of the 5 (equal) intervals [10,12]x...x[10,12].

 

The range of this addition function (for all possible values of the kittens' weights) is then the interval [50,60]. This function may be called W, the dependent variable for the second function.

 

Actually this became interesting to me as I tried to make sense of it, but my sense is probably not what the teacher has in mind.

 

I hope this has some interest for you, as an illustration of just what variables and the other terms actually refer to.

 

I have also tried to see and reveal the correctness of your child's intuitive take on the meaning of the domain, as the actual litter. It was that insight that led me to see that the so called "independent variables"Ki, are actually themselves dependent variables of another more basic preliminary function, from the litter to the interval [10,12].

[mathwonk]

aha! actually there are one or two more functions involved in this problem.

 

the third function is the "maximize" function, that has domain the total weight interval [50,60] , and out put the maximum of these values, or 60.

 

Then the fourth possible function has domain the one number 60, and has output an actual basket which will hold that weight! this last function is not necessarily single valued, since many baskets may work, so is not called a "function" in elementary math books, which pretend that such animals do not exist.

 

I.e. the goal is to choose a basket, and the steps involve 4 stages, kittens, individual weights, sum of weights or total weight, maximum total weight, and finally a choice of basket!

 

So there are 4 functions, 4 domains, and 4 ranges, and at each stage the role of independent and dependent variable undergoes an interchange. I.e. dependent variable in each function becomes the independent variable in the next function.

 

So you see why these terms are misleading and the driver of the process is the function being considered at each stage.

[EKS]

Forgive me, this sort of thing sets off my mathematical nonsense detector.

 

I am a college math professor and this problem makes little sense to me. I am tempted to say it is primarily asking for jargon. I would say this is an estimation problem - the total weight of 5 kittens weighing 10-12 ounces each is between 50 and 60 ounces, so the basket needs to support at least 60 ounces, unless you hold it from the bottom of course.

 

:iagree:

 

[mathwonk]

notice that until you describe what function you are considering, it is impossible to determine the domain and range.

 

your child gave as domain the litter and as range the interval [50,60]. Ok that is correct if the corresponding function is the one assigning to the collection of kittens in the litter, their total weight.

 

If the teacher wanted as an answer that the domain was (5 copies of) the interval [10,12], then that would be correct for the addition function assigning to 5 individual weights from the interval [10,12], their sum.

 

However if the teacher wanted as an answer the domain as being the interval [10,12], and the range being the interval [50,60], then in my opinion technically this can only be the domain for one of the variables, say K5.

 

Hence this can only be correct for a somewhat artificial partial function such as the one which assumes that say the first 4 kittens' weights are already known, and then we look at the function assigning to the fifth kitten's weight K5 say, the total weight K1+...+K5.

 

I.e. if the domain is a single interval, like [10,12], then the function can only have one variable.

 

If the function has 5 variables, as seems the case here, then the domain must consist of 5 tuples of numbers, so it should be a product of 5 intervals, even if those intervals are the same.

 

(This agrees with what Kendall said.)

 

So I am kind of wondering what your teacher thinks the answer is here, and why. It is necessary to read carefully the description given in the book or course of "domain" and "range" and "variable", (and hopefully "function").

[stephanie]

Ok, ladies. I've got it...lol.

Teacher says the independent variable = # kittens in the basket

Dependent= total weight in basket

 

Domain=0-5 because she doesnt HAVE to put any kittens in the basket.

Range=0-60 because if none of the kittens were in the basket then there would be 0 ounces in the basket .

 

I understand that, but I assumed as did ds that if she's getting a basket she's going to at least put one in it! Go figure!

[mathwonk]

with all due respect, this is not what i expected.

 

If that interpretation is considered correct, then there are many other equally valid ones that must also be considered correct.

 

perhaps the teacher just wanted any conceivable interpretation that involved numerical domain and range? But this cannot possibly be argued to be the one correct answer, unless there were more instructions we do not know about.

 

my idea that i logged on here to offer as an attempt to justify what i assumed to be the teacher's answer, was to let the independent variable be the average weight of the kittens, so that then the function was y = 5x, with domain [10,12] and range [50,60].

 

 

but when the basket is supposed to be chosen to hold the weight of the entire litter, as was specified, ("Jill chooses a basket that can support the total weight of the litter.") then I do not see how one can say that the number of kittens it should hold is somewhere between 0 and 5.

 

this is becoming not so much a math problem, but a debate with imprecise conditions, and arguable conclusions. please consult euler's elements of algebra for some algebra problems I would recommend more highly.

[mathwonk]

"Teacher says the independent variable = # kittens in the basket

Dependent= total weight in basket"

 

Let me pose one further question. Is a "function" from a given domain to a given range supposed to have just one value at each domain point? (This is the usual meaning of "function" in mathematics.)

 

 

If so, then the answer given above by the teacher, cannot be correct unless all kittens have the same weight. I.e. if e.g. some two of the kittens weigh different amounts, then just knowing the number of kittens in the basket does not determine their total weight, for any number less than 5.

 

thus the total weight of the kittens in the basket, even if proper subsets of the litter are allowed, is not a single valued "function" of the number of kittens in the subset.

 

of course i wasn't present in the class, so maybe multiple valued "functions" are allowed?

 

of course i realize the word "function" has not occurred in this problem, but that is the usual context for the words "domain" and "range". is this possibly a problem about multiple valued correspondences rather than functions?

 

or to put it in the less precise language of variables, is the dependent variable in this problem allowed to take more than one value when the value of the independent variable is fixed? that would seem to be needed to rescue the teacher's answer.

 

I.e. the teacher's answer is conceivably correct, but only with somewhat unusual assumptions.

 

I have thought of a way to rescue it another way - let the function have as input the number of kittens, and as output the largest possible weight of that number of kittens from the litter. then again we have a single valued function.

 

 

I want to emphasize again that the key information is "what is the function?" only then can one decide what is the domain and range.

[creekland]

I have thought of a way to rescue it another way - let the function have as input the number of kittens, and as output the largest possible weight of that number of kittens from the litter. then again we have a single valued function.

This is the simple answer they want. It's the way I saw it (I work in high school) all along, but like the OP, I wasn't thinking of "no" kittens as an option this early in the morning, so I was wondering what the correction was going to be as I read through the thread.

 

We teach IV as the variable "I" change. There's no way the individual would change the weight of any kitten. The individual does choose the number of kittens to add to the basket. The DV totally depends upon the IV - as the weight does here.

 

As you mentioned also, if the IV were the weight of each kitten, we wouldn't have a function, we'd have a relation as two kittens can weigh the same amount, but the total would differ.

 

Input and output are often used as terms when teaching but as long as domain and range stay on standardized tests they will remain in classes.

[mathwonk]

of course, standardized tests! that explains this whole exercise. thank you, I get it now.

[creekland]

of course, standardized tests! that explains this whole exercise. thank you, I get it now.

Frustrating, isn't it? But life... I have no idea how many years it takes to change standardized tests. I'll likely be out of the school system by then.