Quick Math Problem Help Needed :) :)

[TheAttachedMama]

Hi Everyone,

I am sitting at the dining room table with DD (4th grade)  helping her with math.   She has the following problem:

A cube has the volume of 64cm(cubed).   Find the length of one edge.

She has not learned about exponents or logarithms yet.   So I am not sure how to guide her to solve this besides asking her to do trial and error.   Example:  "What three numbers would multiply together to give you 64?  Let's try 1, does that work? (1 x 1 x 1= 1)  How about 2? (2 x 2 x 2) etc. etc."   But that doesn't seem very eloquent!   I know the answer, but I am not sure how I am supposed to guide her to see it.   

 At first, she kept trying to DIVIDE 64 by 3, and I finally was able to explain why that wasn't going to give her the same answer.    But I am not sure how to guide her to solve this other than trial and error.   I am probably missing the obvious.  

[Syllieann]

You could try having her make a factor tree and using it to find triplets.

[Kiara.I]

It doesn't need to be elegant.  I think the elegance is in the discovery, for this one.  Any chance you have 64 centimetre cubes around the house?  Because that might be the best way:  let her discover it for herself.

If you don't have centimetre cubes, do you have popsicle sticks and a snip?  They wouldn't be thick enough to truly show a cube, but you could at least lay them out and manipulate them.

[RootAnn]

Does she understand what volume is? 

I'd go for manipulatives if I had them. If not, I'd do the trial and error once she understands how volume of a cube is calculated.

[Miss Tick]

Legos? Sugar cubes? Blocks of cookie dough?

Perhaps pause and talk about how multiplication is repeated addition and exponents are repeated multiplication. Show how 5^3 can be expanded to 5x5x5 and both equal 125, then set up the equation for 64 and see if that clicks.

[sweet2ndchance]

Does she have her text book she can look at that explained this type of problem to her and how it expects her to solve it? That is where I would point a 4th grader to look first.

If there isn't a textbook with her math program, I would assume since you said she hasn't learned exponents and cube roots yet, that it wants her to factor 64 to get the answer. I would guide her by asking her what do we know about volume and what do we know about cubes and what do we know about the number 64.

We should know that volume is length times width times height and that a cube is a 3-D square. Since it is a square, all the sides are equal.

With that information we know that we are looking for one number that multiplied by itself 3 times will give us 64.

If she knows her multiplication facts, she should know, nearly instantly, that 8x8 is 64. And that it is an even number

So we now know we are looking for one number multiplied by itself 3 times is 64 and that 64 has the factors 8 and 2.

With that information we can greatly reduce the amount of numbers needed to guess and check or we can factor. If we factor, we can proceed two ways. We can factor 8x8 and look for triplets or factor 32x2 and look for triplets. Either way will get you the same answer. It's just which ever path looks easier to her.

That's how I would guide her. But I would let her supply the information about the problem and let her do the factoring. If she was just really really stumped, I might model for her how I figured it out or use a different perfect cube number as an example and show her how to solve it and then have her apply that knowledge to her problem.

[Gil]

20 hours ago, TheAttachedMama said:

Hi Everyone,

I am sitting at the dining room table with DD (4th grade)  helping her with math.   She has the following problem:

A cube has the volume of 64cm(cubed).   Find the length of one edge.

She has not learned about exponents or logarithms yet.   So I am not sure how to guide her to solve this besides asking her to do trial and error.   Example:  "What three numbers would multiply together to give you 64?  Let's try 1, does that work? (1 x 1 x 1= 1)  How about 2? (2 x 2 x 2) etc. etc."   But that doesn't seem very eloquent!   I know the answer, but I am not sure how I am supposed to guide her to see it.   

 At first, she kept trying to DIVIDE 64 by 3, and I finally was able to explain why that wasn't going to give her the same answer.    But I am not sure how to guide her to solve this other than trial and error.   I am probably missing the obvious.  

I would start by asking her questions to get her thinking about what the question is asking her.

She needs to consciously recall the meaning of the words cube and volume or she's not going to understand the question due to lack of reading comprehension. If you read the sentence " The diet of a Grey Fox consists of a mix of vegetation and small mammals" but have only a vague idea of what a fox is, kinda-know what the word diet means but don't know what the words "consists", "vegetation" and "mammal" are, then you won't understand that sentence.

So get her to think through the words directly so she can realize what the question is saying. In Gil-land that conversation involves me asking questions like:

"What does volume mean?"

"What is a cube?"

"Good, what is the difference between a cube and a rectangular prism?"  (she should be able to recall and express that a cube is made up of squares)

"Okay, and what do we know about the sides of a square?"

"So what does that tell you about the sides of a cube? -- or asked another way -- "If a squares sides are all the same length and width, and a cube is made up of all squares, then how do the sides of a cube compare to one another?"

"Good, now we've got "cube" unlocked, what is volume of a shape?"

"That's right, so how do we find the volume of a cube?" (she'll probably come up with l*w*h)

[draw out that equation:

Volume = length * width * height or

___ = ___ * ___ * ____ ]

Once you have that drawn out, then I'd return to the problem and read it again "A cube has the volume of 64cm(cubed).   Find the length of one edge."

"Good, so we understand the problem now. and what information are we given?"

(She should realize that she's given the volume, so I'd have her write that in it's spot in out equation. So we now have

Volume = length * width * height or

64cm(cubed) = ___ * ___ * ___.

Once that's written down, then she needs to read the problem again and realize that she's asked to find the length of one edge.

So at this point you ask

"Okay, kiddo, if we're looking at a cube, are the length, width and height related? How are they related?"

So, she would be seeing that the lenght-width and height are all the same, so at this point you can say "Good, so essentially what number multiplied by itself three times will give us 64?"

(Before I turn kids lose on "guess and check" I almost always have them use 10 and 5 as starting points.

What is 10*10*10? Okay, that's WAAAY to big.

What about 5*5*5? Okay, that's also too big, so I'd only let them do "guess and check" after they'd found an intelligent range to "guess and check")

It shouldn't take her long to find that the answer is 4.