Correcting my DD's 5th grade math and I don't know one of the answers

[cruisnfamily]

Here's the problem:

Mrs. Jones had some white paint and some green paint and a bunch of wooden cubes. Her class decided to paint the cubes by making each face either solid white or solid green. One kid painted his cube with all 6 faces white, another kid painted her cube solid green, but another painted 4 faces white and 2 faces green.

How many cubes could be painted in this fashion so that each cube is different from the others? Two cuves are alike if one can be turned so that it exactly matches, color for color on each side, the other cube.

Answer = ________ different cubes can be made.

DD has the answer as 7 but this seems too easy to me, yet I can't think of any other way. A little help please?

 

[lacool]

I'm no math magician, but I think your DD is right.

1 - Solid white
2 - One green face
3 - Two green faces
4 - Three green faces
5 - Four green faces
6 - Five green faces
7 - Solid green

Perhaps you are trying to make the question harder than it is. I am always trying to read further into word problems.

 

[floridaminnie]

It's actually twelve. YOu have 6 faces of the cube and two different colors. So you take six times two and come up with twelve. No cube will be the same.

 

[lacool]

But a cube with 5 white faces is identical to a cube with 1 green face. 4 white identical to 2 green, etc. They cancel each other out and will only count as one design. I stand by 7 as the answer.

 

[floridaminnie]

It's called the counting principal. Here's a link for an exampleexample

 

[cruisnfamily]

Originally posted by lacool
Perhaps you are trying to make the question harder than it is.

I'm sure I am!

I thought there should be a formula(as Suzanne pointed out) but I agree with you that they cancel each other out. It just seems too easy but I'm letting her go with 7 as her "final answer" unless somebody can convince me otherwise.

 

[robsmom]

I am usually fairly good with math but get different answers than both the folks above. This is tough for a 5th grader because I am not sure if it is suppossed to be about probablity or the geometry of a cube.

Mathematically if each side of the cube where unique you would actually have 6 items for which you have 2 choices. that would be 2 to 6th power or 64 unique combinations. So let's say that each of the cubes sides had a number written on it (like a dice) and then you did the painting. You could come up with 64 different combinations.

But in the actual question, there is no differentiating a side of a cube so if you paint one side it doesn't matter which one it is. Based upon this I get 10 combinations. I can't come up with 12 unique options per answer above.

1. There is only one way to paint in with zero greeen (all white)
2. There is only one way to paint it with one green.
3. Two green sides touching each other
4. Two green sides opposite each other on the cube (not touching)
5. Three green sides running side by side around the cube
6. Three green sides with 2 side by side and one on top or bottom.
7. 4 green sides running all the way around the cube
8. 3 green sides running side be side with one green on top or bottom (total 4 green)
9. 5 green sides
10 6 green sides.

I am not 100% convinced, but if i look at the options for zero, one, five, or six greens there is only one way to do them on a cube. For the 2, 3, or 4 sides, I come up with 2 unique ways each time.

Lisa

 

[Danauk]

I think I agree with robsmom and the snswer is 10. I'm a teacher from England so am not sure about the ages in your grading system. How old are children in 5th grade? I think it is quite a hard question.

 

[cruisnfamily]

Originally posted by Danauk
How old are children in 5th grade? I think it is quite a hard question.

The children in 5th grade are 10 and 11 years old. This is not part of the regular curriculum, this is an extra thing called "superstar Math" or sometimes called "sunshine math". It's problem solving. The kids aren't actually graded on this, they get the equivalent of some extra credit for it. Not all the kids in the class are required to complete this only about 7 in a class of 23 are required. There are about 8 problems each week and there's usually one or two that I can't figure out myself. I decided to post this one to see if anyone could help.

I am now more confused than when I started out...is it 7? or 10?? or 12??? I think I'm going to bring up the "2 green next to each other or opposite from each other" thing to her and then just let her go with her best shot at it.

We are not supposed to help them get the right answer on this, it's all about the problem solving process. We're supposed to "put them on the right track" or something but not work through it with them.

 

[robsmom]

The counting pricinple as documented is sort of the way to the answer but you have to apply not as 2 X 6 but as 2 to the 6th or 2X2X2X2X2X2 or 64. But because of the shape of a cube many of the 64 combinations would match, hence the lower number. Have not come up with a good mathematical way to get to the 10 but when I draw the possibilities keep coming back to that.

 

[robsmom]

When you get the official answer let us know! I love puzzles and have spent 15 minutes drawing cubes and using my data switch box (shaped like a cube) to figure this out. Would love to know the right answer!!!

 

[cruisnfamily]

Originally posted by robsmom
When you get the official answer let us know! I love puzzles and have spent 15 minutes drawing cubes and using my data switch box (shaped like a cube) to figure this out. Would love to know the right answer!!!

It was so sweet of you to put that much time and effort into this!

She's currently throwing balled up pieces of paper into a trash can 9 feet away. She has to do this 100 times and record the results and then do something with them. I haven't been asked for input on this one so I'm letting her muddle through the paper in trash can one by herself.

The page is due on Tuesday and they usually correct them together on Tuesday or Wednesday. I'll let you know what the correct answer is when I find out although I'm currently leaning towards 10.

 

[lacool]

I had to laugh because when you first posted the question I thought, "This looks just like Sunshine Math." DD is in 2nd grade, and anytime we got an answer wrong it was for overthinking the problem.

My favorite was:
Mary has a cat that has 5 kittens, and a dog that has 5 puppies. If she gives away two kittens and 3 puppies, how many pets does she have left. Well we came up with 3 kittens + 2 puppies + 1 cat + 1 dog = 7 pets. We were told the answer was 5 (just the kittens and puppies) and that we were overthinking to add in the parents of the animals. But didn't she have a cat and a dog to start with???!!!! Sunshine math is the bane of my existence!!!!

That said, 10 makes sense, as explained, but I will be shocked if the 5th graders are expected to come up with that answer. But you have a good basis for argument if it is marked wrong. Not that it will do you any good!

 

[cruisnfamily]

Originally posted by lacool
Sunshine math is the bane of my existence!!!!

Alot of parents actually HATE the Sunshine Math. I happen to like it. It's particularly good for kids like my DD who is weak with problem solving.

DS is in 2nd grade and has no trouble whatsoever with the sunshine pages(his entire classs is required to do them). He just "gets" math.

Of course the 5th grade sheets are much much more difficult than the 2nd grade ones but DD has been struggling with this type of thing since the 1st grade, she never "got" it, even when they were easier.

So thanks all! Maybe I'll start posting the one I consider to be the hardest each week....wouldn't that be fun?

 

[robsmom]

Can't believe that you were told the initial cat and dog don't count!! Now I am even more curious as the right answer. I will feel really bad if they just wanted her to come up with the 7!

Cruisinfamily - it was fun and no problem at all!! My 4 year old refuses to nap on weekends even though he takes 2 1/2 hours each day during the week. So as typical, he crashed just as we were about to eat dinner and will be out cold until morning. Good time for me to surf a little bit.

 

[lacool]

Originally posted by cruisnfamily
Maybe I'll start posting the one I consider to be the hardest each week....wouldn't that be fun?

I think we'd enjoy the challenge. I'll post the ones DH and I don't agree on. The irony is that he is was a math major and I was an accounting major, so we are not intimidated by math. Sunshine math, however, seems to cause the most trouble of all homework. It is hard to help DD if even DH and I can't agree on the answer.

 

[cruisnfamily]

By the way, DD's final answer after rethinking the problem was 12 . I don't think it's correct but she's put in enough effort in the right direction that I'm going to leave it and see what happens.

I'll let you all know.

 

[cruisnfamily]

The correct answer was 10

This week had a few really challenging ones but they were very visual....not something I could describe for you.

I'll try to post some stumpers next week!

 

[robsmom]

thanks for letting us know!