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Help with a Year 4 maths problem please
DH & I have several different answers


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#1 ~*Amethyst*~

Posted 11 February 2013 - 06:42 PM

Can anyone help in how to work out a 'Family Maths Question' please.

Family Maths Challenge 2

At your party you have decided to serve triple decker ice creams!
* There are 5 yummy flavours - peppermint, chocolate, strawberry, banana and tutti frutti.
  * How many combinations of three flavours could you create?
  * How many combinations of three flavours could you create if one flavour is always chocolate?
  * How many combinations all together (including 3 scoops the same, 2 the same and one different)?

XxxAmethyst


#2 secret~sammy

Posted 11 February 2013 - 06:49 PM

1) 5 chose 3 = 10

nCr = n! / (n - r)! r!

nCr = 5!/ (5 - 3)! 3!
nCr = 5!/ 2! 3!
nCr = (5 * 4 * 3 * 2 *1) / (2 * 1)(3 * 2 * 1)
nCr = 120 / (2 * 6)
nCr = 120 / 12
nCr = 10

2) 4 choose 2 (because 1 is always choc) = 6 by the formula above

3) 5^3 = 125

#3 Georgie01

Posted 11 February 2013 - 06:50 PM

QUOTE
How many combinations of three flavours could you create?


5x4x3=60 (you have 5 choices for the first flavour, then 4 for the second, 3 for the third since you aren't allowed to repeat any flavours)

QUOTE
* How many combinations of three flavours could you create if one flavour is always chocolate?


1x4x3=12 (1 choice is chocolate then 4 (all except chocolate) then 3 (not chocolate and not the second flavour)

QUOTE
How many combinations all together (including 3 scoops the same, 2 the same and one different)?


5x5x5=125 (because you can choose any of the five flavours for each scoop)

(hoping that I haven't done something wrong, seems to make sense original.gif )

#4 CrazySingleMum

Posted 11 February 2013 - 06:51 PM

OMG I can't understand that formula ... it's not really a Year 4 question???
ETA: Georgie01, that answer makes more sense to me, still seems difficult for the age, but that could be because of my lack of maths skills.

Edited by CrazySingleMum, 11 February 2013 - 06:52 PM.


#5 Peppery

Posted 11 February 2013 - 06:54 PM

1. 15

2. 6

3. 125

Honestly these are guesses, my father was a mathematician (retired) would be absolutely horrified at my lack of mathematical reasoning

#6 agnodice

Posted 11 February 2013 - 06:56 PM

Georgie's answer is correct.

I remember doing combinations in primary school.

#7 libbylu

Posted 11 February 2013 - 07:00 PM

Does the order of the flavours matter? If not, then the first poster is correct, if not, then the second poster is correct!
Does seem very complex for year 4.

#8 jayskette

Posted 11 February 2013 - 07:01 PM

1) 5*4*3
2) 4*3*2 - edited to say - oops... should be 4*3
3) 5*5*5

This is actually an extension maths question... unless the grade 4 people are smarter than when I did this as an extension when I was in year 4... lol

Try this one (another "extension" question on ratios that I actually got in year 4)

There is a piece of orchestral music that is played by 60 Strings, 60 Woodwind and 40 Brass, and it lasts 2 minutes 35 seconds.
How long will the music take to be played if it is played by 40 Strings, 30 Woodwind and 20 Brass?

ROFL

Edited by jayskette, 11 February 2013 - 07:03 PM.


#9 Georgie01

Posted 11 February 2013 - 07:05 PM

My grade 4 has done a little bit of this sort of thing - I work through it with him the way that I did here. It can help to use a diagram or find five different things an do a bit of a model to understand the reasoning.

I haven't had to use factorials with him as the worksheets ask him to explain how he thought things through and I'm fairly sure he hasn't learned factorials/combinations/permutations formally.

QUOTE
Does the order of the flavours matter? If not, then the first poster is correct, if not, then the second poster is correct!


Ahhh, thank you! I need to brush up.

Yes, my answers assume that choc/strawberry/banana is different to choc/banana/strawberry, Secret~Sammy's solution calls those the same...

Reading the question again Secret Sammy is right because the question asks for combinations so it's implied that the order doesn't matter and choc/strawberry/banana=strawberry/banana/choc etc.  Not sure how I'd help a year 4 work through that logically other than with a chart (assuming they haven't actually been taught the formula)

Edited by Georgie01, 11 February 2013 - 07:23 PM.


#10 amabanana

Posted 11 February 2013 - 07:06 PM

QUOTE (jayskette @ 11/02/2013, 08:01 PM) <{POST_SNAPBACK}>
There is a piece of orchestral music that is played by 60 Strings, 60 Woodwind and 40 Brass, and it lasts 2 minutes 35 seconds.
How long will the music take to be played if it is played by 40 Strings, 30 Woodwind and 20 Brass?


roll2.gif


Edited by amabanana, 11 February 2013 - 07:07 PM.


#11 secret~sammy

Posted 11 February 2013 - 07:10 PM

Whilst I still think I'm right  and the order of the flavours doesn't matter  cool.gif  -  Now that I think about it I suspect for a year 4 question the answer they are looking might be Georgie's one.

#12 secret~sammy

Posted 11 February 2013 - 07:13 PM

Whilst I still think I'm right  and the order of the flavours doesn't matter  cool.gif  -  Now that I think about it I suspect for a year 4 question the answer they are looking might be Georgie's one.

#13 ~*Amethyst*~

Posted 11 February 2013 - 07:14 PM

This was in DS homework book to be done tomorrow night as a family - no guidance - no instructions.

DH & I have spent the last 2 hours working on it & still aren't sure that we have calculated it correctly.

The answers are:

10

6

41

So it seems secret-Sammy was closest & Georgie's answer is incorrect?

How on earth are we supposed to explain this to our 9 year old & what is the purpose of such homework?

I find it very frustrating.

XxxAmethyst

#14 ~*Amethyst*~

Posted 11 February 2013 - 07:14 PM

This was in DS homework book to be done tomorrow night as a family - no guidance - no instructions.

DH & I have spent the last 2 hours working on it & still aren't sure that we have calculated it correctly.

The answers are:

10

6

41

So it seems secret-Sammy was closest & Georgie's answer is incorrect?

How on earth are we supposed to explain this to our 9 year old & what is the purpose of such homework?

I find it very frustrating.

XxxAmethyst

#15 HeroOfCanton

Posted 11 February 2013 - 07:24 PM

This is why I hated mathematics in primary school (and subsequently in secondary).

If you ever came across this in real life, would you care how many combinations you could make, or just be glad you could have 3 flavours of ice cream at once? Tounge1.gif

#16 PatG

Posted 11 February 2013 - 07:24 PM

Are you saying that the answers given are 10, 6 and 41?

If you are happy with 60 (5*4*3) as total permutations (order does matter) then try the following:

Each permutation of a, b, c can be written in 6 different ways (a, c, b etc).  Therefore to get the total combinations you need to divide 60 by 6 to get rid of the repeats, leaving 10.

Do the same with chocolate start - 1 x 4  x 3 = 12 , divide by 2 combinations of the second two scoops = 6

My solution to part c - total variations including multiple of the same flavour:

10 different ways to have 3 different flavours
5 different ways to have all the same flavour
20 ways to have 2 scoops the same and one diff  (4 different ways to have 2 scoops of chocolate and one other, multiply by the 5 flavours you could have two scoops of)

Total:  35.

I don't know what the other 6 are.....  The part b answer (6) is included in part a.

this webiste seems to agree with me 35 as an answer  I'm guessing I'm mis interpreting something

Edited by PatG, 11 February 2013 - 07:53 PM.


#17 ZombieMum

Posted 11 February 2013 - 07:30 PM

Ok I cheated and googled it.
http://www.docstoc.com/docs/134459705/Family-Maths-Challenge

There are 10 flavours of 3 combinations.
There are 6 combinations if one flavour is always chocolate.
There are 41 combinations altogether.


#18 ~*Amethyst*~

Posted 11 February 2013 - 07:30 PM

Yes PatG.  I got the second answer, DH the first & neither of us the last!

XxxAmethyst

#19 Lucretia Borgia

Posted 11 February 2013 - 07:31 PM

The answer is 47


#20 Peppery

Posted 11 February 2013 - 07:32 PM

QUOTE (ZombieMum @ 11/02/2013, 08:30 PM) <{POST_SNAPBACK}>
Ok I cheated and googled it.
http://www.docstoc.com/docs/134459705/Family-Maths-Challenge

There are 10 flavours of 3 combinations.
There are 6 combinations if one flavour is always chocolate.
There are 41 combinations altogether.


Woohoo I got one right!!!!!!

#21 PatG

Posted 11 February 2013 - 07:35 PM

Sorry, have been adding to my prior post.... missed some of the updates.

#22 ZombieMum

Posted 11 February 2013 - 07:36 PM

The key word is combination.
QUOTE
Mathematicians eat ice cream just like anyone else.
But sometimes they take longer to make up their mind about what flavour of ice cream they would like to have, especially when they want a double scoop ice cream and there are 31 different flavours to choose from.
If I want a double scoop ice cream cone how many possible double scoop cones are there to choose from?

Now that’s a problem!!!


It has to do with things called  ‘COMBINATIONS’ and ‘PERMUTATIONS’.

If you think it doesn’t matter which flavour is on
top and which one is on the bottom,
then you are thinking about COMBINATIONS.


But if you think that a double scoop ice cream cone with strawberry on the top and lemon on the bottom is not the same as lemon on the top and strawberry on the bottom, then you are thinking about PERMUTATIONS.

There is a big difference.


#23 Georgie01

Posted 11 February 2013 - 07:43 PM

Oh, who knew there were solutions online! A couple of those maths challenges have taken us hours too.

What I will do when my year 4 comes home with that one is to sit down with 5 coloured textas and a big piece of paper and work through it.



#24 ~*Amethyst*~

Posted 11 February 2013 - 07:45 PM

I can't access that website on the iPad Zombiemum? It wants me to download something & then to enter my credit card details?

XxxAmethyst

#25 ZombieMum

Posted 11 February 2013 - 07:48 PM

It didn't explain it, just had the answers, so you don't need to view it online - plus you already knew the answers anyway. original.gif




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