Urgent help please with maths homework

[Dancingdreamer]

Here is rhe question my 8 year old has come home with:

3 monkeys ate a total of 25 nuts. Each ate a different odd number of nuts.

How many nuts did each of the monkeys eat? Find as many different ways as you can.

We are busy doing number lists here and are sure there must be an easier way to work this out. Now run out of ideas. Anybody able to help please?

[JumpingJetFlash]

If list the odd numbers up to 25 and then look at 3 numbers that add together to make 25. Repeat using 3 different numbers - can you change one and adjust the others accordingly.
HTH

[Dancingdreamer]

That's what we have been doing but the list seems to go on forever and then we have to remember to take out the numbers we have already included eg 1, 3, 21 and then remember to remove 3, 1, 21.

Or do we include these as this is a different pattern as a different monkey has a different number of nuts even if it is the same pattern? Aargh!

[ClayDavis]

A systematic approach is best and probably what the teacher will be looking for. So:

1+1+23
1+3+21
1+5+19
etc.

[purplemurple1]

If monkey A has 1nut monkey b 3nuts monkey c 21

Then each time you increase monkey b decrease monkey c

1. 3. 21
2. 5. 19
3. 7. 17

Etc

(3. 1. 21. Is already done)

1. 5. 17
2. 7. 15

Etc

1. 7. 13

Etc

Etc

Some beads or counters could help explain it.

[ClayDavis]

I think the question would suggest that each monkey could have a different number of nuts, so 1+3+21 would be a different answer to 3+21+1. There are situations where those two would be the same answer, but I don't think this is one of them.

I would do a table and label the columns as Monkey A', 'Monkey B' and 'Monkey C'

[spanieleyes]

I would leave repeats in as different monkeys are eating different numbers of nuts, I think the teacher might not expect every single combination but ( certainly in my case) would like to see evidence of logical and systematic thinking, so

1,1,23
1,2,22
1,3,21
1,4,20
1,5,19
1,6,18 and so on before moving onto

2,1,22
2,2,21 etc

but rather long winded homework!

[meala]

I would think that 1, 3, 21; 3,1,21; 21,3,1; 21,1,3; 1,21,3; 3,21,1 would all class as the same solution. Otherwise your list will be huge!

[purplemurple1]

Remember all are diff so you can't have

1. 1. 23
2. 3. 19

Etc

[spanieleyes]

Sorry, didn't see the "odd" but the theory would be the same!

[Dancingdreamer]

Forget my DS - he has now gone to bed! My DH and I have now spent over an hour and a couple of large glasses of wine on this. We think there are 60 permutations. Surely the school can't be expecting my DS to list all these? He is supposed to write the answers on the margins of his worksheet.

[TeenAndTween]

clay and purple have the way to go.

My DD2 did this homework a couple of weeks ago!

I let my DD2 experiment for a bit, then I helped her write them out in order so she could see the structure and help her find some more.
DD needed to use coins to assist.

[ClayDavis]

It's stupidly long winded homework. If you're going to set a task like this to develop or show logical and systematic thinking it should have a relatively small number of possible answers. Otherwise what you are actually testing is 'how many can I write down before I get bored of this slightly pointless activity'.

[TeenAndTween]

There aren't 60. 1 3 21 is the same as 3 1 21 for this homework.

1 3 21
1 5 19
1 7 17
1 9 15
1 11 13
3 5 17
3 7 15
3 9 13
5 7 13
5 9 11

job done.

if you must to the different orders you will end up with 60 (because 3 items can be ordered in 3! ways (3!=3x2x1=6) but they will not expect that for this homework. All monkeys look the same so they don't count!

[Dancingdreamer]

ClayDavis absolutely agree. Seems pointless to me. DS knows his number bonds and has no prob with addition ir subtraction at this level. Could understand it if my older DS came back with this as some sort of exercise to develop a formula. As it is DS did get bored whilst DH worked out all the possible permutations.

I wanted to send DS back with just a few examples but DS said there was a merit mark for the person who could get the most variables!

[AnAdventureInCakeAndWine]

All monkeys don't look the same to other monkeys.

[stardusty5]

Sorry to be a PITA but the question does say to list the combinations "you can think of" not "all possible" combinations. I'm not sure the intention was for you or your child to spend so long on a task- just demonstrate that he gets the point?

Thats how i would interpret that anyway.

[TeenAndTween]

Just to say I thought this was a good homework for my DD. Not only did she get to practice her adding (which is clearly not as good as Dancing's DS) but it got her to start thinking about solving problems in a logical way rather than just randomly trying different things. This is a really good skill to develop, and for some children doesn't come naturally.

AnAdventure OK monkeys don't all look the same, but really I do not think this homework is aimed at finding all the extra rearranging of the piles. Though it is quite easy. Call the columns in my earlier answer ABC. Then for each row rearrange in the following additional 5 ways:
ACB
BAC
BCA
CAB
CBA

extra complicated job done.

Would not take more more than 15 minutes to write out. Dancing - you and your DH may have been faster without the wine!

[Dancingdreamer]

AnAdventure - lol. Agree maybe the wine was a bad idea!

[ClayDavis]

I might agree in year 1, but at 8 years old (assuming year 4) 'find as many different ways as you can' does mean 'find all the different combinations using a systematic method'. It is what the teacher will be looking for. The 'find as many as you can' bit is just used as a method of differentiation, so lower attaining children will find a few and higher attaining children will find more. It's the maths version of differentiation by outcome.

I disagree with TeenandTween the monkeys might look the same but they are different monkeys. Every version of this question I have seen worded like this has had 1+3+21 and 21+3+1 as different answers in the mark scheme.

OP count yourself lucky, there's a question in the same style as this that has several hundred different combinations.

[juliemaths]

This sort of question needs a logical approach and look for patterns to help. One such way is to start with the first one having the smallest possible amount (assuming 0 not possible)
1 , 2 , 22
then increase the first by 1 giving
2,3 20 ( I am assuming that 1,2,22 is the same as 2,1,22)
Then increase by one again giving
3,4,18
Continue until you have all this type ( with two of them 1 apart) the final one being 11,12,2 then start with the ones 2 apart
1,3,21 next comes 2,4,19 etc
then all the ones 3 apart:
1,4,20 and 2,5,18 etc
Continue increasing the gap.
You will find that each time you do a new set in the list there will always be one more which you can't use ( ie. the first list has 1 you can't use, the second list 2 etc ). When you find you are starting with one you can't have (I think it is 1,9,15 - which you had in the list of numbers 6 apart ) then you know that you have all the possibilities.

[TeenAndTween]

OK. If you must find all the orderings as well, then you still need to start with all the unique combinations (see my first list) and then rearrange them logically too (see my second list).

But no way my DD2 could have done that in a reasonable amount of time.

[stardusty5]

I see what youre getting at Clay, but surely you can demonstrate that you are able to apply a systematic method to problem solving without having to list every possible answer?

For example, you are usually asked to extend a pattern of numbers (e.g. 3, 6, 9, _, 15........) by offering 3 or 4 examples, not continuing the numberline ad nauseum.

The 'merit awarded for the most' condition as well implies that the teacher is not expecting the majority of the class to find them all.

[Dancingdreamer]

Can I just point out that whilst on its own this does not seem a lot, this was actually his 3rd piece of homework tonight. He had 2 pages of proof reading, spellings and this was one of 2 maths problems. I haven't bothered with the reading he is supposed to do every night.

[ClayDavis]

And that's exactly why this is a reasonably pointless task IMO, particularly with the added 'bonus' of a prize for the most answers. You don't need many combinations to show that you can work systematically, in a logical manner. As it isn't open ended and there is finite total number of combinations what you end up doing is rewarding the children who enjoy writing out long lists of numbers. Everybody else will have probably given up once they got bored.

[stardusty5]

Dreamer, if the teacher is really expecting this amount of work every night then you need to be speaking to him/her. However, i still don't think it was asking you for as many examples as that. Imagine the marking!!