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## Can someone help with this KS2 homework??

(63 Posts)That is a ridiculous question and I"m only here to learn something.

I'll wait till' someone better than I am comes along.

Can you just clarify the questions, the photo is cut off..

'when is the first time that all three lights will be ....

'when is the next time that all three lights will...

I would get your daughter to draw on squared paper - 3 on, 3 off on one line, 4 on, 4 off on another line etc and then count? She should be able to see the pattern then.

Surely First question is whenever you switch them on. Or 1 second As they would all come on at the same time wouldn't they. Second question ill work out now .

Bleurgh my dd is also in ks2 and sometimes I just googled the homework lol

I would draw it visually....

so o=on n = off

o o o n n n o o o n n n o o o n n n o o o n n n o o o n n n

o o o o n n n n o o o o n n n n o o o o n n n n o o o o n n n n

o o o o o n n n n n o o o o o n n n n n o o o o o n n n n n

so if the question is 'when is the first time all the lights will be off' - then that's when the 'n' all line up vertically - so 6 seconds in.

next time the lights all come on together is when the 'o' line up vertically - so 25 seconds in.

That's my interpretation anyway!

So glad our answers match!

I think this question is really about common multiples. At least if the last question is 'when will they all come on at the same time'.

The first light comes on when the number of seconds passed is a multiple of 6: (0 seconds first), then 6 seconds, then 12 seconds etc.

The second light comes on when the number of seconds passed is a multiple of 8: (0 seconds first), then 8 seconds, then 16 seconds etc.

The third light comes on when the number of seconds passed is a multiple of 10: (0 seconds first), then 10 seconds, then 20 seconds etc.

So you need to find the lowest number that is a multiple of 6, 8 and 10. That is, the 'lowest common multiple'. The way to do this is to factorise each number into its primes: 6 = 2x3; 8 = 2x2x2; 10 = 2x5. Then you can see that the lowest common multiple will be 2x2x2x3x5 = 120. So the answer is at 120 seconds - i.e. at 2 minutes.

That is if the second question is when the first time is (after 0 seconds) when all the lights come on together.

But this seems too complicated for KS2. I like the suggestion to have your dd just draw a sort of timeline with the lights going on and off along it. I will need to be quite long though to get to the answer to the second question!

If she draws a graph as above she'll notice that A and B come on first together at 24 seconds.

If you look at 6 and 8 and split them down to their lowest numbers (i.e. 6 = 2x3, and 8 = 2x2x2, then the lowest number that can be divided by them both needs 2x2x2 (to make the 8) and one 3 (so that 2x3 can make 6) = 2x2x2x3 = 24, as per the diagram.

Since 10 split in the same way is 2*5 she needs to multiply the 24 by 5 giving 120, which she can also show graphically.

Not sure if this helps.

Ah! Maybe I am misunderstanding the question (or wrongly guessing what it is asking!). If it is just asking when they will all be on together, then ... well, they will be all on together for the whole of the first 3 seconds? But then if the question is when will they **next** all be on together, then I guess I agree with the pp... though what exactly is meant by 'next' is a bit unclear (I guess, after all the lights have gone off at least once?).

But if the question is 'when do the lights all next **come** on together' - as in all come on at the same moment, then I think it is 2 minutes.

Well - when I say I agree with the pp, I hadn't read them right! The first time that all lights will be off will begin at 5 seconds (and last for 1 second).

And the first time that all lights will be on together having each been off at least once (which would be a weird question to be asked) will start at 24 seconds.

The first time all lights will be off will begin at 5 seconds - i.e. after 5 whole seconds have passed. They will be off all together for the whole of the 6th second.

Sorry, I posted then pootled off to peg washing & chat to the neighbours!

Questions are; first time they will all be off, and next time they will all come on together.

I think I'm more baffled than when I started . Maths never was my strong point! **@Nesssie**, I think your idea might be the simplest - they've just started working on graphs though so maybe that's what her teacher is after?

(I am able to grown up on my own, honest )

**Nessie's** idea is great. Your dd will need to do it for a good while, though, to get to the answer to the second question!

One more point, and then I will shut up! When your dd does it Nessie's way, she will find that it is on the 121st column that they all come on together. This might make her think that they come on together 121 seconds from the start. This is not quite right. They come on together in the 121st second, which begins 120 seconds from the start.

HTH

Still look you ladies are confusing me. Lol

You also need to account for the distance in between lighthouses regarding the speed of light. So the real answer is error insufficient data.

**@user1471433035** that would probably cause more confusion than it's worth!

All **come on** together or all **be on** together? First would be badgers answer, second would be Nessies.

Suspect for KS2 they're actually wanting to know when they will be on, as badgers explanation seems a bit advanced.

So, the first light comes on every 6 seconds, the second every 8, the third every 10. So what the second part of the question is asking is: what is the lowest number (other than 0) that is divisible by 6, 8 and 10? (It’s 120 btw). Badger’s explanation is right.

I can’t read the first part of the question as it’s cut off, sorry!

As it’s KS2I’d say it’s probably trying to get them to work it out by plotting a graph then see where the lines cross over

For KS2 draw the picture done by **Nessie** and **Balloon**

For the *coming* on together (as opposed to being on together) it is a lowest common multiple question for numbers 6, 8, 10

2x2x2x3x5=120s.

How old is your DD, OP? My 8 year old would never be able to do this. I had some trouble myself!

It’s KS2, it’s going to be 6 seconds & 25 seconds, easy to see on a graph.

Mine looks like Nessie’s 😊

120 is overthinking it for KS2, especially when they’re learning to do graphs.

But it is the correct answer for **coming on** together...

Also the '25 seconds' answer (should be 24 really - they are all on together **throughout the 25th second** which starts 24 seconds from the beginning of time!) is the answer to a very convoluted question which I don't think they can have intended to ask. After all, the lights are all on solidly for the first 3 seconds. So a question like 'what is the first time when all the lights are on?' should be 'at 0 seconds', and 'what is the next time when all the lights are on' should be met with the answer ??? The time which is closest to zero seconds without being zero seconds, and there is no such time because of time being continuous!'. (Don't let your dd say this, it sounds annoying even from an adult!).

I think a much more sensible question is 'when (after time 0) do the lights all come on at the same time?', and the answer to that is at 120 seconds.

Not sure how they would expect a KS2 child to answer this except by doing a diagram or something along **Nessie**'s lines, and this would get pretty unwieldy and big, and your dd might make mistakes with it (I probably would).

Do children learn about 'lowest common multiples' in KS2?

And it is 5 seconds for when the lights are all off together! They are all off together throughout the 6th second, which begins 5 seconds after the start time.

I get 6 for all off and 25 for all being on at the same time

**Demented pixie** you get '6' for all being off, because as your diagram rightly shows, in the 6th second they are all off together. But that means that they are first all off together 5 seconds from the start time.

This is confusing, but it's the same with lots of things that we count. E.g. I am in my 44th year (sob) but I'm only 43, because we count your age by the number of years you've completed - not the year you are in. And it's the same with rulers. When you look at a ruler, you can see that '2cm' say really means '2 cm all completed here'. The 3rd centimetre begins at the 2cm mark. And it's the same with time. 5 seconds from the start with when the 6th second begins. So I think that your diagram shows that the lights are all off together first at 5 seconds.

'is', not 'with'

Thank you all for your help; we sat down and worked it out on a very messy chart of o's and x's - I'm not sure whether to hand that in or not so we've shoved it in so her teacher can see we've sat down and worked it out (with a little MN help )

Some of the homework my 8 year old is getting is ridiculous like this too, I feel very strongly that if they (the child) doesn’t understand it themselves and can complete without assistance then it shouldn’t be sent home. Also check out these spelling we got this week, I repeat again he is 8. I asked him if they learn the words at school or use them in sentences and his response was “no”. What’s the point in learning to spell words you don’t understand the meaning of???

**Scottsy100** - yep, that's ridiculous in my opinion.

The maths question I think is not totally ridiculous. The first part at least you can work out quite simply as people have shown. The second part you can also work out simply if you are prepared to make a very long chart! Or you can at least have a good think about it.

But why learn to spell words that you can't use?

**You also need to account for the distance in between lighthouses regarding the speed of light.**

The speed of light has nothing to do with whether the lights are on or off.

A very deceptive puzzle.

At first it seems easy, until you look more deeply!!

For this discussion, lets assume:-

The lighthouses all turn on as the stopwatch is started. (ie =0)

Thus 3-second lighthouse (L3) turns ON at 0s and OFF at 2.999s

and 4-second lighthouse (L4) turns ON at 0s and OFF at 3.999s

and 5-second lighthouse (L5) turns ON at 0s and OFF at 4.999s

At the 24 second mark, lights L3 and L4 are both turning on.

24s is divisible by both 6 and 8 (ie ON/OFF period of lighthouses)

But lighthouse L5 had turned ON at 20s and will turn OFF at 24.999s

Thus all 3 lighthouses are on between 24s and 24.99s

Just for completeness:

The times the all 3 lighthouses are ON are:-

24 - 24.999s (1s)

32 - 32,999s (1s)

42 - 43.999s (2s)

50 - 50.999s (1s)

72 - 74.999s (3s)

80 - 80.999s (1s)

90 - 91.999s (2s)

104 - 104.999s (1s)

114 - 114.999s (1s)

And everybody’s favorite: 120-122.999s (3s)

etc, etc, etc

I have a nice graphic that explains this problem much more simply,

but because of MumsNet newbe policy was unable to attach it. Sorry!

I am bit buffled. Isn't it simple as first one, common multiples, 3 x 4 x 5 = 60 will be on together so 61 seconds for off together, then next one on together is 120? Am I missing something?

No... first one off together is 6 seconds by making a diagram/chart/graph what ever it's called. Now I am totally buffled how to figure it out.

The cycle lengths are 6, 8 and 10, **irvine**, not 3,4,5.

Yes, of course! Thank you, Balloon.

*Scottsy100 I can't remember the last time dd2 brought spellings home tbh! I know they have spelling books in class so presumed they did them during class time - I'll ask in the morning.

Dd1 (11yo) brings them weekly & barely looks at them - I get the impression everyone gets the same & don't think she finds them challenging really.

I agree with the comment that if the child isn't able to understand and complete the homework then it shouldn't be sent home. Dd2 doesn't usually struggle, and we sit together while she does her homework, but this confused both of us until I asked here!!

We made it onto the Daily Fail website

Maybe their journalists will be more successful with it...

After having a quick look, perhaps they should have read my username properly...neither M is capital yet they gave Mam a capital one

Shall I register just to comment & point it out to them

3————>1st Lighthouse

0-3, 7-9, 13-15, 19-21, 25-27, 31-33, 37-39, 43-45, 49-51

4————>2nd Lighthouse

0-4, 9-12, 17-20, 25-28, 33-36, 41-44, 49-52

5————>3rd Lighthouse

1-5, 11-15, 21-25, 31-35, 41-45, 51-55

Numbers marked are when the lights are on.

Numbers not included are when the lights are of.

1st time they are all off->5.0 seconds, for 2 seconds.

Next time they are all on->25.0 seconds

The numbers are 6 sec for off together and 25 sec for on together again. Just look at each individual second.

Lighthouses

Sec 3 second 4 second 5 second

1 on on on

2 on on on

3 on on on

4 off on on

5 off off on

6 off off off ALL OFF at 6 SECONDS

7 on off off

8 on off off

9 on on off

10 off on off

11 off on on

12 off on on

13 on off on

14 on off on

15 on off on

16 off off off

17 off on off

18 off on off

19 on on off

20 on on off

21 on off on

22 off off on

23 off off on

24 off off on

25 on on on ALL ON at 25 SECONDS

Google “mathematical challenges for able pupils”. I’m fairly sure this is where it’s from and it should have solutions at the end of the document that will help you to help her.

Your numbers were right. When you look, you see that they are off together for only 1 second at 6 seconds. Then they are on together at 25 seconds. This is so detail oriented.

What makes you so complicated? Some diagrams. It is necessary to find a common dividend for which the result of division is even for all. Example: the first one that suits us 60 .. 60/3 = 20 (goes out) 60/4 = 15 (not extinguished) 60/5 = 12 (goes out) the option is not suitable. Then 120 .. 120/3 = 40 (go out) 120/4 = 30 (go out) 120/5 = 24 (go out) => answer: at the same time they will extinguish every 120 seconds, sunbathe simultaneously at 121 (if not included in the calculation ).

sorry for my english he is not very good

What are questions like this actually testing, other than patience?

It's from 'Mathematical challenges for able pupils'. I never set this problem because I couldn't work it out myself. Otherwise I loved the challenges and found them excellent for problem solving.

The decision is 3*4*5*2. Imagine this task as a chart. The point where all these cuts cross is 3*4*5. Lets check their state: chart 3 will be repeated 4*5 times. This multitude is even therefore it is off in this point. But 4 will be on: 3*5 is odd. So we have to multiple all of them on 2 '- the second place where all charts cross. Hope, my reasoning is clear)

It is too easy. I write C# program, my result 6 and 120:

static void Main(string[] args)

{

bool[] lightson = new bool[3]{true, true, true};

int[] lights = new int[3]{3, 4, 5};

int nON = 0;

int nOFF = 0;

for(int i = 1; i < 150; i++){

Console.WriteLine(" " + i);

for(int c = 0; c < 3; c++){

lights[c]--;

Console.WriteLine(lightson[c] + " " + lights[c]);

if(lights[c] == 0){

lightson[c] = !lightson[c];

if(c == 0) lights[c] = 3; else if (c == 1) lights[c] = 4; else if (c == 2) lights[c] = 5;

}

}

if(lightson[0] == false && lightson[1] == false && lightson[2] == false && nON == 0)nON = i + 1;

if(lights[0] == 1 && lights[1] == 1 & lights[2] == 1 && lightson[0] == false && lightson[1] == false & lightson[2] == false && nOFF == 0)nOFF = i + 1;

}

Console.WriteLine("Time ON: " + nON);

Console.WriteLine("Time OFF: " + nOFF);

}

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