Eyes down! Pencils sharp! A KS2 Maths SATS Q:

[ampere]

30 children are going on a trip.

It costs £5 including lunch.

Some children take their own packed lunch.
They pay only £3.

The 30 children pay a total of £110.

How many children are taking their own packed lunch?

How should a Y6 child answer this correctly? What should their -ahem- methodology be?

distant he-e-elp!

This is certainly a level 5 type question
ds3 is here with me but will be back shortly

y6 teacher here.....

Ummm, would this work?

30 children all paying £5 would equal £150.

£150 is £40 more than was paid.

Divide that £40 by 2 (the 2 less pounds iyswim)

40 divided by 2 equals 20

So 20 children paid £3 and 10 children paid £5.

It works out to £110 but I am not sure if this is the best method.

Not any sort of teacher but, here gores....

I would calculate cost of all 30 @ £5, which is £150

Then find out difference between this maximum and the actual paid i.e. £40.

Then divide this amount between the difference of provided lunch and packed lunch i.e £40 / (5-3) which is 20

Therefore 20 children had packed lunch.

Don't think it matters how you answer it since logic isn't age dependant

Although looking back, this doesn't sound very clear or logical at all for an answer!

LadyGooGoo, that was my method exactly. I am now reassured. Thank you!

We could look at it as a ratio and proportion type question.

If 30 children pay £110 then 3 children pay £11.

This is easier to work with.

It must be one child paying £5 and 2 paying £3 pounds, so multiply these by 10 to scale it back up again.

So 10 children pay £5 and 20 children pay £3.

Cost one one lunch is £5 - £3 = £2

Cost of the trip is £3 * 30 = £90

Cost of total school lunches £110 - £90 = £20

Number of pupils taking school lunch is £20/£2 = 10, therefore number of pupils taking packed lunch is 20.

you've got the right answer but I used algebra

lunch= x and packed lunch=y

so
5x + 3y = 110

and you know that
x + y =30

and then you balance the equations out

so that
x=10 and y= 20

you are all scaring me now.

i'm with dg.

don't let me near the algebra. letters are for literacy, not numeracy.

Back!

All correct

However, many children would probably not go straight to the methods that we, as adults, are able to do. Just thinking of my maths group - they would probably do some sort of trial and improvement method.

Sothey would probably start with £5x 30 to see what it would be if all paid £5 - so £!50.

The more able would then probably start taking off £2 at a time so comeup with something like:

30x5 and 0x3 = 150
29x5 and 1x3 = 148
28x5 and 2x3 = 146

and continue until they got to
10x5 and 20 x3 = £110.

Some pupils would realise whilst taking off the £2s, that they could perhaps jump from 30x5 and 0x3 = 150
to
25x5 and 5x3 = 140

Other pupils would start with

1x5=5 and 29x3= 87 which makes £92
2x5=10 and 28x3= 84 which makes £94

and work through that way.

All acceptable (if a little time consuming.

What is importan is that they write down their methods clearly.

I would think that only the brightest would leap to do 30x5=150
150-110=40 etc as we as adult realise.

HTH

I have a middle band group if that is relevant

The majority of my Set 6 (of 7 sets) worked it out using the first method:

30 x 5 = 150
150 - 110 = 40
40/2 = 20

but these are some of the brightest children and hopefully at least half of them will get 4a/5 in May.

From the post SATs report on this question:

The main focus of this question is using and applying mathematics to solve a problem involving ratio and proportion. Children are required to identify and use the appropriate operations to solve the problem. Children are asked to record their working.

Methods
? Of those children who got a correct answer, 15% calculated the cost of all the children on the trip having lunch then worked out the difference.
? Of those children who got a correct answer, one-quarter used a trial and improvement method.

I know some of my high flyers answered the question the way I explained it because we did it last week! Most of the others either used the finding the difference method or trial and error.

I just challenged my Y4 DD - having got her to fetch a piece of paper first.

She just did it in her head within about 20 seconds .

I think it took me a bit longer.

I like Hana's algebra method the best. Would the children have been introduced to algebra by that age?

Thanks all!
The stupid thing is DS1 actually got it right BUT he put the 'Mark 350g on this scale' wrong! He put it at 250g. Also, he got this wrong:

If 3/4 is 48 what's the whole? He put 16.

Wot?

ampere I was always doing stuff like that in maths. I was really, really good at maths at primary school. And I knew it. So I got all the really complicated stuff right, because I found that interesting. But made stupid mistakes on the easy stuff because I wasn't paying attention.

It all went to pot when I reached about age 16 and hit a brick wall with the weird and esoteric stuff you have to do beyond that!

thinking about it more, hana's method is simultaneous equations. I think this is probably KS3 rather than KS2

I initially turned to trial and improvement method because I was tired and my brain freezes when numbers are mentioned (I can do maths, just have the number phobia thingy). I got it correct, and did more mental jumps etc, but figured many childrn would do it this way.

In terms of logic, I like the one which compared the difference between the cost of a packed lunch with the cost of the trip and how much was spent. My head considers this more straight forward... heaven protect my children... (notes I can do maths... really...).

I'd have done the same as ampere's DS too... written what a 1/4 is rather than the whole... That is simply incomplete thinking!

I would go for trial and error with this one. Then adjust according to whatever you got.