Problem Solving on maths 11+ papers

[fatbananas]

I've read on here that being very familiar with all the different ways of presenting a maths problem as you can, will stand one in good stead, particularly for CEM which is still a bit of an unknown quantity (think there's a pun in there, somewhere!).

I've been looking at the City of London School for Girls paper from 2010. The problem solving type questions (examples below) are really frightening me . I had thought I'd be able to help DS, but looking at this, I have NO IDEA how to go about these. Are there standard ways/ formulae for approaching these questions?

ABCD is a four digit number
* Its first digit is 1/4 of its last digit
* The second digit is 1 less than its first digit
* When you multiply ABCD by 4, its digits appear in reverse order
* None of the digits are the same.
What is the number?

Some fairy cakes are delivered for Janey's party.
Janey can use big plates or small plates to put the cakes on.
If she uses big plates she can put 7 cakes on each plate with 5 left over.
If she uses small plates she can put 5 cakes on each plate with 3 left over.
What is the smallest number of cakes that were delivered for Janey's party?
The smallest number of cakes are delivered for Janey's party.
(a) If she only used big plates for the cakes, how many big plates would she need?
(b) If she only used small plates for the cakes, how many small plates would she need?

[ToadMum]

In the first-

A must be 1 or 2; B=A-1, so A =2 and B=1.
A times 4 to give D=8.
8x4=32, so C must be something which gives 1 as the unit (to be the mirror of B); trial and error gives 7.

Therefore ABCD is 2178, which times 4 equals 8712.

Late for school sports so have not tried the other one yet.

[mystery]

Ooh they look fun. Just done the first one but yours is better Toadmum

[fatbananas]

Thank you Toadmum. You are clearly a whizz at these things! I'm sorry to ask further questions, but

I don't understand why A must be 1 or 2
Why do you times A by 4?
and why must C be something that gives 1 as a unit. I don't understand the bit about mirroring B either.

[Okanagan]

Some fairy cakes are delivered for Janey's party.
Janey can use big plates or small plates to put the cakes on.
If she uses big plates she can put 7 cakes on each plate with 5 left over.
If she uses small plates she can put 5 cakes on each plate with 3 left over.
What is the smallest number of cakes that were delivered for Janey's party?
The smallest number of cakes are delivered for Janey's party.
(a) If she only used big plates for the cakes, how many big plates would she need?
(b) If she only used small plates for the cakes, how many small plates would she need?

The number can be written as 7b+5 (b= number of big plates) - so 5 12 19 26 33 40 ....
or as 5s+3 (s= number of small plates) - so 3 8 13 18 23 30 33 38 ....

The first one which appears in both sequences is 33

[fatbananas]

Brilliant, Okanagan, thank you. I haven't actually refreshed my memory about algebra/ formulae yet, so, hopefully I might recognise that type of question when I come to going through it with DS ...

[mystery]

I've read on here that being very familiar with all the different ways of presenting a maths problem as you can, will stand one in good stead, particularly for CEM which is still a bit of an unknown quantity (think there's a pun in there, somewhere!).

I've been looking at the City of London School for Girls paper from 2010. The problem solving type questions (examples below) are really frightening me . I had thought I'd be able to help DS, but looking at this, I have NO IDEA how to go about these. Are there standard ways/ formulae for approaching these questions?

ABCD is a four digit number
* Its first digit is 1/4 of its last digit

TThis means that D is 4 x A, so could be 1 and 4, or 2 and 8 , can't be 3 and 12 as 12 is a two digit number etc

* The second digit is 1 less than its first digit
so the first digit can't be 1 as this would make A zero
* When you multiply ABCD by 4, its digits appear in reverse order

So the number is 21C8

And 21C8 times 4 is 8C12. Now look at the comment about trial and error etc that Toadmum made to work out what C is. Imagine doing 21C8 times 4 as a short multiplication - when you get to 4 x C it has to result in a number which ends in a 1 when you add the carry 3 to it from 4 x 8 as 1 is the number in the tens column in the answer we need to get to (8C12). The only numbers C can be are 3,4,5,6,7 and 9 as all the numbers have to be different. The only number this will work with is 7 as 4 x 7 = 28 plus 3 = 31
* None of the digits are the same.
What is the number?

Some fairy cakes are delivered for Janey's party.
Janey can use big plates or small plates to put the cakes on.
If she uses big plates she can put 7 cakes on each plate with 5 left over.
If she uses small plates she can put 5 cakes on each plate with 3 left over.
What is the smallest number of cakes that were delivered for Janey's party?
The smallest number of cakes are delivered for Janey's party.
(a) If she only used big plates for the cakes, how many big plates would she need?
(b) If she only used small plates for the cakes, how many small plates would she need?

[fatbananas]

Mystery, THANK you! I understand about the 1/4 bit now.

What category/ heading of maths would this come under? Really need to work on it.

It's not boding well for 2014 is it. Thank the Lord I'm not sitting it!

[mystery]

Well I don't remember any of the GL assessment maths questions in Kent being as hard as this.

Not really sure what branch of maths it is --- it's kind of challenging puzzles which don't involve too much actual maths knowledge. I would suspect that there are a lot of children in the top 25% in Kent who would not be able to do these questions correctly in the time given - so the paper cannot be made up exclusively of these types of question otherwise they won't be able to interpret the test results and work out who should pass and who should fail!

I don't think CEM questions to sort out the top 25% could all be this hard either.

Sorry have edited my red stuff a bit more above as it didn't make too much sense. It's very hard showing working on here clearly.

I don't know if my year 4 child can do this type of thing or not either - I suppose it's a case of finding some problems where there is a bit of "trial and error" involved rather than just working through a "set piece" from start to finish and ending up with one answer.

Good questions but not the kind of thing that I would have liked to do at that age under pressure in an exam.

[Kingfisher]

Fatbananas, if your DD is trying for CLSG, she will need to be able to do some of these, I am afraid. My DD is at a school in the same consortium so she sat the same paper as CLGS, but these are for the Consortiums 1 and 2. If you are not sitting for these independent schools, I should focus on questions which are more suited to your own tests.

If she is only in Year 4 I should not even be trying these problems yet; focus on building up her skills as she is likely to be intimidated. If she is already in Year 5, you will need another strategy. She has to take them step by step. Some children are just naturally good at these type of questions but most will need to practise. To be honest, they seem to be 'IQ testing' type of questions; my DD had hers tested by an educational psychologist and she covered many like this. She is at a comparable school to CLSG and when she went up for interview they asked her even more of these type of questions.