need help please:)

[Kiwimum]

3[12]24 6[24]36 5[?]32

I would explain this as the first number times 4 gives the second number then add 12 to the second number to get the third number:

3 x 4 = 12...................12 + 12 = 24

6 x 4 = 24...................24 + 12 = 36

5 x 4 = 20...................20 + 12 = 32

Except that we are trying to find the number in the middle?

The answer could simply be R-12, where R is the right hand number. Surely a methodology of (RL)/(R/4) is too much to expect of an 11 year old. But it seems a bit odd to use just one of the numbers, though I've seen a few examples where you can work an answer either using just one of the numbers, or by using both numbers in a more complex pattern. Do we have any evidence that the three stage questions actually appear in 11+ papers, and if so, in what areas?

While my reasoning may be more simple and is perhaps not the right method, it still comes out with the correct answer and would score a point!!!

[patricia]

68[14]17 76[14]19 49[?]7 answer is 17

A 2 operation question, which could easily be found on real VR tests. Each section starts off with a few simple ones followed by a couple at the end which are a tad harder like this example. Once practiced my children would polish this one off within 20 to 30 seconds.

Number in the middle is smaller than at least one of the outside numbers so the 1st operation is probably going to be subtraction or division.

Subtraction does not work. No need to panic straight to dividing. I always teach my children to take a good guess and then make sure their guess is right by completing a quick multiplication sum [old fashioned way not grids!] Children of this age should easily be able to divide by 4 [half and half] at school they will have completed much work on doubling and halving and near doubles / halving.

68 divided by 17 = 4
How do I get from 4 to 14 = add 10
4 add 10 = 14

76 divided by 19 = 4
How do I get from 4 to 14 = add 10
4 add 10 = 14

49 divided by 7 = 7
We now know the rule is add 10
7 add 10 = 17


3[12]24 6[24]36 5[?]32 answer is 20

A 3 stage question which can also appear in real tests. I would agree this one is an Extreme VR question! However again I teach my children the old fashioned way of multiplication [ and division] Lets hope Guest55 is not reading this

Subraction and Division does not work. Do not panic, straight to multiplying or adding.

24 x 3 =72
How do you get to 12 = divide by 6
How do you find the number 6 using the numbers either side = 3 doubled or 24 divided by 4

36 x 6 = 216
6 doubled = 12
216 divided by 12 = 18

Does not work, try second possibility.

36 x 6 = 216
36 divided by 4 = 9
216 divided by 9 = 24

5 x 32 = 160
32 divided by 4 = 8
160 divided by 8 = 20

Type K questions are the hardest of the 4 maths to master however with plenty of practice and keeping to basic rules they become relatively easy. Once my children are confident with the rules I constantly time them. Two stage operations within 30 seconds. Three stage is a tad variable [even for me!]

If a 3 stage question was to appear then it would be at the end of the section. They do not appear very year. I only started teaching them 2 years ago.

I insist on note taking, it is no use trying out various methods in your head, by the time you get to the 3rd set you have forgotten which operations/numbers you are dealing with, totally wasting your time and open to errors.

Rules and Notes. Rules and Notes. Rules and Notes...

Patricia

[Sally-Anne]

I think the length of Patricia's reply probably says it all about these two questions!

[Guest55]

Lets hope Guest55 is not reading this

Now Patricia - go and sit on the naughty stair

[patricia]

I think the length of Patricia's reply probably says it all about these two questions!

Yes it was rather long winded !

But the fact remains that this level of difficulty [in particular the 1st question] will appear in the tests as part of those questions at the end of each section, the ones that “separate the wheat from the chaff”

Out of interest I took both questions out with me this evening:

Question 1

Child A took 22 seconds
Child B took 26 seconds
Child C took 24 seconds

Question 2 predictably took longer

Child A took 37 seconds
Child B took 40 seconds
Child C - I was kind to and hinted it was a 3 stage one, took 27 seconds.

Lets hope Guest55 is not reading this

Now Patricia - go and sit on the naughty stair

I can be found regularly on those stairs...

Patricia

[mitasol]

Question 2 predictably took longer

Child A took 37 seconds
Child B took 40 seconds
Child C - I was kind to and hinted it was a 3 stage one, took 27 seconds.

That is terribly depressing because it took me a very long time to work out the answer using the correct method. Far longer than would be practical in an exam.

What did immediately jump out at me was the sequence. 3[12]24 6[24]36 5[?]32

3 [12] 24
4 [16] 28
5 [20] 32
6 [24] 36

However, I had to discard this as it's not the correct method. It was very frustrating because there was so obviously a pattern/relationship but the number of variables just kept eating up the time. I also tried this on year 9 DS who is in the top set maths at GS and has very good number manipulation skills. It took him just short of three mins to get to 3*24/6 but he derived the 6 from doubling 3 and then got distracted when doubling didn't work for the second set.

I genuinely think that the children who are able to do this using the correct method and under exam conditions will be quite exceptional, even within those selected for GS. I think I will amend my usual advice to DC from "work methodically through the options and aim for 100%" to "...aim for 100% but know when to draw the line and move on."

For both DS and DD, I only used the standard GL type papers; Tutors, SD, GL (i.e. none of the harder papers) and neither had any difficulty with this type of question - at that level. These types did come up when DS did his exam but nothing that he couldn't tackle, so presumably nothing more difficult than he had encountered before.

I have a DD sitting 11+ later this year and I'm not going to stress over the vague possibility that anything this time consuming will appear. (I used up my full stress quota the first time around and don't have any left! )

Good luck to all the DC. The parents are all strictly forbidden to fret unnecessarily!

[patricia]

Dear Mitasol

I agree that the 3 stage maths are somewhat extreme and thankfully rare [at the moment]

I start showing my children once they have mastered the 2 stage. I have made up 30 questions I then repeat those 30 questions a month later and again a month later. [mixing them up each time] The children therefore start getting an "eye" for what to look for.

We are only a week away from their real tests, therefore my children will have completed 90 questions , or more of this this type, therefore they are starting to become second nature. If I had given them this question 6 months ago they too would have found it hard.

I have made it quite clear to my students that they are always to assume 1 or 2 operations, its only when they have exhausted their rules on 2 stage that they can start trying out a 3 stage sequence.

Patricia

[999 mum]

3[12]24 6[24]36 5[?]32

Hi Patricia,

I am trying to understand why this question can't be answered as the first number times 4.

If I have read what you said on previous posts, the solution is

Left times right divided by a quarter of right.

so mathematically

L*R/(R*0.25)

simplifying the equation, (canceling R)

L*1/0.25

which is the same as L* 4

(isn't this the same as Kiwi Mum said a few posts ago)

999 mum

PS I would love to know where the question came from and whether it was standard or multiple choice.

[patricia]

Yes you and Kiwimum are quite right, but...

There are other 3 stage questions where that would not work.

The questions state that the numbers in each group are related [all 3 numbers in each group] so I always teach the children using all 3 numbers.

The last thing I would want to do is panic parents, therefore to make my comments regarding these 2 questions completely clear and realistic.

Based on over 15 years experience of the Bucks VR tests.

This 2nd question is without a doubt extreme, but 3 stage maths remain a possibility.

The 1st question is typical of the difficulty found towards the end of a section, and for me or anyone else to say otherwise would be a disservice to parents helping their children.

Patricia

[vchin]

The luxury/convenience of doing it as 1 or 2 operation was possible only if all the operations used are any of multiplication, division, square and sq. root when attempted as 3 or more operations. If one of the 3 operations is to be add/subtract, it will not work MOST of the times (this sum being an exception or a well created one dare I say, see my explanation below). But worth a try only if that one operation again is only in that times/division set (see my ex. later).

Somebody mentioned this already: 1/4 of 2nd number in this ex. is also add 3 to the 1st. So it can have an 'add' and yet has a quick solution. Have a concern to particularly to do this as 3 operation, as the 2nd times give rise to a big number 216 (3rd one may be easy once we find out the rule using 1 and 2) and then what 216/? is 24 could be difficult. So to have some comfort pls. don't yet multiply, keep it as 6 * 36 and now divide(not literally) by 24 to help get the actual number which is 6 4s and 4 9s giving out 9. OR, try to see the factors for 24 in 6 * 36 as 6 * 4 * 9, giving rise to 9. It could as well be the way some are trying, but i thought i mention just in case and help not to put us off seeing big numbers like that.

I copy an ex. from Walsh paper 6 No. 70 that can be done as a 2 operation instead of 3 operation.
16[12]3 49[14]2 100[?]3

If you can recognise your sq. numbers, it is sq. root of 1st multiplied by the 2nd.
Otherwise, if you start your first operation involving both the numbers it takes 3 operations: times followed by division with the sq. root of 1st.

So, I feel if numbers are such that it strikes without wasting a lot of time (and it involves both the numbers like in this ex. and unlike the previous ex., it is safe) then it saves time of not starting your 1st operation on both the numbers ...

Just to prove my point I created this sum: 3[12]24 6[15]30 5[]50
Answer here is not 'add 9 to the 1st number'. AVOID add/subtract in finding quick answers. It is correct though to have seen it as 2nd number divided by 2. Trying it out as our infamous 3 operation, it is times followed by dividing with double of 1st (OR half of 2nd times with 1st and divide by 1s, pointless so half of 2nd is correct and quick) . Yes, it has all 3 operations from times/division set too, but still can fall foul of 3 add 9, 6 add 9 if we see it that way first.

So I guess the moral is not to find (or avoid) quick answers involving just one number with an add/subtract of some constant, until such time there can be such an example to disprove this, but also gives correct answer which is bonus.

One suggestion though is not to look at this type of Maths question as involving a sequence/series (as someone tried to see it), it could lead to wrong answers.