11 Plus Exams Forum

Type K as identified by IPS

[ 36 [6] 6] [56 [ 7] 8] [49 [?] 7]

There are THREE basic rules

1] The number in the MIDDLE is made by using the numbers on either side.

2]Sometimes you use ONE operation, sometimes you use TWO.

3]The RULE found for the first set MUST apply to the second set.

To get started the child must look at the number in the MIDDLE of the first set

If the number is BIGGER than the numbers on either side, then the child says to themselves “The CHANCES are I will be ADDING or MULTIPLYING.”

If the number is SMALLER than one or both numbers on either side, then the child will say, “The CHANCES are I will be TAKING AWAY or DIVIDING.”

They always say, “The Chances Are” because occasionally you DO have to use the opposite operations.

The Above Example

The number in the MIDDLEis smaller than one of the numbers on either side ”The chances are that I will be TAKING AWAY or DIVIDING

36÷6=6

MUST check that it works for the second set 56÷8=7

The rule goes for both sets, therefore can use for last set 49÷7=7

Another Example

[25 [16] 7] [29[27]25] [49[?]]23]

The number in the MIDDLEis SMALLER than at least one of the numbers ”The chances are that I will be TAKING AWAY or DIVIDING

25-7=18 how do I get to 16, I take away 2 does this rule work for the second set NO

25÷8= cannot do, must be a whole number.

I must NOT give up, I just try the other TWO operations

25+7=32 how do I get to 16 I half the number 32 does it work for the second set.

29+25=54 how do I get to 27 I half the number 54

The rule works for both sets, therefore I can use for the last set

49+23=72 half of 72 = 36

Common Mistakes

The child forgets to check the RULE works for BOTH sets.

The child tries to USE the middle number as part of his/her calculations to find THAT middle number.

The child tries the obvious 2 operations, cannot find the answer, then panics, forgetting they CAN use the other two operations.

Knowledge Required

This type of question is ALWAYS the most dreaded BUT at the end of the day it ONLY uses the four basic maths operations + ÷ x -

All my tutored children have to complete times table squares on a weekly basis [2-15]

I tell ALL mums that they should try to ensure that the child can add up and take away basic numbers under 100 VERY QUICKLY before they come to me.

A good knowledge of doubling and halving is also very important.

It’s basically, firing quick questions at them, in the car, out for walks at the kitchen table.

Hope this helps

Patricia

The way I got my daughter to answer these questions,


is to write the answers to the 4 first steps in a consistant pattern like this

11 30 15 56 + x
6 [34] 5 7 [60] 8 a [ b] c
1 - 1 - - /

compare 1 and 2, the answer becomes obvious, this also works for bigger numbers as it is obvious not to multiply numbers greater than the 12 times table, in the example above subtraction and division is eliminated immediately, the main advantage is it provides an ordered and structured way to tackle the question, and then answer the question without getting mixed up beacuase the first step is always laid out the same way. PS look at the top right answers and add 4!!
My daughter is hopeless at maths she went from getting 1 of these right to never getting them wrong.

11 ......30 _______15 .......56 _____+....... x
.6 [34] 5 _________7 [60] .8 _____a [ b] c
.1 .......NA ________1 ......NA ______-....... /

If you say they wont have time to do all the first steps and write them down. The extra time writing the options is totally outweighed by the clarity it offers and the associated time saving of visual thought rather than muddled mental maths.
I suggest you give up and came back when they can do tables and number bonds, instantly.

When I say tables, I mean multiplication tables as well as division tables, if they cant do it both ways, start practicing

7x8=56
56/7=8
56/8=7

Thanks for the techniques. Great advise!!!!!!

But, Mary Poppins how would you apply your technique to a K TYPE question from another thread?

ie..........

(9 [20] 18 )............(2 [6] 4)............(3 [ * ] 18 )



P.S the answer to * = 24

Just the same.


27.......NA...............6......8
(9 [20] 18 )............(2 [6] 4)
9...........2................2......2..

If you complete the calculations and still cant see the answer after doing stage one, dont bother taking the elevenplus!!!!

(3 [ * ] 18 )
.............6


18+2,4+2, the only way both work is to divide and add the result

18+6=24

Hope this helps, this IMHO is one of the easier questions, and in no way should be scary, as it once was, as proved by my daughter

Thanks Mary Poppins,

Didn't understand previous bottom line of example, i.e

.1 .......NA ________1 ......NA ______-....... /


Your method does indeed clearly throw up the answer when written out as

27.......NA...............6......8
(9 [20] 18 )............(2 [6] 4)
9...........2................2......2..