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
257=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 [215]
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
