Hi Jane,
I posted an image of the bar model to represent the two stpes of the calculation.
Algebraically:
S = amount Sam has
C = amount Charles has
S = N + £463
C = N
Difference is: S  C = (N + £463)  N = £463
Charles gives Sam £246
So no
C = N + £463 + £246
S = N  £246 (Sam now has £246 less than before)
Difference is: S  C = (N + £463 + £246)  (N  £246)
= N + £463 + £246  N + £246
Difference = £463 + £246 + £246
Using countable objects you can see that if C had 6 objects and S had 5 the difference is 1.
If S gives 1 object to C then S has 1 more than before and C has 1 less than before so the difference is actually 3. (The original difference + double the amount given by S)
C xxxxxx
S xxxxx
C xxxxxxx
S xxxx
It an interesting problem to explore.
So what would happen next if C gave S another one object when the difference is 3?
