Gap & Difference
Eggsellers A and B have the same number of eggs. A puts 30 on every tray and uses them all up; B puts 25 on every tray, needs 6 more trays than A, and still has 10 eggs left over. How many eggs did each have?
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The pattern behind it: Gap and difference
Share the same things two ways. One way leaves too many, the other too few.
In this one. Match B's trays one-for-one against A's: over those trays B is 5 eggs short each time, and every one of those missing eggs has to be somewhere else — in B's 6 extra trays or loose on the table — so 6 × 25 + 10 = 160 counts the same shortfall as 5 × (A's trays).
How to spot it
Objects are grouped two different ways with a leftover in one arrangement and a shortage in the other, using words like 'left over' and 'short of'.
Common mistake
Children combine the leftover and the shortfall in the wrong direction. The gap must then be divided by the difference in group size, not by either group size.
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