Question P3–P4 Gap and difference
Today’s problem — free all day, every step. Every day has one.
A librarian packs storybooks into boxes of 5, with 3 books left over. If she packs them into boxes of 7 instead, she is short of 5 books for the last box. How many storybooks does she have?
Answer
23 storybooks (in 4 boxes).
Share the same things two ways. One way leaves too many, the other too few.
In this one. The number of boxes is the same both ways, so the swing from 3 spare to 5 short is a gap of 3 + 5 = 8 books — and that gap is built 2 books at a time, one box at a time (7 − 5 = 2), so there are 8 ÷ 2 = 4 boxes.
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'.
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.
Worked examples of all 33 patterns and skills, in a booklet you can print.