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Library shelves — more books, fewer per shelf
In a library, books were arranged on shelves with exactly 8 books on each shelf. The librarian brought 4 more books into the library and rearranged all the books. There are now exactly 6 books on each shelf and 10 more shelves than before. How many books are there in the library now?
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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. The 10 extra shelves need 60 books, but only 4 books are new, so the other 56 books must be the 2 books freed from each old shelf.
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.
Try one like it
Challenging Chairs — rearranged into rows of 7 In a school hall, chairs were arranged in rows such that there were exactly 9 chairs in each row. For a concert, Mr Ong brought 6 …The 33 problem patterns
All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.
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