Today’s problem — free all day, every step. Every day has one.
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 more chairs into the school hall and rearranged all the chairs. There are now exactly 7 chairs in each row and 12 more rows than before. How many chairs are there in the school hall for the concert?
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 12 extra rows hold 12 × 7 = 84 chairs, but only 6 chairs were brought in — so the other 78 must have been taken out of the old rows, 2 from each (9 − 7 = 2), which fixes the old number of rows at 78 ÷ 2 = 39.
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 Flower pots rearranged in rows — the nursery In a garden nursery, flower pots were arranged in rows with exactly 15 pots in each row. The gardener bought 10 more pots and rear…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.
A PDF, and a note when new solutions go up.