Question P4–P5–P6 Gap and difference
Today’s problem — free all day, every step. Every day has one.
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?
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.
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.