Question P3–P4 Gap and difference
Today’s problem — free all day, every step. Every day has one.
A teacher packs pencils into boxes of 6 and has 4 pencils left over. If she uses boxes of 8, she is short of 6 pencils. How many pencils does she have?
See all 7 steps
MathBrush is being tested with a few parent groups, and every solution on the site is open to them — one household, all children. If you were given a code, it goes in once and this device remembers it.
I have a code → See a free one like it
65 worked examples are free without a code, two from every pattern. No account, either way.
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 4 spare to 6 short is a gap of 4 + 6 = 10 pencils — and that gap is built 2 pencils at a time, one box at a time (8 − 6 = 2), so there are 10 ÷ 2 = 5 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.