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P4–P5–P6 Gap and difference

Today’s problem — free all day, every step. Every day has one.

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 rearranged all the pots. There are now exactly 10 pots in each row and 8 more rows than before. How many flower pots are there in the nursery now?

One step of the worked solution to Flower pots rearranged in rows — the nursery, drawn in pencil.
7 steps, drawn in pencil

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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 extra rows' capacity minus the pots actually added is the number of pots redistributed from the old rows.

5 to a row3 chairs left over4 rowsfive chairs in eachspare3 chairs with no row7 to a row5 places short4 rowsseven in each — wider rowsgaps5 empty places, not 5 chairsThe swing3 over + 5 short = 8per roweach row gains 2, so 8 ÷ 2 = 4 rows

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 …
All 3 with this pattern →

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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