Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
A Day with Grandpa
Stage: 2 Challenge Level:
It is easy to get confused by these sorts of calculations.
Fortunately Felipe from Quarry Bay School and Toby, Liam, Abi and
Livvy from Shute Community Primary School didn't get confused, and
all came up with the correct solutions.
The first rug measures $2$ yards $1$ foot by $1$ yards $1$ foot.
$2$ yards $1$ foot = $(2\times 3) + 1 = 7$ feet and $1$ yard $1$
foot = $(1\times 3) + 1 = 4$ feet. Therefore the area of the rug is
$7\times 4 = 28$ square feet.
Many of you correctly realised that if $1$ yard is $3$ feet then
$1$ square yard is $3\times 3 = 9$ square feet. $28 = 3\times 9 + 1
= 3$ square yards $1$ square foot. So Grandad was correct.
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NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.