My friends and I love pizza. Can you help us share these pizzas
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
There are a number of coins on a table.
One quarter of the coins show heads.
If I turn over 2 coins, then one third show heads. How many coins are there altogether?
There were many replies to the puzzle of
the bursting balloons. You needed to be very clear about what you
were being asked in this problem. Here is some advice about how to
make sure you are clear from Joey and Vincent, both from Colindale
Primary School in London:
We read the passage again and again until we understood the
We know that at the beginning of Katie's
seventh blow the balloon popped. The question was how many puffs
did it take Will to burst the balloon? Some people told us how many
puffs of air he blew in before it burst and others said which was
the puff of air that was just too much for the balloon to take.
Several different answers were submitted. Was
this the type of problem that has a single answer or do you think
there could have been several solutions?
Different strategies and approaches were
taken. Some people used their knowledge of addition, others used
multiples and another group of problem solvers used their
understanding of fractions to arrive at their solutions.
Allison explains a strategy using first
a fraction and after that using addition.
To find out what was happening with Katie, we did this
$24 + 12 = 36$
$36 + 12 = 48$
$48 + 12 = 60$ ...
And so on ... $24, 36, 48, 60, 72, 84$ then Bang!
Half of $14$ is $7$.
You use this information and add.
So, $14 + 7 = 21$.
As Crewe, Errington and Porter and Croft
Jadie from Tattingstone School, shows
how division was the operation that helped her find and
Joey and Vincent made use of what they
know about fractions to find a solution:
Verity explains her answer by finding a
common multiple of 12 and 7:
I worked it out by working out the size of Katie's balloon as
she blew it up. The numbers went up in the $12$ times table. With
Will's balloon, the numbers went up in the $7$ times table. I wrote
out my $7$ times table until I found a number that was the same as
in Katie's list.
My lists looked like this:
Tom as well as Emily C, Emily G,
Gabrielle and Rebecca
from The Mount School think Will did $11$
puffs before his balloon burst. Or, as Verity puts it, what burst the balloon was the $12$th