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?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
This problem encouraged a huge number of
responses. There were different strategies used to solve the
problem and many suggestions for other words that could be used to
make a spelling circle.
Chen used the guess and check method for problem solving.
I moved randomly ... which eventually led me to the answer.
This can work quite well, but sometimes you
have a hunch there is a method or piece of information that will
help you. This happened withCaroline, Gabriella, Hanna, Natalie and
Rebecca all from The Mount School:
We think it has something to do with $5$ and $7$ not going into
In fact as the members of
Thomas , Robert and Keiichi from Moorfield Junior School used what they know about
Richard and Luke , also
from Moorfield, used the same method:
Did counting in fives work for the
second circle? Christopher , Chris and James found five didn't work and they:
... decided to count on in sevens because it is not a multiple
All of the people who sent in their solutions
agreed with these boys.
But was there a second solution?
, a pupil at Balderstone Primary School in
Blackburn, wrote that she had found five and seven worked but
having tried other numbers Ruth reports:
We couldn't do it any other way.
Thank you for your solutions,
explanations and willingness to be mathematical problem
solvers: Adam ,
, Anthony , Steve ,
, Matt B , Hanah ,
and Joanne (Phew!) all from Moorfield Junior School.
, Carla ,
Georgia and Thomas (who cleverly made a spelling circle using the name of
the school, Tattingstones). Also, well done to
Eastbury Farm School in Northwood.
Oh yes, so what were the words? Over
to Ruth :
The first one is MATHEMATICAL counting in fives
The second one is MEASUREMENTS counting in sevens.
Here are some words sent in by the readers
above. Put the letters to put into a twelve-section circle with the
first letter in the $12$ o'clock position and see if you can
discover what they are.
I, C, T, I, R, N, E, N, T, E,O, S (It's a word out of a maths
D, A, O, E, D, O, H, N, C, R, D, E
I, U, D, L, V, Y, D, N, A ,E, L, I
G, H, O, C, R, L, P, E, I, G, A, A
These final ones are the same word but using a different ** in
D, C, E, F, L, I, C, S, I, T, F, U
D, L, F, I, I, S, U, I, T, F, E, C
Here are series of possible words
from Burgoyne Maths Club :
Let me leave you with this question: If the
spelling circles don't work with multiples of $12$, will they also
work when counting by $8$, $9$, $10$ or $11$? After all, they are
not factors of $12$.