EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Find a great variety of ways of asking questions which make 8.
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
Hmmm, let's see if we can figure out the
solution by seeing how you might solve the problem. There seemed to
be two ways that this problem was tackled. One way was to use
manipulatives - tools - to help discover the number of people who
took part and Rocco's position in the race.
from Moorfield Primary School used
manipulatives. Here they explain what they used and how:
We started of by using multi-link cubes. We arranged the cubes
so there was an odd number and Rocco was one before the middle. We
tried it first with $5$ cubes but that didn't work. We kept adding
on $2$ so that the number stayed as an odd number. We kept it as an
odd because if you put one runner from behind in front, Rocco will
be in the middle. Seven didn't work so we tried $9$. This did work
so everything fitted in to place. This showed that Rocco came
Someone else said:
The other strategy used was 'guess and check'.
This can be combined with using manipulatives. You have to have a
number to start with that seems reasonable. Let's see how some
people used 'guess and check'.
of Moorfield Junior School
We started off with $5$ people but it didn't work so we then
tried $15$. That didn't work because there were $6$ people in front
of him and $8$ behind him. Then we tried $9$ and it worked. When
you move $1$ in front of him it made him in the middle and when you
move one behind him it makes $2$ in front and $6$ behind, $2
\times3 = 6$. Rocco came $4$th.
Robin, also of
Moorfield Junior School, did a great job in showing how you can
combine 'guess and check' with drawing a diagram to help you
thinking through the problem. Robin writes:
I knew that it had to be an odd number if Rocco was to finish in
the middle of the race to make the same number of runners in front
as behind. Starting at five we placed Rocco second in the race but
this didn't work because when a runner finished after Rocco the
amount of runners behind was not $3$ times the runners in
Then we tried $9$ runners, it would look like this: - - - - R -
- - - -
So based on these diagrams, Rocco starts off in fourth place
If one more runner finishes before him it would look like this:
- - - - R- - - -
and in this case there is an equal number of runners in front and
If one runner finished behind him, however, it looks like this:
- - R - -- - - -
Rocco has $2$ people in front of him and six people behind. $6$
is three times $2$.
At the finishing line, Rocco came fourth in the race.
Thomas here did so
well, despite being frustrated by the computer - perhaps it was the
font you chose Thomas!