George and Dominic from St Nicolas C of E
Junior School sent us very clearly explained solutions to this
problem. Thank you! Here is what they wrote for the first
part:
1. For the first question I worked it out by seeing that number 3 was at
180° and that meant I needed to divide 180 by 3, giving the angle in
between each number. The answer was 60°. By knowing this I could work out
that number 2 was 120° away from zero anticlockwise and was 240° clockwise
from zero.
2. To work this out I did almost the same as I did with question 1 except
that I divided 180 by 4 instead. This gave me 45° between each number. By
multiplying 45° by 3 (which is how many numbers 5 is away from zero ) I got
135°. This meant that I would have to either turn the dial 135°
clockwise or 225° anticlockwise.
3. This was a little easier to work out because number 3 was a quarter of
the way round the dial meaning to get to it I either had to turn it 90°
anticlockwise or 270° clockwise.
4. This was harder than the previous questions because there wasn't a
number at the 180° point. To work it out I divided 360° by 9. This gave me
how many degrees I would have to turn the dial to get to the next number.
The answer was 40°. This showed me that to get to number 3 I had to turn it
either 120° anticlockwise or 240° clockwise.
5. At first sight this looked really tricky but after thinking about it
wasn't. Number 12 is 180° away from zero. Half of 12 is 6 and half of 180
is 90, meaning that to get to the number 6 I have to either turn the dial
90° anticlockwise or 270° clockwise.
George and Dominic continued to explain how
they had gone about the second part of the solution:
The next five were the hardest questions because we couldn't see where
the zero was at the start.
A. For this question I worked out that 12 was 180°
from zero and 180 divided by twelve is 15. This means that each section is
15° wide. There are 9 spaces between zero and nine which means that to work
out the answer we have to times 9 by 15 which equals 135. So to get to 9 I
have to turn the dial either 135°anticlockwise or 225° clockwise.
B/ We found this one quite easy because again 6 was a quarter of the way
round, so this meant that we had to turn the dial 90° clockwise or 270°
anticlockwise.
C/ First I worked out that 360 divided by 6 is 60 meaning that each
section is 60° around the dial. Using this information I worked out that I
would have to turn the dial either 120° clockwise or 240° anticlockwise.
D/ On this one I knew that 6 was at 180° but you had to work out what 5
was. So I did 180 divided by 6 which equals 30. Then I did 180-30 which
equals 150° so it was 150° anticlockwise and 210° clockwise.
E/ Firstly for this I divided 360 by 9 which gave me 40. I then multiplied
40 by 5 which gave me 200. Knowing this I could work out that to get to 5 I
either have to turn the dial 200° anticlockwise or 160° clockwise.
We ended the lesson by writing down 3 instructions for someone else to
follow which would give our combination. Sophie, another girl in our
group, wrote down:
Using dial D, turn the dial 240° anticlockwise. Then from that point,
turn the dial 210° clockwise. Then from this point, turn the dial 90°
anticlockwise. What's my combination?
We worked out that it was 8 1 4.
Very well done to you both. You
obviously worked hard on this activity. Thank you too, to Eve and
Rachel from Castle Carrock Primary who also sent in
well-explained solutions.