Which times on a digital clock have a line of symmetry? Which look
the same upside-down? You might like to try this investigation and
This investigation explores using different shapes as the hands of
the clock. What things occur as the the hands move.
Do you know the rhyme about ten green bottles hanging on a wall? If
the first bottle fell at ten past five and the others fell down at
5 minute intervals, what time would the last bottle fall down?
The time where the 2 watches are 10 mins apart is 9:20.
At 7 o'clock they're 3 mins apart
At 8 o'clock they're 6 mins apart
9 o'clock, 9 mins.
For 1 minute you divide 1 hour by 3, as 20 is 3 times as small as
Then you add 9:00 and 0:20 to make 9:20, which is when they are 10
Stuart and Mark (Lower Juniors at Cummersdale,
Cumbria) also say 9:20. They used this technique:
Every hour the difference between the two watches increases by 3
That gives us 3 hours and then divide 60 into 3 to make 20
3hours + 20mins = 3 20mins
6:00 a.m. + 3hrs 20 mins = 9:20 a.m.
George (Rosebank Primary School, Leeds) drew diagrams to show
I knew that it would take them 3 hours and something because
every hour they got three minutes apart. That meant that it will
have minutes as well as hours. I knew that Stuart's and Adam's
watches went three minutes apart every hour. Now I needed to know
how many minutes apart the boys' watches go in one minute. For this
I drew a scale.
Then I marked how much they'd be apart.
This showed me that it must be between 15 and 30 minutes. When I
divided it into even smaller parts I got the answer.
This got me to the answer, which is 3 hours and twenty
Daniel (Anglo-Chinese School - Primary, Singapore),
Thomas (Tattingstone School) and Timothy
(Munsang College, Hong Kong) gave very
similar explanations. The one below is Timothy's:
Stuart's watch loses 2 min every hour and Adam's watch gains 1
min every hour,
so they are 1 + 2 = 3 min apart after the 1st hour and 3 more mins
after every hour.
When they arrive at the airport, their watches are 10 mins apart,
so they travel:
10/3 hours = 60 x 10/3 = 200min = 3hours and 20mins
They start at 6:00am, so they arrive at 9:20am.