### Clock Hands

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.

### Ten Green Bottles

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?

### A Child Is Full of ...

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

# Times

##### Stage: 2 Challenge Level:

I've been thinking about the time for some time now! What a funny thing to say. Let me explain. Often during the day I have to look at my watch to see what the time is.
"Am I late?''
"Will I get there on time?''
"This is very boring, is that all the time is?''
"I can't wait, I wonder what the time is now?''
and so on.

I have a digital watch on my wrist, one in the car and one by the side of my bed. For quite a while I've been fascinated by the way the digital numbers are displayed and the patterns they show. Some of my friends also get caught up in this. I'll explain more ...

When it's:-

I'm very likely to say, "Well, that's interesting, if you put a mirror down where the dots are you find you get symmetry; there's definitely a line of symmetry down the middle.''
So I'll then look for another, and here's one:-

Is it the next one or are there some in between?

Whatever the next one is, I wonder how long it is between the two times?

So there we go, the first challenge is to find times on a 24 hr digital watch/clock that have this line of symmetry down the middle. You might find some rather different ones in which you have to decide whether they are allowed or not, that's all part of doing investigations.

But, you know, there are other sorts of shapes that fascinate me. What about this one for instance:

This is just good because when you stand on your head, or show someone else your watch [with your watch upside down to them], you find it can say the same time. Maybe we have to start ignoring the dots in between the hours and minutes, so we take it to look like:

As before there are others like:-

which we may prefer to see as simply:-

I wonder just how many there are?
Can we use the seconds numbers as well?
Does it help to always have your watch set to being a 24 hour display?

Well all of that was something to do with shape.
What about the actual numbers, or digits?
Here's an idea which I've used when running a residential course for youngsters. I told them that we would have a break and the next time that we would meet would be when the digits added up to 10. [We did not include the seconds.] So after the lunch break we met at 1:54.

Here are three times that add up to ten:

Have a go yourself and see what others you can come up with; you may think about changing the rule later on.