Times
Problem
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.
I've had a go at times that add up to 12!
Well, that's it.
"I wonder what would happen if ...?''
Do enjoy this. Looking at the time may never be the same again!
Remember to send in ideas, even if you do it on your own and not through a school.
Getting Started
You may find it helpful to have a mirror handy.
Don't be afraid to turn your paper!
Student Solutions
Even though this challenge is about times on clocks, the display on a calculator will help you to explore the patterns more easily than trying to write the numbers on paper. So grab a calculator and punch in some "times". A little hand mirror can help check for symmetry and reflections too.
Let us know what you find by emailing primary.nrich@maths.org! Please don't worry that your solution is not "complete" - we'd like to hear about anything you have tried. Teachers - you might like to send in a summary of your children's work.
Hurrah! In 2015 we had a solution come in from Jake at St George's C of E primary schoolTimes
You have to have 1 at the start otherwise it won't work.
Then when I started to think about it, I realised you could have 0 or 2 to start. You can't have a number greater than 2 because it is a 24 hour clock.
If you used 8 (which has symmetry) you would have 18:81 and you can't have 8 in the minutes as the highest number you can have is 59 in the minutes.
I then worked out you could have these times:
0 1:1 0
02:50
05:20's good
1 0:0 1
1 1 . 1 1
1 2:5 1
1 5:2 1
20:05
2 1:1 5
22:55 Jake
Thanks, that's a good answer, sorry your previous submission got lost in the airways.
Teachers' Resources
Times
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.
I've had a go at times that add up to 12!
Well, that's it.
"I wonder what would happen if ...?''
Do enjoy this. Looking at the time may never be the same again!
Remember to send in ideas, even if you do it on your own and not through a school.