# The time is ...

Can you put these mixed-up times in order? You could arrange them in a circle.

Can you put these $12$ mixed-up times in order? You could arrange them in a circle.

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You can download a copy of the times on this sheet which can be printed out.

If you feel happy to try the same thing with a $24$-hour digital clock, try these $12$ times. They are on this sheet.

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You might find it a good idea to put all the times in the same format - that is make them all digital times or all clock times. This sheet of clock faces might help.

If you are unsure about $24$-hour times, take $12$ from the hour digit given so 13.15 becomes 1.15.

I think that some of you didn't notice that the times shown on the clock faces weren't the same as the digital times underneath the clocks so some solutions only included half the number of times we'd given.

Sophie offered this helpful advice:

I did this by looking at the numbers and ordering them earliest to latest. At first I was stuck on the time 00:17, but then I thought: in 24 hour clock, 1 o'clock in the morning is 01:00 so what is midnight?'I realised 00:00 must mean midnight.

Katie from Hymer College Junior School sent us this picture of the order of the 12-hour clocks:

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Katie explained what she'd done:

First I labelled them with either "am" or "pm"so it was possible to put them in order.Then I had to work out what each time said on the clock. With this I could put them in order [earliest - latest] easily.

I felt it was easier to set it out in lines like I have. I put arrows on so it was easy to follow.

I also found it was easier to do this on paper than on the computer.

With the 24 hour clock I would do the same except not label them with "am" or "pm".

I wonder whether this is the only solution?

How about the order of the 24-hour times? If you have a solution for this part of the problem, let us know!

### Why do this problem?

This problem assesses and extends children's understanding of telling the time. Many children have difficulties with this, which is not surprising when you realise that analogue clocks are two dials super-imposed on one another.

### Possible approach

The clock pictures and digital times can be downloaded here. These can be printed (and possibly laminated), then cut into separate cards. You could provide a set of cards for each pair, or they could be enlarged and used by a group of up to four children.

This task is probably best introduced with a minimum of teacher talk. Simply give each pair or group the cards and invite them to order the times. Give them plenty of time to tackle the challenge and try to step back. You may wish to stop them after some time to discuss what they have done so far so that ideas are shared among the whole class. This sheet of empty clock faces could be useful if children prefer to put all the times in the same format. The 24 hour clock times could be tackled by those who finish earlier than others. [Download here].

In the plenary, encourage children to explain how they went about the task, rather than only focusing on their final answer. Listen out for children who realise that the hour hand or hour digit/s is the one to look at first. If there are disagreements about the order, invite pairs or groups to try and justify their thinking. None of the times mention am/pm (in the twelve-hour version) so it
will be interesting to see how the children cope with this and whether it comes up in their conversations. This may mean that there are several different solutions to the task and this is where children's justifications of their decisions are key.

### Key questions

What does that hand tell you?

Which of the clocks shows the earliest time? How do you know?