### Learning to Tell the Time

Telling the time is a rather abstract concept to begin with and some children find it extremely difficult to get to grips with. To be able to tell the time or solve time problems, children need to have understanding in many different areas of mathematics. Although it can be difficult, if you take it one step at a time, learning to tell the time can be engaging and fun - it is a fantastic mathematical concept that can easily be linked to a child's real-world and time problems can greatly enhance their problem solving skills. This post talks about common misconceptions and difficulties that children may experience. It also highlights different areas of maths that are involved in learning to tell the time and ideas for activities that can be done at home or at school in order to improve a child's time-telling skills.

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Misconceptions / Difficulties

If you stop to really consider time and think about what it would be like to look at a clock face (or digital clock) with no previous understanding of time, it is easy to think of many difficulties that you might come across. For example:
• Time uses numbers to represent something other than a physical quantity - up until this point, children will have been using numbers to quantify a group of physical objects. When learning to tell the time, children need to be able to count an abstract concept; something that they cannot physically see. It is also a leap into continuous numbers - children need to comprehend that there is something between 1 and 2. Not only that, we are also now expecting children to count up to 12, and then start again at 1, rather than continue to 13. All of these concepts go against what we have been trying to get children to understand about numbers. It is important to be patient and appreciate that it is a big jump for children to be able to use and really understand numbers in such a different context than what they are used to. It helps if they have had practice counting other non physical quantities such as steps or (one of my personal favourites) the number of sleeps left until an exciting event.
• The day starts at 12 o'clock - up until this point in a child's life, we have always started counting at 0 or 1, depending on the situation. However, now they need to learn that a day starts at 12 o'clock and after an hour has passed we go back to 1 o'clock. Even if you consider midnight to be 0 o'clock, as some digital clocks do, there is still the issue that 11:59 is morning (am) but 12:00 is afternoon (pm) and one minute after 12:59 pm is 1:00 pm. I suppose you could overcome these difficulties by using 24 hour format, but then the child needs to understand that the 2 on the clock face represents 14 if it is in the afternoon. If your mind is a bit boggled now, imagine how a child must feel when first being introduced to the concept of telling the time.
• There are two of each time in a day - not only does the day start at 12 o'clock, but there are two of them in one day. Children need to recognise that the day is split up into two 12 hour chunks and, as a result, the hour hand on a clock will do two complete rotations in one day. They need to appreciate that 2 o'clock can mean two different things and are at two very different times of day. This leads to the need to be specific about am and pm (or at least morning and afternoon). However, a young child may struggle with the concept of "2 in the morning", because to them that is in the middle of the night and not morning at all.
• Each number on a clock has two meanings - when reading an analogue clock, the meaning of each number depends on which hand is pointing to it: for example, the 4 on a clock face represents 4 o'clock when the hour hand is pointing to it but should be regarded as 20 minutes past when the minute hand points to it. This can be a very difficult concept for children to grasp - we are not only using number for a new, abstract concept but each number now has a double meaning.
• The hour hand is usually between hours - children need to grasp the concept that although the hand is between the 7 and the 8 (for example) it is still 'something' past 7. For example, at "5 to 8" the hour hand is almost touching the 8 but it is still 7:55 - to begin with many children think that this must mean 8:55 (as the hour hand is so close to the 8 that it may as well be on it). They need to perceive that the hour hand is constantly moving between the hours and that it doesn't suddenly jump to the next hour. However, this presents a lovely opportunity to emphasise how "5 to 8" is almost 8 o'clock, as the hour hand is almost on the 8.
• 60 minutes in an hour & 24 hours in a day - 60 and 24 are not standard numbers that children will be used to using for grouping things. On top of this, children need to be able to group the day into two 12 hour chunks in order to understand the meaning of a time. It can be difficult for a child to achieve this as they will naturally want to start grouping things in 10s. A good sense of time will help them crack this concept.
• We also use words for quarter or half hours - children need to have knowledge of basic fractions to get to grips with this concept, particularly halves and quarters. To switch fluently between describing the time as 7:15 or as "quarter past seven" they must be able to work out that half of 60 is 30 and a quarter is 15. An analogue clock face can really help with this concept, but it helps if the students have had previous practice finding halves and quarters of pictures (particularly circles).
• To or past the hour - children need to be able to describe time as either 6:35 or "25 to 7" (for example). They also need to recognise that although it is common to state a time as "25 past 7" it is not normal convention to state a time as "35 past 7".
• The big hand is for the minutesintuition often leads children to assume the big hand is for the hours, as hours are bigger (or more significant) than minutes.
• Time is often not stated exactly - if you ask someone the time and it is 8:14, they will probably tell you that it is "quarter past 8". This doesn't help children to accurately tell the time, if they can see a clock face at 8:14 but are being told it is quarter past 8.
• Everyday phrases that are related to time are often used incorrectly - for example, phrases such as "in a minute" or "give me 5 minutes" are often used loosely and the time frames are not followed. It is easy to use these phrases without thinking, but they can really obscure a child's sense of time.
• 24 /12 hour clock and analogue vs digital - not only are there all these new, abstract and sometimes obscure concepts for children to get to grips with, they will also eventually be expected to read and convert time between 12 and 24 hour format or between analogue and digital.
Links to other areas of maths

Learning about time gives children the opportunity to practise (in a practical context) basic fractions and counting in 5s. It will also help to improve their ability to recognise numerals, to count up to 60 and to recall the 5 times table. The visual clock face presents the opportunity to advance comprehension of addition and subtraction. It helps children realise that "25 past" is 25 "more than" the hour and to achieve this on a clock, they move the minute hand forward 25 minutes. To achieve "25 to" children move the hand backwards 25 minutes and this is 25 before or "less than" the hour. This also presents a perfect opportunity to help children understand the link between addition and subtraction - move 5 minutes forward in time and then 5 minutes back and you end up where you started so taking away 'undoes' adding - it is the opposite. The time format encourages children to practise and remember number bonds to 60, which will aid children with other number bonds and mental arithmetic.
Learn with an analogue clock first

Digital clocks are everywhere these days (on phones, computers, electrical appliances...) and it is becoming less and less common to see analogue clocks hung on walls or people wearing analogue watches. However, it is actually easier to learn to tell (and really understand) the time on an analogue clock. The constantly moving hands help children to get a sense of the passage of time, and the numbers on the clock face help children block time into 5 minute intervals. The clock face also provides a visual picture of the current time: when the big hand is half way round, we can see that we are half past the hour. This is a really important concept for kids to get to grips with, as they have to get used to 60 being the whole hour, 30 being half and so on. It also means that at other points such as 10 past, it is easier to 'see' what fraction of the hour has passed and will later help them link this to talking about "10 to" the hour, rather than 50 minutes past.

The following are the stages that children go through when learning to tell the time (with the approximate year in which they learn them, as described in a post by busythings). These are learnt over a matter of years rather than days, so it is important to make sure that a child has a deep and fundamental understanding of one stage before moving on to the next.
1. Tell the time to the hour and half past the hour (year 1)
2. Tell the time in 5 minute intervals including quarter past/to (year 2)
3. Know the number of minutes in an hour and hours in a day (year 2)
4. Tell the time from an analogue clock to the nearest minute (year 3)
5. Tell the time on an analogue clock that uses Roman numerals (year 3)
6. Tell the time in 12 or 24 hour format (year 3)
7. Read/write and covert time on analogue and digital clocks in both 12 and 24 hour format (year 4)
Tasks to help kids learn to tell the time

Get a sense of time
Life will be much easier for a child if they have some sense of time before trying to read the time on a clock. There are many activities that can be done to help children develop an awareness of the passage of time. These activities should be done frequently and for as long as possible before moving on to telling the time. For example:

• Constantly talk about time: bed time, lunch time, morning, afternoon, story books with a time theme. This gets the children used to the idea of 'blocking' sections of time.
• Time a child's favourite/common activities. For example, ask them to time 2 minutes to brush their teeth. Give them an analogue clock timer for activities that matter to them (time out, having a friend over, cooking food with them). This will build up their sense of time and allow them to see how the timer changes during certain time intervals, improving their ability to read analogue clocks.
• After/when doing an activity (drawing a picture, going to the park) ask the child how long they think it took or will take. Afterwards talk about how long it actually took. The child should get more and more accurate as they develop a better awareness of time.
• Give your child 5/10/15 minutes to do something (make a Lego model, play football, anything they like doing) and see how much they can get done in that time. Talk about it afterwards and discuss how much more time they may have needed or wanted.
• Do not use time phrases incorrectly ("in a minute, in a sec") if you don't really mean it. This will obscure a child's sense of time. Instead, if you really mean "in a minute", get the child to tell you when they think it has been a minute, and compare to how long it has actually been.
• Ask the children to plan their day. This will help them separate their day into time sections and will improve their sense of how long activities take and how many hours are in a day.
• Once children are more aware of time, ask them to tell you when it is time to do something (e.g. we will go to the park at 4 o'clock, let me know when it's time to go).
Make a 'double agent' clock
The act of making their own clock face can help children to understand how many sections the clock is broken up into and gives them the opportunity to practise their skills in counting up to 12 and counting in 5s up to 60. It also means they will then have a visual and kineasthetic aid to help them learn to tell the time and to solve time problems. You could even make the clock face when learning to count in 5s (rather than when learning to tell the time). When you then come to use the clock later on, the children will more easily be able to relate their knowledge of counting in 5s to telling the time.

It is a great idea to make 'pie slices' on the clock face by drawing lines from the centre of the clock to each of the 12 numerals at the edge. By colouring in each section a different colour, it really emphasises the 12 sections of a clock and can help children to become more aware that although the hour hand is constantly moving, it is still past the same hour until it moves into the next section.

I first saw the idea of a double agent clock in "Learning to Tell Time" by Karen Cicero from Parents Magazine. I think that it is a fantanstic idea that excites and engages children and helps them to get to grips with the two meanings of each number on a clock face. Essentially, it is about getting the children to realise that each number has a second, secret identity that comes out when the minute hand points to it.

To make a double agent clock, I like to make each number from 1 to 12 into a little door and behind each door is the second identity. This means that the clock face looks like a normal clock face, but to begin with children can look behind the door to check the second meaning. After a bit of practise, you can start asking the child to guess what is behind the door before checking (eventually, they won't need to look behind the door at all). The fact that the second meaning is hidden means that a child won't rely on just reading it off the clock face but will learn to remember and associate each number with its second meaning on their own. As a result they will then be able to tell the time on a normal clock that only has the numerals 1 to 12 written on it. (Later on, the clock face can be used to emphasise and practise the 5 times table.)

Practise telling the time or showing the time on an analogue clock
Start with o'clock first, making sure that you discuss the difference between am and pm and the fact that there are two of each time in the day. Then move on to half past the hour and quarter past/to emphasising the fact that the hour hand will be between (rather than on) the hour. Use the clocks that the children have made so that they are physically able to move the hands round - this will link to the words that they are using. Once the kids have a strong grasp of this it is not too big a leap for them to move on to telling the time to the nearest 5 minutes, especially with a double agent clock. It may be more difficult for them to describe a time as "25 to" rather than 35 past, but this will come with time (and frequent reminders). It's worth considering using the clock face to practise the number bonds to 60.

There are many fantastic worksheets, games and apps available online that are engaging and offer the opportunity for children to practise their new skills. More importantly, it is vital for children to consistently think about time and link it to their own activities and daily lives. Fortunately, time is something that is easy to constantly point out and remind the children of. It is simply a matter of encouraging the children to look at the clock before, after and during activities. Not only will this help the children to read the time from an analogue clock, but it will improve their awareness of elapsed time.

 NCETM Mastery Assessment
A great mastery question that encourages greater depth of understanding is to give children a picture of a clock with no minute hand. Ask them to draw on the minute hand to work out the current time (using o'clock and half past times). This requires the children to really understand the position of the hour hand (as well as the minute hand) and allows them to realise that the hour hand alone can give an estimate of the time, and the minute hand is used for accuracy.

Solve Time Problems
To be able to solve time problems, children not only need to be able to tell the time but also need to be confident with the idea of elapsed time. This can be a difficult concept to grasp, but can be made easier through the following activities:
• Use a timer or stop watch to get a sense of elapsed time during a child's favourite activities. Link this to the child's home made analogue clock. Start with simple intervals such as 5 minutes/30 minutes/1 hour and then talk about how the clock has changed.
• Ask the child to tell you when their time is up for a chore or when it is time to do something fun - encourage them to think about what the clock will look like when time is up. They will inevitably keep an eye on the clock and get used to seeing time passing. This will also improve their sense of time.
When attempting time problems, don't introduce children to rote methods for working out elapsed time. Even if they remember the method correctly, they may not be able to apply them to other situations, such as when you go over an hour, or through 12 o'clock. Instead, let the children develop their own strategies, and use their discussions and ideas to lead them towards methods that will always work, no matter the problem.

The children can use the clock they made earlier to physically move the hands, and keep track of how much they have moved each hand. When they understand and have got used to it, they will then be able to apply these strategies on paper or by visualising the hands turning.

One of my preferred techniques to solve time problems is to use a time number line. Of course, this is another new concept for kids to understand, as it is essentially linearising time. However, if they have a good concept of the hours in a day (1 comes after 12) and how many minutes are in each hour, the transition should not be too tricky. You can start with labeling the hours on a number line and then filling in the major intervals between each hour. It is important to finish drawing the number line before attempting the problem, otherwise many children start drawing irregular intervals to suit the question, which doesn't help to accursolve the problem. Perhaps encourage children to make and keep a time number line that they can keep coming back to whenever solving time problems.

When using a time number line, children are able to make jumps that they are comfortable with (hours, half hours, 5 minutes) until they are close to the answer. They can then make jumps of a minute at a time until they get to where they need to be. All they then need to do is add up all the jumps. The good thing about this method is that it can be adapted for the use of all sorts of time problems including going forward in time, going backward in time and finding the difference between two times.

Discuss the Circular Nature of a Clock
Discussing and helping children to understand why a clock is circular can help them to more easily create time number lines and linearise time problems. Asking children why they think we use a circular clock to tell the time encourages them to think about how specific times are repeated, even though time has elapsed and we are in a new hour or a new day. It will emphasise that there are 60 minutes past every hour before time moves on to the next hour and the minutes start again at zero.  It will also help children to think about how the hours are repeated twice a day, everyday. This aids children's understanding of the repetitive pattern of time which will, in turn, support the process of learning to tell the time. The children should be able to  come to the conclusion that a time number line would have to go on forever, as time never stops but using a circular clock allows us to repeat the times each day.

Telling the time can be a very difficult concept for children to really understand. There are so many different things that they must get to grips with and a lot of opportunities for misconceptions to arise. However, children are often very keen to understand and talk about time and if we help them develop a good sense of time and how this is represented on an analogue clock, learning about time can be a very fun and engaging process.