# Dear Family, your Operation Maths guide to Time

## Dear Family, your Operation Maths guide to Time

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Dear Family, below is a brief guide to understanding the topic of time, as well as some practical suggestions as to how you might support your children’s understanding at home. Also below, are a series of links to digital resources that will help both the children, and you, learn more about length. The digital resources are organised according to approximate class level:

#### Understanding Time

Although time plays a very important role in everybody’s life, it can be quite a difficult concept to grasp:

• Unlike our number system, time is not built around a base-ten system. All of the other maths topics in measures (i.e. money, weight, capacity and length) are all built around units of ten, one hundred, one thousand and so on e.g. 100 c in €1; 1,000m in 1 km etc. But time is totally different: 60 seconds in a minute; 60 minutes in an hour; 24 hours in day; 7 days in a week; 4 and a bit weeks in each month; 12 months in a year etc.
• While we can’t see or touch time, we have ways to record and show it, but again, there are many different ways to do this: sand timers, sun dials, analogue clocks and watches, digital watches and displays (which can be either 12 or 24 hour), calendars etc.
• Time is not the same all around the world; each country belongs to a time zone and the time is different in each time zone.
• Judging how much time has passed can be quite difficult, as it depend on what we are doing; we all have experienced how time can drag, or it can fly when having fun.

#### Practical Suggestions for all Children

• Talk about time all of the time! When you wake up your child in the morning, (or he/she wakes you!) announce the time and day; how many school days left before the weekend; how long before you need to leave the house; the start time for the sport’s practice or music lesson; dinner time etc. Give your child a set amount of time to complete a task or chore. Try to become a type of talking clock yourself, constantly announcing the time of day and the time left/needed to do something. This will help develop your child’s own internal sense of time.
• What are we doing today? Involve your child in planning trips, visits and outings: what time do we need to leave to arrive there on time; what time do we need to get up at? How long is it going to take you to get ready? Highlight the importance of punctuality and being on time as a valuable life skill: we need to leave the house at 20 to 9 if we are going to get to the school for 9, etc.
• Lots of clocks! Try to have plenty of time devices around your home, and of different types, for your child to become familiar with the many different ways to measure time. It is never too soon to have a clock in your child’s own room and/or for them to wear their own watch; however, first clocks and watches should be of the analogue type (i.e. with hands and a face) rather than digital. Even if your child is not able to read the time on the analogue clock face yet, noticing and becoming aware of the movement of the hands and their direction (clockwise) helps develop your child’s sense of the passage of time, a valuable learning experience that will be built upon when ready.
• Buying a clock: While children need to be flexible, and to be able to tell time using a variety of different time devices, if you decide to buy a first clock or watch for your child, there are some clock features you should consider before you buy (click here to see some suitable examples):
• All the numbers 1-12 (not roman numerals) shown clearly.
• Minute intervals (i.e. little lines) shown clearly around the edge of the face.
• A minute hand that is long enough to show that it is pointing beyond the numbers (which mark the hours) out to the minutes around the edge (the purpose of the long minute hand is to point out to the minutes).
• Hour is key: When your child asks “what time is it?” ask them to try to work out what the time is roughly for themselves. When looking at an analogue clock, they should always look first at the short hour hand: which number is it pointing to (or closest to)? Then, that is the (nearest) hour. The minute hand only helps us refine that approximate time. When looking at an digital display, they should always look at the first digit; that is the hour that it was last. This is another example of why analogue is better than digital: it is possible to gauge the actual time more accurately using only the hour hand on an analogue clock, than using only the hour on a digital display.
• Mark the date: Have calendars and/or weekly charts/diaries visible around your home. Use the calendar to mark events that would be important to your child, like birthdays, holidays, Christmas, school concert etc. Involve your child: if there is space available to do so, he/she can mark these important dates using words and/or pictures. Also try to have calendars that start with Monday, since Monday is officially the first day of the week (read on here for more interesting info on this). On weekly charts, mark repeat events like sports practices, lessons etc.
• Dot, dot NOT dot! When writing or texting a time in digital format (e.g. See you at 6:30) always use a colon (two dots) rather than a single dot (i.e. don’t write 6.30). Firstly, a colon is what is used most often on actual digital displays. Secondly, a dot is identical to a decimal point (e.g. 2.5 meaning 2 and a half or the decimal point used when writing money e.g. €1.20) which, mathematically, is used with numbers on the base-ten system. And time, as we said earlier, does not work on a base-ten system. So using a single dot for writing time, may only confuse children.
• 24 hour & 12 hour: For the older children, draw their attention to 24 hour time and encourage them to translate 24 hour to 12 hour with a.m. or p.m. and vice versa. Most phones, devices and smart watches have the option to display either version, so perhaps set these to 24 hour time to provide your child with more opportunities to become familiar with it.
• When is it on? When does it leave? Highlight also any timetables and schedules that the household might use, or refer to, for example TV listings on an Electronic Programme Guide (EPG), cinema timetables, transport timetables (e.g. bus and train), flight arrival and departure times. In the case of an upcoming flight for a family vacation, encourage the children to identify the arrival and departure times and to use this information to calculate flight time. If there appears to be a difference between the outgoing and incoming flight times, can the child explain this, i.e. does he/she notice that flight arrival and departure times are always given as local time and that the destination may be in a different time zone?

#### Digital Resources for Infants

NB: By the end of senior infants, children are expected to be able to tell time to the nearest hour.

BBC Bitesize – Time: Nice images and a song to explore the structure of the typical day for a young child.

White Rose Maths – Time: A lesson for Year 1 on Time to the Hour.

Matholia – Time: A video lesson on Telling Time to the Hour.

Telling the time in words: Look at the clock and find the matching time in words. Do the first level only, reading time to the nearest hour.

I Know It! – Days of the Week: Answer questions about the Days of the Week.

Seasons and Days of the Week. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum.)

#### Digital Resources for First and Second Classes

NB: By the end of second class, children are expected to be able to tell time to quarter hour intervals.

White Rose Maths – Time: Lessons for Year 1 on Time to the Hour, Time to the Half Hour, Writing Time and Comparing Time. Lessons for Year 2 on o’Clock and Half Past and Quarter To and Past.

Matholia – Time: A series of video lessons, including Telling Time to the Hour, Telling Time to the Half HourQuarter Past and Quarter To

Khan Academy – Time: Watch the video to learn about time and then answer the practice questions. You can also register for a free Khan Academy account to record your progress and explore other areas of Early Math.

Let’s make a Calendar: From Starfall, this builds an interactive calendar for the current month and asks questions. NB: This is a US site so the calendar starts with Sunday, not Monday and includes the US holidays and feasts.

Using a calendar: From Maths Frame, 3 levels of questions about the current month. Start on level 1 and move up a level when confident.

Calendar Clowns: Answer a host of questions based on the calendar given.

Telling the time in words: Look at the clock and find the matching time in words. 5 different levels: reading time to the nearest hour, half hour, quarter hour, five minutes or minute, which can be played as timed or untimed games.

Telling the time: Read the time on an analogue clock. Lots of choice over levels, including: reading time to the nearest hour, half hour, quarter hour, five minutes or minute. Options include using a 24 hour clock and seeing how many correct answers you can get in a given time.

Time Tools: Match analogue and digital times, on the hour and half hour. Click on start to learn more about time (tell me more tab), telling time to any minute interval and to try out other challenges and games (other tabs along top).

Time Matcher: Memory game where you match equivalent amounts of time eg 1 week, 7 days etc

Time Teller: Tell the time game with 6 different levels, from half hour to minute intervals, and solving elapsed time problems in hours and/or minutes.

Adding Time Problems: Quiz game where you’ve to read the problems and work out the answer. Lots of options and levels.

Hickory, Dickory, Clock: Read the time at the bottom of the screen and chose the matching clock. Three levels available.

Clock Splat: Find the digital time that matches the analogue time and Splat! Options include hours, half hours and quarter hours.

That Quiz – Time: This quiz has lots of options, on the left hand side, that can be changed to suit the ability of the child. Ensure that the level is set to 1. Each time do the set 10 questions, if you get 10 or 9 correct go up a level, if not stay at that level. There are lots of different types of activities: For Simple clock (it automatically starts on this) you must type in the digital time; if you set it to Time passed you must identify the amount of elapsed time from first to second time.

I Know It! – Time: Scroll down to Time to do any of the activities. There are some more advanced activities in the second grade section.

Time: a selection of games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum.)

Math Games: a whole suit of times games, for all class levels; choose the skill you want to practice.

#### Digital Resources for Third to Sixth Classes

Time: Background information on money from Maths is Fun, including Analog and Digital Clock Animation,  Time: AM/PM and 24 Hour Clock, Adding and Subtracting Time  and World Time Zones

White Rose Maths – Time: Lessons on Telling Time to 5 Minutes 1, Telling the Time to 5 Minutes 2, Hours and Days, Durations of Time, Compare Durations of Time. For 5th and 6th, check out Converting Units of Time & Timetables.

Matholia – Time: Lessons on Telling Time (Past & To), Telling Time AM & PM, Duration of Time 1 and Duration of Time 2

Khan Academy – Time: A unit of work exploring time, including how to read time to minute intervals, time on a number line and elapsed time. You can also register for a free Khan Academy account to record your progress and explore other areas and/or try more difficult material.

Splash Learn – Time Games:  for Third Grade.

Elapsed time number lines: A video from the Avery Bunch, showing how Marshall and Amanda solve elapsed time problems using number lines.

Using a calendar: From Maths Frame, 3 levels of questions about the current month. Start on level 1 and move up a level when confident.

Calendar Clowns: Answer a host of questions based on the calendar given.

Telling the time in words: Look at the clock and find the matching time in words. 5 different levels: reading time to the nearest hour, half hour, quarter hour, five minutes or minute, which can be played as timed or untimed games.

Telling the time: Read the time on an analogue clock. Lots of choice over levels, including: reading time to the nearest hour, half hour, quarter hour, five minutes or minute. Options include using a 24 hour clock and seeing how many correct answers you can get in a given time.

Time Tools: Match analogue and digital times, on the hour and half hour. Click on start to learn more about time (tell me more tab), telling time to any minute interval and to try out other challenges and games (other tabs along top).

Hickory, Dickory, Clock: Read the time at the bottom of the screen and chose the matching clock. Three levels available.

Time Matcher: Memory game where you match equivalent amounts of time eg 1 week, 7 days etc

Time Teller: Tell the time game with 6 different levels, from half hour to minute intervals, and solving elapsed time problems in hours and/or minutes.

Adding Time Problems: Quiz game where you’ve to read the problems and work out the answer. Lots of options and levels.

Find the start time: Quiz game where you’ve to read the problems and work backwards to identify the correct start time. Lots of options and levels.

Clock Splat: Find the digital time that matches the analogue time and Splat! Options include hours, half hours and quarter hours.

I Know It! – Time: (Third Grade) Scroll down to Time to do any of the activities. There are some more advanced activities in the fourth grade section.

That Quiz – Time: This quiz has lots of options, on the left hand side, that can be changed to suit the ability of the child. Ensure that the level is set to 1. Each time do the set 10 questions, if you get 10 or 9 correct go up a level, if not stay at that level. There are lots of different types of activities: For Simple clock (it automatically starts on this) you must type in the digital time; if you set it to Time passed you must identify the amount of elapsed time from first to second time; other options are arithmetic and conversions, which includes time zones for 5th and 6th.

Time: a selection of games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum.)

Math Games: a whole suit of times games, for all class levels; choose the skill you want to practice.

## Digging Deeper into … Time (all classes)

Category : Uncategorized

For practical suggestions for families, and links to useful digital resources, to support children learning about the topic of time, please check out the following post: Dear Family, your Operation Maths Guide to Time

Time is an integral element of our daily lives and therefore an essential, “need-to-know” topic in primary maths, particularly for those children with special educational needs or learning difficulties. However, it is also a very difficult mathematical concept, and one with which many children struggle, for a number of reasons:

•  Time is abstract; it cannot be touched, or manipulated, or seen (although we can see its effects when we look in the mirror!).
• The standard units of time do not reflect the familiar structures of our base-ten place value system i.e. 60 seconds = 1 minute, 60 minutes = 1 hour, 24 hours = 1 day, 7 days  = 1 week etc.
• It can be displayed in analogue and digital forms and, furthermore, digital times can use a 12 or 24 hour system.
• It is not uniform around the globe; each country belongs to a time zone and the time is different in each time zone.

Furthermore, there is a distinct difference between identifying a particular instant/moment in time (i.e. the skill of reading or telling the time) and understanding the concept of duration and the passage of time. In many cases, children may know how to tell the time, without having any real understanding of the concept of duration. Remember, that just because a child can read the digits on a digital clock/watch, or even read time from an analogue clock/watch, this does not mean they understand time as a concept.

As explained in all of the previous Digging Deeper posts, Operation Maths is based on a CPA approach. And, while we acknowledge that given the abstract nature of time is can be difficult to represent it concretely, Operation Maths does introduce the empty number line as a way to pictorially represent elapsed time (see below in post).

### Telling Time

Telling time requires the children to:

• develop an understanding of the size of the standard units of time eg days, weeks, hours, minutes
• be able to estimate and measure using units of time
• read and tell the time using both analogue and digital displays (12 hr & 24 hr).

The analogue clock has its own features that can further complicate matters; there is a “past” half and a “to” half; when reading times on the hour, the hour is said first (eg 3 o’clock) but when reading all other times the hour is said last (eg half past 3). Other valid questions that a child might have about the conventions of reading time include:

• Why do we only say half past; why not half to? (Interesting point: the German for half past three, translates literally into English as half to four)
• Why do we say half past; why not 30 past?
• Why do we say quarter past/to; why not 15 past/to?

More often than not, when teaching analogue time, teachers tend to get the children to focus on the position of the long/minute hand and to use that to tell the time eg “if the minute hand is at 12, it is o’clock”, “if the minute hand points at 6, it is half past” etc. However, this type of explanation can in itself be very confusing, with many children interpreting half past any time as 6 o’clock, quarter past any time as 3 o’clock etc.

In fact, the first thing a child should be able to read is the bigger unit of time i.e. to identify the hour (hence, the first mention of telling time in our Primary Mathematics Curriculum is telling time to the hour, in senior infants . To do this, the children should, logically, look at the hour hand, which, although it is shorter than the minute hand, can often be wider on real analogue devices, emphasizing its significance. When the hour hand points straight at a number, then it is that time; when it points half way between two numbers, it is half past the previous hour (also the lesser number). In this way, the children will be enabled to tell time in relation to the hour eg “it’s nearly 2”, “it’s just gone past 7”, “it’s around half 5”, etc. Consider also how many children, when drawing hands on a clock to show time, will often have the hour hand pointing straight at the number even if it is half past, quarter past or a quarter to the hour. Focusing initially on the hour hand rather than the minute hand, highlights the fact that the hour hand also travels around the clock as the hour passes, and doesn’t jump from one hour to the next. A real or made clock with only the hour hand can be very useful here to teach this concept. Or use the Operation Maths Clock eManipulative (pictured below), and ask the children to look only at the red hour hand. The Two Clocks problem from NRICH can also be used to reinforce the importance of the hour hand.

Next, draw the children’s attention to the blue minute hand and to the blue minute markings around the edge of the clock. Logically, the minute hand has to be the longer hand because it points, beyond the numbers, at the minute markings which are furthest out from the centre, whereas the hour hand points to the hours (numbers) which are typically closer to the centre, and thus the hour hand is shorter. Emphasise that the minute hand enables us to become more accurate in our measurement of time. “O’clock” is actually an abbreviation of “of the clock”, so then when the minute hand points to the top of the clock , it is o’clock. Avoid saying “when the minute hand points to 12 it is o’clock” as the minute hand is actually pointing to the minute markings around the edge and not to the hours, which instead is the purpose of the hour hand.

At this point, it can be useful to use a cut-out paper circle (see below) to represent the clock and fold it in the centre to show both halves of the clock. Thus we can explain that when the minute hand points at the bottom/base of the clock, it is half past, as the minute hand has now passed through half of the clock. In a similar way, use the paper circle to make quarters and emphasise that when the minute hand has passed a quarter way through the hour, it is a quarter past, and when the minute hand is a quarter away from the next hour, it is quarter to. However, it should be acknowledged that, while it would be mathematically correct to say it is three quarters past the last hour (which prepares them for digital time), the convention used is to describe time in terms of how it relates to the next hour once it has passed the half-way point, at the bottom of the clock. Return to the paper circle at this point and label each half “past” and “to”. “Past” and “to” are also clearly labelled on the Operation Maths Clock eManipulative (see above), along with arrows to indicate the clockwise direction in which the hands travel.

When the children are ready, they should begin to measure time in minutes also (reading time in 5 minute intervals is on the curriculum for third class). Again, focus their attention on the blue minute hand and on the blue minute markings around the edge. In this way, the children may initially begin counting  the minutes in ones around the edge before realising that it is more efficient to count in groups of five, which co-incidentally, are also marked by the hour numbers. Creating and using peek-a-boo clocks can help reinforce this idea.

It is essential that when teaching digital time that the connection between analogue and digital is emphasised from the start. The Operation Maths Clock eManipulative is very useful in this regard as both clock types can be shown concurrently (see below). It is also includes the feature to hide/reveal the time in word form, as well as the feature to produce a random time on either clock, which can then be displayed manually on the other clock to match. For ease of use the teacher can also select the options that best suits the class level and ability eg hours only, time to half hours, quarter hours, five minutes, individual minutes.

### Time as Duration

It is very important that the concept of time as duration is emphasised from the start. Duration of an event requires noting the starting and finishing points of time.
Developing a solid understanding of duration develops from a child’s experience  and understanding of:

• Sequencing activities (eg pictures  of familiar/daily events, seasons etc)
• The language of time such as before, after, soon, now, earlier, later, bedtime and lunchtime
• The standard cycles of time (seconds, minutes, hours, days, months, seasons etc ) which in turn follows from the sequencing of daily events.
• Measuring duration (using non-standard units initially, and then standard units)
• How long does it take to …..? Estimate & measure
• How many ….can you do in …? Estimate & measure
• What if you do it faster/quicker…? (this in turn develops an understanding of the relationship between speed and time)
• Comparing the duration of two events, (using non-standard units initially, and then standard units) eg what takes longer/shorter? How much longer/shorter is ….. than …..?

Developing an understanding of duration also requires the ability to visualise the passage of time in some way. For this purpose, empty number lines, one of the key problem solving strategies used in Operation Maths, are extremely useful. This can start with drawing an empty number line on the IWB or on the Operation Maths MWBs, to which class/question appropriate details can then be added:

• What hour is after 9 o’clock? 11 o’clock? 12 o’clock?
• Ann’s school starts at 9 o’clock. What time is it 2 hours later? 2 hours earlier? 5 hours later?
• If Ann’s school finishes at 2:30 for how long is she at school?
• Umair’s school starts at 9:30 and finishes at 3:00. For how long is he at school?
• How long is it from the start of the 11 o’clock break to the start of the next break?

In Operation Maths, empty number lines are presented as a viable alternative, to the traditional column method approach, for calculating time. In many other countries, the traditional column method used for calculations involving units, ten, hundreds etc., is not encouraged, or not used at all, for calculations involving hours, minutes etc. However, as our Primary Mathematics Curriculum here in Ireland, still specifies the use of subtraction to solve elapsed time problems, Operations Maths has opted to present both ways in the books.

To view an excellent video of students solving elapsed time problems using an empty time line, please click here.

### Other tips and suggestions for teaching time

• Refer to, and use, aspects of time as much as possible during the school day, as appropriate to the class level e.g.:
• Assign times for tasks and show interactive count-down timers on the IWB. This loop timer is particularly useful for timing stations in class.
• Reference calendar facts such as the current, previous and next day, date, month, season, etc every morning.
• Have a calendar visible in the classroom, marked with significant dates eg school play, outing, pupil birthdays etc. Ask the children to tell you how long it will be (in hours, days or weeks) until certain events (try to only use calendars that start with Monday as the first day)
• Encourage the children to wear watches themselves, with a preference for analogue, as an awareness of analogue time better develops the children ability to appreciate the passage of time.
• If buying a new clock for your classroom, try to ensure that it has the necessary features to help the children better understand how to read time.
• When writing time in digital format always use a colon (as seen on digital displays) as opposed to a dot i.e. 10:30 as opposed to 10.30. Using a dot, which is identical to a decimal point, doesn’t help the child to recognise that the system of measuring time is inherently different from our base-ten place value system.