Time Matters - Book 2 (Years 4 to 6)

RIC-6123 35/7

Time matters: Australian Curriculum Mathematics Book 2 (Years 4–6) Published by R.I.C. Publications® 2015 Copyright© Linda Marshall and Paul Swan 2015 ISBN 978-1-92501-08-6 RIC– 6123

Titles in this series: Time matters: Australian Curriculum Mathematics Book 1 (Foundation to Year 3) Time matters: Australian Curriculum Mathematics Book 2 (Years 4–6)

Also in this series: Money matters: A teachers handbook for developing money concepts (Ages 5–10+)

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Contents Introduction Issues

Introduction

4

Curriculum links

5

Issues to consider

6–10

Time equivalents

11

Likely difficulties with time

12

The language of time

Language (including children’s literature)

Language abbreviations Children’s literature Time-related displays Days of the week

Periods of time

Timing/Duration (including estimation)

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19–20

Seasons

22

The calendar

23–24

Organising your time

25–26 27

Telling the time

28–32

12- & 24-hour time

42–48

Clock bingo

49–53

Time concentration game

54–59

Time dominoes

60–65

Self-checking time cards

66–69

Race around the clock game

70–71

Skateboard racing game

72–79 80

Linking fractions and time

81–84

Sequencing events

85–95

Sequencing shadows

96

Sequencing time lines

97–101

Using timetables

102–106

Timing/ Duration

107–112

Adding time intervals game

113–120

Making a tocker

121

Candle clock

122

Making a sand timer

123–124

Making a water clock

125–126

Playing with pendulums

127–128

Rates

129–130

Time projects

131–132

Greenwich Mean Time

Applications

18 21

Close your eyes (Time problems)

Sequencing

15 16–17

Months of the year

Year planner

Telling the time (Clock reading – digital and analog)

13–14

133

Time zones

134–136

International Date Line

137–138

Lunar month: Phases of the moon

139

Sequence of the moon

140

Time on different planets

141

3

Time matters Book 2 (Years 4–6)

Introduction

B

ook 2

Most of us, if asked to consider the topic of time, would think about telling the time. This is a very important aspect of the topic; however, there are many other aspects of time that we need to consider. These include: time equivalents; days of the week, months of the year etc.; sequencing events; timing and duration; planetary time and so on.

Time is an interesting topic in that it is a non-tangible item. We cannot ‘see’ half an hour or ten seconds; we cannot hold it in our hands or measure it directly as we can with other measurement activities such as measuring length, area, volume, capacity or mass.

The development of understanding of the various aspects of time may be gradual. We would not, for example, consider teaching the telling of time to the nearest five minutes if the students cannot tell the time to the halfhour. We would also not consider using a stopwatch to time a particular event if the students did not have a ‘feel’ for how long one minute, five minutes, or even one second is.

In the early years, students may use arbitrary units to measure duration; for example, how many claps it will take to put some books on a shelf.

Later, students may make their own timing devices such as water clocks, candle clocks and tockers. Eventually the need for a standard unit of time, and the ability to measure this accurately, will lead to timing events using minutes, seconds, a stopwatch etc.

We have decided to produce two separate Time matters books, as the topic is more extensive than we first realised. The first book looks at teaching aspects of time for Foundation through to Year 3. The second book takes these ideas and continues them through from Year 4 to Year 6.

Because there are many aspects of time that are important for all year levels, there are sections in this book that are also in the first book.

The Australian Curriculum has expectations in the teaching of time from Foundation through to Year 6. All of these content descriptions have been addressed in the two books.

Time matters Book 2 (Years 4–6)

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Curriculum Links Description Compare and order the duration of events using the everyday language of time (ACMMG007)

Foundation Connect the days of the week to familiar events and actions (ACMMG008)

Tell time to the half-hour (ACMMG020)

Year 1 Describe duration using months, weeks, days and hours (ACMMG021)

Tell time to the quarter-hour, using the language of ‘past’ and ‘to’ (ACMMG039)

Year 2

Name and order months and seasons (ACMMG040)

Use a calendar to identify the date and determine the number of days in each month (ACMMG041)

Year 3

Tell time to the minute and investigate the relationship between units of time (ACMMG062)

Convert between units of time (ACMMG085)

Year 4 Use am and pm notation and solve simple time problems (ACMMG086)

Year 5

Compare 12- and 24-hour time systems and convert between them (ACMMG110)

Year 6

Interpret and use timetables (ACMMG139)

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5

Time matters Book 2 (Years 4–6)

Issues to Consider Time is an intangible – it can be measured, but not actually seen. We can think of it as an ‘invisible’ measure. You cannot ‘see’ ten minutes or one hour. You cannot feel it or hold it.

T Much of the teaching about time can be incidental, especially in the early years. Teachers can refer to the time of day frequently, with such statements as, ‘It’s nearly 12 o’clock, almost lunch time’.

Students need to be aware that there is no ‘zero o’clock’. Also, there is no 60-minute place on an analog or digital clock.

ime is not decimal

Time is one of the few measures that is not decimal. It uses many different bases: 60 (seconds in a minute; minutes in an hour), 24 (hours in a day), 7 (days in a week), 4 (weeks in a month), 52 (weeks in a year), 12 (months in a year), 365 (days in a year), 366 (days in a leap year). The only base ten units are 10 years in a decade, 10 decades in a century and 10 centuries in a millennium.

Although most measures of time are not decimal, timing of some sporting events can go into tenths or hundredths of a second. For example, in Olympic running or swimming events, the difference between the first and second places may be as little as 0.03 of a second.

These times are also recorded in decimal format, e.g. Australian Robert Hurley won the men’s 400 metres freestyle race at the World Shortcourse Championships in August 2010 in a time of 3:41.58; that is 3 minutes and forty-one point five eight seconds. The 0.58 is 58 hundredths of a second.

This is a strange mix of Base 60 and decimal.

Writing of time in a mathematical context should use a colon between the hours and minutes; for example, twelve o’clock should be 12:00 not 12.00. This helps emphasise the fact that time is not decimal.

U

The word ‘minute’ has several meanings. It can mean something that is very small. It can also be one-sixtieth of an hour or a measure of a very small angle (one-sixtieth of a degree). The first meaning is pronounced differently, but spelt the same. They are related in that the two measures are very small (i.e. they are minute).

T

There have been attempts to introduce a decimal time system. See Metric time on page 132.

Time matters Book 2 (Years 4–6)

se of fractions

There can be confusion when fractions are used for segments of time, e.g. 3.25 hours is not 3 hours and 25 minutes but 3 hours and 15 minutes, as 0.25 indicates a quarter, and one quarter of one hour is 15 minutes.

Also, we can have 0.75 of an hour, which is 45 minutes (3/4 of an hour); this can be confusing as there are less than 75 minutes in an hour.

ime is relative

Time is quite subjective. Five minutes can seem like a long time if you are waiting for something good to happen, but seems to be over in no time at all if you are engaged in something really interesting or exciting.

This makes estimation of time quite difficult, even for adults.

Time is also subjective in terms of how long a time period is compared to how long a person has lived. For example, six months is one eighth of the life of a four-year-old; but only a small portion (one seventieth) of the life of a 35-year-old.

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Issues to Consider

M

ore than reading clocks

W

hat is a clock?

‘Time’ is not just about telling the time and reading clocks, although that is important. It incorporates many other important aspects including sequencing; the duration or passage of time; time passed and time still to come; calendars, days of the week, months of the year etc.; time lines, and geographical position and its relationship to time.

There are two basic elements in any clock:

• It has a repeated, regular, constant action or process that marks off equal periods or increments of time.

• It has a way of keeping track of periods of time and displaying the result.

P

rerequisites

A

dual system

A

nalog clock issues

Early understanding of time concepts will encompass many activities that are not obviously about time. For example, children need to know concepts such as clockwise and anticlockwise (also known as counterclockwise), be able to count to twelve, have experience with the use of spinners and be exposed to rhythmic patterns. As they progress to reading clocks to the nearest 5 minutes, they will need to be able to count by 5s. In order to read a digital clock, they need to be able to count and understand numbers to 60.

Roman numerals 1 to 12

1 2 3 4 5 6 7 8 9 10 11 12

I II III IV V VI VII VIII IX X XI XII

To facilitate children’s understanding of the connections between reading analog and digital clocks, it is recommended that both types of clocks be present in every classroom.

Some analog clocks have two hands (hour and minute) and others three (hour, minute and second). There are even some that only have the hour hand, and readers have to estimate the minutes according to the position of the hand between two hour markings.

Teachers need to be careful when choosing clock faces to teach telling the time. It is better to have dials where the hour hand moves in relation to the minute hand (geared clocks). For example, if a clock is showing 7:30, the hour hand should be half way between the 7 and the 8.

Analog clocks are one of the few situations nowadays where Roman numerals may still be used. Another place students may see Roman numerals is in dates, e.g. the year a movie was made. Generally, it is better to avoid analog clocks that use Roman numerals when students first learn to tell the time.

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Time matters Book 2 (Years 4–6)

Issues to Consider

S

aying/Stating the time

Children may hear various alternatives when telling the time, for example, 2:35 could be said as two thirty-five or twenty-five to three. We would recommend that teachers only use the former, but we need to be aware that children may be exposed to both forms. Our recommendation is that the only occasion where ‘something to’ is used is with ‘quarter to’, as this may be an early introduction to reading time to the nearest half-hour and quarter-hour.

1

2-hour and 24-hour time

Many digital clocks have a 24-hour display, or an option to use 12-hour or 24-hour time. For children still coming to terms with basic telling the time, the 24-hour clock is an added problem. There are many adults who may interpret, for example, 16:45 as 6:45 pm rather than as 4:45 pm.

Even in 12-hour time, there are several ways to express a particular time; see example at the bottom of the page. In 24-hour time we could add 0315 or 1515 depending on whether it was morning or afternoon.

V

erbalising 12-hour and 24-hour time

The spoken time reflects the written digital time, e.g. in 12-hour time format, 11:28 would be said as eleven twenty-eight, not twenty-eight minutes after/past eleven. The time 7:31 would be said as seven thirty-one, not twenty-nine minutes to eight, or thirty-one minutes after/past seven.

With times such as 11:05, whether we say oh instead of zero or whether we verbalise the zero at all depends on community practice. However, the zero must be used in the written form. When ‘am’ and ‘pm’ are used, they are simply spoken as the letters am or pm.

When using the 24-hour time format, times on the hour generally are said as ‘hundred’, e.g. 1100 would be eleven hundred and 0500 would be zero five hundred. Other times with a zero at the end would be spoken in tens, e.g. 1120 would be eleven twenty and 0530 would be zero five thirty or oh five thirty.

If telling time to the nearest second, it would be written as, for example, 0530 and 22 seconds, and said as zero five thirty and twenty-two seconds or oh five thirty and twenty-two seconds.

3:15 fifteen minutes after three

Time matters Book 2 (Years 4–6)

three fifteen

8

quarter past three

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Issues to Consider

T

he calendar

The calendar we use is not the only one in current use in the world.

For example, there is an Islamic calendar in which the 12 months have different numbers of days to ‘our’ standard one. The Balinese have two parallel calendars that are both different again; one has 12 lunar months (Sasih), where each month begins on the day after the full moon; and the second (Pawukon) where there are six months in a year, 35 days in a month and 210 days in a year.

L

Reiterating the difficulties faced with the use of decimals for timing; the time of 3:41.58 would need another 0.42 of a second to become 3:42, not 0.02 of a second (i.e. hundredths of a second, not Base 60). This is another very good reason to use the colon to separate the hours and minutes, and help avoid confusion.

When doing calculations involving the time of day, the way that causes less trouble to students is to do them mentally— maybe jotting down part-calculations as you go.

ater is longer

Young children find it confusing when asked to compare the times of events, if one event begins before the other. They will often choose the ‘longer’ duration according to the finish time rather than the total time.

For example, if one train trip goes from 2:15 to 3:00 and another goes from 2:30 to 3:05, children will often believe that the second trip is longer because it finishes 5 minutes later than the first, whereas in fact the first trip is longer as it takes 45 minutes while the second trip takes only 35 minutes.

A

rbitrary measures of time

M

easuring time

We can use arbitrary or standard units of time. When timing actions we can use units such as heartbeats, claps, pendulums, the amount of time it takes to fill a jug with water etc. The standard units are seconds, minutes, hours etc.

Time can be measured using a variety of instruments, from stopwatches for small passages of time and calendars for medium passages of time, through to measures of lunar and solar motion for long durations of time.

C

alculations with time

Calculations of time difference can be quite difficult because of the non-decimal nature of time. For example, if using a timetable and calculating how long before the next bus, a calculator may actually hamper the process. If the bus arrives at 4:25 and it is currently 3:47, you cannot simply key 4.25 into a calculator and subtract 3.27; the result would be 0.78, which a child could incorrectly interpret as 78 minutes. In this case, the number of minutes until 4:00 would be calculated first (from 3:47 to 4:00 is 13 minutes), and the extra 25 minutes until the desired time (4:25) added to give a total waiting time of 38 minutes.

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Time matters Book 2 (Years 4–6)

Issues to Consider Calculations of durations other than hours and minutes are also difficult due to the non-decimal nature of time. For example, when working with a calendar, if a child is asked in late February how many days until Anzac Day, the calculation needs to take into account the total number of days in February, the number of days left in February, the number of days in March, add them together and then add the 25 days into April when Anzac Day occurs.

Events linked to the sun and moon will vary according to the time of year. For example, the times for sunrise and sunset will vary day-to-day and month-to-month. They will also vary according to the geographical position; for example, sunrise in Broome will be quite different to sunrise in Albany on the same day. Also, sunrise will be a different time for places in different states, according to where they sit in the World Time Zones.

The date for Easter each year is determined by phases of the moon. Easter Sunday occurs on the first Sunday after the Paschal Full Moon (PFM) following the Northern Hemisphere’s Vernal Equinox for the year. It is always one of the 35 dates from 22 March to 25 April.

In Australia, most states switch to Daylight Saving Time in summer, but not in Western Australia, Northern Territory or Queensland. This means that a city such as in Tweed Heads in northern New South Wales can have the same time as another city in southern Queensland, such as Coolangatta, for some of the year, but be one hour different when NSW moves into Daylight Saving Time and Queensland doesn’t.

Time matters Book 2 (Years 4–6)

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Time Equivalents Students need to recognise and recall time equivalents.

The generally used conversions are:

They also need to be able to convert between them.

60 seconds (s)

=

1 minute (min)

60 minutes

=

1 hour (h)

24 hours

=

1 day

7 days

=

1 week

2 weeks

=

1 fortnight

52 weeks 1 day

=

1 year

52 weeks 2 days

=

1 leap year

365 days

=

1 year

366 days

=

1 leap year

12 months

=

1 year

10 years

=

1 decade

100 years

=

1 century

1000 years

=

1 millennium

As measures of time are not generally in Base Ten (i.e. they are not decimal), conversion from one measure to another can be problematic.

For example, if we want to know how many minutes there are in 41⁄2 days, we need to undertake a number of small calculations.

1. There are 24 hours in a day, so there are 4 × 24 hours in 4 days. This is 96 hours.

2. There are 12 hours in half a day. We need to add this to the 96 hours, giving us 108 hours.

3. There are 60 minutes in an hour, so there are 108 × 60 minutes in 4½ days. This is 6480 hours.

So there are 6480 minutes in 41⁄2 days.

Generally, the bigger the time gap for the units of time being converted, the greater the number of small calculations to be done.

P

ut in order

A

pplication

Put a number of different time periods onto individual cards, and students place them in order from the shortest to the longest time period.

• Have I been alive for one million seconds?

• A dragonfly usually lives for about 2688 hours. How many days is that?

How many weeks? How many months?

Students may use the internet to create problems that involve different time periods and time conversions.

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Time matters Book 2 (Years 4–6)

Likely Difficulties with Time This section is designed for students who are experiencing some difficulty with time concepts. It is not designed for students with severe learning difficulties.

One of the issues with teaching time is that there is often little consensus within a school as to the progression of how time is taught. For example, should you teach analog or digital time first, or team them together? This lack of consensus can cause issues when trying to enlist parental support for the teaching of time concepts.

In this book we have specified a sequence and language for teaching time that we believe should remove some of these issues.

Consider that time includes the idea of a point in time that may be measured and the duration of a time period (elapsed time) that may also be measured. Each may involve scale or dial reading and possibly some conversion.

We have grouped the main issues with developing time concepts into some basic groups.

T

he language of time

The language related to time concepts can be a little loose. For example, lunchtime for one person may be twelve noon, whereas someone else may not each lunch until two o’clock, so it is not a ‘fixed time’. Words such as ‘earlier’ and ‘later’ need some sort of qualifier. How much earlier? or How much later? When we say it is ‘nearly’ or ‘about’ a certain time, that involves some sort of judgement or estimation.

Some students cannot read the visual clues associated with time. An example of this is the writing of digital time without a colon to separate the parts (in a mathematical context).

N

umber skills

S

cale or dial reading

Initially, students will need to be able to count to twelve and later to sixty by ones, and then by fives. Students will require some basic fraction knowledge, particularly ‘quarter’ and ‘half’.

Reading a scale on a circle is not an easy task. Realising that the 1 on the scale may represent 5 and that 2 represents 10 is an extremely difficult concept. Digital clocks present some issues as well, including the need to read numbers to 59 and interpreting what 00 means.

Clearly there is quite a bank of knowledge that students must possess before they can tackle the intricacies of telling the time.

Some of the sidebars included in this publication are designed to alert teachers to likely difficulties and offer suggestions for overcoming these difficulties.

Time matters Book 2 (Years 4–6)

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The Language of Time Remember, a student might use a word but not really understand what it means. Encourage students to explain what a word or phrase means.

Where possible ask the students to write the word and use the word or phrase in a sentence.

The most common beginning for a story, particularly a fairy story, is ‘Once upon a time …’

It is important that students are ‘tuned in’ to the topic of time. One way to do this is by focusing on the language associated with time. There are several groups of words or time-related phrases that may be used.

1

Time phrases There are many phrases that are used that relate to time and timekeeping. Here are a few that include the word time: • One day at a time

• Like a ticking time bomb

• On time

• No time like the present

• Time’s up

• Double time, time and a half, half time

• Time flies when you are having fun

• Doing time

• Time drags

• A timely event

• Time flies

• (To be) time poor

• From time to time

• Wouldn’t give the time of day

• Waste time • Time’s a wasting • Killing time • Passing the time of day

• Time to kill • Marking time • Before time began

• A time of peace (or war) • Spend your time wisely • Third time lucky • I made it to the BIG time • The time of your life • Time out • Time is of the essence • Time well spent • Saving time • In the nick of time • No time to lose • Running out of time • Find the time to …

• It is just a matter of time • Time is on your side • Time is against us • Take time to smell the roses • Time after time • Time marches on

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Time matters Book 2 (Years 4–6)

The Language of Time

2 3

Clock phrases Here are others that refer to clocks: • Watching the clock

• (Rock) around the clock

• Clock on; clock off

• Beat (against) the clock

• Clock-watcher

• Race against the clock

Relate to more specific times • Once upon a time

• In a jiffy

• In the blink of an eye

• On the hour

• In a minute

• The hour is nigh

• Got a minute?

• His/her finest hour

• Wait a minute

• Red letter day

• Just a minute

• From day to day

• Spare a minute

• Take it one day at a time

• It will only take a second

A proverb is a short saying (phrase) that aims to convey a particular belief.

A stitch in time saves nine refers to the act of fixing something quickly before it needs more comprehensive repairs.

So, if we don’t make a small mend in a torn garment straight away, we may have to do a lot more sewing (stitches) as the tear gets larger.

4

Proverbs Ask the students to try to explain what is meant by the following proverbs. There are several websites that you may use to search for the origins of proverbs or find more. Here are just a few: • A stitch in time saves nine • A watched pot never boils • Time heals all wounds • It is never too late • There is a time and place for everything • Only time will tell • There is always a first time (There is a first time for everything) • Procrastination is the thief of time • Strike while the iron is hot • The early bird catches the worm • Carpe Deim (seize the day) • Time and tide wait for no man (or woman)

Time matters Book 2 (Years 4–6)

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Language Abbreviations For interest Some time spans are so long that they are referred to as periods.

For example, scientists refer to the Jurassic Period when dinosaurs roamed the earth.

A

• All symbols are written in lower case, e.g. hr, min etc.

• The plural forms (add ‘s’) are used with the unit names, but not with symbols. For example: two minutes, but 2 min; 5 seconds, but 5 sec.

• There is always a gap between the numerical value and the unit, for example 3 hr, not 3hr.

There are many abbreviations associated with time. Here is a sample:

am pm yr h (or hr) min s (or sec) BC BCE

Conventions for abbreviations

• We do not use a full stop after measurement abbreviations, unless it is at the end of a sentence.

bbreviations and acronyms

AD CE GMT UTC

L

ante meridiem (Latin for before noon or midday) post meridiem (Latin for after noon or midday) year hour minute second Before Christ Before our common era. Often used in preference to BC Anno Domini (Latin for year of our Lord).

This book was first published in 2015 AD Common Era. Often used in preference to AD Greenwich Mean Time Coordinated Universal Time

engths of time

Write the following lengths of time on card and ask the students to order them from the shortest to longest time period.

Second, minute, hours, day, week, fortnight, month, year, decade, century, millennium (epoch, era, aeon or eon).

Once the students have agreed on the order, ask them to suggest some other words that might fit at either end or between the words. For example, millisecond could be place before second, season between month and year.

According to Wikipedia, we are currently living in the Holocene epoch of the Quaternary period, of the Cenozoic era, of the Phanerozoic eon.

V

ery long times

Aeon (eon) means ‘an age’. In geological terms, it is generally considered to be around a billion years; the largest of the time divisions.

An epoch is a geological time span based on rock layering, usually measured in millions of years.

An era is a commonly used word for a long period of time. Geologically it is a clearly defined length of time such as the Mesozoic era.

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Time matters Book 2 (Years 4–6)

Children’s Literature There are a number of children’s storybooks that can be used as an introduction to lessons on time. Here we focus on just five of them.

Clocks and more clocks lends itself to problem solving, where the children work out why the times are different for each room, and by how much.

•

Clocks and more clocks

by Pat Hutchins (1974) This tells the story of Mr Higgins, who buys a new clock only to find that the time it shows is different to the time shown on another clock in a different room of his house. He continues to buy more clocks until the Clockmaker helps him work out why the times differ.

•

The very hungry caterpillar

by Eric Carle (1970) This very popular book tells the tale of a caterpillar who munches his way through various snacks, each on a different day of the week.

•

The bad tempered ladybird

by Eric Carle (1977) A bad-tempered ladybird takes on challenges against other animals, each taking place at different times of the day. The time of each event is shown on analog clocks.

•

Tick tock

by James Dunbar (2004) This is less a storybook, and more a book of interesting facts related to time. It provides an opportunity to talk about units of time such as seconds, minutes, hours, days, weeks, months, years, decades and seasons. It also gives examples of timing in the two forms: time passed and time still to come. It has excellent pictures that illustrate many of the unusual facts presented.

Children could be encouraged to write their own stories • A day in the life of …

•

Year on our farm

by P Matthews and A McLean (2002) This book illustrates months of the year and the four seasons in a distinctly Australian setting. So instead of January being illustrated by snowmen and sled rides, it shows a hot farmyard.

• Choose key times in the day, and write and illustrate the story.

• A group of children write a page each for a story with a set order.

• Groups of children write a serial by each group undertaking a chapter.

Time matters Book 2 (Years 4–6)

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Children’s Literature

•

A week of birthdays Monday’s child is fair of face, Tuesday’s child is full of grace, Wednesday’s child is full of woe, Thursday’s child has far to go, Friday’s child is loving and giving, Saturday’s child works hard for a living, But the child that is born on the Sabbath day, Is bonny and blithe and good and gay.

•

My shadow

by Robert Louis Stevenson I have a little shadow that goes in and out with me, And what can be the use of him is more than I can see.

He is very very like me from the heels up to the head; And I see him jump before me, when I jump into my bed.

Robert Louis Stevenson is best known as the author of Treasure island, Kidnapped and The strange case of Dr Jekyll and Mr Hyde.

The funniest thing about him is the way he likes to grow – Not at all like proper children, which is always very slow; For he sometimes shoots up taller like an india-rubber ball, And he sometimes gets so little that there’s none of him at all.

He hasn’t got a notion of how children ought to play, And can only make a fool of me in every sort of way.

He stays so close beside me, he’s a coward you can see; I’d think shame to stick to nursie as that shadow sticks to me!

One morning, very early, before the sun was up, I rose and found the shining dew on every buttercup; But my lazy little shadow, like an arrant sleepy-head, Had stayed at home behind me and was fast asleep in bed.

Source: The golden book of poetry (1947)

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17

Time matters Book 2 (Years 4–6)

Time Related Displays These ideas are designed to ‘tune students in’ to the language and concepts to be developed in a unit of work or series of lessons on time.

To build appreciation for the topic of time, displays (teacher or student made) can be created to focus on an aspect of time. Here are some suggestions.

I

n the olden days

Choose a time period—e.g. 100 years ago—and compare and contrast different fashions, inventions etc. For example, mobile phone versus telegraph/telegram.

C

locks, clocks and more clocks

Create a display of real clocks and pictures of clocks (an image search will help). Aim to add different clock faces, shapes and types of clocks to the display.

P

ast, present, future

Drawings, photographs or objects may be placed in one of three sections. For example, transport may be horse and cart, aeroplane, and spaceship. Alternatively, use yesterday, today and tomorrow.

T

ime mobile

Use time mobiles to display connected ideas such as hour, minute, second and millisecond.

W

ord wall

B

ook/Poem display

W

orld records

Words and phrases may be added to a word wall. For example, ‘In the nick of time’, ‘save time’ and ‘waste time’. See section on words and phrases for further ideas, pages 13 and 14.

Make a book display of time related books, e.g. Pat Hutchin’s Clocks and more clocks. For a list of time related literature see page 16.

Use the Guinness book of world records or the internet to research time-related world records. Illustrate them and make a display. At the time of writing, the world record for eating a 30-centimetre pizza with a knife and fork was just over 41 seconds!

Time matters Book 2 (Years 4–6)

18

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Days of the Week Students need to be aware that there are 7 days in a week. They should know the names of each of them, and the order in which they occur.

Students need to be aware that a week is a period of 7 days, and it may be, for example, from a Wednesday to the following Tuesday. So we can talk about ‘a week from Wednesday’.

They should also be aware that there are about 4 weeks in a month.

Students need to be fluent in reciting the days of the week, and know what day comes before or after a named day.

It is useful for students to know the common abbreviations for each of the days:

Sun. Mon. Tues.

Wed. Thurs.

Fri. Sat.

Discuss the types of things that students do during and after school on different days of the week. A one-week chart could be set up. Regular events that happen for students on weekends could also be included.

This could lead to a discussion about the fact that there are some activities that happen on a regular basis, and others that vary from week to week.

Mon.

Tues.

Wed. Science

Thurs.

Music

Library

Phys Ed

Emma: dancing class

John: piano Jean: Bella: lessons picked up swimming after school lessons by granny

Fri.

Sat.

Sun.

Tim: swimming lessons

Nat: netball

Assembly Sport

Barry: football

Jane: T-ball Ron & Josh: Little athletics

Students could make and illustrate a poster of what they did the previous weekend.

What I/we did last Saturday

What I/we did last Sunday

Note: a third column could be added for ‘what I plan to do next Saturday/ Sunday.

S

pecial days

Students could be encouraged to look for special days that always fall on the same day of the week, e.g. Good Friday, Easter Sunday, Queen’s Birthday (always a Monday long weekend) etc. Other holidays are taken on the day they fall, e.g. Christmas Day, Anzac Day etc. In many instances, if they fall on a weekend, the holiday is taken on the following Monday.

Students could investigate what day of the week these events occur for the particular year, and discuss what day they might be next year or what day it was the year before. This may be affected by the occurrence or otherwise of a leap year.

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19

Time matters Book 2 (Years 4–6)

Days of the Week Origins of the names of the days of the week

Sun. Mon. Tues.

Wed. Thurs.

Fri. Sat.

I

nvestigation • Students could investigate where the names of the days of the week are derived. Note: that they are taken from Norse mythology.

Sun’s Day Moon’s day Norse god Tyr Norse god Wodan Norse god Thor

O

Norse god Frig Saturn’s Day

Saturday was originally the start of the week, but was changed to Sunday.

The Greeks also named their days of the week after the sun, moon and the five known planets.

The recommended form for writing the date is 25 April 2015; this can be shortened to 25.4.15 or 25/4/15.

Many forms require the use of two digits for the date and the month, so our example would appear as 25.04.15 or 25/04/15. Note, the use of ordinal numbers is oral but not written; in our example, we would say ‘The twenty-fifth of April 2015’, but we don’t write it as ‘25th April 2015’. In Australia, writing the month before the date is not encouraged, so we don’t put April 25, 2015, 04.25.15 or 04/25/15.

f interest • Different countries have experimented with weeks of different lengths. The Republican Calendar in France (1793) had a ten-day week. The seven-day week was re-established in 1801.

• From 1929–1931, the Soviet Union tried a five-day workweek. There were 72 weeks in a year, plus 5 additional national holidays; making 365 days in a year. In 1931, they changed to a 6-day week. Every 6th day was a state rest day. They kept the 5 national holidays; but to retain the 365 days in a year, there were some weeks that had 7 days and some with 5. A seven-day week was re-introduced in 1940.

E

arlier calendars

Students could investigate early calendars used in the Baltic region (9-day week); also Celtic calendars (number of days varied); and Chinese, Japanese and Korean (10-day weeks).

Note: there is an international standard The ISO 8601 date order with fourdigit years: YYYY-MM-DD (introduced in ISO 2015), is specifically chosen to be unambiguous. The ISO 8601 standard also has the advantage of being language independent and is therefore useful when there may be no language context and a universal application is desired (for example, expiration dating on export products). Many Internet sites use YYYY-MM-DD, and those using other conventions often use -MMM- for the month to further clarify and avoid ambiguity (2015-MAY-09, 9-MAY2015, MAY 09 2015 etc.).

Time matters Book 2 (Years 4–6)

20

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Months of the Year Students need to be aware that there are 12 months in a year. They should know the names of each of them, as well as the order in which they occur.

They should also be aware that there are about 4 weeks in each month, and that the number of days in a month may be 28, 29, 30 or 31.

Students need to be fluent in reciting the months of the year, and know what month comes before or after a named month.

It is useful for students to know the common abbreviations for each of the months:

Jan. Feb. Mar. Apr. Aug. Sep. Oct. Nov. Dec. It is best to avoid abbreviations for the months that have four or fewer letters (May, June and July).

Much of the teaching of the names of the months of the year would be incidental. For example, as part of a morning routine, the date would be recorded, and this would be a good time to discuss what month it is, what month it will be next, what month it was previously etc. It also offers the opportunity to record it as a digit (e.g. 11.10.15) or in the abbreviated form (11 Oct 2015), as well as using the full word (11 October 2015).

Discussion can take place about special days that occur in certain months: • In which month does Christmas fall?

• In which month is Anzac Day? • Australia Day is in …?

Students could be encouraged to work out how many more months there are until a certain event, or how many there have been since a particular event: • How many more months is it until Easter?

• How many months ago was the sports carnival?

• Ben’s birthday is in April. How many months away is that?

O

rigin of names of months

H

ow many days in each month?

Students investigate the origin of the names of the months. Ask questions such as: Why is it that September is the 9th month when ‘sept’ indicates the number 7? What about October (‘oct’ for 8); November (‘nov’ for nine) and December (‘dec’ for 10)?

The verses below can be used to recall the days in each month.

Thirty days have September,

Thirty days hath September,

April, June and November.

April, June and November.

February has twenty-eight;

All the rest have thirty-one;

And thirty-one the others date.

Excepting February alone,

But if a leap year to assign,

Which has twenty-eight days clear,

Then February twenty-nine.

And twenty-nine in each leap year.

By clenching both fists alongside each other, the days in all the months can also be recalled by checking the knuckles and the gaps as shown in the diagram.

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21

J MMJ

AO D

F A J

S N

31 days 30 days or less

Time matters Book 2 (Years 4–6)

Seasons A mobile showing the seasons of the year can be made using a strip of card, staples and fishing line or string. Fold the paper strip into 4 equal pieces.

The children can label each of the segments, and illustrate each season on the mobile. The card can then be stapled to make a loop, and suspended using the fishing line or string.

Generally it is accepted that there are 4 seasons in a year: summer, autumn, winter and spring. However, some tropical areas have only 2 distinct seasons: a wet or rainy season; and a dry season. Teachers need to adjust the activities on seasons according to their local situation.

Many Aboriginal cultures have different ways of breaking up a year into seasons. For example:

ING

• The Yolngu people of the Northcoast identify six seasons • The Anangu Pitjantjajara people of central Australia identify five seasons

Sort class birthdays into seasons.

• The Noongar people of the Southwest coast identify six seasons

• Which has the least?

• Which season has the most birthdays?

• How many seasons are there?

Discussion can take place about the type of weather we can expect in each season: • In which season do we get the most rain?

• Which season is the driest?

• Our hottest days are usually in …?

Many sports are seasonal. For example, football and hockey are usually winter sports, and cricket and baseball are usually summer sports. There are other sports that are played all year round, e.g. tennis, golf, basketball etc.

Students could collect data on the above and graph the results.

Time matters Book 2 (Years 4–6)

22

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The Calendar A number track can be constructed for each month. This may precede a formal monthly calendar.

Children need to be aware that different calendars have different ways of showing each month, or the whole year.

September 1

3 4 5 6 7 10 11 12 13 14 17 18 19 20 21 24 25 26 27 28 31

Su M Tu W Th F Sa

3

4

5

6

7

8

9

29

Jan. July

Feb.

Mar.

Kim

Roy

Aug.

Sept.

Apr.

May

June

Oct.

Nov.

Dec.

Other events can be added to the calendar as they arise; for example, national holidays such as Anzac Day, Easter and Christmas, school holidays and excursions etc.

4

11

18

25

6

12

19

26

6

13

20

27

7

14

21

28

1

8

15

22

29

• How many Sundays are in this month?

2

9

16

23

30

• On what day of the week does Anzac Day fall this year?

3

10

17

24

For reasons of space, some calendars show the final days in the month at the beginning of the month. This can be very confusing for young children, and may need to be explained. See example below:

30

A classroom calendar can be set up, and all the children’s birthdays written in. This can take the form of a frieze along the wall.

Su M Tu W Th F Sa 1 2 8 9 15 16 22 23 29 30

2

Discussion can take place about the abbreviations for the months of the year.

Investigate the variation in the number of days in each month. Ask questions such as:

• What will be the date two weeks from now?

• The interschool carnival is on 17 April. What day of the week is that?

P

roblem

A

blank calendar

If you have a tea towel with this year’s calendar on it, how many years will it be before it is relevant again?

Su M Tu W Th F Sa 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Two other forms of calendars students may encounter are desk calendars, where a page for each day is turned over, and electronic diaries (e.g. on smart phones or tablets).

It is useful for students to consider how the dates/days are arranged on a calendar for each month. Looking at the different ways this is done is useful, but so is having a blank calendar and asking students to fill in the relevant details. This activity can also be used as an assessment tool to find out the level of understanding they have about the layout of a calendar. See the following page.

Research: finding out about the origins of the names of the days of the week and the months in a year are interesting projects (see page 20).

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23

Time matters Book 2 (Years 4–6)

Blank Calendar The teacher will let you know what month the calendar below is to represent.

Put the name of the month at the top, and fill in the days of the week along the first row.

Put the 1 for the first of the month in the correct place, and then fill in the rest of the days of the week. You need to make sure your month has the correct number of days.

You can now ask each other questions about the days in your particular month.

The month is Tues.

Time matters Book 2 (Years 4–6)

24

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Organising Your Time People use a variety of paper and electronic means to keep track of appointments and special events. Some events such as birthdays and anniversaries occur on the same date but different days each year.

National holidays occur on a specific date, whereas the date for Easter will vary from year to year. While the date for Easter may change, Good Friday will always fall on a Friday.

To manage time effectively involves planning. Students will be familiar with the typical classroom timetable so it makes sense to begin by reconstructing a school timetable.

The timetable may then be extended to include after school activities and weekend activities. (See template on page 26.)

Time

Mon.

Expose students to electronic diary programs on computers, tablets and phones. Discuss the idea of ‘syncing’ to make sure that appointments are not missed or two appointments are not set for the same day and time.

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Wed.

Thurs.

Fri.

Sat.

Sun.

MORNING TEA

LUNCH

Discuss the need for ‘down time’ when planning how to allocate time to complete tasks and for recreation.

Issues such as allowing ‘lead time’ for certain events and allowing enough time between ‘back-to-back’ appointments need to be discussed when planning a weekly/monthly diary.

Students will need a standard calendar to look up the dates for certain events. They should note that some dates such as Christmas Day are fixed, whereas others such as Easter move from year to year.

Tues.

AFTER SCHOOL

AFTER DINNER

After completing a weekly timetable, show how some events will repeat on a regular basis during the week (generally events that occur during the week), whereas some events will vary, e.g. weekend events such as attending parties.

A year planner will have a bearing on events that vary from week to week.

Students can use a perpetual year planner to help sort out key events in a year (see over). A standard calendar can be used to fill in weekends, special holidays and birthdays. Family holidays can be marked on the calendar and any other significant events such as weddings may be added.

25

Time matters Book 2 (Years 4–6)

Time

Monday

Time Tuesday

Time matters Book 2 (Years 4–6)

Lunch Break

Morning Break

Wednesday

26

After School

Afternoon Break

Time

Time Thursday

Time Friday

Weekly Timetable

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June

July

Aug.

Sept.

Oct.

Nov.

27

Dec.

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May

Apr.

Mar.

Feb.

Jan.

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

A year planner can be handy when looking at events that happen within a particular year, or it may be used as a perpetual calendar. The days of the week are not specified, but when the planner is updated for a particular year, you would generally shade in the Saturdays and Sundays so they stand out. As the number of days in each month varies, the planner has a possible 31 days, but the ‘impossible’ days are blanked out. These ‘impossible’ dates are 30 and 31 February and 31 April, June, September and November. February usually has 28 days, but in a leap year it has 29 days, so the 29 February is lightly shaded to allow for either possibility.

Year Planner

Time matters Book 2 (Years 4–6)

Telling the Time The term o’clock literally means ‘of the clock’.

S

ome basics

Students need to recognise the difference between clockwise and anticlockwise (also referred to as counter-clockwise). The hands on an analog clock turn in a clockwise direction. They need to know what clockwise means before they can tell the time accurately on an analog clock.

Students should be aware that the hour hand on an analog clock travels slowly and its movement cannot be seen; the minute hand travels more quickly and can sometimes be seen moving.

Students may use the term ‘quarter past’ and ‘quarter to’, and know that this is the same as the digital time of ##:15 and ##:45; e.g. quarter past ten is the same as 10:15, and quarter to two is the same 1:45.

It is important that students become aware that when it is quarter past or quarter to a particular hour, the minute hand is will be on the 3 (for quarter past) or 9 (for quarter to), and the hour hand will be a quarter of the way between two numbers on the dial for quarter past, and threequarters of the way between two numbers on the dial for quarter to.

It is recommended that the hands on a clock are always called the ‘minute hand’ and ‘hour hand’. This is preferable to calling them the ‘big hand’ and ‘little hand’, as this does not assist with students’ understanding of the function of the two hands. Later the ‘second hand’ may be introduced.

Writing the time

Also look for students who do not make the connections between ‘quarter past’ (e.g. quarter past 3) and ##:15 (e.g. 3:15); and not making the connections between ‘quarter to’ (e.g. quarter to 5) and ##:45 (e.g.

4:45).

Note: the hour given is different for digital and analog times for ‘quarter to’. In the example above, quarter to 5 is giving a different ‘hour’ time to 4:45.

We suggest that the use of ‘quarter to’ is the only time that students have the option of reading times as ‘to the hour’. When they learn to read the time to the nearest 5 minutes, or nearest minute, we recommend using the digital method; e.g. for 5:35, saying ‘five thirty-five’, not ‘twenty-five to six’.

A colon should be used to separate the hour from the minutes when writing the time in digital form in mathematical context, e.g. 2:00, 3:45 etc. This highlights the fact that time is not decimal.

We recommend that an analog and a digital clock be on display at the front of the classroom at all times so that students become familiar with both, and see different times in both formats.

Of interest In the Northern hemisphere, shadows cast by the sun move in a clockwise direction. Because of this, the hands on an analog clock were made to move in the same direction— clockwise.

Time matters Book 2 (Years 4–6)

28

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Telling the Time There is a ‘hierarchy’ of types of analog clocks to be read.

• A circular clock with all 12 digits shown.

• A circular clock with only 3, 6, 9 and 12 shown.

• A circular clock with no digits, but all 12 places shown.

• A circular clock with no digits, and only marks for the 3, 6, 9 and 12.

A

hierarchy of ‘telling the time’ skills When learning to tell the time, students pass through many stages.

These will include:

• Identifying the two hands on an analog clock: the hour hand and the minute hand.

• Counting to 12.

• Knowing the terms hour and minute; and later, seconds.

• Reading the time on the hour, and being able to place the hour and minute hands on a clock correctly to show the o’clock times.

• Other shaped clocks; e.g. square, rectangular etc.

• Recognising that the o’clock times on an analog clock appear as ##:00 on a digital clock; e.g. three o’clock on an analog clock is the same as 3:00 on a digital clock.

• Clocks using Roman numerals.

• Distributing the digits 1–12 evenly around a blank clock face.

• Understanding the concept of clockwise.

• Understanding about the fraction ‘one half’.

• Reading the ‘half-past’ times, and being able to place the hour and minute hands on a clock correctly to show the half-past times.

• Understand that, as the minute hand passes around the clock, the hour hand moves only a small distance. Being able to judge the distances the hour hand moves for times other than o’clock.

• Recognising that half-past times on an analog clock appear as ##:30 on a digital clock; e.g. half past five on an analog clock is the same as 5:30 on a digital clock.

• Distinguishing between morning (am) and afternoon (pm).

• Understanding about the fraction ‘one quarter’.

• Counting multiples of fives to 60.

• Reading the quarter past and quarter to times, and being able to place the hour and minute hands on a clock correctly to show these times.

• Recognising that when the minute hand moves from one digit to the next, five minutes have passed. Counting by 5s around the digits on the clock; thus understanding, for example that when the minute hand is on the 7, the time is ##:35, or 35 minutes after the hour.

• Counting by ones to 60.

• Recognising that quarter-past times on an analog clock appear as ##:15 on a digital clock; e.g. quarter past eleven on an analog clock is the same as 11:15 on a digital clock.

• Recognise that quarter-to times on an analog clock appear as ##:45 on a digital clock; e.g. quarter to eight on an analog clock is the same as 7:45 on a digital clock.

• Recognising that the hour shown on quarter to times is one more than that shown on a digital clock—quarter to seven is 6:45—and understand why this is the case.

• Reading time to the nearest five minutes, and being able to place the hour and minute hands on a clock correctly to show these times.

• Reading time to the nearest minute, and being able to place the hour and minute hands on a clock correctly to show these times.

• Understanding 24-hour time, and converting between 12- and 24-hour time.

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29

Time matters Book 2 (Years 4–6)

Telling the Time Identifying time related data and producing a graph using that data.

A discussion could take place about the types of clocks and watches we see. Where do we find digital time displays, especially in the home? For example, they are used on ovens, microwaves, DVD players, mobile phones, iPads™ and electronic tablets, cameras, computers etc. Where do we find analog clocks? These may be more difficult to identify, although clocks on buildings and many wall clocks are analog.

A couple of generations ago, watches were expensive items and rarely worn by children. The clockwork mechanisms were generally hand made, hence the expense. They were often given as a present on a special occasion, e.g. 21st birthday or retirement. With the electronic age, digital watches became more affordable.

W

atch graph

Students could be classified according to whether they wear a watch to school, and if so, whether it has a digital or analog time display. A class graph could be constructed with the data collected. The teacher provides a large sheet of light card, with three columns each divided into rectangles, and intervals up the y-axis. Using one colour, students who wear an analog watch each colour one rectangle in the first column, then students with a digital watch each colour one rectangle in the next column (using a different colour). Finally, students who are not wearing a watch colour one rectangle in the third column in a different colour. Label the graph and discuss the results.

Types of watches in our class 17 16 15 14 13 12 Number of students

Purpose

11 10 9 8 7 6 5 4 3 2 1 Analog

Digital Type of watch

None

Discuss the issue of watches that have both analog and digital displays • Do we add an extra column?

• Do we include it in both ‘analog’ and ‘digital’ columns (i.e. twice)?

Time matters Book 2 (Years 4–6)

30

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Telling the Time The one-handed clock can be used alongside a geared two-handed clock to show the movement of the hour hand as the minute hand travels a full circle around the clock.

O

ne–handed clock

This can be a useful device to help students understand that the hour hand does not remain static from one hour to the next. With a one-handed clock, students look at the hour hand and judge how far it has travelled between two digits, and can approximate the time to the nearest quarter hour or to the nearest 5 minute.

Geared clocks The hands on a geared clock move in the same way that a real clock does; that is if the time is four thirty, the hour hand points half way between 4 and 5, while the minute hand points to 6.

Small clocks with independently movable hands are available. When students use these make sure they position the hands in a similar way to a regular clock.

Write-on wipe-off clocks These generally include a clock face printed onto plastic. Students may then use whiteboard markers to draw in the hands.

Some of these clocks include a place to write the digital time.

About 4 o’clock.

T

Halfway between 10 o’clock and 11 o’clock.

A little bit past 2 o’clock.

elling the time to five minutes; then to the minute

Once the students are able to tell time to the quarter hour, they can proceed to telling the time to five minutes; and then to the minute. They need to be able to connect the analog and digital representations of all of these times.

A ‘five-minute clock’ can be introduced to help students make the connections between the digits on a clock face and five-minute intervals.

They could begin with counting by 5s around the clock as the teacher points to the hour digits. This is probably best used as an oral activity; asking students to tell the time at varying 5-minutes intervals.

Of course, students could make their own analog clocks; either on a paper plate, or on paper or light card that could be laminated.

Students practise writing and drawing times to the five minutes, then to the minute in both analog and digital form, converting between the two.

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31

Time matters Book 2 (Years 4–6)

Telling the Time With times such as 10:05, whether we say the oh instead of zero depends on community practice. However, the zero must be used in the written form. The time 10:05 makes sense—10:5 does not.

F

ive-minute time cards and one-minute time cards

On pages 33 and 34 there are time cards that the students can put in order; and then write the digital time under each of them.

11

12

11

1

10

2

9

3

8

11

6

12

2 3

8

11

6

12

2 3

Rounding the time

11

6

12

2

In most instances, we do not need to know the exact time, and we round it to the nearest 5 minutes. This is a skill that should be encouraged in students.

When using an analog clock with a second hand, students will be aware that is easy to see this hand moving around the clock, unlike the hour hand or even the minute hand.

am pm

3

8

11

6

12

2 3

8

4 7

T

6

5

3

11

1

10

2

6

12

3

8

4 7

6

5

12

11

5

2 3

11 3

6

1

4 7

4 7

12

8

2

8

3 5

10

1

10

2 4 6

9

5

9

1

10

1 3

6

12

5

9 7

2

11 2

9

12

3

6

8

4 7

1

10

3

8

2 4

11

1

10

1

10

5

9

5

12

5

9 7

2

6

6

8

4

11

1

4 7

9

12

10

12

8 7

9

5

3

10

3

11

1

5

9

5

8

4 7

3

11

1

10

2

6

2 4 7

2

6

1

8

4

11

1

4 7

9

12

10

12

8

12

10 9

5

10

7

9

5

6

9

5

8

4 7

3

11

1 3

11

1

8

2 4 7

2

6

11

1

8

4 7

9

12

10

12

10 9

5

9

5

10

3

6

8

4 7

2

11

1

10

11

1

4 7

5

9

12

10 9 8

4 7

6

12

5

1

10

2

9

3

8

4 7

6

5

o the nearest second

It is rare that we need to tell time to the second; but if needed, students need to be aware that the second hand is used for this. One example where we use the second hand on an analog clock is when timing an event that needs a high level of accuracy. See page 6.

ante meridiem post meridiem

From the Latin words meaning before and after noon (or midday).

When using am or pm, to avoid confusion, it is recommended that ‘noon’ (or ‘12 noon’) or ‘midnight’ (or ’12 midnight’) be used instead of 12:00.

The use of ‘am’ and ‘pm’ pertain to the digital form of time, and are generally not used with the o’clock form. For example, we would not say ‘quarter past two pm’, but ‘quarter past two in the afternoon’.

a

m and pm

Up until now, students have not formally distinguished between morning and afternoon using the am or pm notation, although they will realise that 11:00 in the morning is quite different to 11:00 in the evening.

Familiarity with the am and pm notation is an important prerequisite to reading 24-hour times.

Discussion could centre on what activities we do at certain times of day, and then decide if the times would be am or pm. Much of this could be treated informally.

B

lank clocks templates

For a sheet of blank clocks for practising drawing hands on an analog clock, see pages 35, 37 and 39.

For a sheet of blank clocks for practising writing times on digital clocks, see pages 36, 38 and 40.

For a sheet of blank clocks for practising writing analog and digital times, see page 41.

Another way to practise the skill of telling time to the five or one minute, both on analog and digital clocks, is to extend the games Clock bingo, Time concentration and Time dominoes to include appropriate times.

This should be in analog (using variations of pictures of analog clocks, and using words, e.g. six fifty) and in digital form (e.g. 6:50). See pages 49, 54 and 60 for these instructions for these games. Also see pages 53 and 65 for blanks for these games where the teacher or students can write in their own times. In doing this, you need to make sure that there are matching cards for each of the times used.

Time matters Book 2 (Years 4–6)

32

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Five-minute Time Cards Cut out the time cards below and place them in the correct order.

Write the times on each card to help you.

11

12

11

1

10

2

9

3

8

11

6

12

8

2 3

8

11

6

12

11 2

9

3

8

4 6

5

R.I.C. PublicationsÂŽ www.ricpublications.com.au

6

12

2 3

33

6

3 4

11

4 5

1

9

1

8

12

5

2

7

9

6

10

5

10

7

4

8

4

1

10

7

3 7

3

11 2

5

1

9

1

9

12

5

2

7

10

6

10

5

8

4 7

12

4

8

4

11

3

11 3

1

9

1

9

6

2

7

2

7

9

12

1

10

5

10

5

10

6

12

8

4

8

4

12

3

11 3

11

9

1

9

6

2

7

2

7

10

5

10

11

1

8

4 7

12

6

12

5

1

10

2

9

3

8

4 7

6

5

Time matters Book 2 (Years 4–6)

One-minute Time Cards Cut out the time cards below and place them in the correct order.

Write the times on each card to help you.

11

12

11

1

10

2

9

3

8

11

6

12

8

9

3

8

11

12

3

8

3

8

4 5

Time matters Book 2 (Years 4–6)

6

12

11

9

3

8

4 6

12

2 3 7

34

6

3 4

11

4 5

1

9

1

8

12

2

7

9

6

10

5

10

5

4 5

8

4

1 2

7

3

6

3

11 2

7

1

9

1

9

12

2

7

10

5

10

12

6

10

5

8

4

11 3

6

9

1 2

7

2

7

9

11

6

4 5

8

4

1

10

5

10

12

8

4

12

6

3 7

3

11 2

5

1

9

1

9

12

2

7

10

6

10

5

8

4

11

9

11

3

1 2

6

9 7

10

7

2

12

4 5

8

4

11

10

5

3

1

3

11

9

6

9

1 2

7

2

7

10

5

8

4 6

12

12

1

8

4 6

12

10

5

8

4

11 2

7

3

1

3

11

9

6

9

1 2

7

2

7

10

5

10

12

11

1

8

4 6

12

10

5

8

4

12

3

11 3

11

9

1

9

6

2

7

2

7

10

5

10

11

1

8

4 7

12

6

12

5

1

10

2

9

3

8

4 7

6

5

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Draw the Times Set 1: analog

11

12

11

1

10

6

11

12

11

(b)

6

12

11

12

(g)

1 2 3 4

7

5

quarter to nine

R.I.C. Publications® www.ricpublications.com.au

12

8

4 6

5

6

9

3 7

4

10

2

8

3

11

9

1

quarter to five

1

10

12

2

7

5

2:15

(c)

quarter past eight

8

4 6

6

9

3 7

5

10

2

8

4

11

9

(d)

(f)

1

10

3 7

5

half past ten

11

2

8

4 7

1

9

3

8

12

10

2

9

5

6

6:45

(e)

1

10

4 7

5

10:30

(a)

3

8

4 7

2

9

3

8

1

10

2

9

12

(h) 35

5

6

1:45 Time matters Book 2 (Years 4–6)

Draw the Times Set 2: digital

(a)

half past six

(e)

quarter past five

(b)

quarter to eight

(f)

quarter past six

(c)

quarter to one

(g)

quarter past two

(d)

quarter past eleven

(h)

quarter to four

Time matters Book 2 (Years 4–6)

36

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Draw the Times Set 3: analog – five minutes

11

12

11

1

10

(a)

6

12

(b)

12

9

11

12

(g)

9

(d)

twenty past one

12

1 2 3

8

4 7

5

eight forty

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6

9

4 6

4 5

10

3 7

3

11 2

8

2

7

1

10

1

8

5

11:55

(c)

12

9

4 6

2:10

10

3 7

5

6

11 2

8

4

(f)

1

10

3 7

5

twelve thirty-five

11

2

8

4 6

1

9

3 7

12

10

2

8

6

11

9

5

6:05

(e)

1

10

4 7

5

three twenty-five

11

3

8

4 7

2

9

3

8

1

10

2

9

12

(h) 37

6

5

10:50 Time matters Book 2 (Years 4–6)

Draw the Times Set 4: digital – five minutes

(a)

twenty past seven

(e)

nine forty

(b)

five past two

(f)

five thirty-five

(c)

twelve twenty-five

(g)

four fifty-five

(d)

ten past one

(h)

six fifty

Time matters Book 2 (Years 4–6)

38

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Draw the Times Set 5: analog – one minute

11

12

11

1

10

(a)

6

12

12

9

(c)

12

(d)

6

8:02

1 2 3

8

4 7

5

three eighteen

R.I.C. Publications® www.ricpublications.com.au

12

9

4 6

5

10

3 7

4

(g)

2

8

3

11

9

1 2

7

1

10

12

8

5

twelve thirty-three

11

6

9

4 6

5

10

3 7

4

11 2

8

3

(f) seventeen minutes past one

1

10

2

7

5

six forty-seven

11

1

8

4 6

12

9

3 7

twenty-six past nine

10

2

8

5

6

11

9

(b)

(e)

1

10

4 7

5

four fifty-two

11

3

8

4 7

2

9

3

8

1

10

2

9

12

(h) 39

5

6

5:59 Time matters Book 2 (Years 4–6)

Draw the Times Set 6: digital – one minute

(a)

nine forty-eight

(e)

nine past four

(b)

twelve thirty-seven

(f)

two fifty-one

(c)

twelve past seven

(g)

six twenty-four

(d)

one minute to two

(h)

one minute past five

Time matters Book 2 (Years 4–6)

40

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Blanks for Matching Times Draw the hands on the analog clocks and write the numerals in the digital clocks for each time.

11

12

11

1

10

2

9

3

8

11

6

12

8

9

3

8

11

12

11 2

9

3

8

4 6

5

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6

12

2 3 4 6

41

3 4

11

5

1

9

1

8

12

2

7

9

6

10

5

10

7

4 5

8

4

1

10

7

3 7

3

11 2

5

1

9

1

9

12

2

7

10

6

10

5

8

4 6

12

4 5

8

4

11 2

7

3

1

3

11

9

6

9

1 2

7

2

7

10

5

10

12

1

8

4 6

12

10

5

8

4

12

3

11 3

11

9

1

9

6

2

7

2

7

10

5

10

11

1

8

4 7

12

6

12

5

1

10

2

9

3

8

4 7

6

5

Time matters Book 2 (Years 4–6)

12- and 24-Hour Time The use of 24-hour time has become more prevalent as more people travel overseas and interstate. It is often used in airline, train and bus timetables to avoid confusion between morning and afternoon times. For example, 7 am is clearly different from 7 pm in 24-hour time (0700 and 1900).

1

2- and 24-hour comparisons

There are two graphics that can help students to compare or convert times from 12 to 24-hour formats. Both of these formats show the hours from 12 midnight (0000 in 24-hour time) to 11 pm (2300). For times that are not on the hour, the two digits for the minutes would replace the ‘00’ in the times, e.g. for 5:34 pm we would change 5 pm to 1700, then ‘add’ the 34 minutes, getting 1734 in 24-hour time.

1. Day/night comparisons

Converting between 12-hour and 24hour times can be difficult because of the non-metric nature of time. So 1630 is not 6:30 pm, but 4:30 pm. To convert 12-hour times past 12 noon to 24-hour time, we add 12 to the hour. So 6:15 pm + 12 hours gives us 1815. To convert 24-hour times past 12 noon to 12-hour time, we subtract 1200. So 1630–1200 gives us 4:30 pm.

When writing 12-hour time, we use a colon between the hours and minutes; for example, five o’clock should be 5:00 not 5.00. When writing 24-hour time, we generally do not use a colon, but use four digits; for example, 10:54 pm would be written as 2254. For times before 10 am, there is a zero at the start in 24-hour time in the written form; e.g. 0245 for 2:45 in the morning.

Whether we say ‘oh’ or ‘zero’ depends on community practice.

Note: some sources do use a colon in 24-hour time.

See page 44 for a full-page BLM of this.

2. Clock face format

When using the 24-hour format, times on the hour generally are said as ‘hundred’; e.g. 1300 would be thirteen hundred, and 0400 would be zero/oh four hundred. Other times with a zero at the end would be spoken in tens; e.g. 1540 would be fifteen forty and 0330 would be zero/ oh three thirty.

See page 45 for a full-page BLM of this, with a few exercises for students to complete.

Time matters Book 2 (Years 4–6)

42

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12- and 24-Hour Time Memory Game Purpose

A game for 2–4 players

Students will be able to practise matching times in analog and digital formats.

Use the two sets of cards on pages 46 and 47. Photocopy, enlarge and laminate the cards on two different coloured pages. Students shuffle each set of cards, and then place each set facedown on the table. Students take turns to flip over a card of each colour. If the 12-hour and 24-hour times on the two cards match, the student keeps the cards and has another turn. If they do not match, the cards are placed facedown again, but not shuffled. It then becomes the next student’s turn to flip one card of each colour and try to match them. The winner is the student who has the most cards when all have been matched.

To extend the game, two sets of cards could be used for each group.

A further extension would be for the teacher and/or the students to write their own matching sets of cards. A blank set is included on page 48, but remember that you will need two sets (one 12-hour and the other with matching 24-hour times), preferably copied onto 2 different coloured pages.

Zulu time The military use a version of 24-hour time called ‘zulu time’. Zulu is the NATO phonetic alphabet name for the letter z. Zulu time is also used in aviation. This is to ensure that pilots are all using the same 24-hour clock; thus saving confusion when flying across time zones. It is the same as Greenwich Mean Time (GMT), or Coordinated Universal Time (UTC), but not necessarily the same as the time in the United Kingdom because of daylight saving.

0059

9 :5

12 am

Of interest Reykjavik always uses UTC and does not have daylight saving. So zulu time is also always the same as the time there.

See page 133 for more on GMT and UTC.

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43

Time matters Book 2 (Years 4–6)

12- and 24-Hour Comparisons 12-hour clock

24-hour clock

12 am

0000

1 am

0100

2 am

0200

3 am

0300

4 am

0400

5 am

0500

6 am

0600

7 am

0700

8 am

0800

9 am

0900

10 am

1000

11 am

1100

12 pm

1200

1 pm

1300

2 pm

1400

3 pm

1500

4 pm

1600

5 pm

1700

6 pm

Time matters Book 2 (Years 4–6)

am

pm

1800

7 pm

1900

8 pm

2000

9 pm

2100

10 pm

2200

11 pm

2300 44

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The 24-Hour Clock The am hours are shown in the inner ring and the pm hours are shown in the outer ring.

12:01 am

0001

1:00

0100

2:00

0200

3:00

0300

4:00

0400

5:00

0500

6:00

0600

7:00

0700

8:00

0800

9:00

0900

10:00

1000

11:00

1100

12:00 noon

1200

23 11 22 10

24 12

1

13 2

21 9 20

14 3 15

8 19

7

4 6 18

5

16

17

1:00 pm

1300

2:00

1400

3:00

1500

4:00

1600

5:00

1700

6:00

1800

7:00

1900

8:00

2000

9:00

2100

10:00

2200

11:00

2300

12:00 midnight

2400

Example 1 What is 8:35 am in 24-hour time?

Look at the 24-hour clock. 8:00 am is shown as 0800, so 8:35 am would be shown as 0835.

Example 2 What is 8:35 pm in 24-hour time?

Look at the 24-hour clock. 8:00 pm is shown as 2000, so 8:35 pm would be shown as 2035.

1. Write the following 12-hour times as 24-hour times. (a)

3:00 am

(b)

5 pm

(c)

11:47 pm

(d)

12 noon

(e)

12:00 midnight

(f)

5:55 am

(g)

1:03 am

(h)

11:21 pm

2. Write the following 24-hour times as 12-hour times. (a)

1234

(b)

2345

(c)

1644

(d)

0059

(e)

0101

(f)

1127

(g)

2005

(h)

0713

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45

Time matters Book 2 (Years 4–6)

12- and 24-Hour Memory Game Set 1

9:50 am

8:33 pm

4:40 am

3:42 am

1:15 am

2:22 am

6:13 pm

8:09 am

12:45 pm

11:28 am

11:29 pm

7:42 pm

2:42 pm

4:58 pm

7:00 am

5:51 pm

3:42 pm

12:59 am

1:01 am

6:03 am

5:12 am

10:30 pm

10:37 pm

9:04 pm

Time matters Book 2 (Years 4–6)

46

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12- and 24-Hour Memory Game Set 2

0950

2033

0440

0342

0115

0222

1813

0809

1245

1128

2329

1942

1442

1658

0700

1751

1542

0059

0101

0603

0512

2230

2237

2104

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47

Time matters Book 2 (Years 4–6)

12- and 24-Hour Memory Game Set 3: blank

Time matters Book 2 (Years 4–6)

48

R.I.C. Publications® www.ricpublications.com.au

Clock Bingo Purpose Students will be able to practise matching times in analog and digital format.

Make the Bingo boards on a 3 × 3 grid (next page) and have 9 clock faces showing different times in each grid. You can adjust the difficulty of the game by varying the representations of time; e.g. to the nearest hour, half-hour, quarter-hour, nearest 5 minutes or nearest minute.

For every time shown on the Bingo boards, you need a matching card in the teacher’s set.

M

aterials

R

ules

You will need a Clock bingo board (3 × 3 grid; see next pages) for each player. Each player will also need 9 counters. The teacher will need a set of time cards that match the times used for the Bingo boards.

• The teacher turns over a clock card and either reads out the time, or holds the card so that the students can see the time shown.

• If a student has the corresponding time on their Bingo board, they cover it with a counter.

• The first person to cover all their times is the winner.

It is a good idea to have the cards with different representations to the Bingo board. For example, if the Bingo board has analog clock faces, the cards may have the times in digital format or in words.

You could mix and match the representations of time on the cards and on the Bingo boards.

Students could be asked to make their own Bingo boards or cards. Also, you could use some of the cards from the Time concentration game.

With this board, you might use cards with words for the times, e.g. ‘quarter past 9’.

For older, or more advanced children, you could use a mix of 12- and 24-hour times, or just 24-hour times.

Watch for …

When children draw their times, look for whether they show the movement of the hour hand in relation to the minute hand; e.g. is the hour hand halfway between the 6 and the 7 when they draw 6:30?

With this board, you might use cards with analog and/or digital times.

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49

Time matters Book 2 (Years 4–6)

Bingo Board 1: Analog Add in your own times.

11

12

11

1

10

2

9

3

8

11

6

12

8

2 3

8

4 7

6

5

Time matters Book 2 (Years 4–6)

12

2 3

6

3 4

11

4 5

50

1

9

1

8

12

5

2

7

9

6

10

5

10

7

4

8

4

11

3

11 3

1

9

1

9

6

2

7

2

7

9

12

1

10

5

10

5

10

6

12

8

4

8

4

12

3

11 3

11

9

1

9

6

2

7

2

7

10

5

10

11

1

8

4 7

12

6

12

5

1

10

2

9

3

8

4 7

6

5

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Bingo Board 2: Digital Add in your own times.

R.I.C. Publications® www.ricpublications.com.au

51

Time matters Book 2 (Years 4–6)

Bingo Board 3: Analog and Digital Add in your own times.

11

12

11

1

10

2

9

3

8

11

6

12

11 3

8

12

2 3

8

4 7

6

5

Time matters Book 2 (Years 4–6)

12

8

11

8

6

12

5

1

10

2

9

3

3

8

4 6

4

1 2

7

3 7

9

1 2

5

10

12

9

4 6

6

5

10

3

11

9

11

9

1

10

1 2

7

4 7

10

5

3

5

8

4

11

12

2

8

4 6

1

9

3

1

9

6

9

12

10

2

7

2

7

10

5

10

11

1

8

4 7

12

4 7

5

52

6

5

R.I.C. Publications® www.ricpublications.com.au

Bingo Board 4: Blank Add in your own times.

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53

Time matters Book 2 (Years 4–6)

Time Concentration Game Purpose Students will be able to practise matching times in analog and digital format.

The two pages of each set of cards can be photocopied onto two pieces of different coloured paper, so that students turn over; for example, one blue card and one green card. All the blue cards may be the analog ones, with the green ones being the digital representations. As you add the new variations, keep the colours constant, e.g. blue for analog and green for digital. The word cards could be a third colour, e.g. yellow. Using different cards for different groups of students will help to differentiate the curriculum.

Watch for …

Many students are confused with the two ways of saying or reading the ‘quarter to’ times. For example, they confuse 9:45 (nine forty-five) and a quarter to 10, wrongly saying or reading it as ‘a quarter to nine’.

M

aterials

R

ules

At the most basic level, you will need a set of 24 laminated time cards (see following pages). It is suggested that the pages are enlarged to A3 before photocopying and laminating.

• Place all of the time cards facedown on the table.

• Player 1 turns over two cards, one of each colour. If the two cards match—e.g. an analog and digital clock each showing 8:15—the player keeps both cards and has another turn. If they do not match, the player turns the cards back over without shuffling them and the next player has a turn.

• When all the cards have been matched, the person with the most cards is the winner.

Variations There are four variations on this game.

• Game variation 1: Use the half-hour and quarter-hour analog and digital cards. Analog clock faces may vary (see p. 29).

• Game variation 2: Add in the half-hour and quarter-hour analog, digital and word cards • Game variation 3: Use the 5-minute and 1-minute analog and digital cards • Game variation 4: Mix previous sets of cards.

Note: As students become more proficient, and as a means of differentiating the curriculum, you could add each new variation to the previous set, or keep them separate.

Alternatively, ‘Snap’ can be played for a set period of time. At the end of the time, the player holding the most cards is deemed the winner.

Time matters Book 2 (Years 4–6)

S

nap

Two sets (48) of the same cards can be used to play ‘Snap’, although for this game you may wish to have all cards the same colour. The cards are shuffled and dealt out equally. Players take it in turns to turn over a card and place it onto a central pile. If the new card matches the current one on top of the pile, then the first player to cover the cards with his or her hand keeps the whole pile. Play continues until one player has won all the cards; or after a set time, the player with the most cards wins.

54

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Time Concentration Game Set 1: analog half past, quarter past and quarter to

12

XII

11

12

1

10 9

3

IX

III

2

9

3

8 7

6

VI

XI XII I

11 12 1

VIII IX X

II III IV V

VI

4

10

6

5

2 3

9

4

8 7

VII

12

6

5

XII

11

12

1

10 9

3

IX

III

2

9

3

8 7

6

VI

XI XII I

11 12 1

VIII IX X

II III IV V

VI

VII

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4

10

6

5

2 3

9

4

8 7

55

6

5

Time matters Book 2 (Years 4–6)

Time Concentration Game Set 1: digital half past, quarter past and quarter to

11:15

2:45

8:15

3:45

10:30

5:30

9:30

6:30

12:45

4:15

1:45

7:15

Time matters Book 2 (Years 4–6)

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Time Concentration Game

Note: if you are using these word cards with both the analog and digital cards from the previous 2 pages, you will need two sets of them.

Or you can use one set with either the analog or digital cards. (There needs to be the same number of cards of each type and colour.)

Set 2: half past, quarter past and quarter to in words

quarter past eleven

quarter to three

quarter past eight

quarter to four

half past ten

half past five

half past nine

half past six

quarter to one

quarter past four

quarter to two

quarter past seven

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57

Time matters Book 2 (Years 4–6)

Time Concentration Game Set 3: nearest 5 minutes – analog

12

XII

11

12

1

10 9

3

IX

III

2

9

3

8 7

6

VI

XI XII I

11 12 1

VIII IX X

II III IV V

VI

4

10

6

5

2 3

9

4

8 7

VII

12

6

5

XII

11

12

1

10 9

3

IX

III

2

9

3

8 7

6

VI

XI XII I

11 12 1

VIII IX X

II III IV V

VI

VII

Time matters Book 2 (Years 4–6)

4

10

6

5

2 3

9

4

8 7

6

5

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Time Concentration Game Set 3: nearest 5 minutes – digital

11:35

2:10

8:50

3:50

10:05

5:40

9:20

6.35

12:55

4:25

1:25

7:05

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59

Time matters Book 2 (Years 4–6)

Time Dominoes Purpose

A game for 2–4 players

Students will be able to recognise and match digital and analog time to the nearest half and quarter hour, and to the nearest 5 minutes.

Time dominoes are played in the same way as normal dominoes. When students play the different variations of the Time dominoes game, they need to be able to recognise the rounding of time: to the nearest half and quarter hour, and then to the nearest 5 minutes.

M

aterials

R

ules

A set of Time dominoes (see following pages)

• Dominoes are placed facedown on the table, and seven are given to each player. Each player looks at his or her dominoes, and the person with the highest hour shown places that domino on the table face up. If two players have the same time, the person with the highest hour on the other side of the piece starts.

There are many variations to the traditional dominoes game. If your students know a different set of rules for dominoes, you may want to let them continue with these rules.

• Players take turns, playing one domino at a time, by matching one of their pieces with either end of the chain of dominoes. New pieces can only be placed at either end of the chain of dominoes. The chain of dominoes can be turned to fit onto the playing surface, but the line essentially can only be built on at the two ends.

Of interest

• When a player cannot match one of the ends of the line, he or she takes another domino from the ones facedown on the table. This becomes the end of his or her move. If there are no pieces left, the player misses that turn.

The dominoes in the centre of the table are sometimes known as the ‘bone-yard’, taken from the original dominoes that were made from pieces of bone.

• Play ends when a player has no dominoes left, or when no further moves can be made.

• The winner is the player with no dominoes left; or in the case where no further moves can be made, the one with the least number of dominoes remaining.

Variations There are four variations on this game.

• Game variation 1: Sets 1A and 1B: Use the half-hour and quarter-hour analog and digital dominoes • Game variation 2: Sets 2A and 2B: Use the 1-minute and 5-minute analog and digital dominoes • Game variation 3: Mix the first two sets • Game variation 4: Students or teacher make sets of Time dominoes using the blank template on page 65.

9

100

111 122 1

8

1:05

IX

VI

XII

III

4:37

2

7

3 6

5

4

1:0

5

Time matters Book 2 (Years 4–6)

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Time Dominoes Set 1A: analog and digital half past, quarter past and quarter to

12 1 12 11 11

XII 2 4

6

IX

5

3:30

VI

11

12

XI XII I

1

10

2

9 4 7

6

5:45

6:30

3

3:30

2:45

4:15

III

6:30

3:30

3:30

3:30

5:45

3:30

6:30

4:15

6:30

1:15

3

8

II III IV

1:15

1:15

III

VII

7

1:15

1:15

3

8

IX X VIII

9

5

VI

V

10 10

12

2:45

2:45

9

6

12 1 12 11 11 10 10

2:45

9

3

8

IX

4 7

11

3:30

XII 2

6

12

5

VI

1

10

2

9

3

8

4 7

6

5

XI XII I IX X VIII

4:15

VI

V

4:15

II III IV

4:15

VII

12 12 11 11 1

12

5:45

5:45

9

3

2

9

3

8

4 7

6

R.I.C. Publications® www.ricpublications.com.au

6:30

10 10

61

6

6:30

5

Time matters Book 2 (Years 4–6)

Time Dominoes Set 1B: analog and digital half past, quarter past and quarter to

XII

7:30

11

IX

III

8:45

7:30

12

1

10

2 3

9:30

7:30

12:15

9 8

4 7

VI

6

5

XI XII I IX X VIII

7:30

VI

V

10:45

II III IV

7:30

VII

12 12 11 11 1

12

9

3

8:45

8:45

8:45

9:30

10 10

2

9

3

8

4 7

6

6

5

XII IX

III

11:15

12:15

8:45

9:30

9:30

VI

11

9:30

10:45

9:30

11:15

12

1

10

2

9

3

8

4 7

6

12:15

5

XI XII I IX X VIII

II III IV VI

11:15

10:45

10:45

12:15

12:15

12:15

V

10:45

VII

12

11:15

11:15

11:15

9

3

6

Time matters Book 2 (Years 4–6)

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Time Dominoes Set 2A: analog and digital, 1 minute and 5 minutes

12 1 12 11 11 10 10

XII 2

9

1:05

3

8

4 7

1:05

3:12

5

6

1:05

5:51

1:05

3:12

3:12

XI XII I

2

9

3

8

4 6

9

1:05 1:05

11:25

3:12

5:51

5

4:37

12 1 12 11 11 3

3:12

11:25

10 10

2

9

3

8

4

6

7

XII

11

V IX

III

4:37

7:59

5:51

5:51

7:59

7:59

7:59

11:25

6

12

1 2

9

3

8

4 6

4:37

5

10

7

VII

VI

5:51

III

1

12

II III IV

IX X VIII

3:12

12

10

7

4:37

IX VI

11

VI

1:05

11:25

5

5:51

11:25

11:25

11:25

XI XII I IX X VIII

II III IV V

VI

VII

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63

Time matters Book 2 (Years 4–6)

Time Dominoes Set 2B: analog and digital, 1 minute and 5 minutes

12

2:43

2:43

9

6:02

3

2:43

8:44

2:43

12:28

6:02

9:16

6

12 12 11 11 1

9:16

2:43

2:43

10 10

2

9

3

8

4 7

6:02

6:02

6:02

6

5

8:44

XII

6:02

11:25

6:02

12:28

IX

III

8:44

VI

11

8:44

12

1

10

2

9

3

8

4 7

6

8:44

10:35

8:44

12:28

10:35

9:16

12:28

5

XI XII I IX X VIII

VI

V

9:16

II III IV

9:16

VII

12

10:35

10:35

10:35

12:28

9

3

12:28

6

Time matters Book 2 (Years 4–6)

64

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Time Dominoes Set 3: Blank

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65

Time matters Book 2 (Years 4–6)

Self-Checking Time Cards Students work in pairs, taking turns. Time cards are placed, writing side up, in a pile. Player 1 has a clock with movable hands; Player 2 the Time card. Player 1 reads the time and makes it with the clock. Player 2 then turns over the card to show the correct time on the back of the card, and determines if the answer was correct.

Players then change ‘jobs’. The cards can be matched to the students’ abilities in telling the time. They may need to be enlarged and laminated.

Set 1: quarter past and quarter to Front

quarter past 6

Back 11 9

3

8

4 7

8

4

8

Time matters Book 2 (Years 4–6)

5

1

10 9

3

8

4

11

12

5

9 8

4

11

6

12

8

8

4 7

11

4

12

5

1

10

2

9

3

8

4 7

6

12

5

1 2 3

8

4 6

12

5

1

10

2

9

3

8

4 7

66

6

9

12:45

5

1 3

11 3

12

2

1

9

6

5

9

7

2

6

4

5

10

7

3

10

11:15

3 7

2

11 2

1

10

1

10

12

5

8

quarter to 10

2

6

9

quarter past 11

4

6

7

11

3

7

4

1

9

12

3

8

7

2

6

9

5

10

11

quarter to 8

12

1

10

9:15

3

12

2

11

9

6

11 10

1 2

7

quarter past 10

12

5

10

11

4:45

6

Back

quarter to 4

2

7

12:45

1

10

11

3:15

12

Front

6

5

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Self-Checking Time Cards Set 2: five-minute times Front

Back 11

5:55

ten fifty-five

9 8

4

11

11

Note: These cards can be added to the previous sets to get a combination of different times.

6

12

2:05

8

4 6

12

9:35

8

4

8

one fifty

4

12

3

8

4

11

6

12

5

9

4:55

3

8

4

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4

67

12

5

1 2

9

3

8

4 6

12

5

1

10

2

9

3

8

4 7

6

12

5

1

10

2

9

3

8

4 7

5

6

10

11 2

6

8

1

10

7

3

11

9

1 2

1

eight twenty-five

12

9

7

2

6

5

10

5

10

7

4

11 3

11

3

8

1

9

1 2

7

2

12

5

9

5

10

6

10

11 3

6

4

1

9

12

8

7

2

6

3

5

10

1

9

11 3

12

5

2

1

9

6

10

7

2

7

4

5

10

7

11:50

10:20

4 7

3

11 3

8

2

8

1

9

1

9 7

2

11

twelve thirty-five

12

12

10

5

10

7

7:25

six forty

3

11

3:05

11 2

6

Back

1

10

7

ten past 11

12

Front

6

5

Time matters Book 2 (Years 4–6)

Self-Checking Time Cards Set 5: one-minute times Back 11

5:03

one minute after ten

2

9

3

8

4

11

8

4

11

12

8

1

9

3

8

4 5

seven forty-three

9 4

11

6

12

8

4 6

8

4

11

5

12

5

1 2

9

3

8

4 7

6

12

5

1 2

9

3

8

47 minutes after 2 68

6

10

4

11

3

1 3

1

9

12

2

7

2

6

9

5

10

7

4 5

10

9:21

3

8 7

3

11 2

1

10

1

10

12

5

2

7

2

12

4 6

8

5

10

6

8

9

eight fifty-six

4

12

3

11

3

1

9

1

9

12

5

2

7

2

6

10

5

10

6

4 7

10

3:14

4

12

8

11

8 6

3

1 3

7

2

7

9

1

9

5

2

11

Time matters Book 2 (Years 4–6)

6

10

7

9 minutes past 12

11:52

12

10

11 3

7

11

1

9

11

7:59

12

5

Back

27 minutes past 4

2

7

1:32

6

10

11

12:36

1

10

7

sixteen minutes past six

12

Front

6

12

5

1

10

2

9

3

8

4 7

6

5

R.I.C. Publications® www.ricpublications.com.au

Note: These cards can be added to the previous sets to get a combination of different times.

Front

Self-Checking Time Cards Set 6: blank Front

Back 11

12

Front

11

1

10 9

11

12

9

12

11

8

11

12

12

11

11

8

12

5

1 2

9

3

8

4

R.I.C. Publications® www.ricpublications.com.au

6

10

3

6

4

1 2

7

3

8 7

9

1 2

5

10

12

5

9

4

12

6

10

3

8

11

4

1

9

6

3 7

2

7

2

5

10

1

8

4

11

12

5

9

3

6

4 6

10

2

7

3

11

1

8

2

7

9

1

8

4

11

12

9

5

10

6

5

10

3

6

4

1

8

Note: Add your own times to these cards.

8

2

7

3 7

9

1 2

5

10

12

5

9

4

12

6

10

3

11

4

1

9

6

3 7

2

7

2

5

10

1

8

4

11

12

5

9

3

6

6

10

2

7

4

11

1

8

3 7

5

10

2

8

4 6

1

9

3

8

12

10

2

7

Back

4 7

5

69

6

5

Time matters Book 2 (Years 4–6)

Race Around the Clock Game Purpose This game will help students count the minutes on a clock; and help them see the connection between the 12 digits on the clock and the 5-minute marks of the 60 minutes in an hour. For example, it helps connect the 11 on a clock to 55 minutes when the minute hand is on that place.

A game for 2–4 players

M

aterials • One game board clock face per player (see next page) • 1 × six-sided dice • 1 × set of cards per player (5, 10, 15 … to 60. See next page) • 1 small counter per player, placed on the 12

R

ules 1. Player 1 rolls the dice and moves that many places (minutes) around their clock face. If they land on one of the clock digits (1–12) they place the appropriate card on that digit. For example, if they land on the 3, they place the 15 card over the 3; if they land on 8, they place the 40 card over the 8 etc. If they land on a non-digit place, they do not place a card.

2. When each player has completed one full circuit of their clock board, they add up the total value of all the cards they have covered. For example, if they had landed on the 3, and later on the 8, but no other digit places, they add the 15 and 40 to get a total of 55.

3. The player with the highest score is the winner.

Variations • Game variation 1: The teacher nominates the number of times the players go around their boards. The player with the highest score is the winner.

• Game variation 2: The teacher gives a set time for the game, and the students continue the game until that time is up.

The player with the highest score is the winner.

• Game variation 3: Students continue the game until one player has covered all 12 digits. That player is the winner.

Time matters Book 2 (Years 4–6)

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Race Around the Clock Board

11

12

1

10

2

9

3

8

4 7

5

6

5

10

15

20

25

30

35

40

45

50

55

60

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71

Time matters Book 2 (Years 4–6)

Skateboard Racing Game Purpose Students will complete time calculations.

A game for 2–4 players; plus a judge

M

aterials • One different-coloured counter per player

• One game board • Time problem cards, shuffled and placed facedown on the table • 1 × six-sided dice • Judge’s answer board

R

ules 1. Put all the players’ counters on ‘Start’.

2. The teacher nominates how many laps students need to complete during the game; alternatively, the game can run for a set amount of time.

3. Player 1 rolls the dice and moves forward that number of places. He or she then picks up a time problem card and answers the question. Each card is numbered, but they do not have to be answered in numerical order. The number on the card is for the judge to find the correct answer on the Judge’s answer board. If the player has answered the question correctly, his or her counter stays where it is. If the answer is incorrect, they move their counter back 3 places.

4. Players take turns to roll the dice and complete their move by answering the question. (Remind students to use ‘am’ or ‘pm’ in their answers for Set 1, or 24-hour time for Set 2.) There are also blank cards and a blank Judge’s answer board for the teacher and/or students to write their own problems and solutions.

5. The winner is the first player to complete the nominated number of laps of the circuit, or, if being played for a set amount of time, the player nearest to the start.

Time matters Book 2 (Years 4–6)

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Skateboard Skate e Racing Game

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73

Time matters Book 2 (Years 4–6)

Skateboard Racing Game Set 1: time problem cards – am and pm times

1

Jean ran a minimarathon in the time of 2 hours and 35 minutes. She finished the race at 2:46 pm.

2

James heard his baby brother wake up at 11:25 pm. The next morning, he was told that his brother woke again 45 minutes later.

What time did she start?

3

It was 5:55 am when Timothy started delivering papers. He finished one and a half hours later.

What was the time then?

What time was it on the second occasion?

4

Jane started making her lunch at 11:34 am.

She was interrupted by a phone call and didn’t get back to making her lunch until 12:05 pm.

5

6

Ann booked in to get her hair cut at 4:25 pm. She arrived half an hour early.

The flight from Sydney to Melbourne left at 10:50 pm. The flight took one hour and thirty-five minutes.

What time did she get there?

What time would it arrive?

How long was the phone call?

7

Bill looked at the clock in his bedroom.

It read 12:27 am. He knew the clock was 32 minutes fast.

What was the real time?

10

Joseph looked at his watch when he left the movies; it was 9:55 pm. The movie went for 1 hour and 20 minutes.

8

9

What is the difference between these two times?

10:45 am and 3:20 pm

11

When Kim’s granny arrived, it was 9:40 am.

She stayed for 2 hours and 10 minutes.

What time did she leave?

Rob needs to catch a train at 4:17 pm. It takes him 25 minutes to walk to the station.

What is the latest time he should leave home?

12 What is the difference between these two times?

1:55 pm and 11:24 pm

What time did it start?

Time matters Book 2 (Years 4–6)

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Skateboard Racing Game Set 2: time problem cards – 24-hour times

13

The bus from school to Sean’s house takes 50 minutes. It leaves the school every day at 1535.

14

The football game was due to start at 1130 on Saturday. It usually goes for one and a half hours.

15

Rosie got home from school at 1605, and went to bed 4½ hours later.

What time did she go to bed?

What time should it get to Sean’s house?

16

Harry took his dog for a walk, leaving at 0745. He returned home one hour and 17 minutes later.

What was the time then?

19

Sarah went fishing at 0415 and stayed out for three hours and 50 minutes.

What time should it finish?

17

Two friends met for lunch at 1140 and left at 1335.

How long did they take for their lunch?

20

18

Jim’s family drove to their holiday cottage, leaving at 1730. The trip took 2 hours and 45 minutes.

What time did they arrive?

21

Graham finished gardening at 1440. He had been working for one hour and 45 minutes.

Sport time at school is 1350 on Thursday, and goes for one hour and 20 minutes.

What time did he start?

What time does it finish?

What time did she come back?

22

23

Jason’s favourite show started at 2050 and went for 45 minutes.

Cathy caught a train at 1025. The trip took three hours and 25 minutes.

What time did it finish?

What time did it arrive?

24 What is the difference between these two times?

1955 and 2324

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75

Time matters Book 2 (Years 4–6)

Skateboard Racing Game Set 3: time problem cards – blank

25

26

27

28

29

30

31

32

33

34

35

36

Time matters Book 2 (Years 4–6)

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Judge’s Answer Board Set 1: am & pm Remember, where applicable, times MUST be given with am or pm.

Problem

Solution

1

Jean ran a mini-marathon in the time of 2 hours and 35 minutes. She finished the race at 2:46 pm. What time did she start?

12:11 pm

2

James heard his baby brother wake up at 11:25 pm. The next morning, he was told that his brother woke again 45 minutes later.

What time was it on the second occasion?

12:10 am

3

It was 5:55 am when Timothy started delivering papers. He finished one and a half hours later. What was the time then?

7:25 am

4

Jane started making her lunch at 11:34 am. She was interrupted by a phone call and didn’t get back to making her lunch until 12:05 pm.

How long was the phone call?

31 minutes

5

Ann booked in to get her hair cut at 4:25 pm. She arrived half an hour early. What time did she get there?

3:55 pm

6

The flight from Sydney to Melbourne left at 10:50 pm. The flight took one hour and thirty-five minutes. What time would it arrive?

12:25 am

7

Bill looked at the clock in his bedroom. It read 12:27 am. He knew the clock was 32 minutes fast. What was the real time?

11:55 pm

8

What is the difference between these two times?

10:45 am and 3:20 pm

9

Rob needs to catch a train at 4:17 pm. It takes him 25 minutes to walk to the station. What is the latest time he should leave home?

3:52 pm

10

Joseph looked at his watch when he left the movies; it was 9:55 pm.

The movie went for 1 hour and 20 minutes. What time did it start?

8:35 pm

11

When Kim’s granny arrived, it was 9:40 am. She stayed for 2 hours and 10 minutes. What time did she leave?

11:50 am

12

What is the difference between these two times?

1:55 pm and 11:24 pm

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4 hours & 35 minutes

9 hours & 29 minutes Time matters Book 2 (Years 4–6)

Judge’s Answer Board Set 2: 24-hour time Remember, where applicable, times MUST be given in 24-hour format.

Problem

Solution

13

The bus from school to Sean’s house takes 50 minutes. It leaves the school every day at 1535. What time should it get to Sean’s house?

1625

14

The football game was due to start at 1130 on Saturday. It usually goes for one and a half hours. What time should it finish?

1300

15

Rosie got home from school at 1605, and went to bed 4½ hours later.

What time did she go to bed?

2035

16

Harry took his dog for a walk, leaving at 0745. He returned home one hour and 17 minutes later. What was the time then?

0902

17

Two friends met for lunch at 1140 and left at 1335. How long did they take for their lunch?

1 hour & 55 minutes

18

Jim’s family drove to their holiday cottage, leaving at 1730. The trip took 2 hours and 45 minutes. What time did they arrive?

2015

19

Sarah went fishing at 0415 and stayed out for three hours and 50 minutes. What time did she come back?

0805

20

Graham finished gardening at 1440. He had been working for one hour and 45 minutes. What time did he start?

1255

21

Sport time at school is 1350 on Thursday, and goes for one hour and 20 minutes. What time does it finish?

1510

22

Jason’s favourite show started at 2050 and went for 45 minutes. What time did it finish?

2135

23

Cathy caught a train at 1025. The trip took three hours and 25 minutes. What time did it arrive?

1350

24

What is the difference between these two times?

1955 and 2324

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Judge’s Answer Board Set 3: blank Remember, where applicable, times MUST be given with am or pm, or 24-hour time.

Problem

Solution

25

26

27

28

29

30

31

32

33

34

35

36

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Time matters Book 2 (Years 4–6)

Close your eyes (Time problems) Purpose To encourage students to visualise the hands on a clock, and how they relate to each other at certain times.

If some of these ideas are made into cards, consider how the students will self-correct. The solutions could be on the back of the cards, or there could be a master sheet with all of the problems and their solutions. If the students make the problem cards themselves, they should provide the solutions.

1. Close your eyes and visualise where the hands would be at 3:00. What angle is formed? (A right angle) How many degrees is that? (90°) 2. How many degrees does the minute hand travel in five minutes? (15°) 3. What is the angle formed by the two hands at 12:30? (It is not 180°, but a bit less as the hour hand will be between the 12 and the 1. In fact, it is 172.5°) 4. When the minute hand travels from 3:20 to 3:50, how many degrees has it travelled? (180°) 5. Are there any times when the angle formed by the hour and minute hands is 180°? What about 90°?

6. Write down some times (from when to when?) that the minute hands travel 45°. (There are many solutions, such as from 4:05 to 4:20. The minute hand needs to travel between 3 digits on the clock; i.e. three sets of 15°. The times do not need to be in 5-minute increments; e.g. the minute hand travels 45° from 8:41 to 8:56.)

7. Nominate some times when the angles made between the hour and minute hands are obtuse.

8. Have the students write some ‘Close your eyes’ time problems for each other. Place them on cards, and you could end up with a bank of good time problems.

Time matters Book 2 (Years 4–6)

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Linking Fractions and Time Purpose To help students make links between simple fractions and divisions on a clock.

Fractional language is often linked to clock reading. For example, we refer to ‘quarter past’, ‘quarter to’ and ‘half past’. It is of interest that we never refer to three-quarters past.

The angle between each five-minute interval on the clock is 30 degrees. A five-minute interval is one-twelfth of an hour. A ten-minute interval is one-sixth of an hour.

We have the Babylonians to thank for our angle system and the links to a circle. The Babylonians used a sexagesimal base 60 system, which was convenient as it contained a lot of factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. This made it simpler to calculate.

There are obvious links between angle measure and time measure.

For example, we refer to degrees, minutes and seconds when measuring angles. A circle is divided into 360 degrees and most clock-faces are circular.

M

aterials • 2 × six-sided dice • Some clock fraction masters (see next page)

A fraction may be formed by rolling two dice, using the larger number as the denominator and the smaller number as the numerator. For example, if a six and a one are rolled then the fraction 1⁄6 may be formed. One sixth of an hour represents 10 minutes of time.

There are 12 distinct times that may be represented in this way.

Equivalent fractions such as 1⁄2 and 2⁄4 represent the same time. Challenge the students to find all the different times that may be represented. These may be represented in a table. Encourage students to work systematically to record all the distinct possibilities. Below is the start of the table.

Dice numerator

Dice denominator

1

6

1

⁄6

10 min

1

5

1

⁄5

12 min

1

4

1

⁄4

15 min

1

3

1

⁄3

20 min

1

2

1

⁄2

30 min

1

1

1

60 min (1 hr)

2

6

1

2

5

2

4

1

2

3

2

2

2

2

3

…

2

Fraction

Time

⁄3

20 min

⁄5

24 min

⁄2

30 min

⁄3

40 min

⁄2

60 min (1 hr)

Encourage students to investigate combinations of fractions that make up one hour. A BLM of clock circles showing twelve points may be used to explore various combinations. A few examples are given below.

1

⁄5 ⁄

⁄

⁄5

1 6

15

⁄

⁄12

1

1 12

⁄

1

⁄6

1 6

1

⁄

1 12 1 12 1 12

⁄

⁄

⁄

⁄

1 5

1 5

⁄

81

1 12

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Time matters Book 2 (Years 4–6)

Blank Clock Face

Time matters Book 2 (Years 4–6)

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Fractions of Time Game Purpose

A game for 2–4 players

To help students make links between simple fractions and divisions on a clock.

This game builds on the understanding developed in the previous activity linking fractions and time.

Students may have noted when completing the previous activity that some combinations of fractions tend to fit together better than others.

They may wish to have the circles they shaded in the previous activity as a reference for this game.

Students may have noted that thirds typically don’t go with fifths. Similar issues occur with fourths (quarters) and fifths, so students will need to be strategic in the way the shade their clocks.

Students can discuss their various strategies after playing a few games.

M

aterials • 2 × six-sided dice • 1 × Fraction clock game board per player (see next page)

R

ules

Players take turns to roll two dice and form a proper fraction (a fraction where the numerator is less than or equal to the denominator).

The appropriate section of a clock is shaded on the player’s board.

The first player to shade 6 hours (6 circles) is the winner.

Players may shade parts of various different circles and do not have to complete one circle before shading another on their board.

Variations Students must finish the game with the exact fraction. For example, if 1⁄6 is required to complete a set of six clock faces then you might allow the student to win with a roll of 1⁄2 as it more than covers the 1 ⁄6. Alternatively, you could demand that the exact fraction has to be thrown.

Allow fractions to be split across two or more clocks. For example, 1⁄2 might be split as 1⁄3 and 1⁄6; or 1⁄6, 1⁄6 and 1⁄6.

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Time matters Book 2 (Years 4–6)

Fractions of Time Game Boards

Time matters Book 2 (Years 4–6)

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Sequencing Events Not all cartoons lend themselves to sequencing. It is best to choose ones where there is a very clear sequence.

The level of difficulty can be altered according to the number of frames in the cartoon.

As well as putting pictures of familiar stories into the correct chronological order, students can use cartoon strips and order the frames.

Making recipes gives the opportunity for students to measure quantities.

Chocolate crackles Makes approximately 28 Ingredients • • • • •

4 cups Rice Bubbles® 1 cup icing sugar 1 cup desiccated coconut 5 tablespoons cocoa powder 250g melted Copha®

Method Mix all ingredients together.

Spoon into patty cases.

Refrigerate until set.

Most procedural texts lend themselves to sequencing activities.

•

Recipes The list of steps for simple recipes could be written in separate boxes. The students then sort them into a logical sequence.

Measure the icing sugar, coconut, Rice Bubbles® and cocoa.

Measure the Copha® and melt it in a saucepan over gentle heat.

Mix all the ingredients together.

Spoon the mixture into individual patty cases.

Put the filled patty cases into the fridge to set.

•

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Art and craft activities A similar idea could be used for activities that have clear procedural steps; for example, making a clay model or a stained glass window.

85

Time matters Book 2 (Years 4–6)

A School Day (with clocks) Cut out the pictures and place them in order from the earliest in the day, to the latest.

10

11

12

1 2

9

3 8

4 7

Time matters Book 2 (Years 4–6)

6

5

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Sequencing Clocks Cut out the pictures and place them in order from the earliest to the latest.

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Time matters Book 2 (Years 4–6)

Sequencing Longer Events In early years, sequencing of daily events with reference to what we do in the morning, or evening; and in what order we do a series of activities such as getting out of bed, having breakfast, brushing teeth, going to school, going home, eating dinner, bedtime, will all have been covered.

Purpose Sequencing longer events such as timetables.

Students need to be able to sequence events that occur:

W

eekly events

Reference to a weekly classroom timetable can help students understand the cyclic nature of certain events. For example, they see that Japanese is on Wednesdays, Science is on Thursdays and Sport is on Fridays. They may also notice aspects that are the same most schooldays, such as fitness first thing every morning, mathematics every morning after fitness, quiet time straight after lunch etc.

• Daily • Weekly • Seasonally • Annually

Period

Monday

Tuesday

Wednesday

Thursday

Friday

Weekly classroom timetable

1

Maths

Health

Physical Education

Maths

English

2

Music

English Computers English

Sport

Recess 3

English

Maths

Japanese Reading

Health

4

Physical Education

Music

English

Science

Maths

Other discussions about weekly events may include activities that are completed after school on certain days—e.g. sports practice, dancing classes etc.—and activities that take place regularly on weekends. Some families will have routine activities that happen at set times on weekends, while others may not.

One way for students to ‘see’ longer durations is to watch something grow. Planting seeds—for example, broad beans—gives them an opportunity to notice changes on a twice-weekly or weekly basis, and taking photos of them gives access to the activity long after the plants have died. Students can graph the heights of the plants, and later place the photos in order from the germination of the seeds to the stages of growth and eventual death of the plant.

Lunch Creative writing

Arts & craft

Maths

Creative writing

Study group

8

Story group

Story group

Creative writing

Story group

Arts & craft

Friday

Thursday

Wednesday

Tuesday

Monday

Sunday

Saturday

Friday

Thursday

Wednesday

Tuesday

Monday

Centimetres

5

Day of the week

Time matters Book 2 (Years 4–6)

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Sequencing Seasonal and Annual Events

S

easonal events

These may begin with discussion about the names of the seasons and their order. The different types of weather that are typical for each season would follow, and students could find pictures of the types of clothes and related activites/events they would use in the different seasons and glue them onto a poster.

Seasonal events

A

Spring

Summer

Autumn

Winter

nnual events

School terms, national holidays etc. can be placed onto a calendar, along with students’ birthdays and other relevant events such as sports carnivals, swimming carnivals, the school fete etc.

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Time matters Book 2 (Years 4–6)

Sequencing Events According to Duration Purpose Calculating interval between two time periods.

Calculating durations Students often become confused when deciding the order of events according to their duration when the start and finish times vary. They may believe that the event that finishes last will be the longest, even if the start time is later.

Calculations of time difference can be quite difficult, because of the nondecimal nature of time. Sometimes a calculator may actually hamper the process. For example, if a train arrives at 9:31 and it is currently 8:47, you cannot simply key 9.31 into a calculator and subtract 8.47; the result would be 0.84, which a child could incorrectly interpret as 84 minutes. In this case, the number of minutes until 9:00 would be calculated first (13 minutes), and the extra 31 minutes until the desired time (9:31) added to give a total waiting time of 44 minutes.

This serves to reminds us that we should use a colon between the hour and minute digits when writing time in a mathematical context (e.g.

10:47), not a full stop or decimal point.

In order to sequence events according to their duration, students need to be able to calculate the duration of each of the events.

C

alculating relatively short durations

For calculating relatively short durations of time, the easiest method is to calculate the amount of time until the next hour and the number of full hours to the finish time, then add on any remaining minutes. Students may need guided practice at this. For example, if an event starts at 10:48 am and finishes at 2:31 pm, students might say: • 10:48 am until 11:00 am is 12 minutes • 11:00 am until 2:00 pm is 3 hours • 2:00 pm until 2:31 pm is 31 minutes

In order to calculate the total duration; students would add 12 minutes and 3 hours and 31 minutes. This gives a total time of 3 hours and 43 minutes.

Students could be given problems where they are required to work out the duration of various events, and then place them in order from the one that took the least amount of time to the one that took the longest. The teacher can give the problems, or the students can investigate various durations and then order them.

U

sing a ‘time line’ to calculate durations

An empty number line can be a useful tool to calculate time durations.

This is different to creating a time line for a sequence of events (see page 97).

Using an empty number line, we put in the start time of the event (e.g.

9:25 am) and then show a ‘jump’ to the nearest full hour (10:00 am), a ‘jump’ to the nearest full hour before the finish time (4:00 pm), and finally a ‘jump’ to the end time (4:12 pm). An interim ‘jump’ to midday may be used if required, as in the example below. We then add the time periods to get the duration (35 minutes + 2 hours + 4 hours + 12 minutes, giving 6 hours and 47 minutes).

Using an empty number line to calculate duration problems makes more sense to students if they have used them for other number problems.

In the example above, we had a start and finish time and wanted to work out the difference in time (the duration). A number line may also be used when given a start time and the duration, and need to find out the finish time; or, working backwards, when given a finish time and duration and want to calculate the start time.

Time matters Book 2 (Years 4–6)

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Elapsed Time – Analog Calculate how much time has passed between the two time periods.

Beginning 11

12

Elapsed time (Difference) 11

1

10 9

11

12

1

11

9 8

8

11

8

12

8

11

8

12

8

11

8

12

8

11

8

12

1 2

9

3

8

4

4 7

5

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6

5

10

3

6

4

1 2

7

3 7

9

1 2

5

10

12

9

4

11

6

5

10

3

6

4

1 2

7

3 7

9

1 2

5

10

12

9

4

11

6

5

10

3

6

4

1 2

7

3 7

9

1 2

5

10

12

9

4

11

6

5

10

3

6

4

1 2

7

3 7

9

1 2

5

10

12

9

4

12

6

5

10

3

11

4 7

2

6

3

5

10

7

2

8

4 6

1

9

3

8

12

10

2

7

End

91

6

5

Time matters Book 2 (Years 4–6)

Elapsed Time – Analog and Digital Calculate how much time has passed between the two time periods.

Beginning 11

12

Elapsed time (Difference)

End

1

10

2

9

9:35

3

8

4 7

6

5

11

2

9

3

8

4 7

12

2

9

7:20

3

8

4 6

5

11 9

3

8

4

2

9

8:40

3

8

4 6

6

5

1

10

7

1 2

7

12

12

10

11:20 11

6

5

1

10

7

1

10

1:55 11

12

5

11

1

10

9:07

2

9

3

8

4 7

Time matters Book 2 (Years 4–6)

12

92

6

5

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Elapsed Time – Blank Analog Calculate how much time has passed between the two time periods.

Beginning 11

12

Elapsed time (Difference) 11

1

10 9

11

12

1

11

9 8

8

11

8

12

8

11

8

12

8

11

8

12

8

11

8

12

1 2

9

3

8

4

4 7

5

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6

5

10

3

6

4

1 2

7

3 7

9

1 2

5

10

12

9

4

11

6

5

10

3

6

4

1 2

7

3 7

9

1 2

5

10

12

9

4

11

6

5

10

3

6

4

1 2

7

3 7

9

1 2

5

10

12

9

4

11

6

5

10

3

6

4

1 2

7

3 7

9

1 2

5

10

12

5

9

4

12

6

10

3

11

4 7

2

6

3

5

10

7

2

8

4 6

1

9

3

8

12

10

2

7

End

93

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5

Time matters Book 2 (Years 4–6)

Elapsed Time – Blank Analog and Digital Calculate how much time has passed between the two time periods.

Beginning 11

12

Elapsed time (Difference)

End

1

10

2

9

3

8

4 7

6

5

11

12

1

10

2

9

3

8

4 7

11

12

6

5

1

10

2

9

3

8

4 7

6

5

11

12

1

10

2

9

3

8

4 7

11

12

6

5

1

10

2

9

3

8

4 7

6

5

11

12

1

10

2

9

3

8

4 7

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Sequencing Events According to Duration Estimation activities could offer a reason to work out durations of time.

Students estimate how long different events during the day may take; then as they occur, they record the start and finish times. They use these to work out the duration of each activity. Students could then order the events from the one taking the least amount of time to the one taking the most.

Activity

Estimate

Start time Finish time

Duration

Reading a chapter of a book Walking to the canteen Making a cardboard tetrahedron

Television timetables offer an ideal opportunity to look at start and finish times. Students can look at the length of different movies, news programs, sports events etc. They could also discuss their favourite show, calculate the duration of each of them and put them in order from the shortest to longest shows.

Bus, train and airline timetables are another good source of data for activities where the calculations of durations are relevant. This is of special interest if any of the students are about to travel, or have just returned from a trip.

Note: Actual flying times may not be the same as the difference between take off and arrival times if there are different time zones between the arrival and destination points. It may be better to find timetables where this doesn’t occur, or create your own.

Alternatively, students could look at why the difference between a departure time and arrival time does not tally with the flying time given by an airline. For example, if flying from Melbourne to Adelaide, there may be a departure time of 1435 and an arrival time of 1525, but the airline timetable states that the duration of the flight is 1 hour and 20 minutes. This would lead to discussion about the time difference between Melbourne and Adelaide. (See pages 135–136 for more information on time zones.)

A

dding time game

An activity in which students need to add on specific amounts of time would help promote the idea that working out time durations can be done using complementary addition. See ‘Adding time intervals’ on page 113.

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Time matters Book 2 (Years 4–6)

Sequencing Shadows Purpose Observe the movement of the sun via changes to the shadows.

The formula for making an accurate sundial is very complex and beyond the scope of this book. It is affected by the geographic place and the time of year (in relation to sunrise and sunset).

The gnomon is the upright piece of these devices.

The Egyptians used a shadow clock with a gnomon. It used the position of the shadow on a graduated base, marked in hours, to determine the time. In the morning the crosspiece was turned towards the east so that the shadow moved across the long piece. As the sun moved higher in the sky, the shadow moved down the length of the arm towards the gnomon. At noon, the clock was moved to face the west and the shadow got longer as the afternoon progressed.

The use of a shadow stick can give children an opportunity to experience the movement of the earth around the sun in a practical way. Of course, you need a sunny day for it to work!

M

aterials • Paper • Stick; about 1 metre long is ideal • Pencil

P

rocedure • In the morning, lay a large sheet of paper in a sunny, grassy spot.

Place the stick in the ground so that it stands vertically and is centred on the paper. If you don’t have access to a grassed area, plain ground will be fine. If using a paved area, a means of holding the stick vertical will be needed; perhaps a lump of clay or similar.

• At 9:00, trace the shadow of the stick onto the paper and label it with the time.

• At intervals during the day—e.g. every hour—mark in the shadow and label each one with the current time.

• What will be interesting for the students is that the shadow moves around the paper; but also that the length of the shadow varies.

Variations 1. Students could measure the lengths of the shadows of fixed objects such as a flagpole at 12:00 at the start of every month for a term to see the change in lengths. This could be recorded in a table, as below:

February

March

April

May

Flagpole Main gate post Basketball hoop Solstice From the Latin sol meaning ‘Sun’ and stitium meaning ‘stoppage’.

These usually occur close to 21 June and 21 December.

Equinox From the Latin aequus meaning ‘equal’ and nox meaning ‘night’. These usually occur close to 21 March and 21 September. At both these times, the length of night and day are approximately equal.

Time matters Book 2 (Years 4–6)

2. Similar to above, but students measure the length of the objects at noon on the equinoxes and solstices. As schools have usually started the summer holiday by 21 December, students could predict a likely result for that date.

21 Mar.

21 June

21 Sept.

21 Dec.

Flagpole Main gate post Basketball hoop

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Sequencing Time Lines There is an obvious link between time lines and number lines. If students are familiar with number lines, the concept of time lines will be easier.

A time line is a convenient way to show relative time, or the order of particular events. They can be used to show a short time span (events in a day), long periods of time (dinosaur evolution) or anything in between.

When sequencing particular events, the time line offers a graphical representation that is easy to follow.

Students can be given a variety of events and be asked to place them in order on a time line. Examples include: • Major events in their lives, e.g. their birth, taking their first steps, starting school etc.

• Birth years of relatives, e.g. parents, grandparents, brothers, sisters, cousins etc.

• Events in the life of a plant, e.g. apple tree: seed, sapling, young tree, fruiting tree.

The use of photographs or illustrations will help bring a time line to life. For example, if looking at a time line for the area where they live, students may look for photographs and sketches of historical relevance.

My Dad Dad born

Started school

Started work

Married Mum

Brother born

I’m born

1972

1976

1989

1998

2000

2008

Students may use the web to investigate other time lines. These may include: • Life cycle of an insect, e.g. butterfly • Dinosaur periods • Space exploration • Ages of early humans • Evolution of types of plants • History of a particular sport • Evolution of sea life • Settlement of a town, city or state • History of a particular technology • Time line for an historic figure • Time line for a favourite singer or movie star • Kings/Queens of England • Prime Ministers of Australia

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Time matters Book 2 (Years 4–6)

Sequencing Time Lines Major events in the twentieth century World War I

World War II

Sputnik

Apollo landing

First space shuttle

Fall of Berlin Wall

1914–18

1939–45

1957

1969

1981

1989

A morning in the life of a sportsperson Eats breakfast

Training

Training

6:15

8:00

10:30

6:00

6:50

10:00

11:45

Gets out of bed

Goes to gym

Eats healthy snack

Eats lunch

Have the students make their own ‘Day in my life’; both by constructing a time line, as above, and writing more detail alongside.

Time matters Book 2 (Years 4–6)

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Growing Potatoes Cut out the cards below and place them in the correct order.

Glue them onto a blank sheet, arranging them to form a time line.

Take to market

Fertilise the soil

Sprouts appear

Irrigate the soil

Cook the potatoes

Make furrows in the land $5.00 BUCKET

$2.00 PER KG

Harvest the potatoes

Buy potatoes at the market

Plant the potatoes

Plough the field

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Time matters Book 2 (Years 4–6)

Baking Biscuits Illustrate the cards below, then cut out and place them in the correct order.

Glue them onto a blank sheet, arranging them to form a time line.

Pre-heat oven

Put spoonfuls on tray

Take out ingredients

Put in oven

Take out utensils

Remove when cooked

Mix dry ingredients

Cool

Add wet ingredients

Eat

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Blank Time Line Cards

Students may like to plan a sequence on a separate sheet of paper.

Fill in the cards below, then illustrate, cut out and place them in the correct order.

Challenge another class member to put them into the correct order as a time line.

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Time matters Book 2 (Years 4–6)

Using Timetables It is important for students to become familiar with a variety of different timetable formats.

The 12-hour and 24-hour formats are most commonly used. Students need to be familiar with both formats, and then teachers may start these activities using 12-hour timetables, later extending to 24-hour ones.

It is useful for students to be able to convert times with two units; e.g.

2 hours and 17 minutes is the same as 137 minutes. This will help when calculating time durations from two different times on a timetable.

Where possible, base activities with timetables upon real-life situations.

For example, if a student is going on a trip by plane, the opportunity to look at airline timetables may be taken; or if students are going on an excursion by bus, a bus timetable may be accessed, even though the students would not necessarily be using public transport.

Another opportunity to consult timetables is when comparing programs on television. Students may choose their favourite shows, and then determine how long they run for.

Have students list their favourite shows, and then design a TV timetable for one day. They would need to consider start and finish times of each show, the different types of programs, and maybe even factor in advertising breaks.

Use a clock face format to display part of a timetable. This works well for a one-hour time frame, as the five-minute timeslots make it easy to calculate. Providing the information in this format is a way for students to be introduced to circle (pie) graphs. Students could then make their own circle graph for a different one-hour period, either during the school day or after school. (See activity on next page.) Ensure that students understand that the timetable starts at the 12 and continues clockwise for one hour, but the 12 does not mean 12 o’clock. In the example below, the start time is 3:00 pm.

Between 3:00 pm and 4:00 pm

This clock face format may also be used for other time periods, e.g. 12 hours. See activities on next page.

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Using Timetables A clock face timetable can be used to show how much time is spent on different activities.

A one-hour timetable shows minutes spent. 12-hour timetable shows hours spent.

The starting point is always the 12 position on a clock, but this does not necessarily mean 12 o’clock.

1. This is a one-hour timetable for a bus driver. It shows the stops from leaving the depot at 1:00 pm to reaching the station at 2:00 pm. (a)

How many stops were on the route?

(b)

What was the shortest time between stops?

(c)

What was the longest?

(d)

Mary got on the bus at the 3rd stop. What time was that?

2. This is a 12-hour timetable for a plumber. Her workday starts at 6:00 am. (a)

How many jobs did she do that day?

(b)

She went to fix a dripping tap at a shop at 9:30. How many jobs had she already done?

(c)

Her visit to fix a sink at the hairdressers was her longest job.

What time did she get there?

What time did she leave?

(d)

How long was her shortest job?

3. Make your own 12-hour timetable for last Sunday.

Decide what will be the starting time for your timetable.

Note: the 12 does not mean 12:00; just the beginning of the timetable.

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Time matters Book 2 (Years 4–6)

Using Timetables Have students plan a trip for a day out that involves using public transport. If possible, more than one form of public transport could be planned for, thus necessitating calculations about transit times and the viability of getting from one place to another in plenty of time.

Offer students the opportunity to construct simple personal timetables.

This may be for a period of one day, a weekend, a long weekend or the duration of a two-week school holiday.

Monday

Tuesday Wednesday Thursday

Friday

9:00 10:30 12:00 1:30 3:00 Copy the class timetable, or one day from it, and ask students to fill it in as the day progresses. At the end of the day, students could compare their timetables with the regular one, and discuss any differences and why they might have occurred, e.g. it was raining when we were due to have sport on Wednesday morning, so we did it after lunch.

Monday Subject

Timetable

Actual time

Reason

Fitness

9:00

9:15

Collection of excursion money

Maths

9:30

9:40

Fitness started late

Oral language

10:15

10:15

—

Look at timetables for public transport in the local area and discuss features of them. For example: • What is the earliest bus we could catch to the beach?

• Is it earlier or later than the first bus from the city?

• What time is the last bus for the day?

• Why don’t they have any later buses?

• How far apart are the services?

• Does it vary at different times of the day?

• What is the longest time you would have to wait for a bus?

• What is the shortest time?

• Why do you think this is?

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Rail Away: Checking the Timetable Below is the schedule for Cheapie Trains. They have a regular rail service between the city and the mountains and between the city and the coast. The service each way to or from the mountains takes one hour; each way to or from the coast takes two hours.

City to mountains 0500 1100 0630 1630 0700 1700 0730 1730 0815 1745 0845 1800 0915 1820 1000 1840 1040 1900

Mountains to city 0530 1140 0600 1540 0740 1610 0800 1640 0850 1710 0920 1740 1000 1820 1020 1845 1100 1900

City to coast 0510 1535 0535 1635 0555 1715 0625 1735 0645 1755 0715 1805 0745 1845 0845 1945 0915 2005

Coast to city 0545 1405 0630 1440 0715 1520 0755 1545 0835 1625 0930 1705 1020 1725 1105 1835 1125 1915

Example: Carl arrived at the city station at 3:42 pm.

How long did he have to wait to get the train to the coast?

Convert 3:42 pm to 24-hour time: 3:42 pm to 1542.

Look at the timetable above.

The next train to go to the coast after 1542 leaves at 1635.

From 1542 to the next hour (1600) is 18 minutes.

From 1600 there are another 35 minutes to wait until the train leaves at 1635.

18 minutes plus 35 minutes are 53 minutes. Carl had to wait 53 minutes for his train.

Explain your answers to the problems below.

1. Jean wanted to meet some friends at the beach at 7:00 am. What time would she need to get the train from the city to be there in time?

3. James finishes work in the city at 5:25 pm.

It takes him 20 minutes to get to the station. What time does he arrive at the coast?

2. Timothy camped overnight in the mountains. He needed to see a dentist in the city the next day at 2:15 pm. What is the latest time should he catch the train?

4. Jane wanted to get to the mountains by 4:30 pm. She needed to go from the coast, via the city. What time should she leave the coast to arrive in time?

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Time matters Book 2 (Years 4–6)

Super Sports TV Guide Below is the TV guide for two Pay-TV sports channels for Saturday.

Sportz 1 5:30 5:55 6:00 6:45 8:45 9:00 10:45 12:00 3:30 3:40 5:45 6:40 9:00 11:10

News Weather report Basketball highlights Tennis international News break Baseball league Footy coaching Tennis international News break Footy feature match live Tennis highlights Tennis international Sports review Sports preview

5:20 5:45 6:15 6:55 10:35 10:55 1:25 1:40 3:00 6:45 7:05 8:35 10:20 11:00

Sportz 2 Yesterday’s highlights Swimming review News break Golf international News break Swimming championship Sports highlights Golf international Swimming championship News break Lawn bowls report US basketball match of the day Swimming highlights Sports roundup

1. Which sport is given the most airtime?

How long is that altogether?

5. How many highlight shows are there?

How long do they run for altogether?

2. How many different sports have their own shows?

6. Which sport/s have only one show?

3. How many news shows are there? How much airtime is that altogether?

4. What is the longest show? How long does it run for?

Time matters Book 2 (Years 4–6)

7. If you turn on the TV at 1640, what shows will be showing on each of the two channels?

8. If Jake wants to watch live football, when will he need to turn on the TV? What channel will be showing it? How long is the show?

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Timing/Duration Purpose Timing using arbitrary units.

Students should be encouraged to estimate time durations whenever appropriate.

Students need to be aware that duration requires a start and finish time.

Using timing devices helps students establish an appreciation of the duration of time intervals. The types of timing devices used will vary according to the students’ age and experience.

Incidental timing of events can be made throughout the day.

Eventually, the teacher should lead students to realise that arbitrary units such as clapping are not always suitable to communicate durations. An interim unit, prior to the introduction of timing with standard units, may be with the use of a metronome.

Lunchtime at 12:00 indicates a point in time. But knowing that lunchtime is from 12:00 to 1:00, and that this is one hour, indicates elapsed time or duration.

Working out the duration of an event (timing) involves considering the length of time it takes. This may be the duration of an event yet to happen (e.g. How long will it take to run across the oval?) or the duration of an event that has already happened (e.g. How long did it take to get from the library to the classroom?). In order for students to estimate and time an event that has already happened, someone needs to have recorded the start and finish times; then the duration may then be calculated.

There are many devices that will help students to time events. The stopwatch is the most well known of these. However, there are many other devices, both commercial and ones constructed by the students, which can be used for this purpose.

C

omparing times using arbitrary methods

In the earlier years, students can be encouraged to count various events to compare times. The ‘units’ may include: • Claps • Taps • Bounces of a ball • Walking or running a given distance • Picking up a container of blocks, one by one Varying the ‘arbitrary units’ is important.

Finding how many of a particular action can be done in a set time gives students a reason to actively time something.

Teacher poses questions that will encourage students to think about time durations: • Why did you write ‘puppy’ fewer times in one minute than you wrote ‘dog’?

• What do you think would take about one minute from start to finish?

• A short unit may be:

How many times can you click your fingers while Ben collects the books?

• A longer unit may be: How many times can we run around the hoops while the water drips to fill the jar?

Comparing how many of each of the actions can take place within the given duration leads to explanations of why there may be variations.

• How many claps did it take for you to tiptoe from one side of the classroom to the other? Who took the most claps? The least?

• Which takes longer, putting the books back on the shelf or cleaning the paintbrushes?

Students can make a table of their findings.

Cut out shapes Collect books Estimate Actual time Difference

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Fill bottle

35 claps

27 claps

12 claps

42 claps

30 claps

15 claps

7 claps

3 claps

3 claps

Time matters Book 2 (Years 4–6)

Timing/Duration Purpose Timing using standard units.

T

iming using standard units of time For shorter times, ask questions such as:

• How far can you run in one minute?

Students need to be shown how to use a stopwatch correctly.

Timing of short events can also be done using the second hand of an analog clock or watch. Teachers may also use a stopwatch app available on most mobile phones, electronic tablets or interactive whiteboards.

Because of the progression of numerals, a digital clock shows the time ‘now’ and is not suitable for measuring time past or future by counting.

Sports carnivals offer the perfect opportunity to time events.

Comparisons between different event times can be made and graphed, e.g.

What were the best times for the 100 metres, 200 metres and 400 metres races? Did the 200 metres event take twice as long as the 100 metres?

Why? Why not?

• Count backwards from 100 and stop after one minute. What number did you end up at?

• How many times can you throw a ball into a basket in two minutes?

• How long can you bounce a ball for?

• How long will it take for the ball to drop from your desk to the ground?

How long if we drop it from the top of the cupboard?

For slightly longer times: • How long do you think it will take to run around the oval?

• How long do you think it will take to get from the oval to the classroom?

• For how long do you think we played the game of ‘Snap’?

• Note: the time ten minutes before lunch. Cover the clock and try to predict when the bell will go.

O

When there are three or more events being timed, with either arbitrary or standard units, their respective times can be ordered from the event that took the least amount of time to the one that took the most.

Some estimation activities should involve events over which the students have no control, e.g. the time it will take for the bus trip to the swimming pool.

Include some events where students are not asked about the duration in advance (e.g. How long do you think we spent on the oval?); and others where they are given notice (e.g. at the end of singing this song, write down how long you think it took).

Time matters Book 2 (Years 4–6)

rdering times

D

Activity

Estimate

Time taken

Order

Inflate balloon

20 sec

35 sec

1

Do jigsaw

5 min

6 min

3

Skip to oval

4 min

3 min

2

irect and inverse ratios

There is a direct ratio between the number of balloons inflated and the time taken, as they both increase simultaneously.

Direct ratio

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Timing/Duration Inverse ratio There is an inverse relationship between the time taken to put 500 lollies into bags of ten, and the number of students doing the packing; as the number of students increases the time taken decreases.

There are many alternative timing devices that have been used in the past; and some of which would be suitable for students to construct.

Over the next few pages there are details on five such devices. Students could investigate other alternatives on the web. Try using the term horology.

A

lternative timing devices

There are many types of timing devices that can be made by students.

Over the next pages, there is information on the following: • Tockers • Candle clocks • Sand timers • Water clocks • Pendulums

All of the above timing devices can be used as arbitrary units, or can be timed against a stopwatch. There are other timing devices that can be made; a search on the internet will give further ideas.

C

hoosing the timing ‘tool’

Once students have been exposed to a range of timing devices, they should be given the opportunity to choose the appropriate instrument for a particular purpose, rather than the teacher being the one to make the decisions. For example: Choose the best measuring tool for the following: Measuring pulse

Clock, stopwatch, calendar, eggtimer

Running a race

Eggtimer, tocker, stopwatch, sundial

Time of a TV show Baking a cake

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Calendar, sundial, water clock, digital watch Pendulum, eggtimer, stopwatch, shadow stick

Time matters Book 2 (Years 4–6)

How fast can you do them?

1. Work in pairs. The first person starts the timer. Their partner has to point to each of the numbers 1–20 in order and say them out loud. Record how long this took. Now try it a second time and record your time. Then try a third time. Did you improve?

2. The second person now does the same three tries, but saying all of the letters from A to Z, recording how long it took each time. Did it take longer than the counting? Did the times improve?

3. Finally, time each other doing the activity that the partner did and compare your times.

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How quick are you?

Working in pairs, take turns to do the activities and time each other. Have a break between activities, or complete them over several days.

1. Use the 50-metre track on the oval, or mark out 50 metres using a trundle wheel. Take turns running the distance and timing each other. Do this three times and work out your average speed. Put the result in your table.

2. Take turns timing each other walking backwards on the track. Do this three times and work out our average speed.

Put the result in your table.

Materials • A stopwatch • A trundle wheel or access to a 50-metre track • One copy of the table below for each partner

3. Do the same for bunny-hopping and skipping.

4. Compare your results.

Name: 1st try

2nd try

3rd try

Average

1st try

2nd try

3rd try

Average

Running Walking backwards Bunny-hopping Skipping

Name:

Running Walking backwards Bunny-hopping Skipping

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Time matters Book 2 (Years 4–6)

Short and Long Time Durations Scientific notation Scientific notation is a method for writing very large or very small numbers in a compact form. It is named because it is often used by scientists who may look at very small numbers, as in nanotechnology, or who may use very large numbers, as in astronomy where measures of distance can be huge. It involves the use of exponents (powers). The way it works is to use the first non-zero digit of the number, then the decimal point, the rest of the digits of the number, and then multiply it by an appropriate power of ten.

A simple example is 3675 (which does not really need scientific notation as it is simpler in its original form).

We change it to 3.675 and then multiply it by 103 (which is the same as 1000); because 3.675 × 1000 = 3675.

In scientific notation, 3675 is 3.675 × 103 A very large number may appear as 2.42 × 108. This is 2.42 × 100 000 000 which gives us 242 000 000.

S

hort time durations

There are occasions when very short durations of time may need to be considered, e.g. the miniaturisation of technology.

One unit of very short duration is the nanosecond (ns). This is a unit of time that is equal to one billionth of a second (10-9 or 1⁄1 000 000 000). A normal computer has a cycle time of less than one nanosecond.

Light travels about 29.979 centimetres in one nanosecond. It takes approximately 3.335 640 95 nanoseconds for light to travel one metre in a vacuum.

Another unit of short duration is the microsecond (µs); this is equal to one millionth of a second (1⁄1 000 000). There are 1000 nanoseconds in one microsecond. One microsecond is the length of time of a high-speed commercial strobe light flash. It takes approximately 3.335 640 95 microseconds for light to travel one kilometre in a vacuum.

A normal person’s blink of the eye takes about 350 000 microseconds. The flash of a normal camera lights up for approximately 1000 microseconds.

The millisecond is the smallest time that can be measured on most stopwatches. It is 0.001 (one-thousandth) of a second.

There is also an official time span called a jiffy. It is 0.01 (one-hundredth) of a second. So when someone says, ‘I’ll be there in a jiffy’; they would have to move really fast!

L

onger time durations

Sometimes it is useful to consider longer periods of time using scientific notation. These times (below) are compared to the SI base unit for time, the second.

With very small numbers, we use negative powers of ten. So for 0.000034, we show it as 3.4 × 10-5.

Sunlight takes about eight minutes and seven seconds to travel the average distance from the sun to Earth. This is 299 792 458 metres per second, or approximately 3 × 108 metres per second.

A very small number may appear as 5.6 × 10-7. This is 5.6 × 0.000 000 1 which gives us 0.000 000 56.

Some longer units of time, compared to the second are: • Megasecond – 1 000 000 seconds (106; about 11.6 days) • Gigasecond – 1 000 000 000 seconds (109; about 31.7 years) • Terasecond – 1 000 000 000 000 seconds (1012; about 31 700 years) Another large measure of time is the Cosmic Year. This is the rotation period of the sun around the centre of the Milky Way galaxy (approximately 225 million years). The longest measure of time is the kalpa. It is from the Hindu culture, and represents a period of 4320 million years.

Note: A light-year is a unit of measure used mainly in astronomy. It is equal to just under 9 500 000 000 000 or 9.460 55 × 1012 kilometres. It is often used for communicating distances of planets and stars.

The light-year is a measure of distance, not time.

Time matters Book 2 (Years 4–6)

An Astronomical Unit (AU) is the distance from the Earth to the sun (approximately 149 597 870 000 metres). Astronomers use the AU to record the distance from the sun to the other planets. For example, Neptune is about 30 AU from the sun. The Astronomical Unit is also a measure of distance, not time.

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Adding Time Intervals Game Purpose Students perform time calculations.

A game for 2–4 players

M

aterials • Set of Time cards. See pages 114–117 for different time cards

• Spinner with times to be added. See pages 118–120 for different spinners • Counters

R

ules • Shuffle the Time cards and place them in a pile facedown between the players.

• Player 1 takes the top time card and spins the spinner.

• He/She adds the time shown on the spinner to the time on their card, and gives their answer to the other player/s. If correct, the player collects the number of counters that is the same as the hour digit on their card. If incorrect, it is the end of their turn.

• Replace the time card facedown on the bottom of the pack.

• The teacher decides how long the game runs for, or the students set a timer for a time such as 15 minutes. At the end of the time, the person with the most counters is the winner.

Variations for time cards 1. Set 1: quarter past, quarter to and half past cards 2. Set 2: five-minute cards 3. Set 3: one-minute cards 4. Use a mix of all the cards.

5. Blank set; for teacher or students to add their own times.

Variations for spinners 1. Use Spinner 1 for adding 5, 10, 20, 30, 40 or 50 minutes to the time cards.

2. Use Spinner 2 for adding 5, 15, 25, 35, 45 or 55 minutes to the time cards.

3. Use Spinner 3 for adding 2, 17, 29, 31, 48 or 56 minutes to the time cards.

4. Use Spinner 4 for adding 11, 22, 44 or 59 minutes; or, if it lands on one of the stars, add the amount designated by another player to the time cards.

5. Teacher or students write their own time durations on the blank spinner.

Variations for game Instead of students being asked to add a specific amount of time to that shown on their time card; students subtract the amount from it.

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Time matters Book 2 (Years 4–6)

Time Cards Set 1: quarter past, quarter to, half past

12 1 12 11 11 10 10

1:15

2

9

3

8

4 7

11

12

1

10

2

9

3

8

4 7

5

6

6

5

quarter past two

quarter to four

IX X VIII

II III IV

half past six

5:30

V

VII

quarter past seven

11 12 1 10

2 3

9

4

8 7

6

5

half past nine

9

11:15

half past eleven

Time matters Book 2 (Years 4–6)

11

12

9

3

6

10:15

quarter to eleven

3

6

4:45

8:30

4 7

VI

quarter past eight

2

8

III

12

1

10

IX

4:15

XI XII I

VI

XII

5

12

9

3

12:45

6

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Time Cards Set 2: five-minute cards

12 1 12 11 11

1:20

10 10

1:55

2

9 8

4 7

XII

3:05

11

IX X VIII

II III IV

9

5:35

6:50

6

5

3

V

XII

11

12

1

10

7:05

VII

3 6

4:20

4

6

4 7

3

12

2

8

2

7

11 12 1 9

1

8

XI XII I

10

12

5

9

III VI

VI

6

10

IX

2:40

3

IX

III

2

9

3

8

5

4 7

VI

6

5

XI XII I IX X VIII

II III IV

VI

10:40

V

VII

9:05

10:35

12

9

11 12 1 3

11:50

12:35

2 3 4

8 7

6

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6

5

Time matters Book 2 (Years 4–6)

Time Cards Set 3: one-minute cards

1:11

1:27

2:06

2:38

3:23

3:52

4:14

4:44

5:09

5:43

6:21

6:56

7:36

7:41

8:02

8:58

9:17

9:33

10:24

10:59

11:19

11:47

12:08

12:32

Time matters Book 2 (Years 4–6)

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Time Cards Set 4: blank

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117

Time matters Book 2 (Years 4–6)

Time Spinners Set 1: adding 5, 10, 20, 30, 40 or 50 minutes

m

5 es t inu

20 minutes

m 10 i nu t es

50 minutes

mi 40 nu te s

30 tes nu i m

Set 2: adding 5, 15, 25, 35, 45 or 55 minutes

25 minutes

mi 15 nu t es

m

5 es t inu

55 minutes

mi 45 nu te s

Time matters Book 2 (Years 4–6)

35 tes nu i m

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Time Spinners Set 3: adding 2, 17, 29, 31, 48 or 56 minutes

m

2 es t inu

29 minutes

m 17 i nu t es

56 minutes

mi 48 nu te s

31 tes nu i m

Set 4: adding 11, 22, 44, 55 or chosen number of minutes

11 tes inu

119

22 minutes

m

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c ? n ho u m sen m b i nu er o t es f

55 minutes

ch ? nu os e m mi ber n nu te of s

44 tes nu i m

Time matters Book 2 (Years 4–6)

Time Spinners Set 5: blank

Time matters Book 2 (Years 4–6)

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Making a Tocker Purpose To create a timing device for short periods.

A tocker can be used to measure short intervals of up to about 30 seconds.

M

aterials • The lid from an aerosol can • A piece of Blu-tack®

There are commercial tockers that that will rock for a set amount of time. These are useful to demonstrate the notion of tockers, but are not totally accurate. One suggestion is to have only one set, and ask the students to time each of the tockers in the set to see how accurate they are. This introduces the idea of students making their own versions.

• A timing device, e.g. stopwatch

P

rocedure 1. Firmly place a ball of Blu-tack® on the inside of the aerosol lid.

2. On a flat surface, hold the tocker with the ball of Blu-tack® at the top. Let go of the tocker and time how long it takes for it to completely stop rocking.

Note: Students should not count the number of ‘rocks’, rather the time from letting go until it becomes still.

When using commercial tockers, the student holds it with the ‘handle’ laying flat on the table. They then let go of the tocker, and time how long it takes to come to a standstill. There is a natural temptation to count the number of ‘rocks’ it makes, however, what is important is the time it takes to come to a standstill.

Once this first attempt at a tocker has been made, students can investigate how to make it rock for a longer or shorter time; or even for a specified time, e.g. exactly 20 seconds.

This can take the form of a conjecture, where the students try to determine beforehand what to alter to make the time of the rocking different. Variables may include: • The size of the piece of Blu-tack® • Rolling the Blu-tack® into a sausage-shape instead of a ball • The distance inside the lid that the Blu-tack® is placed.

This activity integrates many other learning areas, including science, technology and enterprise, and, if students are asked to write a report on their findings, literacy.

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Time matters Book 2 (Years 4–6)

Candle Clock Purpose • To create a timing device and to measure intervals of time using it.

A candle clock cannot be used to tell the time of day, but rather it is can be used to measure time that has elapsed. The side of a candle is marked at specific intervals and as the candle burns down, a certain period of time will have elapsed.

• To measure length.

Students will require supervision while creating their candle clocks. You will also require adequate ventilation or you risk setting off smoke alarms.

Note: non-tapered candles work best.

The thicker the candle, the longer it will take to burn; so if you want to measure shorter periods of time (minutes), use a thin candle.

Use the same brand of candle when comparing; otherwise melting rates may vary, as the composition of the candle might be slightly different.

It appears that candle ‘clocks’ have been used for hundreds of years.

King Alfred the Great (who reputedly burned the cakes), 849–899 used candle clocks as a means of breaking his day into different timeslots.

M

aterials

P

rocedure

You will need some candles; thin candles like birthday candles are ideal as they melt quickly. It is a good idea to have another larger candle so that children may observe the different rates at which candles melt.

You will also need some permanent markers, some Blu-tack®, a ruler, a clock or timer, a jar lid and some matches.

• Measure the height of one candle.

• Use the Blu-tack® to fix the candle to the lid of a jar.

• Light the candle and let it burn for a fixed amount of time, e.g. 2 minutes. (You will need to test before trying.)

• Blow the candle out.

• Let it cool.

• Measure the candle again and work out how much has burned down.

• Mark intervals along a new candle of the same length as had previously burned and experiment to see if the new candle melts at the same rate.

Note: Marking equal intervals along the second candle only works if the candle is cylindrical, not tapered. If it is tapered, it will take longer to burn down the same distance as it burns lower.

Discuss whether thick candles melt at the same rate as thin ones.

H

alf-hour candle clock • Use larger, thicker candles and measure the height.

• Allow one candle to burn for half an hour and blow out.

• When cool, measure again to determine how much shorter it is now (e.g. 15 mm).

• Mark all the candles at, for example, 15-millimetre intervals. You now have some half-hour candle clocks.

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Making a Sand Timer Purpose • Student will create a timing device to measure short periods of time.

• Students will use a sand timer to measure short events.

Students may already be familiar with sand timers as they are often used to time events like the length of a shower or the time taken to cook something, particularly boiling an egg. Sand timers may be found in many maths storerooms in amongst the measurement materials.

Often sand timers are colour-coded to indicate the length of time to be measured. If the sand timers have been mixed up and you are not sure how long a time period each one measures, let the students sort them out. This is a great problem-solving activity and involves seriating (placing in order) the timers according to the lengths of time they measure.

Sand timers are essentially a timing device and as such are used to measure elapsed time. They do not tell the time of day.

M

aterials • Two plastic drink bottles (same size)

• Some thick card • A funnel Note: Sand timers are also known as hourglasses. Small ones may be called eggtimers and are set to time exactly 3-minutes; the ideal time to cook a soft-boiled egg.

• Scissors • Sticky tape • Some fine sand • A skewer • A cup (to measure the sand) • A timing device, e.g. stopwatch

00 00 M

MIN

S

START SEC

STOP

P

rocedure

Prior to starting, make sure the bottles and the sand are dry, as any excess moisture will interfere with the smooth flow of the sand.

1. Measure a set amount of sand into one of the bottles.

2. Trace around the neck of the second bottle onto the cardboard so that a circle is formed.

3. Cut the circle out.

Nowadays, digital eggtimers can be purchased. They may even have animated falling sand.

4. Make a small hole in the centre of the cardboard circle using the point of the scissors or a skewer.

5. Tape the cardboard circle over the opening of the bottle, being careful not to cover the hole.

This project links science, design and technology, and mathematics.

Students will also use aspects of measurement such as capacity, and circumference and area of a circle.

6. Join the two bottles using the tape.

7. Turn over and watch the sand flow from one bottle to the next.

8. Use a stopwatch or a watch/clock with a second hand to time how long it takes.

9. Adjust the sand timer to measure a set length of time (e.g. one minute with a few seconds tolerance) by either altering the size of the hole or the amount of sand in the bottle.

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Making a Sand Timer

A more traditional-looking sand timer may be made in a similar way to the one above. This time, however, each of the bottles can be cut down to a shape more like a half sphere. Trace around the cut end of the bottle onto two pieces of card to get two circles, and tape each one to the ends of the bottles (first putting the sand into one of the ends).

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Making a Water Clock Purpose • Students will create a timing device to measure short periods of time.

• Students will regulate water flow to measure short events.

A water clock times events according to the flow of water.

M

aterials • A plastic drink bottle

• A polystyrene cup • Scissors • A skewer • Some tape • A bucket • Some water • A timing device, e.g. stopwatch.

P Another name for a water clock is a clepsydra.

rocedure 1. Cut a hole in the top of the plastic drink bottle so that the polystyrene cup fits snugly in it.

2. Use the skewer to pierce a hole in the bottom of the cup so that water can drip through the cup into the plastic bottle. Start off with a small hole; it can be increased later if needed.

Of interest

3. Part-fill the cup with water.

Water clocks have been found as far back as 1500 BC, and, along with sundials, are one of the oldest forms of instruments for measuring time.

4. Use a stopwatch or a watch/clock with a second hand to time how long it takes for the water to empty from the cup into the bottle.

5. Adjust the hole, or the amount of water, to measure a set length of time (e.g. one minute with a few seconds tolerance).

6. Calibrations of various times can be made on the bottle.

This project links science, design and technology and mathematics.

Students will also use aspects of measurement such as capacity, and circumference and area of a circle.

Use the water clock to time certain events. Set challenges for the students such as: • Try standing on one leg until the water runs out.

• See how many times you can legibly write your name until the water runs out.

See pages 107–108 for further suggestions of events to be timed.

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Making a Water Clock A different type of water clock can be made using the lid from a jar and an ice-cream container of water. Using a nail, make a hole in the lid. Once the hole has been made, it is difficult to make the hole smaller, so start off with it quite small. Carefully place it onto the water to float. As the lid fills with water, it will start to sink. Time how long it takes for the lid to sink.

Discuss how it could sink faster (by increasing the size of the hole).

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Playing with Pendulums Purpose Student will experiment with the length of a pendulum and the weight on the end to create a timing device.

Students will also use aspects of measurement such as length and mass.

The plural of pendulum is pendulums, however, pendula is sometimes used in physics.

Note: the mass or weight on the end of the string does not affect the duration of the period—it is the length of the string.

Caution: If students search the internet under the topic ‘pendulum’ they may find references to a band, and the occult.

M

In 1657, Christian Huygens of the Netherlands built the first pendulum clock.

The time (T ) to complete a swing (backwards and forwards) of a pendulum of length (L) is given by

L g

aterials • Some string

• Nuts, washers or other weights that can be tied to the string • Some wood or a wooden 1 metre ruler • A timing device, e.g. stopwatch

P

Of interest

T = 2π

A pendulum is made by suspending a mass on a string. The famous scientist Galileo studied pendulums in the 1600s. As the story goes, his interest in pendulums first occurred when he was sitting bored in church and noticed a lamp swing from the ceiling. He timed the swing using his pulse.

rocedure 1. Place two desks about 80 centimetres apart.

2. Measure the height of the desks.

3. Cut a piece of string slightly longer than the height of the desk.

(Note: that by the time you have tied a weight to the bottom of the string and tied a loop in the string so it fits around the supporting ruler, the string should swing freely without scraping on the floor.)

4. Tie one end of the string to the weight and other to the ruler.

5. Place the ruler between the two desks, with about 10 centimetres at each end resting on the desk. (You may need to place a heavy object on each end of the ruler or tape the ruler to the desks to avoid any movement.)

Where g stands for the acceleration caused by the force of gravity 9.8m/s2

6. Pull the weight back and release (around 15° to the vertical). You should notice that the pendulum swings back and forth in a regular motion.

Oscillation: A complete oscillation refers to swinging back and forth from the original release point.

7. Use a stopwatch or a watch/ clock with a second hand to time how long it takes for each swing. A swing is considered to be from one extreme to the other and back.

This project links science, design and technology, and mathematics.

Adjust the length of the string to see if that makes a difference to the time it takes.

Tie a heavier weight to the string.

Does that make a difference?

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Playing with Pendulums Another way to make a pendulum is to tie the weight to the string and suspend it from a door frame.

Students work in pairs. Hold the weight out and release. One student times the swings while the other counts the number of swings. Count ten swings and stop. Discuss the results.

Now change the length of the swing by holding the weight out at a different distance. Repeat the experiment and discuss the results.

Try changing the mass of the weight. What happens now? What about if you change the length of the string?

A grandfather clock is an old fashioned clock that uses a pendulum to drive it.

The pendulum hangs inside the tall part of the clock. The clock is commonly 1.8 to 2.4 metres tall. It may also be called a longcase clock, tall-case clock or floor clock.

Note: A grandmother clock is more common nowadays, as it is not as tall.

Many ceilings in houses aren’t as high as are needed for a grandfather clock; so it may not fit. However, they are still often sold as grandfather clocks.

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Rates • Students are given an initial exposure to the idea of rates.

Time is often linked with other measures. Typically car speeds are expressed as kilometres per hour or km/h. Bank interest is often quoted as a per annum (pa) or per year figure. Heart rates are expressed as beats per minute (bpm)

• Collect data (pulse rates).

Students should be exposed to different types of rates.

Purpose

Bank interest rates may be calculated in slightly different ways and may include various fees and charges, so in order to compare one bank with another, comparison rates are often used.

Apparently Gallileo used his pulse (heart rate) to work out how pendulums might be used as a time device. As the story goes, he was attending church one day when he noticed a swinging lamp in the Pisa cathedral. He then used his pulse to determine the regularity of the swing.

Note: A pulse should never be taken with the thumb, as it has its own pulse.

E

xercise and heart beat Students will need to be taught how to take a pulse.

They should record their heart rate prior to exercising and straight after exercising. The simplest place to feel a pulse is on the wrist or neck where arteries run close to the surface of the skin.

Two fingers may be placed on the artery that runs down near your palm. The number of beats of a 30 second period may be counted and then doubled to calculate the beats per minute.

A second check may be made after an intense short burst of activity such as ten step-ups.

Students can explore the resting and exercising heart rates of ordinary people and compare them with atheletes.

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Rates Another way to measure your heartbeat is to use a drinking straw, a drawing pin and some Blu-tack®. Cut the straw in half and put some Blu-tack® on the end. Stick the drawing pin into the end of the straw containing the Blu-tack®.

Lay your hand, palm up, on a desk and place the ‘pulse-measurer’ on your wrist. You will notice that the straw moves from side to side. You can now count how many times your heart beats in one minute by counting the movements of the straw. The average person’s heart beats 60–75 times per minute.

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Time Projects Purpose Students research different facets of time.

The first calendars were based on lunar months and hence were called lunar calendars. A lunar month is 29.5 days long and a lunar year is only 354 days long, so the seasons soon became out of synchronisation with the calendar. Jewish people used a lunar calendar in the time of Jesus Christ and that is why Easter is not on a fixed date in our calendar. Every year adjustments have to take place to match the lunar and the Gregorian calendar.

The world calendar was first proposed in 1930. It is a perpetual calendar.

That is, the same calendar may be used year after year without the days and associated dates shifting. Discuss why this calendar has never been adopted?

Some students take everyday items such as clocks and calendars for granted. The following research topics should help students gain an appreciation for other cultures and history.

T

he calendar

Most countries use a Gregorian calendar, but this wasn’t always the case. Explore one calendar that differs from the Gregorian calendar.

Explain: • when it was used and by whom.

• the months and seasons.

• the accuracy of the calendar.

Here are some examples:

• The Hebrew calendar • The Julian calendar • The Islamic calendar • The Chinese calendar • The World calendar

Example: A combined Gregorian and Hebrew calendar

The wristwatch is a relatively new invention. Soldiers in World War 1 found it more convenient to strap a watch onto their wrist rather than keep a watch in their pocket. After the war the practice caught on.

T

imepieces

There are different types of clocks and watches. Explore the difference between:

Most clocks have circular faces because angles are measured in a base 60 system, and there are 60 minutes in an hour.

• Weight-driven clocks • Pendulum clocks • Spring-driven clocks • Quartz clocks • Atomic clocks

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Time Projects

M

etric time

Most countries have adopted the metric system or SI system for measuring things; however, this is not the case for time.

Students may be set the challenge to develop a metric time system.

Groups of students can discuss the problems and think of solutions for metric time. Here are some considerations: • The clock face would need to be changed.

• Speed limit signs would need to be altered.

• 12- and 24-hour time probably wouldn’t make sense. How would you describe morning and afternoon, or would it stay the same?

• Would you need conversion tables from OT (Old Time) to MT (Metric Time)

• Hourly rates of pay would need to be reworked.

• Would you still have 7 days in a week or would the week be converted to ten days?

• What would constitute a ‘work’ week and a weekend?

• What prefixes and suffixes would you use, e.g. deca, deci …

The following website is devoted to Metric or decimalised time <http://zapatopi.net/metrictime/> This website describes various types of metric time and suggests how there might be ten hours in a day and 100 minutes in an hour and so on.

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Greenwich Mean Time & Coordinated Universal Time In England, British Summer Time (BST) is one hour ahead of Greenwich Mean Time and Coordinated Universal Time because of daylight saving.

If stating time in UTC, we add the letter ‘Z’ directly after the digits, without a space. It is the zone designator at zero. So for 10:30 UTC, we would write ‘10:30Z’ or ‘1030Z’.

Because of the use of the ‘Z’, UTC is also known as zulu time. Zulu is the ICAO spelling code word for the letter Z.

The ICAO (International Civil Aviation Organisation) or NATO spelling alphabet

A B C D E F G H I J K L M

Alfa Brava Charlie Delta Echo Foxtrot Golf Hotel India Juliet Kilo Lima Mike

N O P Q R S T U V W X Y Z

November Oscar Papa Quebec Romeo Sierra Tango Uniform Victor

W

hy Greenwich Mean Time (GMT)?

Up until the nineteenth century, most towns and cities had their own times that were built around the sun being overhead at 12 noon.

So within one country, the clocks would often vary depending on the geographical position of the towns. As travel between countries and continents increased, the need for a way of determining the time at different locations became more important. In 1884, representatives of 25 countries met to determine a standard time to alleviate problems when going from one location to another. It was agreed that Greenwich would be the prime meridian (0° longitude), and that international time zones would be linked to this.

The worldwide standard for time was for many years Greenwich Mean Time, often abbreviated to GMT. Since 1 January 1972, the Coordinated Universal Time (UTC) replaced GMT as the time standard. However, many sources use ‘GMT/UTC’, as the difference is not allowed to exceed 0.9 seconds. The UTC still uses the 0° longitude as its starting point.

UTC time is the standard time zone on which all other time zones are based. It is never adjusted for daylight saving. It is a time based on International Atomic Time (TAI), with leap seconds added occasionally to compensate for the globe’s minutely slowing rotation.

Greenwich Mean Time originally referred to mean solar time at the Royal Observatory in Greenwich, London, United Kingdom. However, noon in GMT is not necessarily the exact moment when the sun crosses the Greenwich Meridian (0° longitude) at its highest point. This is because the earth has an uneven speed in its orbit around the sun, and also because the earth is tilted on its axis. This sometimes results in noon GMT being up to 16 minutes away from the sun’s highest point. The use of the word ‘mean’ comes about because of the need to average the annual time when the sun is at its highest point over the Greenwich Meridian.

Whiskey X-ray Yankee Zulu

This Royal Observatory clock is shown in various sites on the web. You may like to project this image and discuss the unusual layout of the timepiece; e.g. use of 0; and Roman numerals to 23 (XXIII).

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Time Zones There are 24 standard time zones on the globe, bounded mostly by the lines of longitude. It can be imagined as like a peeled orange that has the individual segments going from the top of the orange to the bottom. All of the lines meet at the top, and again at the bottom, but they become more spread out as they get near to the widest part of the orange.

Time zones are based on Greenwich Mean Time or Coordinated Universal Time. In the map below, time zones are shown as + or – UTC (or 0° longitude). The numbers beneath the map indicate the number of hours needed to be added or subtracted to determine the current time in any particular region.

Perth is shown as +8, which means it is 8 hours ahead of GMT or UTC. Sydney is shown as +10 and Darwin as +9. California in the USA is –7, which means that you would need to subtract 7 hours from GMT/UTC time to work out its local time.

M

ap of time zones

All of the times shown on the map above are calculated as explained above. If a country or state has daylight saving for some period of the year, differences in the local time may occur, but the GMT or UTC remains constant.

As well as the 24 standard time zones, there are up to 16 other countries, islands or states that have time zones that differ from GMT by increments of 15, 30 or 45 minutes. For example, Newfoundland in Canada has time that is GMT less 3.5 hours.

Interestingly, China, which crosses 4 time zones, uses the same time zone throughout the country.

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Time Zones Another way to look at the different time zones, using the map below, is to consider the degrees of longitude either side of Greenwich. For each 15° of longitude east or west of Greenwich, we ‘add’ or ‘subtract’ one hour. So, for example, if it is 12:00 (noon) GMT or UTC, it will be 8:00 pm in Perth.

Students could investigate different cities around the world, find them on the map above, and work out what time it would be for each of them if it was 12:00 in Greenwich. Teachers could also pose questions about the time in these cities for various times in Greenwich.

T

ime zones in Australia

In Australia, there are three main time zones, and they are designated mostly along state boundary lines. The map on the following page shows these.

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Time Zones These zones are called Australian Western Standard Time, Australian Central Standard Time and Australian Eastern Standard Time.

• Australian Western Standard Time (AWST) covers all of Western Australia and is UTC plus 8 hours (UTC + 8).

• Australian Central Standard Time (ACST) covers South Australia, Broken Hill (which is in northern New South Wales) and the Northern Territory.

It is UTC plus 9.5 hours (UTC + 9.5).

• Australian Eastern Standard Time (AEST) covers Queensland, New South Wales except Broken Hill, Victoria, Tasmania and the Australian Capital Territory. It is UTC plus 10 hours (UTC + 10).

Unofficially, Eucla (in WA, but only about 11 km west of the South Australian border) and its surrounding area have their own time zone that is UTC +8:45.

D

aylight saving in Australia

Daylight saving is where clocks are advanced one hour during the hotter months of the year, and put back for the rest of the year. In Australia, it is observed in New South Wales, Victoria, South Australia, Tasmania and the Australian Capital Territory. It usually begins on the first Sunday in October (forward 1 hour) and ends on the first Sunday in April (back 1 hour). Daylight saving is not observed in Western Australia, Queensland or the Northern Territory.

During the daylight saving period, those areas in the Australian Eastern Standard Time that observe daylight saving move to Australian Eastern Daylight Time (AEDT), where time is UTC + 11. The areas that are in the Australian Central Standard Time and observe daylight saving move to Australian Central Daylight Time (ACDT) where time is UTC + 10.5.

C

alculating times in other time zones

Students can compare the times in other parts of the country or world by using their time zone information and adding or subtracting the appropriate number of hours and minutes. For example, if it is 5 pm (1700) in Brisbane, and we know that New York time is 15 hours behind, the time in New York will be 2 am (0200).

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International Date Line Historically the position of the International Date Line (IDL) has changed according to political and communication needs. The Philippines, for example, were east of the IDL until the 1840s, when Spain’s trading interests moved from Mexico to China. This resulted in a change for the Philippines to the west side of the IDL. When Magellan circumnavigated the globe in 1519–1522, at the end of the journey the crew’s calculations were one day short, even through they kept accurate sailing logs of their journey and times. They travelled from east to west, and thus lost 24 hours.

The IDL first began to be included on maps in the 17th Century. However, even today, there has been no International Treaty or Law that has proclaimed the IDL. It is an artificial, generally agreed upon line. All nations determine their own time zones but these pertain only to their land and territorial waters.

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The International Date Line is an imaginary line that generally runs from the North Pole to the South Pole, passing through the Pacific Ocean. It runs mainly on the 180° longitude that is opposite the prime meridian.

The line shows where the beginning of one day and the end of another come together. It is not a straight line, but has been drawn to avoid going through any territories or island groups. In fact, it runs through no land other than Antarctica; but it splits the Diomede Islands (Little Diomede Island [USA] and Big Diomede Island [Russia] into two separate days, even though they are only 1.5 kilometres apart.

A place immediately to the left of the IDL is always one day ahead of a place immediately to the right of it in the Western Hemisphere.

If you were to head from east to west around the earth, one hour is lost for every 15° of longitude traversed. This would mean losing a full 24 hours in one circumnavigation. To counter this, 24 hours is added when crossing the International Date Line from east to west.

One way to think of this is that when it is sunrise in one location, the sun has already risen in an area to the east of it, and will not yet have risen in areas to the west of it. So in fact, it is always sunrise somewhere on the globe. But once sunrise returns to the original location, it is 24 hours, or one day later.

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International Date Line To the east of Australia, there is a good example of how the IDL has been ‘drawn’ to allow for different island groups to remain together.

Global comparisons are shown below.

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Lunar Month: Phases of the moon The term gibbous refers to a moon that is more than half, but less than a full moon and literally means ‘hunchback’ or ‘bulging’. The dark ‘crescent’ forms one part of the circle and the illuminated piece that completes the circle is gibbous.

The term waxing, when applied to the moon, means that the illuminated portion is getting bigger. A waning moon means that the illuminated portion is becoming smaller.

Early civilisations based their calendar around the moon—hence calendars were known as lunar calendars. From the earth, the moon appeared to change from a round disk to a disappearing crescent. These changes appeared in a repeated cycle over a period of 29.5 days, or a lunar month.

There are eight phases of the moon. Students can be encouraged to keep a pictorial diary of the phases of the moon over one lunar month. The lunar month technically starts with the new moon—that is, the moon is not visible—and progresses to a full moon.

Provide the students with a moon diary to complete. Begin with a fourpoint diary—that is, four circles—and build to an eight-circle diary.

Students may notice that at times the moon is visible during the day.

They could investigate why the moon appears at different times and places in the sky.

Students can research the impact of the moon (and sun) on tides.

Investigate early lunar calendars. The shift from the Julian calendar to the Gregorian calendar is a fascinating story.

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New moon

First quarter

Full moon

Last quarter

The terms first quarter and last quarter can seem a little unusual, as at these points the moon will appear as a semi-circle (or hemisphere). The full moon will be a shiny circular disk in the night sky.

In between two new moons the moon is said to wax and wane. Basically, this means that beginning with the new moon, the light is slowly revealed and the familiar crescent shape becomes apparent. The shape changes from a crescent shape to a gibbous. The following diagram shows the changes that occur over a lunar month.

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Sequence of the Moon Purpose Students will observe and record phases of the moon.

This activity is best carried out over one or two months. It uses daylight sightings of the moon.

M P

aterial • Drawings of landscape, or a silhouette template of one.

rocedure

Students take daylight sightings of the moon’s position in relation to a landmark, e.g. a flagpole. They keep a daily record of their observations over the period of one or two months, showing the size and shape of the moon, and the times of day it comes in line with the landmark.

These observations can be compared to information available on most calendars about the full moon, new moon, crescent moon, etc.

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Time on Different Planets Purpose Students will research and tabulate data on planetary movement.

One day on Earth is the length of time it takes to rotate once on its axis.

One year on Earth is the time it takes for the earth to revolve once around the sun. The length of days and years on other planets are expressed in earth days or earth years so that students can better understand them.

A planet ‘rotates’ on its axis.

A planet ‘revolves’ around the sun or associated star.

Each planet in the solar system rotates at different speeds and revolves around the sun at different speeds; therefore, the length of a day and a year on each planet varies.

The difference between a circle and an ellipse will need to be explained so that students understand why the distances to the sun are approximate.

H

elping students understand the length of a day and a year on other planets

The speed at which a planet rotates determines the length of a day. For example, the planet Venus rotates extremely slowly. One day on Venus lasts the equivalent of 243 Earth days. Venus is unusual in that it takes less time to orbit the sun than it takes to complete a single rotation. A year on Venus takes approximately 225 Earth days to orbit the sun. This means that in Venus time, it takes slightly less than a day to orbit the sun!

Encourage the students to search the internet to gather data to complete the following table. After completing the table the students should pick out interesting or surprising facts. Earth is approximately 150 million kilometres from the sun. We say approximately because the Earth follows an elliptical orbit so, at its closest point it is 147 million km from the sun and at the furthest point it is 152 million km from the sun.

Planet

Distance to sun

Length of day

Length of year

Earth

150 000 000 km

24 hours (1 Earth day)

365.25 days (1 Earth year)

243 Earth days

225 Earth days

Venus

The average distance from the Earth to the sun (150 000 000 km) is also known as an astronomical unit (AU).

Large distances are often stated in astronomical units.

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