m30507 Learn to read, tell the time and write the time from analogue clocks 1.1 2009/07/25 12:14:20.135 GMT-5 2009/07/25 12:23:17.837 GMT-5 gert bezuidenhout gert bezuidenhout gertb@mweb.co.za gert bezuidenhout gert bezuidenhout gertb@mweb.co.za gert bezuidenhout gert bezuidenhout gertb@mweb.co.za Mathematics and Statistics en

Activity 1: To learn to read, tell and write the time from analogue clocks [LO 4.1] To use time measuring instruments, including watches and clocks [LO 4.3] TIME We know that there are 36514 size 12{"365" { {1} over {4} } } {} days in one year. For your calculations in this module you may use 365 days in a normal year and 366 days in a Leap Year. A Leap Year occurs every 4 years (four quarter days = 1 whole day). A Leap Year may be identified by dividing the last two digits of the year by 4. If there is no remainder, the year is a Leap Year. The year 2004 was a Leap Year. The extra day is always put in February. There are 24 hours in one day. There are 7 days in a week There are 60 minutes in an hour. There are 12 months in a year There are 60 seconds in a minute. SHORT FORMS: year = a day = d hour = h minutes = min. (remember: m = metres!) seconds = s month = mo week = wk In this module we shall also come across tenths and hundredths of a second! Analogue clocks and watches show twelve hours only. They do not indicate whether it’s morning or afternoon. Every hour the long hand goes right round the circle once. It counts the minutes.

The long hand tells us the minutes. The short hand tells us the hour. The short hand takes twelve hours to go round the circle once. It tells us the hour. Write down the time on each of the clocks:

Hands on: practical work On the next page you will find two circles. Cut out the first one. Fold it in half. Open it and shade one half. Write PAST in the half on the right and TO in the half on the left. Now paste your cut-out on the circle below. TO PAST When we read the minutes, the first half of the circle shows minutes past the hour. When the long minute hand has gone halfway round the circle, we say it is half past the hour. The second half shows minutes to the next hour. Now cut out the second circle on the “cutting page” page. Fold it in half and in half again. Open the circle and draw dotted lines on the folds. We have divided the hour into 4 quarters. So we get a quarter past the hour and a quarter to the next hour. Write A QUARTER PAST on the right side and A QUARTER TO on the left side and paste your cut-out on the circle below. A QUARTER TO A QUARTER PAST for cutting out Read the instructions very carefully; be sure you understand before you do each step. Now we are going to write in the hours on the clock face. On the next page there are two more circles for you to cut out. Cut out the first one. Fold it in half. Fold it in half again. Do not open it. Now, fold the quarter in three (like an ice-cream cone). Can you predict how many parts there should be when you open it?

Yes, there should be 12 marks. Start with the top mark and label it inside the circle: 12. Then work clockwise and number each fold in the circle. (Your spaces between each number should be accurate because you made folds.) You have now written in the hours. Mark each fold at the edge of the circle and write in the number of the hour. (The first one has been indicated.) Paste it on the first circle on this page.

Now (on the cutting page) cut out the second circle. Mark in the hours as you did in the previous circle. Now you are going to mark in the minutes. There are 60 minutes in an hour, so how many minutes will there be between the numbers? Yes, 5, i.e. 5 spaces. Put little marks to show them and paste the circle on top of circle number 4. You have made an analogue clock face. For cutting out TEST YOUR SKILLS: ANALOGUE CLOCKS Below each of the following clocks, write the time:

On the following clock faces, draw in the long and the short hands carefully to show the time that has been written below:

22 minutes past 2

2.2 17 minutes to 10 (Did you remember that the hour hand is also moving, very slowly?)

2.3 a quarter to four

2.4 twelve o’clock Analogue clocks cannot tell us whether it is morning or afternoon. We have to say it is 9 o’clock in the morning, or 4 o’clock in the afternoon. We use the following short forms: a.m. = in the morning p.m. = in the afternoon Example: A short way of writing 42 minutes past 10 o’clock in the morning is: 10.42 a.m. A short way of writing 36 minutes past 6 o’clock in the evening is: 6.36 p.m. Activity 2: To learn to read, tell and write the time from digital and 24-hour clocks and stop watches [LO 4.1] To use time measuring instruments, including watches and clocks [LO 4.3] Digital clocks tell how many hours and minutes have passed since midnight. They work from midnight to midnight; 24 hours. This is useful because as soon as we see more than 12 hours, we know the time is past noon, e.g. 08:35The first two digits, the 08, tell us the hour if the hour is less than 10.The last two digits tell us the minutes past the hour This clock says 35 minutes past 8 o’clock in the morning (the 08 is less than 12). Midnight would be 24:00. One minute past midnight may be written as 00:01 or 24:01. Noon or midday would be 12:00. One minute past noon would be 12:01. 1. Write as digital time: ten past five in the morning: twenty past four in the afternoon: a quarter to ten in the evening: three minutes to one in the morning: 8 p.m. one minute to ten a.m. Study this example of a digital clock: 16:15 It shows the time, 4.15 p.m. 2.Now read the time on the analogue watch and write it correctly on the digital watch (in the frame on the right): 2.1

(in the morning) 2.2

(afternoon) 3. Draw hands on the analogue clock face to show the same time as is shown on the digital clock. Then write the time below the analogue clock to indicate if it is morning or afternoon. (Use the short form.)

3.1 13.50

3.2 09.10

An international clock is based on the same idea as the digital clock. This clock also works from midnight to midnight. The half of the clock face on the right shows time before noon (midday). The left half shows time from noon to midnight.

4.By looking at this clock, how would you know that the time shown on it is in the morning? A Stop-watch. We use this at swimming galas and athletics and other sports events because we have to measure decimal fractions of a second! 5. Write the time that is shown in the frame: 5.1 Swimming: freestyle relay: 4 x 25m: 1:17,53 5.2 Athletics: 1500m: 5:56,01 Activity 3: To solve problems involving calculation and conversion between the appropriate units of time [LO 4.2] 1. The annual Athletics meeting was held at school. The girls’ times in the 100 sprint were as follows: Joy 14,9 seconds Doreen 15,2 seconds Petra 14,7 seconds Kathleen 14,6 seconds Marie 14,8 seconds Barbara 15,5 seconds 1.1 Who won the race? 1.2 Explain why you give this answer. 1.3 What was the difference between Kathleen and Barbara’s times? 2. Mother puts a chicken into the oven to roast at 11:50. It takes an hour and ten minutes to roast. When will she take it out of the oven? Remember: there are 24 hours in a day. There are 60 minutes in an hour. There are 60 seconds in a minute. 3. Flight 502 leaves East London at 13:10 and arrives at Johannesburg at 15:30. Flight 504 leaves East London at 19:35 and arrives at Johannesburg at 21:50. 3.1 Did the planes arrive in the morning, afternoon or evening? Flight 502 ___________ Flight 504___________. 3.2 Which flight was the faster, and how much faster than the other one was it? Write down your calculations clearly, step by step. . 4. The workers in a car factory start work at 8 a.m. They work until 5 p.m. with a lunch break of one hour and two tea breaks of ten minutes each. For how long do they work each day? Months of the year – old rhyme: Thirty days have September, April, June and November; All the rest have thirty-one, Excepting February alone, which has twenty-eight days clear, And twenty-nine in each Leap Year! 5. When we write dates the short way, we write the year, the month and then the day, e.g. 2003: 01: 24 (24 January 2003) The school year was as follows: School Term Term Starts Term Ends 1 2003:01:22 2003:03:28 2 2003:04:08 2003:06:27 3 2003:07:22 2003:09:26 4 2003:10:06 2003:12:05 5.1 Write the date of the first day of the second term in full (the long way). 5.2 Write the date of the last day of the fourth term in full (the long way). 5.3 How long was the holiday between the first and second terms? Give your answer in weeks and days. 5.4 How long was the holiday between the second and third terms? Write down statements to show how you calculated this and give your answer in weeks and days. 5.5 How long was the holiday between the third and fourth terms? Give your answer in weeks and days. 6. Hannes is a keen fisherman. He was studying high tides because he was planning to go fishing off the rocks in the June holidays. Study this extract from the Table of High Tides in Cape Town and answer the questions that follow. Date June July a.m. p.m. a.m. p.m. 1 0407 1630 2 0443 1707 3 0523 1748 Some dates have been left out here 28 0222 1448 29 0256 1521 30 0331 1555 Study the morning high tides. Describe the pattern. Is it always like that? Do the afternoon high tides have a similar pattern? Write yes or no. . 6.3 High tide at Knysna is 43 min. later. When is the morning high tide at Knysna on 30 June? 6.4 How much time goes by between the morning high tide and the afternoon high tide on 28 June? When we add or subtract time, remember that we are working with hours, minutes and seconds. 60 seconds = 1 minute 60 minutes = 1 hour Example: 1h 45min.+ 2h 36min. You will think of your own way to do this. One way might be: 1h 45min. +2h 36min. = 3h 81min. (Notice: there is 1h hidden in those minutes.) = 4h 21min. 7. Calculate the answers and write down your calculations: 7.1 53 min. and 48 sec. + 14 min. and 34 sec 7.2 14 h 25 min. － 7 h 36 min. Activity 4: To describe and illustrate ways of measuring and representing time in different cultures throughout history [LO 4.4] ASSIGNMENT (RESEARCH-BASED) Your educator will help you to find reference books or take you to the library when you need information in this Assignment. 1. Read the following information. People in the Ancient World did not have clocks and watches as we know them, but they did try to measure time. Some of their instruments for measuring time included: a sun dial; a water clock; a candle clock; burning oil and an hour-glass. Some of them were not very accurate. 2. Look up information in reference books or on the computer to find out what these instruments looked like and how they worked. Also try to find out which people used them and where they lived. 3. Choose four of the instruments named in number 1. Draw them and label each drawing clearly. 4. Explain how any two of them worked. 5. Make either a water clock or a candle clock (or one of the others) and show it to the class. Explain to the class how it works. 6. In the table below write down which people used each of the clocks you have drawn and where they lived: Name of clock People who used it Where they lived 7. Explain why these ancient instruments were not always very accurate. Write your answer below. 8. Try to think of a link between one of them and a modern instrument which we use. Write down your answer .

LO 4 measurementThe learner will be able to use appropriate measuring units, instruments and formulae in a variety of contexts. We know this when the learner: 4.1 reads, tells and writes analogue, digital and 24-hour time to at least the nearest minute and second; 4.2 solves problems involving calculation and conversion between appropriate time units including seconds, minutes, hours, days, weeks, months and years; 4.3 uses time-measuring instruments to appropriate levels of precision, including watches and clocks; 4.4 describes and illustrates ways of measuring and representing time in different cultures throughout history; 4.5 estimates, measures, records, compares and orders two-dimensional shapes and three-dimensional objects using S.I. units with appropriate precision for:mass using grams (g) and kilograms (kg);capacity using millilitres (ml) and litres (l);length using millimetres (mm), centimetres (cm), metres (m) and kilometres (km); 4.6 solves problems involving selecting, calculating with and converting between appropriate S.I. units listed above, integrating appropriate context for Technology and Natural Sciences; 4.7 uses appropriate measuring instruments (with understanding of their limitations) to appropriate levels of precision including:bathroom scales, kitchen scales and balances to measure mass; measuring jugs to measure capacity; rulers, metre sticks, tape measures and trundle wheels to measure length; 4.8 investigates and approximates (alone and/or as a member of a group or team):perimeter, using rulers or measuring tapes.

ACTIVITY 1 1.1 2 1.2 5 1.3 7 Practical work TEST YOUR SKILLS 1.1 20 to 11 or 10.40 1.2 9.25 or 25 past 9 2 Drawing hands on clock faces (see module) ACTIVITY 2 1.1 05:10 1.2 16:20 1.3 21:45 1.4 00:57 or 24:57 20:00 09:59 2.1 06:45 2.2 16:10 3.1 Drawing on clock-face: ten to two in the afternoon 3.2 Drawing on a clock-face: ten past nine in the morning 4. Morning; the hour hand is on the right side of the clock-face; in the afternoon it would be on the left side of this clock-face. 5.1 1 min. 17,53s 5.2 5 min. 56,01s ACTIVITY 3 problems involving time 1.1 Kathleen 1.2 Her time is the shortest 1.3 0,9s 2. 13:00 or 1 p.m 3.1 Flight 502: afternoon; Flight 504: evening Flight 504 was 5 min. faster. 4. 7 h 40 min. 5.1 8 April 2003 5.2 5 December 2003 5.3 10 days 5.4 3 weeks 3 days 5.5 1 weeks 2 day The time from one morning high tide to the next increases; the increase varies from one minute to four minutes The time from one afternoon high tide to the next increases; the increase varies from one minute to 3 minutes. (Note: from morning high tide to afternoon high tide on the same day the time seems to decrease by 1min.each day, but not on 3 July.) 04:14 12 h 26 min. 7.1 1h 8 min. 22 s. 7.2 6 h 49 min. ACTIVITY 4 assignments 1. Read 2. Look up information 3.1 Drawings 3.2 Practical and oral 3.3 Own – practical and oral 3.4 Own – complete table 4. They could not measure seconds and parts of seconds; outside conditions (e.g. wind) influenced the instruments. 5. hour-glass; egg-timer