Reading Clocks to Nearest Minute: 3.25
Supporting materials
Indicator of Progress
At this level students are able to read analogue clock times to the nearest minute and have a fully developed understanding of the relationship between analogue and digital clocks. Students are also able to solve problems involving calculations with durations of time.
Both of these abilities require knowledge of the numbers of minutes in an hour, half an hour and quarter of an hour, and mental calculations, especially based on 60 and on multiples of 5 minutes.
At this stage, students are completing the phase learning to measure time, as shown in the diagram below, and are moving onto learning to calculate with time. See Measurement Phases.
Three phases of teaching measurement
Illustration 1: Connections between analogue, digital and spoken expressions for time
Students at this level can convert freely between digital, analogue and verbal forms of time notation. For example, they can read a digital clock at 7:40 and can say that the time is '20 (minutes) to 8' and know where the hands are on an analogue clock showing this time.
Illustration 2: Calculating duration
Students at this level understand that there are 60 minutes in an hour, and can use this fact to determine the duration of certain time intervals, including over the o’clock times. For example, they can recognise that there are 40 minutes between 6:45 and 7:25. They can also calculate that there are 2 hours and 45 minutes between 4:30 and 7:15 because they know that there are 2 hours between 4:30 and 6:30, a further 30 minutes until 7:00 and then an extra 15 minutes after that.
Before reaching this level students may only be able to deal with durations within the hour interval because they involve only simple subtraction (e.g. there are 25 minutes between 11:10 and 11:35).
Illustration 3: Links to the Mathematics Online Interview
Examples of the types of tasks that would be illustrative of prior knowledge for this indicator, as aligned from the Mathematics Online Interview:
- Question 39c) Telling the time (analogue clock)
- Question 42 Duration Tasks
- Question 43 TV Guide
- Question 44 Linking digital and analogue time
Teaching Strategies
Much of the teaching of reading an analogue clock will occur incidentally throughout the day as the teacher points to the classroom clock. Progressively, the teacher will be modelling reading the clock more accurately (e.g. to minutes). Students also need to be able to see a digital clock simultaneously to connect analogue and digital representations.
Specific attention in number work needs to be given to mental computation that supports working with time, such as multiples of 5, fractions of 60, complements to 60 etc. In turn, students will learn number facts in the time context that they can use in other number work (e.g. 12 fives = 60).
Performing calculations with times is greatly helped by having students visualise movements on the clock face. Teaching calculations with the support of a geared clock builds up this mental imagery.
Note: Clocks show points in time, as opposed to the duration of time given by stop-watches.
Activity 1: Showing times on analogue and digital clocks provides opportunities for students to represent times from a digital display on an analogue clock.
Activity 2: Timetables provides opportunities for students to perform calculations involving durations of time.
Activity 3: Important properties of time notation highlights key points associated with the properties of time notation that should be discussed with students.
Activity 4: Time Bingo is a bingo-like game that builds students’ capacity to connect digital, analogue and verbal representations of time.
Activity 1: Showing times on analogue and digital clocks
Provide students with a commercially available un-geared clock, or they can make their own as described below. A geared clock is not used, because it is engineered to keep the two hands synchronised.
- Provide students with a copy of a clock printed on card. See resource sheet Clock Face (PDF - 19Kb).
- Students need to cut out the hour and minute hands and use a split pin to attach them to the centre of the clock face.
Write a digital time on the board and ask students to make this time on their own clock. Students hold up their clocks to show their responses, after which the teacher demonstrates the correct time on a large geared clock. Repeat with other digital times. A set of suitable sequences is suggested below. They may be done over several days. The process can be reversed – an analogue clock can be shown and students can write down digital time.
Sequence 1:
- Providing times separated only by a few minutes keeps the minute hand moving in a clockwise direction
- Providing times within a one hour period focuses attention on the small movements of the hour hand
- Providing times which are multiples of 5 minutes as well as those which are not, highlights the intermediate position of the minute hand.
Sequence 2:
- Providing times separated exactly by one hour keeps the hour hand moving in a clockwise direction
- Providing times separated exactly by one hour focuses attention on the movements of the hour hand to the same relative position between adjacent clock numbers (here always one quarter of the way from the current hour number to the next hour number)
- Providing times after 12 focuses attention on the cycle 11, 12, 1, 2
- Remind students of the language of 'quarter past 7' as well as '7 fifteen'
Sequence 3:
- Sequence 3 is similar to Sequence 2. Remind students of the language of 'quarter to 8' as well as '7 forty five.'
Sequence 4:
- This sequence highlights 'twenty past' and 'twenty to.' The 0 - 20 - 40 - 0 pattern can be linked to 60 minutes in one hour.
Sequence 5:
- This sequence combines movements of hour and minute hands.
Activity 2: Timetables
This activity provides opportunities for students to perform each of the three types of calculations involving durations:
- Given two points in time (start and end times), students can calculate the duration of the interval
- Given a start time (one point in time) and a duration, students can calculate the other point in time (end time).
- Given an end time (one point in time) and a duration, students can calculate the other point in time (start time).
Provide students with copies of local public transport timetables and ask questions similar to the following:
- How long does it take for the train/bus to travel from High Street to Bayview Street?
- If it takes 12 minutes for the train/bus to travel from Bayview Street to Central and it leaves Bayview Street at 10:51, what time will it arrive at Central?
- If it takes 17 minutes for the train/bus to travel from Central to Mountain Street and you need to be at Mountain Street by 11:14, what is the latest time you should leave Central? Which bus/train should you catch at Central?
Provide students with other problems in different contexts (e.g. cooking, TV guides) to practice using durations:
- What time will the cake be ready, if it went into the oven at 3:12 and takes 45 minutes to cook?
- At what time should the cake be put into the oven if I want it to be ready at 4:20 and it takes 45 minutes to cook?
Illustrate the answers to all of these problems using a geared clock. For example, when students give their answers, ask them to move the hands on the clock appropriately. This builds up students’ capacity to visualise. This capacity to assist in visualising time passing is a great advantage of the analogue clock.
Activity 3: Important Properties of Time Notation
The activities above, and fluency with time numeration, rely on several properties that are worth discussing explicitly with students.
- There are two cycles of 12 hours in a day. Once we reach 12:00, the next hour after this is 1:00. This can lead to a discussion of the use of am and pm, and consideration of 24 hour time.
- Note: 12:00 midnight and 12:00 noon should not be given an am or pm designation. Technically speaking pm means post meridian or AFTER the middle of the day and 12:00 noon IS the middle of the day. However, there is widespread usage of 12:00am for midnight and 12:00pm for noon.
- The next number in the minutes sequence 57, 58, 59 is 00, not 60. As a consequence, calculations involving duration require care. For example, if a bus leaves at 10:51 and travels for 12 minutes, we cannot simply add 12 minutes on to 10:51 to get 10:63 as the answer. Either, students can recognise that 10:60 is the same as 11:00 and so 10:63 is 11:03; or else they can recognise that 9 of the 12 minutes are needed to get the time to 11:00, and there are three minutes after that.
- Fluent conversion between analogue and digital times depends on knowing complements to 60 or being able to calculate them quickly. For example, I know 10:40 is 20 minutes to 11 because I know 40 + 20 = 60 and I know 8:50 is 10 minutes to 9 because I know 50+10 = 60.
- Students need to know that 7.50 (for example) in a TV guide is not the number 7.50 (i.e. 7 and a half). This is a major source of confusion for students as they begin to learn about decimals. The separator between the hours and minutes is not a decimal point. Use a colon : not a dot as the separator between hours and minutes.
Activity 4: Time Bingo
To play Time Bingo, a playing card would be made up with digital, analogue and verbal versions of a fixed set of different times in a 4 × 4 grid (e.g. 8:35, 8:35 on an analogue clock face, and '25 to 9'). Each student has a playing card and some markers to place on the recorded times. The teacher has a list of all of these different times. As the teacher calls out a time or displays it on a digital clock or displays it on an analogue clock, students place a marker on any times on their card that are equivalent to what the teacher says or shows. Students can mark more than one grid position if there are duplicates in different formats. The winner is the first student to fill their card. Teachers can vary the information that they give – on some occasions saying the times only verbally, on other occasions showing a digital time only, on other occasions showing and saying a time etc.