Calibrating Clocks

Purpose

In this unit students construct several simple clocks including water clocks and pendulums. They investigate time as measured by these clocks and make comparisons with standard units of time.

Achievement Objectives
GM3-1: Use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time.
Specific Learning Outcomes
  • Measure time in periods of up to 15 minutes.
  • Compare non standard and standard measurements for time.
Description of Mathematics

Students' experiences with time throughout the learning sequence has two aspects:
duration and telling time.

Telling time must enable them to:

  • develop an understanding of the size of the units of time. This includes being able to estimate and measure using units of time;
  • read and tell the time using both analogue and digital displays.

Standard units
When students can measure the duration of events using non-standard units, they are ready to move to the use of standard units. The motivation for moving to this stage often follows from experiences where the students have used different non-standard units for the same event. They can then appreciate that consistency in the units used would allow for the easier and more accurate communication of duration.

Measuring with standard units involves the introduction of minutes, hours and seconds in addition to reading time on analogue and digital clocks.

Duration
The minute is often introduced first because it is small enough to measure common events. The duration of a minute can be established by watching the second hand on a clock or by constructing a minute sand-timer. An appreciation for the size of a minute can be built up through lots of experience in measuring everyday events. For example, how many minutes does the song play for? How long is morning break? How long does it take to walk around the school building? How many times can you hop in a minute? How many linked cubes can you join in a minute?

As the students become familiar with the size of a minute they should be given opportunities to estimate before measuring. Minutes need to be linked to the movement of the minute hand on the analogue clock and the digits on digital displays.

An understanding of the size of a second can be developed by investigating the relationship between seconds and minutes. This can be done by watching the digital displays on some watches, on stopwatches and on video-recorders. The students should be encouraged to develop their own reference for a second, for example, a counting pattern "one – banana – two – banana – three etc".

Reading and telling time
The underlying number skills should be mastered before teaching students the skill of telling and reading time.

Opportunities for Adaptation and Differentiation

The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:

  • providing support on how to use the timing devices (stopwatches or clocks)
  • pairing the students so that they can be supported at the station tasks
  • reducing the number of tasks that need to be completed at the stations.

The context for this unit can be adapted to suit the interests and experiences of your students. While the focus is on creating “clocks” that measure time, the tasks can be made more engaging by providing a purpose for each clock that connects to the everyday experiences of your students.  The clocks could then be used by your students for that purpose.  For example: 

  • a clock that can be used to time whether an egg is soft or hard boiled
  • a clock that could be used to measure the time allowed for a school's performance at Polyfest 
  • a clock that can be used to measure the time spent cleaning teeth or washing hands.

Giving students the opportunity to suggest their own purposes for the clocks and then adapting the stations so that they can tailor the clocks to those purposes is also likely to increase their engagement in the task.

Required Resource Materials
  • Getting started: Candles (enough for one per group or pair), matches, large dish of sand for candles to stand in.
  • Station One: Plastic containers (e.g. milk bottles, yoghurt pottles), nails to make holes in plastic (variety of sizes), wooden sticks, water, trays or buckets for water collection, water, stopwatches or clocks with second hands.
  • Station Two: Pairs of plastic bottles with the same size openings (e.g. soft drink bottles, water bottles), small squares of cardboard,  nails to make holes in cardboard, salt or dry sand (needs to be dry to run through hole), stopwatches or clocks with second hands.
  • Station Three: String, a variety of weights, place to attach string to (e.g. edge of desk, overhanging shelf in classroom, empty chart holder), stopwatches or clocks with second hands.
  • Reflecting: Variety of timing devices including stop watches, clocks, watches and devices made in the three stations.
Activity

Getting started

This session is taken as a whole class activity with students working in groups or pairs to experiment with the time taken for different candles to burn. The teacher retains control of the matches and the burning candles.

Brainstorm with students the different kinds of clocks they know: watches, wall clocks, oven timers etc. Explain that this week they will be making and experimenting with a variety of different clocks.

  1. Show the students a candle. Ask them to estimate how long it would take for the whole candle to melt. How much would be melted in 5 minutes?
  2. Group or pair students and give each group a candle.
  3. Students record the length of their candle, either by drawing a line to show how long it is, or measuring it in cm. They also draw a mark on the candle to show how much they think will be melted in 5 minutes.
  4. Collect candles together (maybe in a dish of sand so they stand up easily) and burn all candles for five minutes. Students observe and watch to see the accuracy of their five minute marks.
  5. Blow out the candles after five minutes and return them to the students for them to check the accuracy of their mark and record how long the candle is now (either by drawing a line to show how long it is, or measuring it in cm).
  6. Students put three more marks on their candles: showing how much they think will be melted in 5, 10 and 15 minutes.
  7. Collect all candles together and burn for 15 minutes, observing the accuracy of the marks as they burn.
  8. At the conclusion of the activity return candles to students and discuss
    How accurate was your candle clock?
    How could you make your candle clock more accurate?
    What are the limitations of a candle clock?

Over the next three days have students work at the three stations, rotating groups so all students have a chance to try all three activities.

Station One: Water Clocks

In this station students make and experiment with water clocks.

Student Instructions (Copymaster 1)

  1. Use the materials provided to make a water clock like the one in the diagram. The size of the hole you make and the size of the container you use will affect the way your clock measures time.
  2. Estimate the time it will take for the water level to drop from one mark to the next on your clock. Record your estimates in a table.

water moves down

estimated time taken

measured time taken

1 mark

 

 

2 marks

 

 

3 marks

 

 

4 marks

 

 

 

  1. Measure the time taken for the water level to drop from one mark to the next on your clock. Record your results in a table.
  2. Experiment with your clock and the way it measures time.
    What happens if you make the marks further apart?
    What happens if you make the marks closer together?
    Can you make your clock measure 1 minute accurately?
    Can you make your clock measure 5 minutes accurately?

Station Two: Sand Timers

In this station students make and experiment with sand clocks similar to egg timers.

Student Instructions (Copymaster 2)

  1. Use the materials provided to make a sand timer like the one in the diagram. The size of the hole you make will affect the way your clock measures time.
  2. Estimate the time it will take for the sand level to drop from one mark to the next on your clock. Record your estimates in a table.

sand moves down

estimated time taken

measured time taken

1 mark

 

 

2 marks

 

 

3 marks

 

 

4 marks

 

 

 

  1. Measure the time taken for the sand level to drop from one mark to the next on your clock. Record your results in a table.
    Were the times between the marks the same?
    Why / Why not?
    How could you make the time between each mark the same?
  2. Experiment with your clock and the way it measures time.
    What happens if you make the marks further apart?
    What happens if you make the marks closer together?
    Can you make each mark measure the same time period?
    Can you make your clock measure 1 minute accurately?
    Can you make your clock measure 5 minutes accurately?

Station Three: Pendulums

In this station students make and experiment with pendulums to tell the time.

Student Instructions (Copymaster 3)

  1. Use the materials provided to construct a pendulum like the one in the diagram.
    Pend
  2. Start your pendulum swinging to measure time.
  3. To help your pendulum measure the same each time you use it, you will need to
    • make sure you hold the pendulum in the same place each time you release it
    • make sure you let the weight go rather than push it
    • count the number of swings carefully from the highest place in the swing each time.
  4. Estimate the time it will take for the pendulum to swing 5, 10, 15 and 20 times. Record your estimates on a table.

number swings

estimated time taken

measured time taken

5

 

 

10

 

 

15

 

 

20

 

 

 

  1. Measure the time taken for the pendulum to swing 5, 10 15 and 20 times. Record your measurements on a table.
  2. Experiment with your pendulum and the way it measures time.
    What happens if you make the string longer?
    What happens if you make the string shorter?
    What happens if you use a heavier weight?
    What happens if you use a lighter weight?
    Can you make your pendulum measure 1 minute accurately?
    Can you make your pendulum measure 5 minutes accurately?

Reflecting - Comparing Clocks

This session is taken as a whole class activity with students working with different timing devices to time the same event. Equivalent times are recorded and compared.

  1. Explain to students that today they will be using a variety of timing devices to measure the length of set tasks.
  2. Distribute timing devices amongst pairs of students. Use a variety of timing devices including stop watches, clocks, watches and the devices made in the three previous stations.
  3. One student performs a task while all other students time the task.
  4. Record equivalent measures on a chart.

Task

Equivalent measures for time taken

Recite the alphabet

55 seconds

1/2 candle mark

2 water clock marks

3 sand clock marks

20 pendulum swings

Count to 500

2 minutes, 33 seconds

3 1/4 candle marks

6 sand clock marks

52 pendulum swings

 

  1. Continue for several tasks. When complete review and discuss results.
    What are the advantages of the candle clock (and other devices)?
    What are the disadvantages of the candle clock (and other devices)?
    Which measure would be the most useful if you wanted to describe to someone in London how long a task took? Why
    ?
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Level Three