Weather dot com

Purpose

The focus of this unit of work is the world weather and in particular the temperatures in different countries during any given week. 

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
  • recognise the need for a standard unit of temperature
  • measure temperature (degrees Celcius) with a thermometer
  • calculate changes in temperatures
Description of Mathematics

Boiling water is pretty hot. Ice is pretty cold. Fortunately most of the time we live between these two levels of heat at a temperature where we are more comfortable. Temperature gives us a way of saying how relatively hot or cold something is. So the temperature of boiling water is a given a high number and the temperature of ice is a smaller number.

Measuring temperature relies on the fact that if we put one object into something that stays at a constant temperature, then the object becomes the same temperature as the ‘something’. So, for instance, putting an ice cream outside in the summer will mean that the ice cream melts away. It takes on the temperature of the air. Put the same ice cream in a fridge and the ice cream will stay frozen. It takes on the temperature of the freezer.

Similarly when the nurse puts a thermometer under your tongue, the thermometer takes on the temperature of your tongue. The temperature of your tongue is constant for long enough for the thermometer to become that temperature. Taking the temperature of a room or the outside air works on the same principle.

What is a thermometer? It is an instrument that has been set up to measure temperature. These days we use the Celsius system of measurement so that 0 degrees is the temperature where ice and water can exist together without one freezing or the other melting. The other fixed point on the Celsius scale is the 100 degree mark. This is where water boils.

Traditionally thermometers contain the element mercury. However mercury thermometers are not permitted in schools and have been replaced by spirit based thermometers. They work in much the same way as the mercury thermometers in that the liquid expands with heat in a uniform way. The volume of the liquid increases by the same amount for every degree rise in temperature. Its rate of expansion is calibrated on the glass scale.

In 1724 Gabriel Fahrenheit, an instrument maker who lived in Däanzig and Amsterdam, was the first person to use mercury in a thermometer. Fahrenheit described how he calibrated the scale of his mercury thermometer:

"placing the thermometer in a mixture of sal ammoniac or sea salt, ice, and water a point on the scale will be found which is denoted as zero. A second point is obtained if the same mixture is used without salt. Denote this position as 30. A third point, designated as 96, is obtained if the thermometer is placed in the mouth so as to acquire the heat of a healthy man." (D. G. Fahrenheit,Phil. Trans. (London) 33, 78, 1724)

On this scale, Fahrenheit measured the boiling point of water to be 212. Later he adjusted the freezing point of water to 32 so that the interval between the boiling and freezing points of water could be represented by the more rational number 180. Temperatures measured on this scale are designated as degrees Fahrenheit (°F). There are still many countries in the world that use this scale. As you will see from www.weather.com, the United States is one of these countries.

It’s a little surprising that we call the scale that we use in New Zealand, the Celsius scale. After all when Anders Celsius (1701-1744) was playing around with these things he used the reverse scale in which 100 represented the freezing point of water and zero the boiling point of water. It was actually Carolus Linnaeus of Upsula, Sweden, who in 1745 first described a scale in which the freezing point of water was zero, and the boiling point 100, making it a centigrade (one hundred steps) scale.

In 1948 use of the Centigrade scale was dropped in favour of a new scale using degrees Celsius (°C). The Celsius scale is defined by the following two reasonably complicated items that we won’t explain:
(i) the triple point of water is defined to be 0.01 C
(ii) a degree Celsius equals the same temperature change as a degree on the ideal-gas scale.

This is a little more accurate than the old Centigrade scale but it is a bit too subtle a change for daily use. For instance, on the Celsius scale the boiling point of water at standard atmospheric pressure is 99.975 C (in contrast to the 100°C defined by the Centigrade scale). It’s clear that you wouldn’t be able to tell the difference on the average thermometer. It does make a difference though if you are worried about very small changes in temperature and very low temperatures as some scientists are. As far as the ‘person in the street’ is concerned, there is no difference between the Centigrade scale and the Celsius scale.

To convert from Celsius to Fahrenheit: multiply by 1.8 and add 32: °F = °C x 1.8 + 32. You can check this out by remembering that 32°F is the same as 0°C and that 212°F = 100°C. If you find this hard to remember, a simple rule of thumb that is pretty close is "double the °C and add 30". (We give the conversion in the other direction later on.)

Required Resource Materials

Copymaster of Thermometers chart

Thermometers

World map

Activity

Getting Started

In this session we use thermometers to measure the temperature inside and outside the classroom. We also try to guess the temperature of three bowls of water. If possible, position several thermometers around the classroom and at least one outside the room.

  1. Begin the session with a discussion about the temperature of the classroom.
    What temperature do you think it is inside our room today?
  2. Ask questions about the guesses.
    Why do you think it is that?
    How could we check?
    How do you write that?
    What units do we use for temperature?
  3. Check the temperature.
  4. Look in more detail at a thermometer and the calibrations used.
  5. Estimate and check the outside temperature.
  6. Tell the students that they are to monitor the temperature inside and outside the classroom over the week.
  7. Ask for ideas about how this could be carried out.
    When
    Frequency
    By whom
    How to record
  8. Let small groups of students make decisions about how they are going to record the data collected. For example:

Day

 

8:45

10:30

12:00

2:00

3:00

in out in out in out in out in out

Monday

                   

Tuesday

                   

Wednesday

                   

Thursday

                   

Friday

                   

Exploring

Over the next 2-3 days the students gather information about the weather in different countries and cities around the world. Information about the temperature is included in daily newspapers and weather reports on television. However weather.com/en-NZ/ is a wonderful resource, giving current and long-range forecast and temperature predictions for cities and countries around the world. Illustrated below is an example of the information contained on the site. 

  1. Using a world map let the groups of students select a country and 2 or 3 cities to investigate over the next 3 days. Attach a labelled pin to the map to indicate the countries that are going to be surveyed.
  2. As a class make predictions about the temperatures in different parts of the world prior to collecting the information.
    Which countries will have temperatures like NZ?
    Why do you think that?
    Which countries will be very hot? Why do you think that?
    Which countries will be very cold? Why do you think that?
  3. Discuss the collection of weather information over the next 3 days.
  4. Tell the students that they will be expected to record their results for display on the final day of the unit.
  5. In addition collect the long-range predictions for the closest New Zealand city to your school. Compare these with the actual temperatures recorded during the unit.

Reflecting

Today we begin by comparing the temperatures that we collected with the long-range forecast for our locality. We then share the information collected by the groups of students in the class. We use this to plot cities (and countries) on a large classroom  thermometer chart (copymaster). We conclude by adding some other temperature facts to the thermometer.

  1. Discuss the temperatures collected outside the classroom during the week. Display the information on the wall for everyone to look at.
    Which was the highest outside temperature collected?
    Which was the lowest outside temperature collected?
    Which temperature best represents the temperatures this week? Why do you think that?
  2. Place a mark (pin or sticker) against the most representative temperature for our locality on the thermometer chart (copymaster).
  3. Take turns letting the groups add their city to the chart.
    Which city was the hottest?
    What do you think that would feel like?
    Has anyone been there before? Describe.
    Which city was the coldest?
    What do you think that would feel like?
    How could we find out what it really feels like without going?
  4. Conclude the lesson by attaching other temperature facts to the thermometer. (Obviously the thermometer will need to have a "broken" scale to include all these facts. Instead of telling the students the facts you could leave them to investigate the answers.
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