Looking for Patterns: An Integrated Unit of Weather with Algebra

General Information:

Relative humidity – is defined as the amount of moisture in the air compared with the amount that the air can hold.
Capacity – the actual amount of moisture in the air.
Relative humidity – is a comparison of capacity with humidity.


These lessons were adapted and modified from: Friedl, A. E. (1997). Teaching science to children. An inquiry approach.USA: McGraw-Hill Companies, Inc


Lesson 1: Relative Humidity of Air

Purpose: To determine the relative humidity of air.

Materials: Thermometers, Thermometer probes (Optional), piece of cotton cloth, container, water, stop watch

Procedures: Activity 1

1.    Set up two thermometers side by side.
2.    Wrap one end of a short cotton cloth on the bulb of one thermometer and dip the other end of the cloth into a container of water.
3.    Check the two thermometers at intervals of 5 minutes, 10 minutes, 15 minutes etc.
4.    Record the temperature of each thermometer in the table below.
5.    Use an algebraic expression to express the pattern recorded for both thermometers 1 (with wet cotton cloth) and 2 (without cloth).
6.    Graph the results for both thermometers
 
Results:
Investigations could lead to:
1.    Observing temperatures at periodic intervals
2.    Recording observations on graph
3.    Develops concept of Relative humidity: Humidity, Capacity, Relative Humidity

Background Information:
The above activity can allow us to determine the relative humidity of the classroom.

The wet-bulb thermometer will show a cooler reading than the dry-bulb thermometer. The cooler reading is due to the evaporation of water that is on the wet cloth, which makes the thermometer a wet-bulb thermometer.
How does relative humidity relate to the cooling effect of the wet-bulb thermometer?
The lower the relative humidity, the greater the rate of evaporation, and the cooler the temperature. Therefore, the difference in the two readings between the dry and the wet-bulb thermometer can be used to determine the relative humidity of the air.
Evaporation increases the amount of humidity in the air, but rain decreases it.


Pattern Recognition and Expression: Algebraic Expressions

Thermometer 1: With wrapped cotton cloth
Thermometer 2: Without cloth



X – represents 5 minute intervals        Y – represents thermometer 1
X    Y
5    
10    
15    
20    


Activity 2: What are the weather patterns revealed by the relationship between relative humidity, humidity and capacity?

Relative humidity    Humidity    Capacity
50%    5L    10L
50%    10L    20L
100%    10L    10L
100%    5L    5L
        
 
Procedures:
1.    Use the above data to graph the pattern
2.    Derive a formula for the pattern



Student Page

Lesson 1: Relative Humidity of Air

Students will record the temperatures of both the dry and wet-bulb thermometers at 5, 10 and 15-minute intervals in the table below.

Thermometer 1: With wrapped cotton cloth
Thermometer 2: Without cloth

X – represents 5 minute intervals        Y – represents Thermometer 1
X    Y
5    
10    
15    
20    



X – represents 5 minute intervals        Y – represents Thermometer 2
X    Y
5    
10    
15    
20    


X – represents 10 minute intervals        Y – represents Thermometer 1
X    Y
5    
10    
15    
20    


X – represents 10 minute intervals        Y – represents Thermometer 2
X    Y
5    
10    
15    
20    




Describe the observed pattern between the two thermometers for the different time intervals.



Activity 2: Looking at the patterns expressed by the relationship between relative humidity, capacity and humidity.

For this exercise, students will use the analogy of the weatherman carrying a bucket. The weatherman represents an air mass, the bucket represents capacity, and the water in the bucket is the humidity. If we use the first figures as an example, The weatherman carries a 10L bucket. The capacity of the bucket is 10L. However, the bucket contains only 5L of water. This means that the bucket is only 50% full. In weather terms, this means that the air has a holding capacity of 10L. But, it now only contains 5L of moisture. This represents the humidity. Which in essence, makes the air only 50% full. So, the air has a relative humidity of 50%.

Go ahead and explain each of the following relationships using the same weatherman analogy.

Relative humidity    Humidity    Capacity
50%    5L    10L
50%    10L    20L
100%    10L    10L
100%    5L    5L
        


Example 2:



Example 3:



Example 4:

 
Lesson 2: Discovering the dew point

Purpose: To determine why moisture forms on the outside of a cold glass of water

Materials: thermometer, beaker, ice cubes

Procedures:

1.    Place a few cubes of ice into a beaker of water.
2.    Lower a thermometer into the water and carefully observe the temperature.
3.    Stir slowly but constantly.
4.    At what point does dew form on the outside of the glass?
5.    Record the temperature at which dew forms on the outside of the glass.
6.    Extension: Repeat the above procedures outdoors. Compare the difference between the two environments.

Results:
Investigations could lead to:
1.    Record the temperature at which dew is first noticed on the outside of the beaker.
2.    Repeat activity on different days.
3.    Repeat activity in rooms at different temperatures and outdoors.
4.    Develops concept of relative humidity, humidity, capacity, and temperature.

Background Information:
Moisture forms on the outside of a cold glass of water because the cold surface reduces the capacity of the air to hold moisture. If the air can no longer hold the moisture, it condenses into visible dew on the cold surface.
If it is warm, the capacity is large. If it is cold, the capacity is small. This reveals the tremendous variation in air’s moisture holding capacity. Hot summer air has a capacity a hundred times greater than frigid winter air. Capacity depends entirely on temperature.
When the capacity decreases, the relative humidity increases.

Part 2: The table below provides a few examples of how relative humidity, humidity, capacity and temperature are related.

Relative humidity    Humidity    Capacity    Temperature degrees Celsius
90%    9L    10L    15
50%    9L    18L    25
Decreases    9L    5L    5
            

1.    Explain the pattern of the above relationships.


Student Page

Lesson 2: Discovering the Dew Point

This is an activity that can span a day’s lesson or for several days. Students can also take this assignment home and compare their findings with that of the classroom and home environment (must use a specific room, for e.g. kitchen, bedroom). Students can record their findings using the table below.

Environment (Room)    Temperature of Room    Temperature @ which dew forms
Classroom        
Outdoors (Park)        
Cafeteria        
Kitchen        

Explain the observed pattern.





How do you relate the temperature of the room with how dew first forms?




Are there any immediate visible patterns?




How does this relate to the idea of capacity, humidity and relative humidity?



 
Lesson 3: Evaporation

Purpose: To understand how surface area affects evaporation.

Materials: Chalkboard, damp cloth, petri dish, large bowl, test tube

Procedures:
1.    Wipe the chalkboard or a surface with a damp cloth and ask the pupils to observe.
2.    Ask the students to write what happens to the moisture.
3.    Next, put a similar amount of water in a petri dish, large bowl and a test tube.
4.    Leave these for an overnight (at least 12 hours) in a corner of the room.
5.    Ask students to measure the amount of water in each container.
6.    Ask students to compare the new amount of water with the original amount of water and record their results in the table below.
7.    Ask students to describe their findings and observe the patterns between the original and new amounts of water for each container. Explain why.
8.    Extension: Have students observe the level of water in the three containers over a period of 3-4 days.


Volume of water    Original Volume    New Volume
Petri dish        
Large bowl        
Test tube        

Results:
Investigation could lead to:
1.    Observing the moisture disappearing from the chalkboard or surface
2.    Why does the moisture disappear?
3.    Why are the new amounts of water different for each container?

Background information:
The moisture on a chalkboard usually dries so fast that it is easy to see the drying action. The amount of moisture in the atmosphere greatly affects the speed of drying. On a humid day, the drying action is slow. On a dry winter day, the drying action is faster. Surface area also affects evaporation. The water in the large bowl as opposed to the test tube will occupy a larger surface area hence evaporation is expected to occur faster.
Evaporation increases the amount of humidity in the atmosphere but rain decreases it.




Student Page

Lesson 3: Evaporation

Here you will explore the concept of evaporation by using the three scenarios – water in a bowl, a petri dish and a test tube.
Note and record the difference in the level of water between the original and new volume of water in each of the containers.

Volume of water    Original Volume    New Volume
Petri dish        
Large bowl        
Test tube        
 
Explain the pattern observed for the changes between the original and new volume for each container.




 
Lesson 4: The Water Cycle

Purpose: To observe patterns between evaporation, humidity and precipitation.

Materials: large jar, metal pie plate, hot water, crush ice, smoke

Procedures: Part 1
1.    Set up a miniature water cycle in a jar.
2.    Fill a large, wide-mouthed glass or plastic jar with 1 or 2 centimeters of hot water (for best results ensure that the water is as hot as possible).
3.    Cover the top of the jar with a metal pie plate filled with crush ice.
4.    From time to time, add a small amount of smoke inside the container.
5.    See if pupils can identify miniature forms of clouds, air movement, and rain.
6.    Allow plenty of time for results to occur.

Results:
Investigations could lead to:
1.    Observe the formation of clouds, rain and wind
2.    Compare events inside of jar with events in the atmosphere
3.    What are those factors that cause rain?
4.    Factors of evaporation, humidity, precipitation


Background Information:
A convection current is set up inside the jar. Hot water heats the air, so it rises. The cold metal plate cools the air so it descends. The different temperatures power a continuous current inside the jar. The smoke allows for the currents to become more visible.
The moving air produces a water cycle. Warm air carries moisture up to the cold plate. The cold plate causes the water to condense into droplets. After a while enough water forms to fall down as rain. It should be understood that rain forms very slowly.

Part 2:

1.    Observe the patterns between evaporation, humidity, and precipitation.
2.    Graph the relationship between two or more factors.
3.    Can use fathom to obtain information from different site in the U.S and international countries.
4.    Create graphs and then compare with other sites.
5.    Why does the pattern vary?
6.    How are evaporation, humidity and precipitation affected by the different regions?



Student Page

Lesson 4: The Water Cycle

Describe what you see.





Use the applet to observe the patterns between evaporation, humidity and precipitation. (More of this will come when the applets are completed).