Math Activities

How Much Water Is There?

Objectives:

Students will: 
- be able to calculate the fresh water available for human consumption
- make inferences about the importance of using water resources responsibly


Materials:

• 5 gallon aquarium
• water (enough to fill tank)
• measuring spoons (tsp, tbls)
• measuring cups
• eye droppers
• paper towels
• calculators

Background:

Even though 75% of earth's surface is covered by water, not all of it is available for consumption by humans.  In fact, very little of the water is considered potable, or available for consumption.  

Procedure:
1.  Have the students brainstorm the sources of water on the planet.  Create a list on the board.  After allowing students to reveal all sources, complete the list for them, and provide the following information:

(Figures are from The Cousteau Almanac)

2.  Break the students out into small working groups.

3.  Have the students determine which of the water sources could be used for human consumption.  Students should calculate the amount of freshwater potentially available for use.  (Groundwater, Freshwater Lakes, Rivers, and Icecaps/glaciers).   And of course, not all of this would be readily available due to pollution contamination.

4.  Have the students turn their attention to the water filled 5 gallon tank, which will represent the volume of all the water on the earth.  Have the students calculate the amount of water in the tank, in tablespoons.  The students should now calculate the equivalent volume of the quantities on the "Water on Earth" table below.  They should obtain figures similar to the following values:

*Note: 5 gallons = 1280 tablespoons*

5.  Have each team remove 34 tbls of water from the tank and place into a container to bring back to their workstations.   (The 34 tbls of water represents the total possible amount of fresh water available for human consumption.)

6.  Have the students calculate and remove all of the water representing Rivers.  Place the water in a small container and label "Rivers" (approximately 1 drop).  Have the students calculate and remove all of the water representing Freshwater Lakes.  Place the water in a small container and label "Freshwater Lakes" (approximately 1/10 of a tablespoon).   Have the students calculate and remove all of the water representing Groundwater.  Place the water in a small container and label "Groundwater" (approximately 8 tablespoons).  In the container originally containing the 34 tbls, the students should now have approximately (25 tablespoons), which is representing the Ice caps and Glaciers.  Label the container "Ice caps and Glaciers".

7.  The students should now have a good visual understanding of how little water is available for human consumption.  Remind the students that much of the water in the Ice caps is "locked in" and unavailable for immediate use, and that pollutants are being discharged everyday, further decreasing the amount available for human consumption.

Assessment:

Reference

EPA - Office of Wetlands, Oceans, and Watersheds
Water Facts
USGS - Water Science for Schools
Cousteau Almanac

Extension:
To assess how much water your students use on a daily basis, participate in another CIESE project - Down the Drain.




Sense of Scale

Objectives:
Students will:
- brainstorm/research common products and their respective pH levels
- draw a pH scale to scale and place the products under the appropriate pH level on the scale


Materials:

• rolls of white register/receipt tape
• colored pencils
• rulers and yardsticks
• calculator (optional)

Background:

The pH scale is a representation of the balance between hydrogen ions (H₃O⁺) and hydroxide ions (OH^-) in a liquid.  A low pH corresponds to high hydrogen ion concentration, in other words, the more hydrogen ions present, the fewer hydroxide ions present, the more acidic the solution.  Conversely, a high pH corresponds to a low concentration, in other words, the more hydroxide ions present, the fewer hydrogen ions present, the more basic the solution.  This concept is illustrated in the abbreviated pH scale below:
 

The abbreviated pH scale is a common way to represent the concept of pH, but lacks to convey an important concept about pH.  The pH scale is a logarithmic scale, meaning that every step on the scale represents a multiplication of 10.  If the pH of a solution decreases by one pH unit, that represents a tenfold increase in the concentration of hydrogen ions.  For example, Lemon juice, with a pH of 2 (100,000 H₃O⁺ ions) is 10 times more acidic than soda with a pH of 3 (10,000 H₃O⁺ ions).  This aspect of the pH scale is shown nicely in this pH scale graphic.

Even after explanation, this still can be an abstract concept for some students.  This activity is designed to offer a sense of scale to a pH scale for students, showing just how far apart the numbers should be on a true pH scale.  Students will quickly realize why the abbreviated version of the pH scale in found in textbooks.  NOTE: Depending on the student's mathematical abilities, this lesson can be adapted to use Scientific Notation.

Procedure:

1. Have students review a standard (abbreviated) pH scale.

2.  Explain to the class that the pH scale that they are accustomed to seeing is not entirely accurate.  Explain that the pH scale is actually a logarithmic scale, meaning that every step on the scale represents a multiplication of 10 and that they are going to create an accurate representation of the pH scale.

3.  In cooperative working groups or as a class, have students research or brainstorm various products and their corresponding pH. 

4.  Distribute the rolls of register tape, colored pencils, rulers, yardsticks and calculators. 

5.  Have the students unroll and find the approximate middle point of the strip of receipt tape.  NOTE: To conserve class time, complete this step for the students prior to class.

6.  Have the students label the middle point as pH 7 - neutral. 

7.  Have the students measure 10 centimeters to the right of pH 7 and label that point pH 8.  If the students found products with pH 8, have them list the products on the receipt tape.

8.  Have the students measure 10 centimeters to the left of pH 7 and label that point pH 6.  If the students found products with pH 6, have them list the products on the receipt tape.

9.  Have the students calculate how far in centimeters pH 9 will be from pH 8.  Measure to that point and label the receipt tape.  If the students found products with the corresponding pH, have them list the products on the receipt tape.

10.  Have the students calculate how far in centimeters pH 5 will be from pH 6.  Measure to that point and label the receipt tape.  If the students found products with the corresponding pH, have them list the products on the receipt tape.

11.  Continue procedure until students run to the end of the paper (which will happen very quickly).

12.  Have the students continue their calculations to determine how much more receipt tape they would need to complete the pH scale to scale.

Assessment:

1.  Why do you think an abbreviated pH scale is used in textbooks?

2.  How much more acidic is a solution with a pH of 2 than a solution with a pH of 6?

3.  How much more basic is a solution with a pH of 12 than a solution with a pH of 9?

3.  How much more acidic is a solution with a pH of 3 than a solution with a pH of 8?

4.  How much more basic is a solution with a pH of 11 than a solution with a pH of 5?

5.  How long of a piece of paper would you need to draw a complete pH scale (using centimeters)?

6.  Why do you think a change in a body of water's pH level of even one pH unit could be deadly for the organisms that live in the water?

 

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