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Math Activities
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How
Much Water is There?
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Sense of Scale |
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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
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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:
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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:
| Water on Earth |
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| Oceans |
97.2% |
|
All icecaps/glaciers |
2.0% |
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Groundwater |
0.62% |
|
Freshwater Lakes |
0.009% |
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Inland seas/salt lakes |
0.008% |
|
Atmosphere |
0.001% |
|
All
rivers |
0.0001% |
| Total |
99.8381% |
(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:
| Water on Earth |
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| Oceans |
1244.16 tbls |
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All
icecaps/glaciers |
25.60 tbls |
|
Groundwater |
7.93 tbls |
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Freshwater
Lakes |
0.11 tbls |
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Inland seas/salt
lakes |
0.10 tbls |
|
Atmosphere |
0.0128 tbls |
|
All
rivers |
0.0012
tbls |
| Total |
approx 1280 tbls |
*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.
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Assessment:
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- Explain why it is so important for humans to use water responsibly.
Give statistics to prove your position.
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Reference
Atlas of America's
Polluted Waters
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.
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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
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Materials:
- rolls of white register/receipt tape
- colored pencils
- rulers and yardsticks
- calculator (optional)
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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 H 3O+
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.
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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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Overview