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Unit 2

Unit 2 . Analyzing Graphs. Example 1. The title of the graph is “Water Consumption in a Typical School Day.” For what purposes is water used at a school ? What do you think the numbers along the horizontal axis represent?

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Unit 2

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  1. Unit 2 Analyzing Graphs

  2. Example 1 • The title of the graph is “Water Consumption in a Typical School Day.” For what purposes is water used at a school? • What do you think the numbers along the horizontal axis represent? • What might the numbers along the vertical axis represent? Do we have any indication of the units being used? • What could be the reason for the “spikes” in the graph? • What might be the reason for the smaller spikes between the large ones?

  3. Example 1 • The title of the graph is “Water Consumption in a Typical School Day.” For what purposes is water used at a school? Primarily through bathroom use. • What do you think the numbers along the horizontal axis represent? Time of day • What might the numbers along the vertical axis represent? Do we have any indication of the units being used? We have no indication of the units being used. We would assume that these numbers are related, in some way, to a volume of water • What could be the reason for the “spikes” in the graph? Student bathroom use between class periods. • What might be the reason for the smaller spikes between the large ones? Some student use during class time.

  4. Analyzing graphs Scenario #1 • Regular school day hours: 8:00 a.m. - 3:04 p.m. • After school activities: 3:15 p.m. - 5:15 p.m. • Around 10:00 a.m. there is a 13 minute advisory/homeroom period.

  5. Analyzing graphs Scenario #1 • Can you see features of this information appearing in the graph? • Is it possible to deduce the time of lunch at this school?

  6. Analyzing graphs • Can you see features of this information appearing in the graph? Bathroom use before and after activities. • Is it possible to deduce the time of lunch at this school? Around 10:00 a.m. the graph indicates a peak of 80 units.

  7. Analyzing graphs • Around 10:00 a.m. the graph indicates a peak of 80 units. What is the number 80 representing?

  8. Analyzing graphs • Around 10:00 a.m. the graph indicates a peak of 80 units. What is the number 80 representing? Gallons of water used or the amount “used” is measured by the volume of water that drains through the pipes and leaves the school.

  9. Analyzing graphs • How does one actually measure the amount of water flowing out through the pipes precisely at 10:00 a.m.? What does “80 units of water leaving the school” right at 10:00 a.m. mean? (Think about when the bell rings and students “flow” through the door to leave)

  10. Analyzing graphs • How does one actually measure the amount of water flowing out through the pipes precisely at 10:00 a.m.? What does “80 units of water leaving the school” right at 10:00 a.m. mean? The researchers who collected this data watched the school’s water meter during a 12-hour period. The meter shows the total amount of water (in gallons) that has left the school since the time the meter was last set to zero. Since the researchers did not know when this resetting last occurred, they decided, at each minute mark during the day, to measure how much the meter reading increased over the next minute of time. Thus the value “80” at the 10:00 a.m. mark on the graph means that 80 gallons of water flowed through the meter and thus left the school during the period from 10:00 a.m. to 10:01 a.m.

  11. Analyzing graphs • What are the units for the numbers on the vertical axis?

  12. Analyzing graphs • What are the units for the numbers on the vertical axis? Gallons per minute

  13. Analyzing graphs • Ignoring the large spikes in the graph, what seems to be the typical range of values for water use during the school day?

  14. Analyzing graphs • Ignoring the large spikes in the graph, what seems to be the typical range of values for water use during the school day? 15 gallons per minute

  15. BellWork • Suppose the researchers collecting data for water consumption during a typical school day collected data through the night too. • a. For the period between the time the last person leaves the building for the evening and the time of the arrival of the first person the next morning, how should the graph of water consumption appear? • b. Suppose the researchers see instead, from the time 1:21 a.m. onwards, the graph shows a horizontal line of constant value, 4. What might have happened during the night?

  16. Bell work • Suppose the researchers collecting data for water consumption during a typical school day collected data through the night too. • a. For the period between the time the last person leaves the building for the evening and the time of the arrival of the first person the next morning, how should the graph of water consumption appear? Since no toilets are being used, the graph should be a horizontal line of constant value zero. • b. Suppose the researchers see instead, from the time 1:21 a.m. onwards, the graph shows a horizontal line of constant value, 4. What might have happened during the night? Perhaps one toilet started to leak at 𝟏:𝟐𝟏 a.m., draining water at a rate of 𝟒 gallons per minute.

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