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Worksheet Grade 6 Science

Reading the Callan River Gauge: Netherby's Flood Crest

A grade 6 worksheet in which students summarize nine river gauge readings from a storm at Netherby and work out when the Callan River crossed flood stage.

Objectives

  1. Students will summarize a set of river gauge readings using mean, median, and range.
  2. Students will calculate a rate of rise in feet per hour from two gauge readings.
  3. Students will use a rate of rise to predict when a river will reach flood stage.

Vocabulary

Flood stage
Flood stage is the water level in a river at which it starts to overflow its banks and cause flooding problems nearby. Forecasters compare the current water level to flood stage to warn people when flooding is about to happen.
Watershed
A watershed is all the land where rain that falls will drain to the same stream, river, or lake. Everyone lives in a watershed, no matter how far from the water they live.

Also: gauge, crest, rate of rise

Teacher overview

A river gauge reports one number, the height of the water above a fixed point, and forecasters turn that single number into a warning by watching how fast it changes. This worksheet gives students nine gauge readings taken during a summer storm on the Callan River and asks them to summarize the record and then use it to predict a crossing time. The record can also open a class discussion of a common misconception, that a river crests when the rain stops. Students often expect the highest reading at the moment of heaviest rain, when in fact water needs hours to travel from the upper watershed down to the gauge, so the crest arrives well after the storm has moved on.

Reading the Callan River Gauge: Netherby's Flood Crest — Grade 6 Science
Name: ____________________________ Date: ______________

Student Worksheet

The Callan River flows past the town of Netherby. A gauge on the bridge reports how high the water stands. A storm moved across the watershed one Tuesday. The table lists the gauge readings taken every two hours. Flood stage at this gauge is 12.0 feet.

Hours after the storm began Gauge height (feet)
0 3.0
2 4.0
4 6.0
6 9.0
8 13.0
10 14.0
12 11.0
14 7.0
16 5.0
  1. How many gauge readings are listed in the table?
  2. The river stood at 3.0 feet at hour 0 and at 14.0 feet at hour 10. How many feet did the river rise between those two readings?
  3. The nine readings are 3.0, 4.0, 6.0, 9.0, 13.0, 14.0, 11.0, 7.0, and 5.0 feet. What is the mean height?
  4. Using the same nine readings, what is the median height?
  5. Using the same nine readings, what is the range?
  6. The river stood at 9.0 feet at hour 6 and at 13.0 feet at hour 8. What was the rate of rise in feet per hour between those two readings?
  7. Flood stage is 12.0 feet. Between which two readings in the table did the river first pass flood stage?
  8. How many of the nine readings are at or above the flood stage of 12.0 feet?
  9. The river stood at 9.0 feet at hour 6 and rose 2.0 feet each hour after that. At that steady rate, at what hour would the river reach 12.0 feet?
  10. The mean of the nine readings is higher than the median. Explain what it is about this storm record that pulls the mean above the median.
  11. Netherby sounds a siren when the gauge passes 10.0 feet. Explain how knowing the rate of rise, and not just the current height, helps a forecaster decide when to sound the siren.
  12. Suppose the town paves a large shopping center on the flat land beside the Callan River. Explain how that change could make the next crest both higher and earlier.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 9 readings.
    Count the rows in the table, one for each two-hour step from hour 0 through hour 16.
  2. Answer: 11.0 feet.
    Subtract the starting height from the crest height: 14.0 - 3.0 = 11.0 feet.
  3. Answer: 8.0 feet.
    Add the nine readings to get 72.0, then divide by 9. The mean height is 8.0 feet.
  4. Answer: 7.0 feet.
    Put the readings in order as 3.0, 4.0, 5.0, 6.0, 7.0, 9.0, 11.0, 13.0, 14.0. The fifth value in a list of nine is the median, so the median is 7.0 feet.
  5. Answer: 11.0 feet.
    Subtract the smallest reading from the largest: 14.0 - 3.0 = 11.0 feet. The range and the total rise happen to match here because the river started at its lowest point.
  6. Answer: 2.0 feet per hour.
    The river rose 13.0 - 9.0 = 4.0 feet across two hours, and 4.0 divided by 2 is 2.0 feet per hour.
  7. Answer: Between hour 6 and hour 8.
    The reading at hour 6 is 9.0 feet, which is below flood stage, and the reading at hour 8 is 13.0 feet, which is above it. The crossing happened somewhere between those two readings.
  8. Answer: 2 readings.
    Only the hour 8 reading of 13.0 feet and the hour 10 reading of 14.0 feet are at or above 12.0 feet.
  9. Answer: Hour 7.5.
    The river needs 12.0 - 9.0 = 3.0 more feet. At 2.0 feet per hour that takes 3.0 divided by 2.0, or 1.5 hours. Add 1.5 hours to hour 6 to get hour 7.5.
  10. Answer: The two very high readings near the crest.
    The crest readings of 13.0 and 14.0 feet sit far above most of the record, and a few unusually large values pull a mean upward while leaving the middle value where it is. Accept any answer naming the high crest values or describing the record as lopsided.
  11. Answer: The rate of rise tells the forecaster how much time is left.
    A gauge sitting at 9.0 feet is not urgent by itself, yet a river climbing 2.0 feet each hour will pass the siren height within half an hour. Accept any answer explaining that the rate gives warning time, while a single height gives only the present condition.
  12. Answer: Pavement sheds rain instead of soaking it up.
    Water that would have soaked into soil runs straight to the river, so more of the storm reaches the channel and it arrives sooner. Accept any answer naming both a larger volume of runoff and a shorter travel time.

Differentiation

Support

Give students the nine readings already listed in order for items 4 and 5, so the sorting step does not block the median and range work. For item 9, provide a partially drawn number line marked at 9.0, 10.0, 11.0, and 12.0 feet so students can count the rise in whole feet before converting it to hours.

Extension

Ask students to redraw the table as a line graph, mark flood stage as a horizontal line at 12.0 feet, and then estimate from the graph how many total hours the Callan River spent above flood stage. Have them explain why a graph gives a better estimate here than the table alone.

ELL supports

Pre-teach "gauge," "crest," and "flood stage" using a labeled drawing of a bridge with a measuring staff painted on the pier. Provide sentence frames for items 10 through 12, such as "The mean is higher because ___," and "Paving the land near Netherby would ___ because ___."

Extensions

Have students look up the gauge nearest your school on a public river-conditions map, record the height each morning for two weeks, and then compare the calm-weather range they observe with the storm range of 11.0 feet from the Netherby record. A short written comparison of the two ranges makes a strong follow-up assignment.