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Quiz & test questions Grade 9 Math

Corriemoor Brook Storm Week: Flow Rates and Conversions

A grade 9 quiz on six days of fictional gauge readings, covering average rate of change, conversions among cfs, gpm, and MGD, and reading a storm rise.

Objectives

  1. Students will compute and interpret the average rate of change of streamflow over a stated interval.
  2. Students will convert a flow rate among cubic feet per second, gallons per minute, and million gallons per day.
  3. Students will identify a common error in reporting a rate of change from two readings.

Vocabulary

Streamflow
Streamflow is the amount of water moving past a point in a river or stream in a given amount of time. It rises after storms and snowmelt and drops during dry spells.
Baseflow
Baseflow is the water that keeps a stream flowing even when it has not rained for a while. It comes from groundwater slowly seeping into the streambed.

Also: gauge, average rate of change

Teacher overview

This 30-point quiz covers six days of streamflow readings taken during and after a storm on a fictional brook. It mixes two multiple-choice items, three short-answer or explanation items, and six computation items, and it is written for a single 30-minute period. Items 2, 3, and 9 assess average rate of change; items 5, 6, and 8 assess unit conversion among the three flow units a utility uses; and items 10 and 11 ask students to reason about why a stream behaves as the table shows.

Corriemoor Brook Storm Week: Flow Rates and Conversions — Grade 9 Math
Name: ____________________________ Date: ______________

Assessment

Corriemoor Brook is a fictional stream with a gauge above the town's water plant. The table gives the daily flow readings for one storm week. Day 0 is the day before the rain began.

Day Flow (cfs)
0 40
1 120
2 380
3 260
4 150
5 95

Use 1 cubic foot per second = 448.8 gallons per minute, and 1 million gallons per day = 1.547 cubic feet per second.

  1. (2 points) A reading of 380 cfs describes which of the following? (A) a total volume of water, (B) a rate of flow, (C) a depth of water, (D) a water pressure.
  2. (3 points) Find the average rate of change in flow from day 0 to day 2, in cfs per day.
  3. (3 points) Find the average rate of change in flow from day 2 to day 5, in cfs per day.
  4. (2 points) Explain what the sign of your answer to item 3 tells you about the brook.
  5. (3 points) Convert the peak flow of 380 cfs to gallons per minute.
  6. (3 points) Convert the peak flow of 380 cfs to million gallons per day. Round to the nearest tenth.
  7. (2 points) A student reports that the flow rose 340 cfs per day between day 0 and day 2. Which error did the student make? (A) used the wrong two readings, (B) did not divide by the 2 days, (C) used the wrong conversion factor, (D) subtracted in the wrong order.
  8. (3 points) The Corriemoor water plant may withdraw at most 6.0 MGD. Express that limit in cubic feet per second. Round to the nearest hundredth.
  9. (3 points) Find the largest one-day increase in flow between consecutive days, in cfs per day.
  10. (3 points) The brook drains 18 square miles. Explain, using units, why a larger drainage area generally produces a larger peak flow for the same rainfall.
  11. (3 points) Give one reason the flow keeps falling for several days after the rain has stopped.

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: B, a rate of flow. Cubic feet per second is a volume divided by a time, so it measures how fast water passes the gauge, not how much water is present. Choice A is the common confusion between a rate and a total.
  2. Answer: 170 cfs per day. (380 - 40) / (2 - 0) = 340 / 2 = 170 cubic feet per second per day.
  3. Answer: -95 cfs per day. (95 - 380) / (5 - 2) = -285 / 3 = -95 cubic feet per second per day.
  4. Answer: The flow is falling. A negative average rate of change means the readings decreased over that interval, so the brook is receding toward its baseflow after the storm crest.
  5. Answer: 170,544 gpm. 380 cfs x 448.8 gallons per minute per cfs = 170,544 gallons per minute.
  6. Answer: 245.6 MGD. 380 / 1.547 = 245.64 million gallons per day, which rounds to 245.6.
  7. Answer: B, the student did not divide by the 2 days. The difference of 340 is the total rise across two days, so the rate per day is 340 / 2 = 170 cfs per day.
  8. Answer: 9.28 cfs. 6.0 MGD x 1.547 cfs per MGD = 9.282, which rounds to 9.28 cubic feet per second. The plant withdraws a small fraction of the storm peak.
  9. Answer: 260 cfs per day. The consecutive differences are 80, 260, -120, -110, and -55, so the largest one-day rise occurred between day 1 and day 2.
  10. Answer: A larger area collects more rain. Rainfall is a depth per storm, and depth multiplied by area gives a volume, so inches times square miles produces a larger volume of runoff for the same storm. That larger volume passing the gauge over a similar time yields a larger peak flow.
  11. Answer: Water reaches the brook slowly from the soil and shallow groundwater. Rain that soaked into the ground drains toward the channel for days after the surface runoff has passed, so the flow declines gradually toward baseflow instead of dropping at once.

Differentiation

Support

Provide a partially built difference table for this fictional gauge record, with the day-to-day changes computed and only the division by the number of days left for the student. Allow a printed conversion card listing the two factors given at the top of the quiz.

Extension

Ask students to sketch the six fictional readings as a graph, estimate the rate of change at the crest directly from the curve, and explain why an estimate read from a graph and a computed average over an interval need not agree.

ELL supports

Provide the table with a small arrow beside each row showing whether the flow rose or fell from the previous day. Give a sentence frame for item 4: "The sign is ___, which means the flow is ___ between day 2 and day 5."