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Lesson plan Grade 7 Math

Hollenbeck Brook's Stream Gauge: A Grade 7 Conversion Lesson

A 50-minute grade 7 math lesson where students convert a fictional brook's gauge readings between cubic feet per second, gallons per minute, and MGD.

Objectives

  1. Students will convert a stream flow from cubic feet per second to gallons per minute using a published factor.
  2. Students will extend a per-minute rate to gallons per day and to million gallons per day.
  3. Students will find a withdrawal as a percent of stream flow and describe a seasonal change as a negative number.

Vocabulary

Stream gauge
A stream gauge is a station on a river or stream that continuously measures the water level, which is used to calculate how much water is flowing. Scientists and forecasters use the data to track floods, droughts, and water supply.

Also: cubic feet per second, gallons per minute, withdrawal, conversion factor

Teacher overview

Stream gauges report flow in cubic feet per second, while water utilities plan withdrawals in gallons per minute and report them in million gallons per day, which means the same stream is described in three units by the people who share it. This lesson has students move a fictional brook's readings across all three using published factors: one cubic foot per second equals 448.8 gallons per minute, and one million gallons per day equals 694 gallons per minute. The misconception to plan for is that students often treat the conversion as finished after one multiplication, reporting a per-minute figure when the question asked for a daily one, so the closure step asks explicitly which unit of time each answer carries.

Procedure

Hook (5 min): Write "6 cfs" on the board and ask students whether that is a lot of water. After a few guesses, tell them the fictional town of Oxmarsh takes its drinking water from Hollenbeck Brook and needs the same reading in gallons before anyone can answer.

Direct instruction (12 min): Post the two factors, 448.8 gallons per minute for each cubic foot per second and 694 gallons per minute for each million gallons per day. Model a reading that is not on the handout: 6 cfs times 448.8 equals 2,692.8 gallons per minute, then times 60 equals 161,568 gallons per hour, then times 24 equals 3,877,632 gallons per day. Say the unit out loud at every step and write it beside the number.

Guided practice (13 min): Distribute the handout. Work items 1 and 2 together, then let pairs complete items 3 and 4 and check that each answer carries the unit the question asked for.

Independent practice (12 min): Students complete items 5 through 8 alone. Point out that item 6 is a percent and that item 8 asks for a change, which may come out negative.

Closure and exit ticket (8 min): Each student answers on an index card: "A fictional gauge reads 2 cubic feet per second. How many gallons per minute is that?" Collect and check for 897.6 gallons per minute. If more than a quarter of the class answers in a different unit, spend the first minutes of the next class labeling units before computing.

Hollenbeck Brook's Stream Gauge: A Grade 7 Conversion Lesson — Grade 7 Math
Name: ____________________________ Date: ______________

Student Handout

Use the fictional town of Oxmarsh and Hollenbeck Brook for every question. Use these two conversion factors: 1 cubic foot per second equals 448.8 gallons per minute, and 1 million gallons per day equals 694 gallons per minute. On Tuesday the gauge on Hollenbeck Brook read 12.5 cubic feet per second.

  1. Convert Tuesday's reading of 12.5 cubic feet per second to gallons per minute.
  2. How many gallons does the brook carry past the gauge in one hour at that rate?
  3. How many gallons does the brook carry past the gauge in one full day at that rate?
  4. Write that daily amount in million gallons per day.
  5. Oxmarsh may withdraw at most 0.9 million gallons per day. Convert that permit limit to gallons per minute.
  6. That permitted withdrawal is what percent of Tuesday's brook flow in gallons per minute? Round to the nearest tenth of a percent.
  7. By August the gauge fell to 4.0 cubic feet per second. Convert that reading to gallons per minute.
  8. Write the change in the gauge reading from Tuesday to August as a signed number in cubic feet per second.

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: 5,610 gpm. Multiply the reading by the factor: 12.5 times 448.8 equals 5,610 gallons per minute.
  2. Answer: 336,600 gallons. Multiply the per-minute rate by 60 minutes: 5,610 times 60 equals 336,600 gallons in an hour.
  3. Answer: 8,078,400 gallons. Multiply the hourly amount by 24 hours: 336,600 times 24 equals 8,078,400 gallons in a day.
  4. Answer: 8.0784 MGD. Divide the daily gallons by one million: 8,078,400 divided by 1,000,000 equals 8.0784 million gallons per day.
  5. Answer: 624.6 gpm. Multiply the permit limit by the factor: 0.9 times 694 equals 624.6 gallons per minute.
  6. Answer: 11.1 percent. Divide the withdrawal by the flow: 624.6 divided by 5,610 equals 0.11134, which is 11.134 percent and rounds to 11.1 percent.
  7. Answer: 1,795.2 gpm. Multiply the August reading by the factor: 4.0 times 448.8 equals 1,795.2 gallons per minute.
  8. Answer: -8.5 cfs. Subtract the earlier reading from the later one: 4.0 minus 12.5 equals negative 8.5 cubic feet per second, a drop.

Exit ticket answer: 897.6 gallons per minute, because 2 times 448.8 equals 897.6.

Differentiation

Support

Give these students a conversion strip that lists the two factors and the two time steps, times 60 for hours and times 24 for days, in the order the handout uses them. Allow calculators and accept item 6 rounded to the nearest whole percent. If a student stalls at item 4, point out that the only change is dividing by one million.

Extension

Ask students to find how many hours the fictional brook would need to flow at its August rate to carry the same volume it carries in one full day at Tuesday's rate, and to explain why the answer is greater than 24 hours.

ELL supports

Pre-teach "gauge," "flow," "withdrawal," and "per" using a drawing of a brook with a measuring post and an arrow labeled with each unit in turn. Provide the frame "___ cubic feet per second times 448.8 equals ___ gallons per minute" for items 1 and 7.