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Lesson plan Grade 9 Math

Halcyon Ridge Stormwater: A Rational-Method Runoff Lesson

A 50-minute grade 9 lesson where students use the rational method Q = C i A to compare runoff from pavement and lawn at Halcyon Ridge and size a rain garden.

Objectives

  1. Students will use the rational method Q = C x i x A to find peak stormwater runoff.
  2. Students will compare runoff from surfaces with different runoff coefficients.
  3. Students will size a rain garden to hold a roof's storm runoff.

Vocabulary

Rain garden
A rain garden is a shallow planted dip in the ground that catches rain running off a roof or driveway and lets it soak slowly into the soil. Its deep-rooted plants help clean the water.

Also: rational method, runoff coefficient, peak runoff, impervious

Teacher overview

On the fictional Halcyon Ridge campus, a paved lot sheds far more storm runoff than a lawn of the same size. Engineers estimate peak runoff with the rational method, Q = C x i x A, where the runoff coefficient C is about 0.9 for pavement and 0.2 for lawn. In this lesson students use the rational method to compare surfaces, then size a rain garden to hold a roof's runoff from a 1-inch storm. A common misconception is thinking area alone sets the runoff, when the surface type, through C, matters just as much.

Procedure

Launch (7 min): Show two photos, a paved lot and a grassy field, and ask which sheds more water in a storm on the fictional Halcyon Ridge campus. Record predictions on the board.

Model the rational method (13 min): Introduce Q = C x i x A, where C is the runoff coefficient (about 0.9 for pavement, 0.2 for lawn), i is rainfall intensity in inches per hour, and A is area in acres. Work one example: a 0.5-acre parking lot with C = 0.9 and i = 2 inches per hour gives Q = 0.9 x 2 x 0.5 = 0.9 cfs. Note that in these units the answer comes out in cubic feet per second.

Guided practice (10 min): Repeat the calculation treating the same lot as lawn (C = 0.2), then compare the two results and draw out how the runoff coefficient drives the difference.

Independent practice (15 min): Students complete handout questions 1 through 7, including the roof-runoff and rain-garden sizing steps.

Closure / exit ticket (5 min): Students answer handout question 8 on a slip, finding the peak runoff from a smaller pavement area. Scan for correct use of Q = C x i x A before dismissal.

Halcyon Ridge Stormwater: A Rational-Method Runoff Lesson — Grade 9 Math
Name: ____________________________ Date: ______________

Student Handout

All figures below describe the fictional Halcyon Ridge campus.

  1. A parking lot has runoff coefficient C = 0.9, rain intensity i = 2 inches per hour, and area A = 0.5 acre. Use Q = C x i x A to find the peak runoff in cubic feet per second (cfs).
  2. A lawn of the same size has C = 0.2, with the same i = 2 inches per hour and A = 0.5 acre. Find its peak runoff.
  3. How many times more peak runoff comes from the pavement than from the lawn?
  4. Convert the parking lot's 0.9 cfs to gallons per minute, using 1 cfs equal to 448.8 gpm.
  5. The school roof is 8,000 square feet. A 1-inch storm makes runoff of area x inches x 0.623 gallons. Find the roof runoff in gallons.
  6. A rain garden must hold that 4,984 gallons. Using 1 cubic foot equal to 7.48 gallons, find the volume needed in cubic feet.
  7. Explain why replacing pavement with lawn or a rain garden lowers the peak runoff Q.
  8. A 0.25-acre pavement area has C = 0.9 and i = 2 inches per hour. Find its peak runoff Q.

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: 0.9 cfs. Q = 0.9 x 2 x 0.5 = 0.9 cubic feet per second.
  2. Answer: 0.2 cfs. Q = 0.2 x 2 x 0.5 = 0.2 cubic feet per second.
  3. Answer: 4.5 times. 0.9 cfs / 0.2 cfs = 4.5, so the pavement sheds 4.5 times the peak runoff.
  4. Answer: 404 gpm. 0.9 cfs x 448.8 gpm per cfs = 403.9, about 404 gallons per minute.
  5. Answer: 4,984 gallons. 8,000 sq ft x 1 inch x 0.623 = 4,984 gallons of roof runoff.
  6. Answer: 666 cu ft. 4,984 gallons / 7.48 gallons per cubic foot = 666.3, about 666 cubic feet.
  7. Answer: A lawn or rain garden has a lower runoff coefficient C, so with the same rain and area the product C x i x A is smaller, which means less peak runoff.
  8. Answer: 0.45 cfs. Q = 0.9 x 2 x 0.25 = 0.45 cubic feet per second.

Differentiation

Support

Provide the rational-method formula and the two runoff coefficients on a card, plus one fully worked example that is not on the handout. Give the conversion for question 4 in words, and allow a calculator throughout.

Extension

Ask students to find how much the peak runoff drops if half the parking lot is converted to lawn, and to explain the result using the two runoff coefficients.

ELL supports

Pre-teach "runoff," "coefficient," and "rain garden" with a picture of rain hitting pavement and rushing off, next to rain soaking into a garden. Provide a sentence frame for question 7.