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Lesson plan Grade 8 Engineering & Design

Marrow Vale School Parking Lot: A Green Infrastructure Lesson

A 50-minute grade 8 lesson calculating peak stormwater runoff for a conventional versus a green-infrastructure parking lot and testing both against a criterion.

Objectives

  1. Students will calculate peak stormwater runoff for a conventional and a green infrastructure parking lot design using the rational method.
  2. Students will evaluate whether a proposed design meets a stated stormwater runoff criterion.
  3. Students will explain why a permeable surface produces less peak runoff than conventional pavement.

Vocabulary

Permeable pavement
Permeable pavement is a special kind of pavement full of tiny gaps that let rainwater soak straight through it into the ground below, instead of running off like it would on regular pavement. Parking lots and sidewalks can be built with it to reduce stormwater runoff.
Green infrastructure
Green infrastructure uses soil and plants, like rain gardens, green roofs, and street trees, to soak up rainwater where it falls instead of piping it away. It copies the way nature handles rain.

Also: runoff coefficient, criterion, peak runoff

Teacher overview

The fictional Marrow Vale Middle School is repaving its parking lot and must choose between a conventional asphalt design and a green infrastructure design that combines permeable pavement with a small rain garden. This lesson has students step into the role of the district's engineering consultants, calculating peak stormwater runoff for each design using the rational method, a real formula engineers use to estimate runoff, and testing both designs against the town's stormwater criterion.

A common misconception in this math is assuming that a lower runoff coefficient by itself guarantees a design passes any stormwater criterion, without actually comparing the calculated runoff number to the stated limit. The procedure below is built to correct that directly: students must complete the calculation and compare it to the numeric criterion before deciding whether a design passes.

Procedure

Hook (5 min): Show two labeled photos or simple sketches: one of a standard paved parking lot, one of a parking lot built with light-colored permeable pavers and a planted rain garden along one edge. Ask students to predict which lot would send more water rushing into the storm drain during a heavy rain, and why. Collect a few predictions without confirming or correcting them yet.

Direct instruction (10 min): Introduce the rational method formula, Q = C × i × A, where Q is peak runoff in cubic feet per second (cfs), C is a runoff coefficient describing how much of the rain on a surface becomes runoff, i is rainfall intensity in inches per hour, and A is the drainage area in acres. Give students the runoff coefficients this lesson will use: C = 0.2 for grass, C = 0.9 for conventional pavement, and C = 0.3 for the green infrastructure design (permeable pavers plus a rain garden slow and soak up much of the water that would otherwise run off). Work one example on the board using a 1-acre lot at 1 inch per hour of rainfall intensity with C = 0.9, showing Q = 0.9 × 1 × 1 = 0.9 cfs.

Guided practice (20 min): In teams, students calculate peak runoff for the fictional Marrow Vale parking lot, a 1.5-acre lot, using a design storm intensity of i = 2 inches per hour. Each team calculates three values: (1) peak runoff before any construction, when the lot was grass (C = 0.2); (2) peak runoff for the conventional pavement design (C = 0.9); and (3) peak runoff for the green infrastructure design (C = 0.3). Circulate to check that teams are substituting correctly into Q = C × i × A before they move to the next value. Once all three values are found, introduce the district's stormwater criterion: the post-construction peak runoff may not exceed the pre-development (grass) runoff by more than 1.0 cfs.

Independent practice (10 min): Each student individually calculates the district's maximum allowed post-development runoff (the pre-development value plus the 1.0 cfs allowance) and compares it to both the conventional and green infrastructure runoff values their team calculated, deciding in writing which design, if either, meets the district's criterion.

Closure / exit ticket (5 min): Students answer one question on an index card: "In one sentence, explain why the green infrastructure design meets Marrow Vale's stormwater criterion while the conventional pavement design does not." Collect and scan responses for correct use of both calculated runoff values before dismissal.

Marrow Vale School Parking Lot: A Green Infrastructure Lesson — Grade 8 Engineering & Design
Name: ____________________________ Date: ______________

Student Handout

Marrow Vale Middle School is a fictional school repaving its 1.5-acre parking lot. Engineers estimate peak stormwater runoff with the rational method, Q = C × i × A, where Q is peak runoff in cubic feet per second (cfs), C is the runoff coefficient of the surface, i is rainfall intensity in inches per hour, and A is the drainage area in acres. Every question below uses the same design storm, i = 2 inches per hour, and the same drainage area, A = 1.5 acres.

  1. Before construction the lot was grass, with a runoff coefficient of C = 0.2. Calculate the peak runoff Q, in cfs, for the grass lot.
  2. The conventional pavement design has a runoff coefficient of C = 0.9. Calculate the peak runoff Q, in cfs, for that design.
  3. The green infrastructure design, permeable pavers plus a rain garden, has a runoff coefficient of C = 0.3. Calculate the peak runoff Q, in cfs, for that design.
  4. The district's criterion says post-construction peak runoff may not exceed the pre-development grass runoff by more than 1.0 cfs. Using your answer to question 1, calculate the maximum allowed post-development runoff, in cfs.
  5. Compare your answers to questions 2 and 3 against the limit you found in question 4. Which design meets the district's criterion, and which one fails it?
  6. In one sentence, explain why the green infrastructure design meets Marrow Vale's stormwater criterion while the conventional pavement design does not.

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: 0.6 cfs.
    Pre-development (grass) runoff: Q = 0.2 × 2 × 1.5 = 0.6 cfs.
  2. Answer: 2.7 cfs.
    Conventional pavement runoff: Q = 0.9 × 2 × 1.5 = 2.7 cfs.
  3. Answer: 0.9 cfs.
    Green infrastructure runoff: Q = 0.3 × 2 × 1.5 = 0.9 cfs.
  4. Answer: 1.6 cfs.
    Maximum allowed post-development runoff: 0.6 + 1.0 = 1.6 cfs.
  5. Answer: The green infrastructure design meets the criterion; the conventional design fails it.
    Criterion check: the conventional design's 2.7 cfs exceeds the 1.6 cfs limit, so it fails the criterion. The green infrastructure design's 0.9 cfs is below the 1.6 cfs limit, so it meets the criterion.
  6. Answer: Its lower runoff coefficient keeps it under the limit.
    Exit ticket answer: the green infrastructure design meets the criterion because its lower runoff coefficient (0.3 versus 0.9) produces only 0.9 cfs of peak runoff, which stays under the 1.6 cfs limit, while the conventional design's 2.7 cfs exceeds that limit.

Differentiation

Support

Provide a partially completed table with the formula Q = C × i × A written above three rows already labeled "Grass," "Conventional," and "Green infrastructure," and the C values filled in, so students only need to multiply. Allow a calculator throughout.

Extension

Ask students to find the largest runoff coefficient a design could have and still meet Marrow Vale's criterion, working backward from the 1.6 cfs limit and the same 1.5-acre, 2-inch-per-hour storm conditions.

ELL supports

Pre-teach "runoff," "permeable," and "criterion" using the same two photos or sketches from the hook, pointing to each surface type as the word is introduced. Provide sentence starters for the exit ticket: "The green infrastructure design meets the criterion because its runoff, ___ cfs, is ___ than the limit of ___ cfs."

Every figure in this scenario is fictional, chosen so students work with realistic engineering numbers.

Extensions

Have students sketch their own green infrastructure redesign for an actual paved area at their own school, estimating its area and proposing a runoff coefficient for their design, then calculate whether their proposed redesign would meet Marrow Vale's same 1.0 cfs allowance criterion.