Lesson plan Grade 10 Math
Brookfield Crossing Stormwater Runoff Rational Method Lesson
A 50-minute grade 10 lesson using the rational method to compare peak runoff before and after paving a fictional site, then sizing a detention basin's release.
Objectives
- Students will use the rational method to compute peak runoff before and after development.
- Students will determine the peak outflow a detention basin must meet to hold runoff to the pre-development rate.
Vocabulary
- Detention basin
- A detention basin is a dug-out area that fills with stormwater during a storm and then slowly drains empty over hours or days. It holds the water back so streets and streams downstream do not flood.
Also: rational method, runoff coefficient, peak runoff
Teacher overview
When a grassy field becomes a parking lot, less rain soaks in and more runs off, so the peak flow leaving the site during a storm rises sharply. This lesson has students at the fictional Brookfield Crossing development use the rational method to put numbers on that change and then reason about the detention basin needed to control it. A common misconception is thinking runoff depends only on how hard it rains; students learn that the runoff coefficient, which reflects how much surface is paved, multiplies the peak flow just as much as the rainfall intensity does.
Procedure
Hook (5 min): Show a photo of a grassy lot beside a paved lot in the same storm. Ask which sends more water to the storm drain and why. Draw out the idea that pavement lets almost nothing soak in.
Direct instruction (13 min): Introduce the rational method using the fictional Brookfield Crossing site: peak runoff Q (cfs) = C × i × A, where C is the runoff coefficient, i is rainfall intensity in inches per hour, and A is area in acres. Give the typical coefficients: about 0.2 for lawn and about 0.9 for pavement. Model the formula once with a different site: a 3-acre lawn in a 1.5 in/hr storm gives Q = 0.2 × 1.5 × 3 = 0.9 cfs. Do not solve the handout numbers.
Guided practice (14 min): Distribute the handout. Work items 1 and 2 together so students see the before-and-after contrast between the lawn coefficient and the pavement coefficient on the same site and storm.
Independent practice (12 min): Students complete items 3 through 6 on their own, including the unit conversion from cfs to gpm. Circulate and confirm that students keep area in acres and intensity in inches per hour.
Closure and formative check (6 min): As an exit check, ask students to state in one sentence why the developed site's peak runoff is larger even though the storm is identical. Scan responses for the idea that the higher coefficient, not the rain, drove the increase; if many miss it, revisit item 3 next class.
Student Handout
Brookfield Crossing (a fictional 5-acre site) is being developed. Use the rational method: peak runoff Q (cfs) = C × i × A, with C the runoff coefficient, i the rainfall intensity in inches per hour, and A the area in acres. Use C = 0.2 for lawn and C = 0.9 for pavement, and 1 cfs = 448.8 gpm.
The site is currently lawn with C = 0.2. For a design storm of i = 2.0 in/hr over the 5 acres, find the peak runoff in cfs.
After development the site is mostly pavement with C = 0.9. For the same 2.0 in/hr storm over 5 acres, find the new peak runoff in cfs.
How many times larger is the developed peak runoff (item 2) than the lawn peak runoff (item 1)?
Find the increase in peak runoff caused by development, in cfs. Subtract item 1 from item 2.
The town requires that peak runoff leaving the developed site not exceed the pre-development rate. What peak outflow, in cfs, must the detention basin be built to release?
Convert the developed peak runoff from item 2 to gallons per minute using 1 cfs = 448.8 gpm.
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Answer Key
Answer: 2.0 cfs. Q = 0.2 × 2.0 × 5 = 2.0 cfs for the lawn site.
Answer: 9.0 cfs. Q = 0.9 × 2.0 × 5 = 9.0 cfs for the paved site.
Answer: 4.5 times. 9.0 cfs / 2.0 cfs = 4.5, so the developed runoff is 4.5 times the lawn runoff.
Answer: 7.0 cfs. 9.0 − 2.0 = 7.0 cfs is the extra peak flow caused by paving the site.
Answer: 2.0 cfs. The basin must hold the outflow to the pre-development peak, which is the 2.0 cfs lawn rate from item 1.
Answer: 4,039 gpm. 9.0 cfs × 448.8 gpm per cfs = 4,039.2, about 4,039 gpm.
Differentiation
Support
Provide the rational method with the item 1 values already placed (0.2 × 2.0 × 5) so students see how the three factors combine before working item 2 on their own. Give a reminder card noting that lawn uses 0.2 and pavement uses 0.9.
Extension
Ask students to find the runoff coefficient a developer would need to hold the paved site's peak runoff to just 3.0 cfs in the same storm, then explain what design choices, such as adding green space or permeable pavement, could lower the coefficient toward that target.
ELL supports
Pre-teach "runoff," "coefficient," and "detention basin" with a labeled cross-section showing rain hitting pavement, running off, and collecting in a basin. Provide a sentence frame for the exit check: "The developed site has more runoff because ___."
Extensions
Have students map the paved and unpaved areas of the school grounds and estimate a runoff coefficient for the whole site, then apply the rational method to a typical local storm intensity supplied by the teacher. A short written result can compare the school's estimated peak runoff to the fictional Brookfield Crossing figures and suggest one place a rain garden could help.