Math problem set Grade 7 Science

Harlow Heights Roof Runoff: A Rain-Capture Problem Set

A grade 7 science problem set on a fictional school's rooftop rain capture, finding runoff gallons, cistern percent captured, and how surface type changes runoff.

Grade: Grade 7
Subject: Science
Material: Math problem set
Time: 45 min
Prep: No prep
Materials: Calculator

Standards

7.RP.A.2 Common Core Math

Recognize and represent proportional relationships between quantities, including identifying the constant of proportionality and representing proportional relationships by equations.

How this material aligns: Problems 1, 4, and 8 treat roof runoff as proportional to rainfall depth and roof area with the constant 0.623, identifying that constant of proportionality as this standard requires.

All materials for 7.RP.A.2 →

7.RP.A.3 Common Core Math

Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

How this material aligns: Problems 2, 3, and 7 are multistep percent problems finding the percent of runoff a cistern captures and the percent reduction from replacing pavement with lawn, the reasoning this standard develops.

All materials for 7.RP.A.3 →

MS-ESS3-3 NGSS

Apply scientific principles to design a method for monitoring and minimizing a human impact on the environment.

How this material aligns: Problems 2, 3, and 5 size the cistern that captures rooftop runoff, and problems 6 and 7 quantify how swapping pavement for lawn cuts runoff from the same area, the stormwater and land-use impacts this standard's clarification names as impacts to monitor and minimize.

All materials for MS-ESS3-3 →

Download Word file

This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will calculate rooftop runoff in gallons using roof area, rainfall depth, and the 0.623 conversion.
Students will find the percent of runoff a cistern captures and the percent runoff change from swapping surface types.

Vocabulary

Cistern: A large tank that stores rainwater collected from a roof so it can be used later, usually for watering plants.

Also: runoff, runoff coefficient, impermeable

Teacher overview

When rain falls on a roof, most of it runs off instead of soaking in, and that runoff can be captured for reuse or sent to a storm drain. The amount of runoff depends on the roof area, the depth of rain, and a conversion of 0.623 gallons for each square foot of roof per inch of rain. This set follows a fictional school, Harlow Heights Elementary, as it captures rooftop rain in a cistern. A common misconception this set corrects is thinking rainfall in inches is already a volume; students must multiply area by rainfall depth and by 0.623 to get gallons, not read the inches as gallons.

Harlow Heights Roof Runoff: A Rain-Capture Problem Set — Grade 7 Science

Name: ____________________________ Date: ______________

Problems

Harlow Heights Elementary is a fictional school. Its roof is 8,000 square feet. Use the conversion: gallons of runoff equals roof area in square feet times rainfall in inches times 0.623. This gives all the rain that falls on the roof; a real gutter and cistern system collects somewhat less, but for these problems assume all of it flows to the cistern.

A storm drops 1.5 inches of rain on the roof. How many gallons of runoff does the roof shed?
The school's cistern holds 2,500 gallons. What percent of the runoff from problem 1 does a full cistern capture? Round to the nearest tenth of a percent.
How many gallons of runoff overflow past the 2,500-gallon cistern in problem 1?
A smaller storm drops only 0.5 inch of rain. How many gallons of runoff does the roof shed then?
Does the runoff from problem 4 fit inside the empty 2,500-gallon cistern? If so, how many gallons of space are left?
Runoff coefficients describe how much water runs off a surface: pavement is about 0.9 and lawn is about 0.2. For the same area and rainfall, how many times more runoff comes from pavement than from lawn?
The school replaces some pavement with lawn. Because runoff is proportional to the coefficient, the runoff from that area drops from a coefficient of 0.9 to 0.2. What is the percent decrease in runoff for that area? Round to the nearest tenth.
Over a year the roof receives 40 inches of rain in total. How many gallons of runoff does the 8,000-square-foot roof shed in a year?

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: 7,476 gallons.
8,000 times 1.5 times 0.623 = 12,000 times 0.623 = 7,476 gallons.
Answer: 33.4%.
2,500 divided by 7,476 times 100 = 33.44 percent, which rounds to 33.4 percent.
Answer: 4,976 gallons.
7,476 − 2,500 = 4,976 gallons overflow past the cistern.
Answer: 2,492 gallons.
8,000 times 0.5 times 0.623 = 4,000 times 0.623 = 2,492 gallons.
Answer: Yes, 8 gallons of space are left.
2,492 is less than 2,500, so it fits, and 2,500 − 2,492 = 8 gallons of space remain.
Answer: 4.5 times.
0.9 divided by 0.2 = 4.5, so pavement sheds 4.5 times as much runoff as lawn for the same area and rain.
Answer: 77.8%.
(0.9 − 0.2) divided by 0.9 times 100 = 0.7 divided by 0.9 times 100 = 77.78 percent, which rounds to 77.8 percent.
Answer: 199,360 gallons.
8,000 times 40 times 0.623 = 320,000 times 0.623 = 199,360 gallons in a year.

Differentiation

Support

Provide the runoff formula on a reference card and complete problem 1 together, writing each multiplication step. Allow students to reuse the 7,476 gallons from problem 1 in problems 2 and 3 without recomputing it.

Extension

Ask students to find what cistern size would be needed to capture all of the runoff from the 1.5-inch storm in problem 1, and then to estimate how many such storms per year the school could fully capture given its yearly total from problem 8.

ELL supports

Pre-teach "runoff," "cistern," and "coefficient" with a labeled picture of rain hitting a roof and flowing into a tank. Provide a worked unit reminder card showing that square feet times inches times 0.623 gives gallons.