Math problem set Grade 6 Math

Ferncastle Rain Barrels: How Much Roof Runoff to Capture

A grade 6 math set where students use the roof-runoff rule to find how many gallons a fictional roof sheds, and how many rain barrels that runoff would fill.

Grade: Grade 6
Subject: Math
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: Calculator

Standards

6.NS.B.3 Common Core Math

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

How this material aligns: Problems 1, 3, 5, and 7 require multiplying multi-digit numbers by the decimal 0.623, and problems 2 and 8 divide to find full barrels and days of watering.

All materials for 6.NS.B.3 →

6.RP.A.3 Common Core Math

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations, including finding a percent of a quantity and converting measurement units.

How this material aligns: Problems 4 and 6 use proportional reasoning about doubling rainfall and halving roof area, and problem 8 uses a gallons-per-day rate to find how long the water lasts.

All materials for 6.RP.A.3 →

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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 use the roof-runoff rule to calculate gallons of runoff from a roof.
Students will divide to find how many rain barrels or days of watering the runoff supplies.
Students will explain how roof area and rainfall change the amount of runoff in proportion.

Vocabulary

Rain barrel: A rain barrel is a container that catches rainwater from a roof downspout so it can be used later to water plants. It saves drinking water and keeps some runoff out of the storm drains.
Stormwater: Stormwater is rain or melted snow that flows off roofs, streets, and parking lots. In most towns it goes into storm drains and flows to a stream without being treated, carrying whatever it picked up.

Also: runoff, roof area

Teacher overview

When rain falls on a roof, most of it runs off. A common rule says that gallons of runoff equal the roof area in square feet, times the rainfall in inches, times 0.623. This set uses the fictional Ferncastle Community Center, which wants to catch roof runoff in rain barrels. A common mistake is to forget the 0.623 factor and use only the area, or to think a bigger storm changes the runoff by more than its share; the runoff grows in step with the rainfall, not faster.

Ferncastle Rain Barrels: How Much Roof Runoff to Capture — Grade 6 Math

Name: ____________________________ Date: ______________

Problems

Suppose the Ferncastle Community Center has a main roof that is 1,200 square feet. Use the rule gallons of runoff equal area (in square feet) times rainfall (in inches) times 0.623. This rule gives all the rain that falls on the roof; a real rain barrel system collects somewhat less, but use the full amount in these problems.

A 1-inch rain falls on the 1,200 square-foot roof. How many gallons run off? Round to the nearest tenth.
Each rain barrel holds 55 gallons. Using your answer from problem 1, how many full barrels would that runoff fill?
In a bigger storm, 2 inches of rain fall on the same 1,200 square-foot roof. How many gallons run off? Round to the nearest tenth.
Compare problem 3 to problem 1. When the rain doubled from 1 inch to 2 inches, what happened to the gallons of runoff?
The center has a second, smaller roof that is 600 square feet. How many gallons run off the 600 square-foot roof in a 1-inch rain? Round to the nearest tenth.
The 600 square-foot roof is half the size of the 1,200 square-foot roof. How does its runoff compare to the big roof's runoff in the same storm?
Over a whole year, suppose 40 inches of rain fall on the 1,200 square-foot roof. How many gallons could run off in a year?
The center's garden uses about 30 gallons of water a day. If the center saved the full year of runoff from problem 7, for about how many days could that water the garden? Round to the nearest whole day.
Explain one reason catching roof runoff in barrels can help Ferncastle, using a number you found.

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: 747.6 gallons.
Runoff equals area times rainfall times 0.623. 1,200 x 1 x 0.623 = 747.6 gallons.
Answer: 13 barrels.
Divide the runoff by the barrel size. 747.6 / 55 = 13.6, so 13 barrels fill completely and the 14th is only partly full.
Answer: 1,495.2 gallons.
1,200 x 2 x 0.623 = 1,495.2 gallons.
Answer: It doubled.
The runoff went from 747.6 gallons to 1,495.2 gallons, which is twice as much, because doubling the rainfall doubles the runoff.
Answer: 373.8 gallons.
600 x 1 x 0.623 = 373.8 gallons.
Answer: It is half as much.
The 600 square-foot roof is half the area, so in the same storm it sheds half the runoff: 373.8 gallons is half of 747.6 gallons.
Answer: 29,904 gallons.
1,200 x 40 x 0.623 = 29,904 gallons in a year.
Answer: 997 days.
Divide the yearly runoff by the daily use. 29,904 / 30 = 996.8, which rounds to about 997 days.
Answer: Catching runoff saves water the center would otherwise buy, and it keeps runoff out of the storm drains.
Accept any answer that uses one of the runoff numbers, such as saving nearly 30,000 gallons a year for the garden, though a real system would catch somewhat less than all the rain that falls on the roof.

Differentiation

Support

Give students the runoff rule on a printed card and work problem 1 as a class. Provide a filled-in first step (1,200 x 1) so students only need to multiply by 0.623. Allow a calculator for every problem.

Extension

Ask students to find the total yearly runoff from both roofs together, the 1,200 square-foot roof and the 600 square-foot roof, in 40 inches of rain. Then have them decide how many 55-gallon barrels the center would need to hold a single 2-inch storm from both roofs.

ELL supports

Pre-teach "runoff," "rain barrel," "square feet," and "rainfall" with a simple picture of rain hitting a roof and flowing into a barrel. Provide the sentence frame "Area times rainfall times 0.623 equals ___ gallons" for the calculation problems.