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Worksheet Grade 8 Science

Ferngate School Rain Barrels: Modeling Roof Runoff Capture

A grade 8 science worksheet where students build a linear function for roof runoff, predict the most water caught per storm, and connect the model to stormwater control.

Objectives

  1. Students will build and use a linear function relating rainfall depth to gallons of roof runoff.
  2. Students will explain how capturing roof runoff reduces stormwater reaching storm drains.

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

Teacher overview

The fictional Ferngate School wants to catch the rain that runs off its roof and store it for the garden instead of sending it to the storm drain. The gallons of runoff from a roof follow a simple rule: Runoff (gallons) = roof area (square feet) × rainfall (inches) × 0.623. This rule gives the rain that falls on the roof, which is the most the school could catch; a real barrel system collects somewhat less. For one roof of a fixed size, that rule becomes a linear function of rainfall, which students build and use here. A common misconception is that doubling the rainfall more than doubles the runoff; because the relationship is linear through the origin, doubling the rain exactly doubles the gallons.

Ferngate School Rain Barrels: Modeling Roof Runoff Capture — Grade 8 Science
Name: ____________________________ Date: ______________

Student Worksheet

The fictional Ferngate School has a roof that measures 4,000 square feet. Use the rule Runoff (gallons) = roof area (square feet) × rainfall (inches) × 0.623 for every item.

  1. How many gallons run off the 4,000-square-foot roof during 1 inch of rain?
  2. How many gallons run off during 0.5 inch of rain?
  3. Write a linear function G = m × R that gives the gallons of runoff G for R inches of rain from this roof. What is m, the rate of change, and what does it mean?
  4. What is the initial value of your function (the runoff when R = 0), and what does it mean in this situation?
  5. The school installs a cistern that holds 1,500 gallons. Using G = 2,492 × R, how many inches of rain fill the cistern exactly? Round to the nearest hundredth.
  6. A storm drops 2 inches of rain. How many gallons run off the roof?
  7. Complete a table of runoff for R = 0, 1, 2, and 3 inches.
  8. Suppose the school added a second building with a roof of 8,000 square feet. What is the new rate of change m, in gallons per inch, for that larger roof?
  9. Explain how storing roof runoff in barrels and a cistern reduces the amount of stormwater flowing into the storm drain during a storm.
  10. Give one advantage, besides saving water, of keeping roof runoff on the school grounds instead of sending it straight to the storm drain.

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: 2,492 gallons.
    4,000 × 1 × 0.623 = 2,492 gallons.
  2. Answer: 1,246 gallons.
    4,000 × 0.5 × 0.623 = 2,000 × 0.623 = 1,246 gallons.
  3. Answer: m = 2,492 gallons per inch.
    Because 4,000 × 0.623 = 2,492, the function is G = 2,492 × R. The rate of change means each inch of rain produces 2,492 gallons of runoff.
  4. Answer: 0 gallons.
    When R = 0 there is no rain, so G = 2,492 × 0 = 0 gallons of runoff. The initial value means no rain produces no runoff.
  5. Answer: 0.60 inch.
    1,500 = 2,492 × R, so R = 1,500 ÷ 2,492 = 0.6019, about 0.60 inch of rain. This assumes all of the rain that falls on the roof reaches the cistern; a real system collects somewhat less, so a little more rain would be needed.
  6. Answer: 4,984 gallons.
    4,000 × 2 × 0.623 = 8,000 × 0.623 = 4,984 gallons.
  7. Answer: 0, 2,492, 4,984, 7,476 gallons.
    R = 0 gives 0; R = 1 gives 2,492; R = 2 gives 4,984; R = 3 gives 2,492 × 3 = 7,476 gallons.
  8. Answer: 4,984 gallons per inch.
    8,000 × 0.623 = 4,984, so the larger roof produces 4,984 gallons per inch, twice the original roof's rate.
  9. Answer: It holds back water that would otherwise run off.
    Every gallon caught in a barrel or the cistern is a gallon that does not rush into the storm drain during the storm, so the peak flow leaving the school is smaller.
  10. Answer: Reduces flooding or drain overload.
    Keeping runoff on site lowers the surge of water into pipes and streams, which reduces local flooding and erosion; accept any reasonable benefit such as recharging the ground or watering plants slowly.

Differentiation

Support

Work item 1 as a class, then let students reuse that setup for the other items with a calculator. Provide the table in item 7 with the first two rows filled in so students continue the pattern rather than starting from scratch.

Extension

Ask students to graph G = 2,492 × R and the larger roof's function G = 4,984 × R on the same axes, describe how the steeper slope looks on the graph, and state how many more gallons fall on the larger roof during a 2-inch storm, which is the most it could capture.

ELL supports

Pre-teach "runoff," "rain barrel," and "cistern" with simple pictures, and provide the function G = 2,492 × R already written so students focus on substituting values. Allow items 9 and 10 to be answered with a labeled drawing plus a short phrase.