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Math problem set Grade 6 Math

Fenniston Fire Station Roof: Rain into the Cistern

A grade 6 problem set on rainwater harvesting, where students multiply decimals to find roof runoff in gallons and compare it to a cistern's capacity.

Objectives

  1. Students will calculate roof runoff in gallons from an area and a rainfall depth.
  2. Students will multiply and divide multi-digit decimals accurately.
  3. Students will express one roof's runoff as a percent and as a ratio of another's.

Vocabulary

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

Also: runoff, area, rainfall

Teacher overview

Rain that lands on a roof runs off in a predictable amount, and a standard rainwater harvesting conversion multiplies roof area in square feet by rainfall in inches and then by 0.623 to give gallons of runoff. The town of Fenniston, which is fictional, put a cistern beside its fire station to catch that runoff for washing trucks. Students work the conversion in both directions, first finding gallons from a storm and then finding the rainfall a full cistern would take. The misconception this set is built to correct is adding a roof's length and width instead of multiplying them, an error that reports a 2,400 square foot roof as 100.

Fenniston Fire Station Roof: Rain into the Cistern — Grade 6 Math
Name: ____________________________ Date: ______________

Problems

The fire station in the town of Fenniston has a flat roof that measures 60 feet by 40 feet. The cistern beside the station holds 3,000 gallons. To find runoff, multiply the roof area in square feet by the rainfall in inches, then multiply by 0.623. That gives all the rain that falls on the roof. A real system collects somewhat less, but in these problems assume all of it reaches the cistern.

  1. Find the area of the fire station roof in square feet.
  2. A rain of 1 inch falls on the station. How many gallons run off the roof?
  3. A rain of 1.5 inches falls on the station. How many gallons run off the roof?
  4. After the 1.5-inch rain in problem 3, what percent of the empty 3,000-gallon cistern is full? Round to the nearest whole percent.
  5. About how many inches of rain would fill the empty 3,000-gallon cistern? Round to the nearest tenth of an inch.
  6. The garage next door has a roof of 1,200 square feet. How many gallons run off the garage roof in the same 1.5-inch rain?
  7. Write the ratio of the station roof's runoff to the garage roof's runoff in simplest form.
  8. Over one month, 3.2 inches of rain fall on the station roof. How many gallons run off in that month? Round to the nearest tenth of a gallon.
  9. The crew uses 250 gallons each week to wash trucks. How many weeks does a full 3,000-gallon cistern last?
  10. A student found the size of the roof by adding 60 and 40 to get 100. Explain the mistake and state what the student should have done.

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: 2,400 square feet.
    60 feet times 40 feet equals 2,400 square feet.
  2. Answer: 1,495.2 gallons.
    2,400 square feet times 1 inch times 0.623 equals 1,495.2 gallons.
  3. Answer: 2,242.8 gallons.
    2,400 times 1.5 equals 3,600. Then 3,600 times 0.623 equals 2,242.8 gallons.
  4. Answer: 75 percent.
    2,242.8 divided by 3,000 equals 0.7476, which rounds to 75 percent.
  5. Answer: 2.0 inches.
    One inch of rain gives 1,495.2 gallons, so 3,000 divided by 1,495.2 equals 2.006 inches, which rounds to 2.0 inches.
  6. Answer: 1,121.4 gallons.
    1,200 square feet times 1.5 inches equals 1,800. Then 1,800 times 0.623 equals 1,121.4 gallons.
  7. Answer: 2 to 1.
    The runoff amounts 2,242.8 and 1,121.4 both divide by 1,121.4 to give 2 to 1. The station roof is twice the size of the garage roof, so it sheds twice the water.
  8. Answer: 4,784.6 gallons.
    2,400 square feet times 3.2 inches equals 7,680. Then 7,680 times 0.623 equals 4,784.64, which rounds to 4,784.6 gallons.
  9. Answer: 12 weeks.
    3,000 gallons divided by 250 gallons per week equals 12 weeks.
  10. Answer: Area is found by multiplying the two side lengths, not adding them.
    Adding gives 100, which is a distance around part of the roof rather than a surface. The student should have multiplied 60 by 40 to get 2,400 square feet, and the runoff answers would then be 24 times larger than the ones the addition produced.

Differentiation

Support

Give students a three-step recording strip labeled "area," "times inches," and "times 0.623" so each multiplication has its own box, and complete problem 1 together. Provide the product 2,400 times 0.623 as a reference value of 1,495.2 gallons per inch of rain, which turns problems 3, 5, and 8 into a single multiplication or division.

Extension

Ask students to size a cistern that would hold all the runoff from a 2.5-inch storm on both the station roof and the garage roof combined, and to state how many full weeks of truck washing that cistern would supply at 250 gallons per week.

ELL supports

Provide a labeled diagram showing rain falling on a rectangle marked 60 feet by 40 feet, with an arrow to a labeled tank. Give the sentence frame "The roof is ___ square feet, so ___ inches of rain gives ___ gallons" for problems 2, 3, and 8.

Extensions

Students can measure the roof of a real building on their campus from a scaled site map, then use the same conversion to estimate how much runoff a 1-inch rain sends off that roof. Comparing that figure to the fire station's total makes the effect of roof size concrete.