Water for Schools
Menu

Lesson plan Grade 6 Math

Ardleigh School's Green Roof: Volume with Fractional Depths

A grade 6 lesson on a school's planted roof: students find the volume of a growing-medium layer with a fractional depth and compare it with a storm's runoff.

Objectives

  1. Students will compute the volume of a rectangular layer whose depth is given as a fraction of a foot.
  2. Students will convert a volume in cubic feet to gallons using a stated conversion rate.
  3. Students will compare a roof's storage with a storm's runoff and decide whether the storm fits.

Vocabulary

Green roof
A green roof is a rooftop partly or fully covered with soil and plants instead of standard roofing materials. The plants and soil soak up rainwater and slow it down before it can run off, while also cooling the building underneath.

Also: growing medium, runoff, cubic foot, volume

Teacher overview

A green roof is a shallow layer of growing medium and low plants spread across a flat roof, and it holds part of a rainstorm instead of sending it straight to a storm drain. The fictional Ardleigh Middle School has planted one section of its gym roof and is deciding whether to plant a second, deeper section. The misconception this lesson corrects is that a depth written as a fraction of a foot can be treated as a whole number in the volume formula. Students who multiply 30 by 20 by 1 and then "adjust for the half" usually adjust in the wrong direction, so the lesson keeps the fraction inside the multiplication from the first step.

Procedure

Hook (5 min): Pour dry sand into a shoebox until it is about half as deep as the box, then tip a cup of water onto it and let the class watch how much soaks in before any runs to the corner. State the question the lesson answers: how much rain can a layer that shallow actually hold?

Direct instruction (14 min): Draw the roof section of the fictional Ardleigh gym on the board as a rectangular prism labeled 30 feet by 20 feet by one half foot. Work the volume aloud as 30 times 20 times one half, writing the half as a fraction rather than converting to a decimal, arriving at 300 cubic feet. Then model the conversion to gallons using the standard figure that one cubic foot holds 7.48 gallons. Finish by writing the rainfall conversion students will need: one inch of rain falling on one square foot is 0.623 gallons.

Guided practice (10 min): Pairs work a parallel example that is not on the handout: a 10 foot by 10 foot test plot with a depth of one quarter foot. They should get 25 cubic feet and 187 gallons, and they should be able to say which number they would report to a roofer and which to a plumber. Check every pair's setup line before they compute.

Independent practice (21 min): Students complete handout questions 1 through 10. Circulate during questions 5 through 8, where the two conversions can be confused, and ask students who are stuck to label each number with its unit before multiplying.

Closure (5 min): Exit poll with a stated threshold: ask students to write on a slip whether the planted section at the fictional Ardleigh school could hold a one inch storm, yes or no, with one number as evidence. Sort the slips as students leave. If more than five slips say no, or give no number, reteach questions 4 and 5 at the start of the next class.

Ardleigh School's Green Roof: Volume with Fractional Depths — Grade 6 Math
Name: ____________________________ Date: ______________

Student Handout

The fictional Ardleigh Middle School has planted Section A of its gym roof. Section A measures 30 feet by 20 feet, and the growing medium is one half foot deep. Use these two conversions.

  • One cubic foot of space holds 7.48 gallons.
  • One inch of rain on one square foot of roof is 0.623 gallons.
  1. What is the volume of Section A's growing medium, in cubic feet?
  2. How many gallons of space is that volume, using 7.48 gallons per cubic foot?
  3. Section A holds an amount of water equal to one quarter of its volume. How many cubic feet of water is that?
  4. How many gallons of water is the amount from question 3?
  5. Section A covers 600 square feet. How many gallons of rain fall on it in a storm that drops one inch?
  6. Section A holds 561 gallons of water when it is full. Can it hold all of the one inch storm from question 5? Answer yes or no.
  7. How many gallons of rain fall on the same 600 square feet in a storm that drops two inches?
  8. Section A holds 561 gallons. In the two inch storm from question 7, how many gallons spill past the roof's storage and run to the storm drain?
  9. Section B is also 30 feet by 20 feet, but its growing medium is three quarters of a foot deep. What is Section B's volume, in cubic feet?
  10. Section A's volume is 300 cubic feet. By what percent is Section B's volume larger than Section A's?

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: 300 cubic feet.
    Volume is 30 times 20 times one half. Thirty times 20 is 600 square feet, and 600 times one half is 300 cubic feet.
  2. Answer: 2,244 gallons.
    300 cubic feet times 7.48 gallons per cubic foot is 2,244 gallons.
  3. Answer: 75 cubic feet.
    One quarter of 300 cubic feet is 300 divided by 4, which is 75 cubic feet.
  4. Answer: 561 gallons.
    75 cubic feet times 7.48 gallons per cubic foot is 561 gallons.
  5. Answer: 373.8 gallons.
    600 square feet times 1 inch times 0.623 gallons is 373.8 gallons.
  6. Answer: Yes.
    The roof holds 561 gallons and the storm delivers 373.8 gallons, and 561 is greater than 373.8, so the whole storm fits with room left over.
  7. Answer: 747.6 gallons.
    600 square feet times 2 inches times 0.623 gallons is 747.6 gallons.
  8. Answer: 186.6 gallons.
    747.6 gallons minus the 561 gallons the roof holds leaves 186.6 gallons running off.
  9. Answer: 450 cubic feet.
    Volume is 30 times 20 times three quarters. Thirty times 20 is 600, and 600 times three quarters is 450 cubic feet.
  10. Answer: 50 percent.
    Section B is 450 minus 300, or 150 cubic feet larger. 150 divided by 300 is 0.5, which is 50 percent.

Differentiation

Support

Give these students a filled-in setup line for questions 1 and 9, such as "Volume = 30 x 20 x 1/2," so the work is the arithmetic rather than the translation. Provide a unit label card that reads "cubic feet to gallons: multiply by 7.48" and a second card that reads "roof area and inches to gallons: multiply by 0.623."

Extension

Ask these students to find the smallest depth, in feet, that would hold a full two inch storm on 600 square feet without any runoff (about two thirds of a foot), and to decide whether Section B's three-quarter-foot depth at the fictional Ardleigh school is enough. They should reason back through questions 3, 4, and 7 rather than guess and check.

ELL supports

Pre-teach growing medium, runoff, and spill using the shoebox demonstration from the hook, saying each term while pointing at the part of the model it names. Provide a two-column glossary card with the word on one side and a small labeled sketch of the Ardleigh roof on the other, and give this sentence frame for question 6: "The roof can hold ___ gallons, and the storm brings ___ gallons, so the answer is ___."

Extensions

Measure a flat section of the school's own roof from a site plan, or measure a paved courtyard, and have students compute the runoff from a one inch storm on that real area using the same 0.623 figure. Comparing that result with the fictional Ardleigh numbers shows students how quickly runoff grows with area, and it gives the class a concrete number to bring to a facilities meeting.