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Lesson plan Grade 7 Math

Hartsboro Roof Rainwater: A Grade 7 Proportional Lesson

A 45-minute grade 7 lesson where students model a fictional school roof's rainwater capture as a proportional relationship and solve for the rain that fills a tank.

Objectives

  1. Students will show that captured gallons are proportional to inches of rain for a fixed roof.
  2. Students will write and use an equation with the constant of proportionality.
  3. Students will solve an equation to find the rainfall that fills a storage tank.

Vocabulary

Key words: runoff, proportional, constant of proportionality, roof area

Teacher overview

Rain that falls on a roof can be caught and stored instead of running to the storm drain, and the gallons captured depend on the roof size and the depth of rain. This lesson uses the standard capture rule, gallons = roof area × rainfall in inches × 0.623, to build a proportional relationship for a fictional school roof; the rule gives the rain that falls on the roof, and a real system collects somewhat less. A common misconception this lesson addresses is that a bigger storm and a bigger roof combine in some complicated way; for a fixed roof, gallons are simply proportional to inches of rain, and the lesson keeps the roof fixed so that structure is clear.

Procedure

Hook (5 min): Ask students where the rain that lands on the school roof goes now, and whether any of it could be saved. Record a quick estimate of how many gallons one inch of rain might drop on the roof.

Direct instruction (10 min): Introduce the capture rule: gallons = roof area (square feet) × rainfall (inches) × 0.623. Explain that 0.623 is the gallons produced by one inch of rain over one square foot. Point out that if the roof area is fixed, the only thing that changes is the inches of rain, so gallons and inches form a proportional relationship.

Worked example (10 min): Suppose a fictional garage roof is 2,000 square feet. Model computing capture for 1 inch (2,000 × 1 × 0.623 = 1,246 gallons) and for 3 inches (2,000 × 3 × 0.623 = 3,738 gallons), and show the constant of proportionality is 1,246 gallons per inch. This example is for modeling only; students do not record it as an answer.

Guided and independent practice (15 min): Hand out the Hartsboro page and have students complete items 1 through 9 in pairs, each recording their own work. Circulate and confirm students multiply the roof area by 0.623 once to find the constant before writing the equation.

Closure and exit ticket (5 min): As a formative check, students answer this on a slip: "For the 4,000 square foot roof, how many gallons come from 4 inches of rain?" Collect and scan; if more than a quarter of the class misses it, rework the constant-of-proportionality step before moving on.

Hartsboro Roof Rainwater: A Grade 7 Proportional Lesson — Grade 7 Math
Name: ____________________________ Date: ______________

Student Handout

Hartsboro Middle School is a fictional school used for this lesson. Its main roof is 4,000 square feet. Use the capture rule gallons = roof area × rainfall in inches × 0.623 for every question. The rule gives the rain that falls on the roof. A real system collects somewhat less, but in this lesson count all of it as captured.

  1. How many gallons does 1 inch of rain drop on the 4,000 square foot roof?
  2. How many gallons does 2 inches of rain drop on the same roof?
  3. Are the gallons captured proportional to the inches of rain for this roof? Explain how you know.
  4. What is the constant of proportionality, in gallons per inch of rain?
  5. Write an equation that gives the gallons g captured from r inches of rain.
  6. A storm drops 1.5 inches of rain. How many gallons does the roof capture?
  7. The school's tank holds 5,000 gallons. Using your equation, how many inches of rain would fill it? Round to the nearest hundredth.
  8. A second building has an 8,000 square foot roof. What is its constant of proportionality, in gallons per inch?
  9. The 8,000 square foot roof captures twice the gallons per inch of the 4,000 square foot roof. Explain why doubling the roof area doubles the gallons per inch.

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: 4,984 gallons.
    4,000 × 2 × 0.623 = 4,984 gallons.
  3. Answer: Yes, they are proportional.
    Each added inch of rain adds the same 2,492 gallons, so the ratio of gallons to inches stays constant.
  4. Answer: 2,492 gallons per inch.
    The constant is the gallons from one inch, 4,000 × 0.623 = 2,492 gallons per inch.
  5. Answer: g = 2492r.
    Gallons equal the constant times the inches of rain, so g = 2,492 × r.
  6. Answer: 3,738 gallons. g = 2,492 × 1.5 = 3,738 gallons.
  7. Answer: 2.01 inches.
    Solve 2,492 × r = 5,000, so r = 5,000 ÷ 2,492 = 2.006, which rounds to 2.01 inches.
  8. Answer: 4,984 gallons per inch.
    8,000 × 0.623 = 4,984 gallons per inch.
  9. Answer: Gallons are proportional to roof area.
    The capture rule multiplies the area by 0.623, so doubling the area doubles the product, and the gallons per inch double with it.

Differentiation

Support

Provide the capture rule as a filled-in template, "gallons = 4,000 × (inches) × 0.623," so students substitute only the rainfall. Give the constant 2,492 already computed for students who need to focus on the equation and the solving steps.

Extension

Ask students to find the roof area that would capture exactly 5,000 gallons from a single inch of rain, and to explain how they used the capture rule in reverse to find it.

ELL supports

Pre-teach "roof area," "rainfall," "capture," and "constant" with a simple picture of rain landing on a roof and filling a tank. Provide the sentence frame for items 3 and 9: "The gallons are proportional because ___."