Math problem set Grade 6 Engineering & Design

Thistle Hollow Rain-Barrel Storage Design Math

Eight problems where students size a rectangular rain-storage tank for a fictional greenhouse roof, using the runoff formula, fractional volume, and percent capture.

Grade: Grade 6
Subject: Engineering & Design
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: calculator

Standards

6.G.A.2 Common Core Math

Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

How this material aligns: Problems 3 and 6 require finding the volume of a rectangular tank with fractional edge lengths, such as 3 1/2, 2, and 2 1/2 feet, applying V = l w h exactly as this standard specifies.

All materials for 6.G.A.2 →

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 5 and 7 ask what percent of a storm's total runoff, in gallons, a tank's capacity represents, converting measurements and finding a percent of a quantity.

All materials for 6.RP.A.3 →

MS-ETS1-4 NGSS

Develop a model to generate data for iterative testing and modification of a proposed object, tool, or process such that an optimal design can be achieved.

How this material aligns: Problems 6 and 7 change one tank dimension and recalculate its volume and capture percentage, giving students the retest-after-a-design-change step at the core of this standard's iterative approach.

All materials for MS-ETS1-4 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-16.

Objectives

Students will calculate roof runoff in gallons using the area-times-rainfall conversion.
Students will calculate the volume of a rectangular storage tank with fractional edge lengths and convert it to gallons.
Students will find what percent of a storm's total runoff a storage tank can capture, and recalculate after an iterative design change.

Vocabulary

Key words: runoff, volume, capacity, percent

Teacher overview

Thistle Hollow Middle School (a fictional school used for this problem set) wants to capture roof runoff from its greenhouse and reuse it for irrigation instead of letting it drain away during storms. This problem set walks students through finding how much runoff the greenhouse roof produces, sizing a rectangular storage tank to hold as much of that runoff as possible, and testing an iterative design change to the tank. A common misconception in this set is assuming that increasing only one dimension of a rectangular tank multiplies its volume by the same factor as increasing every dimension would; problem 6 gives the teacher a chance to point out that changing only the depth does not multiply the volume the way changing all three dimensions would.

Thistle Hollow Rain-Barrel Storage Design Math — Grade 6 Engineering & Design

Name: ____________________________ Date: ______________

Problems

Use the runoff conversion, area in square feet times rainfall in inches times 0.623 equals gallons of runoff, and the conversion 1 cubic foot equals 7.48 gallons, for every problem in this fictional greenhouse scenario.

The greenhouse roof measures 24 feet by 15 feet. Find its area in square feet.
Using the roof's area from problem 1, find how many gallons of runoff a 1-inch storm produces. Round to the nearest gallon.
The school plans to build a rectangular storage tank measuring 3 1/2 feet long, 2 feet wide, and 2 1/2 feet deep. Find its volume in cubic feet.
Convert the tank's volume from problem 3 to gallons, using 7.48 gallons per cubic foot. Round to the nearest gallon.
What percent of the 1-inch storm's total runoff (problem 2) can the tank (problem 4) hold? Round to the nearest whole percent.
The greenhouse club decides the tank is too small and increases its depth to 3 feet, keeping the same length and width. Find the tank's new volume in cubic feet and in gallons.
With the deeper tank from problem 6, what percent of a 1-inch storm's runoff can now be captured? Round to the nearest whole percent.
A heavier storm drops 2 inches of rain instead of 1. Find the roof's total runoff for this storm, and state whether the deeper tank from problem 6 could hold all of it.

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: 360 square feet. 24 ft x 15 ft = 360 sq ft.
Answer: 224 gallons. 360 sq ft x 1 in x 0.623 = 224.28, which rounds to 224 gallons.
Answer: 17.5 cubic feet. 3.5 ft x 2 ft x 2.5 ft = 17.5 cu ft.
Answer: 131 gallons. 17.5 cu ft x 7.48 gal per cu ft = 130.9, which rounds to 131 gallons.
Answer: 58 percent. 131 divided by 224 equals 0.5848, which rounds to 58 percent.
Answer: 21 cubic feet, or 157 gallons. 3.5 ft x 2 ft x 3 ft = 21 cu ft; 21 x 7.48 = 157.08, which rounds to 157 gallons.
Answer: 70 percent. 157 divided by 224 equals 0.7009, which rounds to 70 percent.
Answer: 449 gallons; no, the tank cannot hold it all. 360 sq ft x 2 in x 0.623 = 448.56, which rounds to 449 gallons. The deeper tank from problem 6 holds only 157 gallons, so about 449 minus 157, or 292 gallons, would overflow. The 449 gallons is all the rain that falls on the roof; a real gutter-and-tank system collects somewhat less, so the overflow would be smaller, but the tank still could not hold it all.

Differentiation

Support

Give students the roof's area (360 square feet) already calculated for problem 1, and provide a printed conversion card listing both "area times rainfall times 0.623 equals gallons" and "cubic feet times 7.48 equals gallons" so they do not need to recall the numbers from memory.

Extension

Ask students to find the minimum tank depth, to the nearest half foot, that would let the 3.5-by-2-foot tank hold at least 90 percent of a 1-inch storm's runoff, keeping the length and width the same as in problem 3.

ELL supports

Provide a labeled diagram of the greenhouse roof and the rectangular tank showing length, width, and depth as separate, clearly marked measurements. Allow students to show their work as numbers and labeled diagrams rather than full sentences.

Extensions

Have students measure, from the ground, a real roof section at their own school, or use a photo with known building dimensions provided by the teacher, and repeat problems 1 and 2 using that real roof's area, comparing the result with the greenhouse figures in this set.