Math problem set Grade 6 Math

Birchgate Elementary's Rain Barrel: Volume with Fractional Dimensions

A grade 6 problem set finding a fictional school's rain-barrel box volume with fractional foot dimensions, converting to gallons, and comparing it to roof runoff.

Grade: Grade 6
Subject: Math
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: Calculator (optional)

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 1 and 3 apply V = l × w × h to rain-barrel box dimensions given as mixed numbers, extending the volume formula to fractional edge lengths exactly as this standard requires.

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 2, 4, and 6 convert cubic feet to gallons and roof area to runoff gallons using given conversion rates, the measurement-unit conversion this standard names.

All materials for 6.RP.A.3 →

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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 find the volume of a rectangular prism with fractional edge lengths.
Students will convert a volume in cubic feet to gallons using a given conversion rate.
Students will compare a container's capacity to a calculated amount of roof runoff.

Vocabulary

Key words: volume, mixed number, cubic foot, runoff

Teacher overview

Birchgate Elementary (a fictional school used for this problem set) is building a rectangular box to catch runoff from its garden shed roof. This problem set has students find the box's volume using fractional foot dimensions, convert that volume to gallons, and compare it to the amount of rain a storm drops on the roof, which is somewhat more than a real barrel system collects.

A common misconception is multiplying only two of the three dimensions, or forgetting to convert a mixed number to a decimal before multiplying. Check each student's setup for problem 1 before they move on, because problems 2, 5, and 7 build on that volume.

Birchgate Elementary's Rain Barrel: Volume with Fractional Dimensions — Grade 6 Math

Name: ____________________________ Date: ______________

Problems

Birchgate's (fictional) original rain-barrel box measures 3½ feet long, 2 feet wide, and 1½ feet deep. One cubic foot holds 7.48 gallons.

Find the volume of the original box, in cubic feet, using V = l × w × h.
Convert your answer from problem 1 to gallons, using the fact that 1 cubic foot holds 7.48 gallons.
The school considers a second, taller box with the same length and width but a depth of 2½ feet instead of 1½ feet. Find its volume, in cubic feet.
Convert the taller box's volume from problem 3 to gallons.
How many more gallons does the taller box (problem 4) hold than the original box (problem 2)?
The garden shed's flat roof measures 200 square feet. Using the fact that roof area (sq ft) × rainfall (inches) × 0.623 = gallons of runoff, find how many gallons of runoff a 1-inch rainstorm produces from that roof. This is all the rain that falls on the roof. A real gutter and barrel system collects somewhat less, so this is the most the box would need to hold.
Would the original box (problem 2) be large enough to catch all the runoff calculated in problem 6? By how many gallons does it fall short, or by how many gallons does it exceed the runoff?
Would the taller box (problem 4) be large enough to catch all the runoff calculated in problem 6? By how many gallons does it fall short, or by how many gallons does it exceed the runoff?
Challenge. Keeping the width at 2 feet and the depth at 1½ feet (the original box's measurements), what length, to the nearest tenth of a foot, would the box need to hold at least the 124.6 gallons of runoff from problem 6?

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: 10.5 cu ft.
V = 3.5 × 2 × 1.5 = 10.5 cubic feet.
Answer: 78.54 gal.
10.5 × 7.48 = 78.54 gallons.
Answer: 17.5 cu ft.
V = 3.5 × 2 × 2.5 = 17.5 cubic feet.
Answer: 130.9 gal.
17.5 × 7.48 = 130.9 gallons.
Answer: 52.36 gal.
130.9 − 78.54 = 52.36 gallons.
Answer: 124.6 gal.
200 × 1 × 0.623 = 124.6 gallons.
Answer: Falls short by about 46.06 gal.
124.6 − 78.54 = 46.06. The original box holds about 46.06 gallons less than a 1-inch storm produces.
Answer: Exceeds by about 6.3 gal.
130.9 − 124.6 = 6.3. The taller box holds about 6.3 gallons more than a 1-inch storm produces.
Answer: about 5.6 ft.
Needed volume in cubic feet = 124.6 ÷ 7.48 ≈ 16.66 cu ft. Length = volume ÷ (width × depth) = 16.66 ÷ (2 × 1.5) = 16.66 ÷ 3 ≈ 5.55, which rounds to about 5.6 feet.

Differentiation

Support (below grade level)

Convert each mixed number to a decimal for students before problems 1 and 3 (3½ = 3.5, 1½ = 1.5, 2½ = 2.5), and provide the volume formula V = l × w × h printed on the page.

Extension (above grade level)

Ask students to find the volume, in cubic feet and gallons, of a box with all three dimensions as mixed numbers of their own choosing, as long as the volume is at least 15 cubic feet, and to show every multiplication step.

ELL supports

Provide a labeled 3-D sketch of the rain-barrel box showing length, width, and depth as separate arrows with their measurements written on each. Allow students to show their work using the diagram and numbers, with minimal written explanation required.