Math problem set Grade 5 Math

Meadow Creek Elementary's Rain Cistern: Volume and Decimal Problems

A grade 5 math set on a school rainwater cistern, applying rectangular-prism volume, gallon conversion, decimal operations, and coordinate-plane graphing.

Grade: Grade 5
Subject: Math
Material: Math problem set
Time: 45 min
Prep: Low prep
Materials: Calculator (optional), Graph paper or a blank coordinate grid handout

Standards

5.MD.C.5 Common Core Math

Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume, including applying the formulas V = l x w x h and V = b x h for rectangular prisms.

How this material aligns: Problem 1 requires students to apply the rectangular-prism volume formula, length times width times height, to the cistern's three measurements, the exact real-world volume application this standard names.

All materials for 5.MD.C.5 →

5.NBT.B.7 Common Core Math

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

How this material aligns: Problems 3 through 7 and problem 9 require adding, subtracting, multiplying, and dividing decimal depth readings and converted volumes to hundredths, the decimal fluency this standard expects.

All materials for 5.NBT.B.7 →

5.G.A.2 Common Core Math

Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

How this material aligns: Problem 8 requires students to plot the week's five depth readings as points in the first quadrant of a coordinate grid and interpret which pair of points shows the largest change, matching this standard's graph- and-interpret task.

All materials for 5.G.A.2 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-15.

Objectives

Students will calculate the volume of a rectangular cistern in cubic feet and convert it to gallons.
Students will add and subtract decimal depth readings to track a cistern's water level over a week.
Students will plot depth readings on a first-quadrant coordinate grid and identify the largest day-to-day change.

Vocabulary

Key words: volume, cubic foot, coordinate grid

Teacher overview

Meadow Creek Elementary (a fictional school used for this problem set) built a rectangular rainwater cistern beside its garden to catch roof runoff instead of letting it wash off the property. The cistern measures 6 feet long, 4 feet wide, and 5 feet deep. This set walks students through finding the cistern's volume, converting that volume to gallons, tracking its water level through a week of rain and garden watering using decimal arithmetic, and graphing the week's readings on a coordinate grid.

A common misconception in this math is stopping after multiplying only two of the three measurements, length times width, which finds the area of the cistern's base rather than its volume. Depth is easy to forget because it is often listed last; problem 1's worked solution flags this directly by showing the base-area result before the final volume step.

Meadow Creek Elementary's Rain Cistern: Volume and Decimal Problems — Grade 5 Math

Name: ____________________________ Date: ______________

Problems

The cistern at Meadow Creek Elementary measures 6 feet long, 4 feet wide, and 5 feet deep. Use these facts for the problems below:

One cubic foot of water equals 7.48 gallons.
The cistern's rectangular base covers 6 ft × 4 ft, no matter how deep the water is.

Find the volume of the cistern in cubic feet. Use the formula Volume = length × width × height.
Convert your answer from problem 1 to gallons. Use the fact that 1 cubic foot equals 7.48 gallons. Round to the nearest whole gallon.
On Monday morning, the water depth in the cistern reads 2.75 feet. A storm that night raises the depth by 1.60 feet. What is Tuesday morning's depth reading?
On Tuesday, the class waters the garden. By Wednesday morning, the depth has dropped by 0.45 feet. What is Wednesday's depth reading?
The garden is watered again on Wednesday and Thursday. Each day, the depth drops by another 0.35 feet. Find Thursday's depth reading and Friday's depth reading.
The cistern's base always covers 24 square feet (6 ft × 4 ft). So each foot the depth drops means 24 cubic feet of water were used. Find the total drop in depth from Tuesday morning (problem 3's answer) to Friday morning (problem 5's answer). Then find how many cubic feet of water that drop represents.
Convert your answer from problem 6 into gallons. Use 7.48 gallons per cubic foot. Round to the nearest whole gallon.
Plot the week's five depth readings on a first-quadrant coordinate grid. Put the day number (1 = Monday through 5 = Friday) on the horizontal axis and the depth in feet on the vertical axis. Between which two consecutive days did the depth change the most? Was that change an increase or a decrease?
Challenge. Suppose no more rain falls. The garden keeps using water at the same rate as on Wednesday and Thursday: 0.35 feet of depth per day. Start from Friday's depth reading (problem 5's answer). About how many more full days can the garden be watered before the cistern's depth reaches 0 feet?

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: 120 cubic feet.
6 ft × 4 ft = 24 sq ft (the base area), then 24 sq ft × 5 ft = 120 cubic feet.
Answer: 898 gallons.
120 cu ft × 7.48 gal/cu ft = 897.6 gallons, which rounds to 898 gallons.
Answer: 4.35 feet.
2.75 ft + 1.60 ft = 4.35 ft.
Answer: 3.90 feet.
4.35 ft − 0.45 ft = 3.90 ft.
Answer: 3.20 feet (Friday); 3.55 feet (Thursday).
Thursday: 3.90 ft − 0.35 ft = 3.55 ft. Friday: 3.55 ft − 0.35 ft = 3.20 ft.
Answer: 27.6 cubic feet.
Total drop: 4.35 ft − 3.20 ft = 1.15 ft. Cubic feet used: 1.15 ft × 24 sq ft = 27.6 cubic feet.
Answer: 206 gallons.
27.6 cu ft × 7.48 gal/cu ft = 206.448 gallons, which rounds to 206 gallons.
Answer: Between day 1 and day 2 (Monday to Tuesday), an increase of 1.60 feet.
The changes across the week are +1.60 ft (Monday to Tuesday), −0.45 ft (Tuesday to Wednesday), −0.35 ft (Wednesday to Thursday), and −0.35 ft (Thursday to Friday). The 1.60-foot rise is larger in size than any of the drops, so it is the week's largest change.
Answer: 9 days (full).
3.20 ft ÷ 0.35 ft/day ≈ 9.14 days, so the garden can be watered at this rate for about 9 full days before the cistern empties, with only a small amount of depth left over for a partial 10th day.

Differentiation

Support (below grade level)

Provide the base-area calculation (6 ft × 4 ft = 24 sq ft) already completed before problem 1, and give students a printed conversion card reading "1 cubic foot = 7.48 gallons" so they do not need to recall it from memory. For problems 3 through 5, provide a blank table with the days already labeled (Monday through Friday) so students only need to fill in each depth as they calculate it, rather than tracking five values in their heads.

Extension (above grade level)

Ask students to design a second, smaller cistern with half the length and half the width of the Meadow Creek cistern but the same depth, find its volume, and explain what fraction of the original cistern's volume the smaller one holds without recalculating from scratch.

ELL supports

Provide a labeled diagram of the cistern showing length, width, and depth as three separate arrows before problem 1, and let students point to each measurement as they identify it. Allow the coordinate-grid answer in problem 8 to be shown as a completed graph with the largest change circled, rather than requiring a full written explanation.

Extensions

Have students research whether their own school or home has a rain barrel, cistern, or rain garden, and if not, sketch a simple design for one sized to fit a real space they know, using the same volume formula to estimate how many gallons it could hold.