Math problem set Grade 5 Engineering & Design

Stannerly School Playground: A Grade 5 Runoff Volume Set

Nine grade 5 problems comparing a sealed mat and a porous pad for a fictional playground, using decimal volume work to pick the surface that meets a limit.

Grade: Grade 5
Subject: Engineering & Design
Material: Math problem set
Time: 45 min
Prep: No prep
Materials: Pencil and paper, Calculator

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: Problems 2 and 5 apply base area times depth to find the rain volume on the playground, and problem 8 solves for a catch tank's missing depth from its volume and its floor area, both forms 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 2, 4, 5, and 7 multiply and subtract decimals to hundredths, such as 2,400 times 0.15 and 360 times 7.48, using place-value reasoning.

All materials for 5.NBT.B.7 →

3-5-ETS1-2 NGSS

Generate and compare multiple possible solutions to a problem based on how well each is likely to meet the criteria and constraints of the problem.

How this material aligns: Problem 6 weighs the sealed mat against the porous pad on the district's stated runoff limit and names the surface that meets it, and problem 9 measures the gap between the two designs.

All materials for 3-5-ETS1-2 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-09-23.

Objectives

Students will find rain volume on a rectangular surface using length, width, and depth in feet.
Students will multiply and subtract decimals to hundredths to compare two surface designs.
Students will name which surface meets a stated runoff limit and by how much.

Vocabulary

Key words: runoff, porous, cubic foot, design storm, criterion

Teacher overview

Every problem in this set draws on one scenario: the fictional town of Stannerly is rebuilding a school playground, and the district must pick between two surfaces that shed rain very differently. The arc runs from the playground's area, through the volume of rain a design storm drops on it, to the runoff each surface would send toward the street, and finally to the size of a tank that could hold the better surface's runoff. Values found in early problems are reused later, so students should keep their work.

The misconception this set is built to correct is a unit mismatch. Rain is normally reported in inches while a playground is measured in feet, and fifth graders often multiply the two straight across: 2,400 square feet times 3 inches, and they write 7,200 of something. Every depth in this set is already given in feet for that reason, and the first thing to say to the class is that all three measurements in a volume must be in the same unit before anything is multiplied. When students later meet rainfall in inches, the fix is to convert the inches to feet first, not to multiply and label afterward. A second, smaller error appears in problem 4: students subtract the soak-in depth from the playground's area instead of from the storm's depth, because both numbers are sitting on the page. Ask them what the answer's unit should be before they subtract.

Stannerly School Playground: A Grade 5 Runoff Volume Set — Grade 5 Engineering & Design

Name: ____________________________ Date: ______________

Problems

Stannerly School's old playground is being rebuilt. The new surface will be 60.0 feet long and 40.0 feet wide. The district's engineer plans for a design storm that drops 0.25 feet of rain on the playground. Two surfaces have been proposed.

Surface A is a sealed rubber mat. No rain soaks through it, so every bit of the storm runs off.
Surface B is a porous gravel and sand pad. The first 0.10 feet of the storm soaks into it, and the rest runs off.

The district set one rule for the new playground: runoff from the design storm must be 400 cubic feet or less.

The playground will be 60.0 feet long and 40.0 feet wide. What is its area in square feet?
The design storm drops 0.25 feet of rain. Using the area from problem 1, what is the total volume of rain that falls on the playground, in cubic feet?
Surface A lets nothing soak in. How many cubic feet of runoff would Surface A send toward the street during the design storm?
Surface B soaks in the first 0.10 feet of the storm. How many feet of the 0.25-foot storm are left to run off?
Using your depth from problem 4 and the area from problem 1, how many cubic feet of runoff would Surface B send toward the street?
The district's rule allows 400 cubic feet of runoff or less. Which surface meets the rule?
One cubic foot of water holds 7.48 gallons. How many gallons of runoff would Surface B send toward the street?
The district wants a catch tank that holds all of Surface B's runoff. The tank will be 10.0 feet long and 6.0 feet wide. How deep must the tank be, in feet, to hold that runoff?
How many more cubic feet of runoff would Surface A send than Surface B?

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: 2,400 square feet.
60.0 feet times 40.0 feet equals 2,400 square feet.
Answer: 600 cubic feet.
2,400 square feet times 0.25 feet equals 600 cubic feet. One quarter of 2,400 is 600, which is a useful check.
Answer: 600 cubic feet.
Surface A lets nothing soak in, so all of the rain volume from problem 2 becomes runoff.
Answer: 0.15 feet.
0.25 feet minus 0.10 feet equals 0.15 feet. The answer is a depth, so it is measured in feet, not in square feet.
Answer: 360 cubic feet.
2,400 square feet times 0.15 feet equals 360 cubic feet. Work it as 2,400 times 15 equals 36,000, then move the decimal two places to get 360.00.
Answer: Surface B.
Surface B sends 360 cubic feet of runoff, which is at or below the 400-cubic-foot limit, while Surface A sends 600 cubic feet and breaks the rule.
Answer: 2,692.8 gallons.
360 times 7.48 equals 2,692.8. Break it up as 360 times 7 equals 2,520, plus 360 times 0.48 equals 172.8, and 2,520 plus 172.8 equals 2,692.8 gallons.
Answer: 6.0 feet.
The tank's floor is 10.0 feet times 6.0 feet, or 60 square feet. Dividing 360 cubic feet by 60 square feet gives a depth of 6.0 feet.
Answer: 240 cubic feet.
600 cubic feet minus 360 cubic feet equals 240 cubic feet more from Surface A.

Differentiation

Support

Give these students a labeled sketch of the playground with the length and width already written in, and a place-value chart for the decimal multiplication in problems 2 and 5. Let them use a calculator for problem 7. Before problem 4, ask aloud what unit the answer should carry, since naming the unit first usually stops the wrong subtraction.

Extension

Ask these students to find the smallest soak-in depth, written in hundredths of a foot, that would let a replacement for Surface A meet the rule, then to design a third surface of their own with a stated soak-in depth and show its runoff. They should also explain why a deeper catch tank is not always the cheaper answer for the district, given that a deeper hole costs more to dig.

ELL supports

Pre-teach "runoff," "soak in," "porous," and "cubic foot" with a sponge and a sealed plastic lid held under a slow pour, so the two surfaces are visible rather than described. Provide a unit strip students can fill in: feet times feet equals square feet, and square feet times feet equals cubic feet. Allow answers written as a number plus a labeled drawing.

Extensions

Students can measure a paved area at school with a trundle wheel or a long tape, then rerun problems 1 through 5 with their own length and width. Comparing their result with the playground's shows how quickly runoff volume grows with area, and a look at where that pavement actually drains connects the arithmetic to a pipe or a ditch students can point at.