Math problem set Grade 6 Engineering & Design

Northgate School Low-Flow Fixture Retrofit Problems

A grade 6 engineering set where students plan a fixture retrofit, comparing shower and faucet flow rates to find water and cost savings with percent and an equation.

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

Standards

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: Students find percent water saved in problem 4 and use a unit price of water in problem 6 to convert gallons saved to dollars, the percent and ratio reasoning this standard targets.

All materials for 6.RP.A.3 →

6.EE.B.7 Common Core Math

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

How this material aligns: Problem 9 asks students to write and solve the one-step equation 18n = 180 to find how many low-flow showerheads fit the budget, exactly the px = q form this standard covers.

All materials for 6.EE.B.7 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will compare fixture flow rates to find gallons and percent of water saved.
Students will write and solve a one-step equation to fit a retrofit purchase to a budget.

Vocabulary

Flow rate: Flow rate measures how much water moves past a point in a certain amount of time, like gallons per minute through a garden hose. Bigger pipes and stronger pushes give bigger flow rates.

Also: retrofit, low-flow, conservation

Teacher overview

Northgate Middle School, in the fictional town of Ardenwood, is planning a fixture retrofit. A retrofit swaps old fixtures for low-flow models that use less water for the same job. Standard showerheads flow at about 2.5 gallons per minute, while WaterSense-labeled models use 2.0 gallons per minute or less. Faucets can be fitted with aerators that cut their flow too.

Students compare flow rates, find the water and money saved, and fit a purchase to a budget. A common mistake is thinking that a lower flow rate means students must shorten their showers. The savings come from the flow rate itself, because gallons used equal the flow rate times the number of minutes.

Northgate School Low-Flow Fixture Retrofit Problems — Grade 6 Engineering & Design

Name: ____________________________ Date: ______________

Problems

Use this scenario for every problem. Northgate Middle School is in the fictional town of Ardenwood. Its gym has 8 showers. A standard showerhead flows at 2.5 gpm, and a WaterSense showerhead flows at 2.0 gpm.

A standard shower runs at 2.5 gpm. How many gallons does an 8-minute shower use?
A WaterSense shower runs at 2.0 gpm. How many gallons does the same 8-minute shower use?
How many gallons are saved per shower by switching to the WaterSense model?
What percent of the standard shower's water does that switch save?
Each of the 8 showers is used for one 8-minute shower per day. How many gallons do all 8 showers save per day?
The school pays $9 for every 1,000 gallons of water. Over a 180-day school year, the 8 showers save 5,760 gallons. What is the cost saved for the year?
Old bathroom faucets run at 2.2 gpm. New aerators bring them to 1.5 gpm. How many gallons are saved for each minute a faucet runs?
The school has 20 faucets, each running about 10 minutes total per day. How many gallons do the faucet aerators save per day?
Let n be the number of low-flow showerheads the school buys. Each costs $18, and the showerhead budget is $180. Write and solve the equation 18n = 180 to find how many the school can buy.
In one or two sentences, explain why a lower flow rate lowers the water bill even when students shower for the same number of minutes.

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: 20 gallons. 2.5 gpm x 8 minutes = 20 gallons.
Answer: 16 gallons. 2.0 gpm x 8 minutes = 16 gallons.
Answer: 4 gallons. 20 - 16 = 4 gallons saved per shower.
Answer: 20 percent. 4 / 20 = 0.20, or 20 percent of the standard shower's water.
Answer: 32 gallons. 4 gallons saved per shower x 8 showers = 32 gallons per day.
Answer: $51.84. Water costs $9 / 1,000 gallons. 5,760 / 1,000 = 5.76, and 5.76 x 9 = $51.84.
Answer: 0.7 gallons. 2.2 gpm - 1.5 gpm = 0.7 gallons saved each minute.
Answer: 140 gallons. 0.7 gallons x 10 minutes x 20 faucets = 140 gallons per day.
Answer: 10 showerheads. Solve 18n = 180 by dividing both sides by 18, so n = 10.
Answer: Fewer gallons flow each minute. Gallons used equal the flow rate times the minutes, so a smaller flow rate uses fewer gallons for the same shower length, which lowers the bill.

Differentiation

Support

Give students a filled example first: a 5-minute standard shower uses 2.5 times 5, or 12.5 gallons. Provide the equation in problem 9 already set up as 18n = 180 with the hint "divide both sides by 18." Allow a calculator for the decimal steps in problems 6 and 7.

Extension

Ask students to find the total yearly water saved if the faucet aerators run every school day for 180 days, then decide which retrofit, showers or faucets, saves more water per year and justify the answer with their numbers.

ELL supports

Pre-teach "flow rate," "retrofit," and "aerator" with a picture of a showerhead and a labeled arrow showing gallons per minute. Provide a sentence frame for problem 10: "A lower flow rate saves water because ___."