Math problem set Grade 6 Math

Wrenfield Water Bills: Cost per Gallon and Fixed Charges

A grade 6 problem set on a fictional town's water rates: students find the cost per gallon, compare two bills, and see how a fixed service charge adds up.

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

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: Problems 1, 5, and 7 find a unit price per gallon, an average price per thousand gallons, and a percent change in use, the unit-rate and percent reasoning 6.RP.A.3 targets.

All materials for 6.RP.A.3 →

6.NS.B.3 Common Core Math

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

How this material aligns: Problems 1 through 6 require adding, multiplying, and dividing multi-digit decimal dollar amounts and rounding to the nearest cent, exactly the decimal fluency 6.NS.B.3 expects.

All materials for 6.NS.B.3 →

Download Word file

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 find the cost of water from a rate given per one thousand gallons.
Students will build a full water bill from a volume charge plus a fixed service charge and compare two households.

Vocabulary

Key words: service charge, volume charge, unit price

Teacher overview

A water bill usually has two parts: a charge for how much water you use, plus a fixed service charge that is the same every month. This set follows two households in Wrenfield, a fictional town, as they read and compare their bills. Students find the price of a gallon, build each bill, and see how the fixed charge changes the math. A common error is forgetting the fixed service charge, or treating the price per one thousand gallons as the price of a single gallon; watch for both, because either one throws off every total that follows.

Wrenfield Water Bills: Cost per Gallon and Fixed Charges — Grade 6 Math

Name: ____________________________ Date: ______________

Problems

The fictional town of Wrenfield bills water two ways. Use these rates for every problem.

Volume charge: $5 for every 1,000 gallons used.
Service charge: a flat $10 each month, no matter how much water is used.
In June, the Alvarez home used 6,000 gallons and the Booker home used 9,000 gallons.

Wrenfield charges $5 for every 1,000 gallons. What is the cost of a single gallon, in dollars?
Find the Alvarez home's total June bill: the volume charge for 6,000 gallons plus the $10 service charge.
Find the Booker home's total June bill: the volume charge for 9,000 gallons plus the $10 service charge.
How much more did the Booker home pay than the Alvarez home in June?
For the Alvarez home, find the average cost per 1,000 gallons once the $10 service charge is included. Divide the total bill by 6. Round to the nearest cent.
In July, the Alvarez home cut its use to 4,000 gallons. Find its total July bill.
Find the percent drop in the Alvarez home's water use from June to July. Round to the nearest whole percent.
The Alvarez home cut its water use by about a third, yet its bill did not drop by a third. Use the numbers from problems 2 and 6 to explain why.

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: $0.005.
$5 divided by 1,000 gallons = $0.005 per gallon, which is half a cent.
Answer: $40.
Volume charge: 6,000 gallons is 6 thousands, so 6 times $5 = $30. Add the $10 service charge: $30 plus $10 = $40.
Answer: $55.
Volume charge: 9,000 gallons is 9 thousands, so 9 times $5 = $45. Add the $10 service charge: $45 plus $10 = $55.
Answer: $15.
$55 minus $40 = $15 more for the Booker home.
Answer: $6.67.
Total bill $40 divided by 6 thousands = $6.666..., which rounds to $6.67 per thousand gallons. The extra above $5 comes from spreading the fixed $10 charge across the water used.
Answer: $30.
Volume charge: 4,000 gallons is 4 thousands, so 4 times $5 = $20. Add the $10 service charge: $20 plus $10 = $30.
Answer: 33 percent.
Use dropped from 6,000 to 4,000 gallons, a fall of 2,000. 2,000 divided by 6,000 = 0.333, which rounds to 33 percent.
Answer: The bill fell from $40 to $30, a drop of $10, which is 25 percent of the June bill, while water use dropped about 33 percent. The bill fell by less because the $10 service charge stays the same no matter how little water is used, so only the volume part of the bill went down.

Differentiation

Support

Give students a two-row bill template labeled "volume charge" and "service charge" with a total line, and work problem 2 aloud before they continue. Remind them that 6,000 gallons is 6 groups of 1,000, so they multiply by 6, and allow a calculator throughout.

Extension

Ask students to find how many gallons the Booker home could use in a month and still keep its total bill at or below $40, and to show the steps that lead to their answer.

ELL supports

Pre-teach "volume charge," "service charge," and "unit price" with a simple bill picture that shows the two parts stacked into one total. Provide the frame "The total bill is the water charge plus the ___," and allow short-phrase answers for problem 8.