Worksheet Grade 6 Math

Harmon Bluff Water Bills: Unit Rates and a Rate Increase

A grade 6 math worksheet using a fictional town's two-part water bill to practice unit rates, writing an expression, and finding a percent rate increase.

Grade: Grade 6
Subject: Math
Material: Worksheet
Time: 30 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: Items 5 and 7 have students find a cost per 1,000 gallons and a percent increase from one rate to another, the rate and percent reasoning this standard targets.

All materials for 6.RP.A.3 →

6.EE.A.2 Common Core Math

Write, read, and evaluate expressions in which letters stand for numbers.

How this material aligns: Items 3 and 4 have students write the bill as the expression 12 + 4g and evaluate it for a given usage, exactly the write-and-evaluate work this standard requires.

All materials for 6.EE.A.2 →

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 write and evaluate an expression for a two-part water bill.
Students will find a unit cost per 1,000 gallons and calculate the percent increase between two rates.

Vocabulary

Fixed charge: The part of a water bill that stays the same every month no matter how much water a family uses. It helps pay for the pipes, meters, and workers the utility needs even when no water is flowing.

Also: unit rate, expression, percent increase

Teacher overview

Most water utilities charge a bill in two parts: a fixed monthly charge that every home pays, plus a usage charge that depends on how much water the home used. This worksheet uses that two-part structure to give students a real reason to write an algebraic expression and to compute a unit rate. Harmon Bluff is a fictional town created for this worksheet, so all of its prices are made up for practice. A common misconception is that the cost per 1,000 gallons stays the same no matter how much water a home uses; the fixed charge actually makes light users pay more per 1,000 gallons.

Harmon Bluff Water Bills: Unit Rates and a Rate Increase — Grade 6 Math

Name: ____________________________ Date: ______________

Student Worksheet

Suppose the fictional town of Harmon Bluff charges for water in two parts. Each home pays a fixed charge of $12 each month. Then it pays $4 for every 1,000 gallons of water used. Use these prices below.

The Ruiz home used 6,000 gallons. Find the usage part of the bill at $4 per 1,000 gallons.
Add the $12 fixed charge. What is the Ruiz home's total bill?
Write an expression for the total bill when a home uses g thousand gallons.
Use your expression to find the bill when g equals 9.
The Ruiz bill was $36 for 6,000 gallons. Find the cost per 1,000 gallons, fixed charge included.
Next year the usage rate rises from $4 to $5 per 1,000 gallons. Find the increase in dollars.
Find the percent increase from the $4 rate to the $5 rate.
With the new $5 rate, find the usage part for the Ruiz home's 6,000 gallons.
Add the $12 fixed charge to find the Ruiz home's new total bill.
Explain why the cost per 1,000 gallons is more than $4 when a home uses only a little water.

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: $24. The home used 6 thousand gallons, and 6 × $4 = $24.
Answer: $36. Add the fixed charge: $24 + $12 = $36.
Answer: 12 + 4g. The $12 fixed charge plus $4 for each thousand gallons, g, gives 12 + 4g.
Answer: $48. Substitute g = 9: 12 + 4 × 9 = 12 + 36 = $48.
Answer: $6 per 1,000 gallons. The bill was $36 for 6 thousand gallons, and $36 ÷ 6 = $6.
Answer: $1. The rate rose from $4 to $5, and $5 − $4 = $1.
Answer: 25%. The increase is $1 on the $4 starting rate, and 1 ÷ 4 = 0.25, or 25 percent.
Answer: $30. At the new rate, 6 × $5 = $30.
Answer: $42. Add the fixed charge: $30 + $12 = $42.
Answer: The fixed charge is spread over few gallons. A light user still pays the whole $12, so each 1,000 gallons carries a larger share of that fixed charge.

Differentiation

Support

Give students a filled example first: for 5,000 gallons, the usage part is 5 × 4 = 20 dollars, plus the 12-dollar fixed charge, for a 32-dollar total. Provide a two-column table with "thousands of gallons" and "usage cost" so students can see the pattern before writing the expression in item 3.

Extension

Ask students to find the number of gallons at which the total bill would first pass 60 dollars under the original prices, then explain their reasoning using the expression from item 3.

ELL supports

Pre-teach fixed charge, usage, rate, and increase with a picture of a sample bill split into two labeled parts. Provide a sentence frame for item 10: "A light user pays more for each 1,000 gallons because ___."