Math problem set Grade 6 Math

Ordley Water Bills: Rates, Totals, and Percent Increase

A grade 6 math set on a fictional utility's water bills, where students find monthly charges, percent increases, and usage from a base plus per-unit rate.

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 4 and 5 ask students to find the percent increase between two usage amounts and between two rates, the real-world percent 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 7 has students write and solve the one-step equation 5x equals 40 to find the water used from a known usage charge, matching this standard's px equals q form.

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 calculate a monthly water bill from a fixed base charge plus a per-unit usage rate.
Students will find the percent increase between two usage amounts and solve a one-step equation for water used.

Vocabulary

Key words: base charge, usage rate, percent increase

Teacher overview

A water bill is not one flat price. Most utilities charge a fixed base amount each month plus a rate for every unit of water used, so a household that uses more pays more. This set uses the bills of Ordley, a fictional water utility, to practice building a bill, finding percent increases, and solving for how much water was used. Water and sewer bills across the country have been rising faster than general prices, which makes reading a bill a useful skill.

A common misconception is to find a percent increase by dividing the change by the new amount instead of by the starting amount. The change is always divided by the original value, not the new one. A student who divides by the larger number will report a smaller percent than the true increase.

Ordley Water Bills: Rates, Totals, and Percent Increase — Grade 6 Math

Name: ____________________________ Date: ______________

Problems

Use this rate plan for Ordley (a fictional utility) in every problem unless a problem says otherwise.

Base charge: $12 each month.
Usage rate: $4 for every 1,000 gallons used.

The Harmon household used 6,000 gallons in June. Find the usage charge (the part of the bill for water used), not counting the base charge.
Find the Harmon household's total June bill, including the base charge.
In July the Harmon household used 9,000 gallons. Find their total July bill.
Find the percent increase in the Harmon household's water used from June (6,000 gallons) to July (9,000 gallons).
Ordley raises the usage rate from $4 to $5 for every 1,000 gallons. Find the percent increase in the rate.
Using the new $5 rate and the same $12 base charge, find the total bill for a household that uses 6,000 gallons.
One household's August bill had a usage charge of $40, after taking out the base charge. At the $5 rate for every 1,000 gallons, write and solve the equation 5x = 40 to find x, the number of 1,000-gallon units they used. Then state the gallons.
Explain why two Ordley households with the same base charge can still get very different total bills.

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.
6,000 gallons is 6 units of 1,000 gallons. 6 units times $4 per unit = $24.
Answer: $36.
Usage charge $24 plus base charge $12 = $36 total.
Answer: $48.
9,000 gallons is 9 units. 9 times $4 = $36 usage charge, plus $12 base = $48 total.
Answer: 50 percent.
The change is 9,000 minus 6,000 = 3,000 gallons. 3,000 divided by the June amount 6,000 = 0.5, or 50 percent.
Answer: 25 percent.
The change is $5 minus $4 = $1. $1 divided by the starting rate $4 = 0.25, or 25 percent.
Answer: $42.
6 units times $5 = $30 usage charge, plus $12 base = $42 total.
Answer: 8,000 gallons.
5x = 40, so x = 40 divided by 5 = 8. That is 8 units of 1,000 gallons, which is 8,000 gallons.
Answer: Because the usage charge depends on how much water each household uses. Two homes pay the same base charge, but a home that uses more water adds more usage charge on top, so its total bill is higher.

Differentiation

Support

Give students a two-column bill template with "base charge" and "usage charge" already labeled, so they add the two parts rather than tracking the whole bill in one step. Provide the June and July usage amounts already converted into units of 1,000 gallons for problems 1 through 3.

Extension

Suppose a household's total Ordley bill is exactly $60 under the new $5 rate. Ask students to find the usage, in gallons, that produces it. Have them write the reasoning as taking out the base charge first, then dividing by the rate, and check their answer by building the bill back up.

ELL supports

Pre-teach base charge, usage, and percent increase with a simple labeled sample bill. Provide the sentence frame "The change is ___ divided by the starting amount ___, which is ___ percent" for problems 4 and 5, and allow answers as a number and unit.