Lesson plan Grade 6 Math

Meadowvale Water Bill Expressions: A Grade 6 Lesson

A 45-minute grade 6 lesson where students write and evaluate an algebraic expression for a fictional town's water bill built from a rate and a fixed fee.

Grade: Grade 6
Subject: Math
Material: Lesson plan
Time: 45 min
Prep: Low prep
Materials: Printed water-bill handout, Chart paper, Markers

Standards

6.EE.A.2 Common Core Math

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

How this material aligns: Students write the bill as the expression 3g plus 12 and evaluate it for several months of use in handout items 1 through 5, the write-read-and-evaluate skill this standard names.

All materials for 6.EE.A.2 →

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: The three-dollars-per-hundred-gallons unit rate that builds the expression is applied in items 2, 3, and 5, the unit-rate reasoning this standard requires in real contexts.

All materials for 6.RP.A.3 →

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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 write an algebraic expression for a water bill using a rate and a fixed fee.
Students will evaluate the expression to find the bill for different amounts of water use.

Vocabulary

Key words: expression, variable, fixed fee, unit rate

Teacher overview

A water bill is usually a fixed monthly fee plus a charge for each unit of water used, which makes it a clear real-world use of an algebraic expression. This lesson uses the town of Meadowvale, a fictional town, so students can write a bill as 3g plus 12 and evaluate it for different months. A common misconception this lesson addresses is treating the fixed fee as if it changed with use; students should see that the fixed fee stays the same while only the rate part grows with gallons used.

Procedure

Hook (5 min): Show students two months of a family's water use, one small and one large, and ask why the bill is not simply zero in a month with no use. Draw out that most bills include a fee that is charged every month no matter what.

Direct instruction (12 min): Introduce the town of Meadowvale, a fictional town, where each bill is a 12-dollar fixed fee plus 3 dollars for every 100 gallons used. Let g stand for the number of hundreds of gallons used. Build the expression on chart paper: cost equals 3g plus 12. Point to each part and name it, the 3g as the use charge and the 12 as the fixed fee.

Guided practice (13 min): Evaluate the expression together for g equal to 5 and g equal to 8, writing every step. Pause for a formative check: ask students to hold up the number of the part, 3g or 12, that changes when a family uses more water, and re-teach if more than a few hold up 12.

Independent practice (10 min): Students complete the handout, writing the expression and evaluating it for several months on their own, then checking with a partner.

Closure (5 min): Students answer one question on an exit slip: "If a family used no water at all in a month, what would its bill be?" Collect and scan for the fixed-fee answer of 12 dollars before dismissal.

Meadowvale Water Bill Expressions: A Grade 6 Lesson — Grade 6 Math

Name: ____________________________ Date: ______________

Student Handout

In the town of Meadowvale, a fictional town, each home's monthly water bill is a $12 fixed fee plus $3 for every 100 gallons of water used. Let g stand for the number of hundreds of gallons used.

Write the expression for the monthly bill using the variable g.
Evaluate the bill for a month when g equals 10, which is 1,000 gallons used.
Evaluate the bill for a month when g equals 20, which is 2,000 gallons used.
Which part of the expression, 3g or 12, is the fixed fee that stays the same every month?
A family used 1,500 gallons, so g equals 15. What is that month's bill?
A family cut its use from g equals 20 down to g equals 15. By how many dollars did the bill drop?

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: C = 3g + 12. The bill is 3 dollars for each hundred gallons (3g) plus the 12-dollar fixed fee.
Answer: $42. 3 × 10 + 12 = 30 + 12 = 42 dollars.
Answer: $72. 3 × 20 + 12 = 60 + 12 = 72 dollars.
Answer: The 12. The fixed fee of 12 dollars stays the same every month, while the 3g part changes with use.
Answer: $57. 3 × 15 + 12 = 45 + 12 = 57 dollars.
Answer: $15. The bill dropped from 72 dollars to 57 dollars, and 72 − 57 = 15 dollars.

Differentiation

Support

Give students a filled-in first row of a table (g equals 5, bill equals 27) worked step by step as a model before item 2. Provide a reminder that "evaluate" means "put the number in place of g, then follow order of operations." Allow a calculator for the arithmetic.

Extension

Ask students to write a new expression for a nearby town whose bill is a 10-dollar fixed fee plus 4 dollars for every 100 gallons, then find how many hundreds of gallons would make the two towns' bills equal. Have them show the work that supports their answer.

ELL supports

Pre-teach "expression," "variable," "fixed fee," and "evaluate" with a labeled sample bill. Provide sentence frames: "The fixed fee is ___." and "When g equals ___, the bill is ___." Allow students to underline the 3g part and the 12 part in two colors.