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Lesson plan Grade 7 Math

Brill Hollow's Tiered Water Bill: Computing Charges and Percents

A 50-minute grade 7 lesson where students compute tiered water bills for a town and explain why higher tiers charge more per gallon to encourage conservation.

Objectives

  1. Students will compute a monthly water bill from a tiered rate structure and a base charge.
  2. Students will explain why a tiered rate charges heavy users more per gallon.
  3. Students will find the percent difference between the top and bottom water rate tiers.

Vocabulary

Key words: tiered rate, base charge, conservation, percent increase

Teacher overview

Many water utilities charge more per gallon as a household uses more, a design called a tiered rate that is meant to reward saving water. This lesson uses the town of Brill Hollow, a fictional town, so students can compute full monthly bills and then reason about why the design charges heavy users a higher rate. A common student misconception is that using four times as much water leads to exactly four times the water charge. The tiers make the water charge grow faster than that, although the flat base charge keeps the total bill from growing as fast as the water charge.

Procedure

Hook (5 min): Ask students to predict whether a household that uses twice as much water as its neighbor pays exactly twice as much for its water, not counting the base charge. Record a show of hands for yes and no, then tell them the town of Brill Hollow uses a rate that will test their prediction.

Direct instruction and model (15 min): Display the Brill Hollow rate structure from the handout: a base charge plus three price tiers. Model one full bill on the board for a household using 6,000 gallons. The base charge is a flat 12 dollars. The first 4,000 gallons cost 3 dollars per thousand, which is 4 times 3, or 12 dollars. The next 2,000 gallons fall in the second tier at 5 dollars per thousand, which is 2 times 5, or 10 dollars. The total is 12 plus 12 plus 10, or 34 dollars. Emphasize reading each tier's range carefully.

Guided practice (10 min): Work handout item 3 together, pausing so students see that the 8,000-gallon household splits its water across two tiers. Have students check the tier ranges with a partner before computing.

Independent practice (15 min): Students complete the Student Handout on their own, using calculators. Circulate and watch for the common error of charging every gallon at a single tier's price. As a formative check, confirm that at least four of every five students correctly split the 12,000-gallon bill across three tiers in item 5 before moving on.

Exit ticket and debrief (5 min): Ask students to answer in one sentence why the town of Brill Hollow might want its highest tier to cost the most per gallon. Collect the cards and read two aloud to close the lesson.

Brill Hollow's Tiered Water Bill: Computing Charges and Percents — Grade 7 Math
Name: ____________________________ Date: ______________

Student Handout

The town of Brill Hollow bills water each month using a base charge plus three tiers:

  • Base charge: 12 dollars per month (always added)
  • Tier 1: the first 4,000 gallons at 3 dollars per 1,000 gallons
  • Tier 2: the next 6,000 gallons (from 4,001 to 10,000) at 5 dollars per 1,000 gallons
  • Tier 3: every gallon above 10,000 at 8 dollars per 1,000 gallons
  1. The Okafor household uses 3,000 gallons, all in Tier 1. Find the water charge only (do not add the base charge yet).
  2. Add the 12 dollar base charge to your answer from item 1. What is the Okafor total bill?
  3. The Nunes household uses 8,000 gallons: the first 4,000 in Tier 1 and the next 4,000 in Tier 2. Find the water charge only.
  4. What is the Nunes total bill, including the 12 dollar base charge?
  5. The Delgado household uses 12,000 gallons: 4,000 in Tier 1, 6,000 in Tier 2, and 2,000 in Tier 3. Find the water charge only.
  6. What is the Delgado total bill, including the base charge?
  7. The Delgado water charge (item 5) is for 12,000 gallons; the Okafor water charge (item 1) is for 3,000 gallons, one-fourth as much. Divide the Delgado water charge by the Okafor water charge. Is it exactly 4 times as much? Explain in one sentence.
  8. Tier 3 costs 8 dollars per 1,000 gallons and Tier 1 costs 3 dollars per 1,000 gallons. What percent more does Tier 3 cost than Tier 1? Round to the nearest whole percent.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 9 dollars. 3,000 gallons is 3 thousands; 3 x 3 dollars = 9 dollars.
  2. Answer: 21 dollars. 9 dollars water charge + 12 dollar base = 21 dollars.
  3. Answer: 32 dollars. Tier 1: 4 x 3 = 12 dollars; Tier 2: 4 x 5 = 20 dollars; 12 + 20 = 32 dollars.
  4. Answer: 44 dollars. 32 dollars water charge + 12 dollar base = 44 dollars.
  5. Answer: 58 dollars. Tier 1: 4 x 3 = 12; Tier 2: 6 x 5 = 30; Tier 3: 2 x 8 = 16; 12 + 30 + 16 = 58 dollars.
  6. Answer: 70 dollars. 58 dollars water charge + 12 dollar base = 70 dollars.
  7. Answer: about 6.4 times, not 4 times. 58 / 9 = 6.44; it is more than 4 times because the extra water falls in higher-priced tiers, so each added gallon costs more.
  8. Answer: about 167 percent. The difference is 8 - 3 = 5 dollars; 5 / 3 = 1.667, which is about 167% more.

Differentiation

Support

Provide a partly completed table with the tier ranges and the "gallons in each tier" already filled for items 3 and 5, so students focus on multiplying and adding. Allow students to stop after item 6.

Extension

Ask students to find the total gallons at which a Brill Hollow bill would first reach 100 dollars, showing how they worked backward through the base charge and the tiers.

ELL supports

Pre-teach "base charge," "tier," and "per thousand gallons" with a labeled sample bill. Provide a filled example bill next to the handout and sentence frames such as "Tier ___ costs ___ dollars per 1,000 gallons" for the explanation items.