Lesson plan Grade 6 Social Studies & Civics
Coldwell Bend: Build a Water Plant or Buy From Aldenport?
A grade 6 lesson where students use a unit rate to compare the yearly cost of rebuilding a small town's water plant against buying treated water from a neighboring city.
Objectives
- Students will convert a town's daily water use into a cost using a rate given for every thousand gallons.
- Students will compare the yearly cost of two supply options and identify which costs less.
- Students will name one benefit besides cost that a town gains or loses under each option.
Vocabulary
Key words: treatment plant, wholesale, unit rate, pipeline, capital cost, operating cost
Teacher overview
Small towns with old treatment plants often face the same question: rebuild the plant, or run a pipeline to a larger neighbor and buy finished water by the thousand gallons. This lesson uses the fictional town of Coldwell Bend, which must choose between rebuilding its own plant and buying from the city of Aldenport six miles away. Students price the purchase with a unit rate, spread each large construction cost across twenty years, and then compare. The misconception this lesson targets is the assumption that the cheaper price per gallon settles the question; students discover that the pipeline itself has to be paid for too, and that adding it flips the answer.
Procedure
Hook (5 min): Ask students what a store means by a price such as three dollars for a dozen eggs, and how they would find the cost of thirty eggs. Establish that a rate lets you price any amount. Tell them a town buys water the same way, by the thousand gallons.
Background and map (10 min): Sketch the two towns on the board. The town of Coldwell Bend has 1,800 residents and a treatment plant built long ago that no longer meets the state's requirements. The city of Aldenport, six miles away, has a newer plant with room to spare and sells treated water at $4.50 for every 1,000 gallons. Explain the two kinds of cost that appear in the lesson: a large one-time construction cost, spread across the twenty years the pipe or plant will last, and a yearly cost to run and staff a plant.
Modeling the unit rate (8 min): Model one purchase on the board. If a town used 20,000 gallons in a day, that is 20 groups of 1,000 gallons, and at $4.50 for each group the day costs $90. Have students explain in their own words why the division comes before the multiplication.
Independent work (20 min): Students complete the nine questions on the student handout. Watch for students who multiply the full gallon count by $4.50 instead of first finding the number of thousand-gallon groups.
Whole-class comparison (5 min): Put both yearly totals on the board and take a vote. Ask what the vote would be if Aldenport later raised its price, and what Coldwell Bend would be able to do about it. Draw out that buying water hands the price decision to another town's council.
Exit ticket (2 min): Students write one sentence naming a benefit besides cost that Coldwell Bend would gain or lose by buying water from Aldenport. Answers vary, so read for whether the sentence names something real from the lesson, such as control of the price, jobs at the plant, or freedom from running a plant at all.
Student Handout
The town of Coldwell Bend has to replace its old water treatment plant. It has two choices. It can rebuild the plant, or it can build a pipeline to the city of Aldenport and buy treated water. Aldenport charges $4.50 for every 1,000 gallons. Show your work.
- Coldwell Bend has 1,800 residents, and each resident uses about 80 gallons of water a day. How many gallons does the town use in one day?
- Aldenport sells water in groups of 1,000 gallons. How many groups of 1,000 gallons does Coldwell Bend use in one day?
- Aldenport charges $4.50 for each group of 1,000 gallons. Using your answer to question 2, what would one day of water cost?
- Using your answer to question 3, what would 365 days of water cost?
- Rebuilding the plant would cost $4,200,000, spread evenly across 20 years. What is the rebuilding cost for one year?
- Running the rebuilt plant would cost another $90,000 each year. Adding that to your answer from question 5, what does the rebuild choice cost for one year?
- The pipeline to Aldenport would cost $1,800,000, spread evenly across 20 years. What is the pipeline cost for one year?
- Add your answer from question 7 to your answer from question 4. What does the buying choice cost for one year?
- Which choice costs less for one year, rebuilding the plant or buying from Aldenport?
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: 144,000 gallons. In the town of Coldwell Bend, 1,800 residents times 80 gallons for each resident equals 144,000 gallons a day.
- Answer: 144 groups. Dividing 144,000 gallons by 1,000 gallons in each group gives 144 groups.
- Answer: $648. Multiplying 144 groups by $4.50 for each group gives $648 for one day.
- Answer: $236,520. Multiplying $648 a day by 365 days gives $236,520 for one year.
- Answer: $210,000. Dividing $4,200,000 by 20 years gives $210,000 for each year.
- Answer: $300,000. Adding the $90,000 yearly operating cost to the $210,000 construction share gives $300,000 for one year.
- Answer: $90,000. Dividing $1,800,000 by 20 years gives $90,000 for each year. This figure happens to match the plant's operating cost, so students should label their work carefully.
- Answer: $326,520. Adding the $90,000 pipeline share to the $236,520 water purchase gives $326,520 for one year.
- Answer: Rebuilding the plant. At $300,000 a year, rebuilding costs $26,520 less than the $326,520 buying choice, even though the water itself looked cheaper before the pipeline was counted.
Differentiation
Support
Give these students a partly finished worksheet with question 1 already answered and with the words "divide" or "multiply" printed beside each of the remaining questions. Allow a calculator throughout, and provide a place-value chart so the large dollar figures are read correctly. Have them check questions 5 and 7 against each other, since both use the same twenty-year division.
Extension
Ask students to find the price for every thousand gallons at which the two choices would cost the same amount in a year and how far Aldenport would have to lower its price for buying to become the cheaper choice, then explain what would happen to Coldwell Bend if Aldenport raised its price after the town had already closed its plant. Students should also state one thing the town would give up by closing its own plant, such as local operator jobs or control over the price.
ELL supports
Pre-teach "plant," "pipeline," "rate," and "spread across twenty years" using a simple drawing of one pipe running between two towns and a calendar strip divided into twenty parts. Provide the sentence frame "One day of water costs ___ because ___ groups of 1,000 gallons times ___ equals ___." Allow the exit ticket to be a labeled drawing with one short phrase.
Extensions
Find out whether your own community treats its own water or buys it from a neighboring system, which is usually stated on the first page of the annual water quality report. If the community buys water, students can look for the name of the seller and discuss what the arrangement means for who sets the price.