Classroom activity Grade 9 Math

Northmill Meter Route: Converting Meter Readings to Gallons per Day

A grade 9 station-rotation activity where teams read six fictional water meters, convert CCF to gallons per day, and rank which address the leak crew should visit.

Objectives

  1. Students will convert a meter reading difference in CCF into gallons and gallons per day.
  2. Students will compare a household's computed daily use against a stated national average.
  3. Students will rank six addresses by daily use and justify which one to investigate first.

Vocabulary

Key words: meter reading, CCF, consumption, leak, gallons per day

Teacher overview

Many residential water meters in the United States register in hundreds of cubic feet, a unit written CCF, so a utility's billing clerk sees a number that a customer cannot interpret without converting it first. This station rotation puts teams of three in that clerk's position for six fictional addresses on a route belonging to the fictional Northmill Water Company. At each station a card shows two meter readings taken thirty days apart, and teams convert the difference into gallons and then into gallons per day. The rotation teaches the concept directly, because telling an ordinary household apart from one with a running leak requires putting every address on the same per-day footing, which is what the conversion chain does. The misconception to watch for is that a CCF is a hundred gallons. Students who carry that assumption report daily totals about seven times too small, and the whole route then looks unremarkable, so it is worth stopping the class on the 748-gallon figure before any team starts rotating.

Activity Directions

  1. Before class, make six meter cards from the table in the Student Handout, one per station, and post them around the room at Station 1 through Station 6. Print one recording sheet per team. Set out a calculator at each station.

  2. Open with the unit itself. Show that one CCF is 100 cubic feet, and that one cubic foot holds 7.48 gallons, so one CCF is 748 gallons. Have the class say what a meter change of 6 CCF means in gallons before any team moves.

  3. Divide the class into teams of three and assign each team a starting station. Explain that each card gives two readings taken thirty days apart, and that the team's job at each station is to record the change in CCF, the change in gallons, and the average use in gallons per day.

  4. Give teams four minutes per station. Call time and rotate teams one station clockwise. Continue until every team has visited all six stations, or until thirty minutes of rotation have passed, whichever comes first.

  5. When the rotation ends, seat the teams and distribute the Student Handout. Teams complete questions 1 through 12 using the readings printed there, which are the same readings posted at the stations.

  6. Bring the class together and build one table on the board with all six addresses and their gallons per day, filled in by asking one team per address to report. Where two teams disagree, work that conversion again in front of the class rather than announcing which team was right.

  7. Close with the debrief question that drives the whole rotation: which address should the leak crew visit first, and what in the numbers justifies sending them there rather than to the address with the second-highest daily use. Ask a second question about the address using the least water, and whether a very low number could also be worth a phone call.

Answer Key

  1. Answer: 6 CCF.
    Subtracting the readings gives 1,210 - 1,204 = 6 CCF over the thirty days.

  2. Answer: 4,488 gallons.
    Multiplying gives 6 CCF x 748 gallons per CCF = 4,488 gallons.

  3. Answer: 149.6 gallons per day.
    Dividing gives 4,488 gallons divided by 30 days = 149.6 gallons per day.

  4. Answer: 33,660 gallons.
    Subtracting gives 700 - 655 = 45 CCF, and 45 x 748 = 33,660 gallons.

  5. Answer: 1,122 gallons per day.
    Dividing gives 33,660 gallons divided by 30 days = 1,122 gallons per day.

  6. Answer: 3.74 times.
    Dividing gives 1,122 divided by 300 = 3.74, so this address used nearly four times the stated average.

  7. Answer: 49.9 gallons per day.
    Subtracting gives 2,043 - 2,041 = 2 CCF, which is 2 x 748 = 1,496 gallons, and 1,496 divided by 30 = 49.87, or about 49.9 gallons per day.

  8. Answer: 288 gallons per day.
    Multiplying gives 0.2 gallons per minute x 1,440 minutes per day = 288 gallons per day.

  9. Answer: 299.2 gallons per day.
    Subtracting gives 884 - 872 = 12 CCF, which is 12 x 748 = 8,976 gallons, and 8,976 divided by 30 = 299.2 gallons per day.

  10. Answer: 409,530 gallons.
    Multiplying gives 1,122 gallons per day x 365 days = 409,530 gallons in a year.

  11. Answer: 43.6 times.
    Dividing gives 409,530 divided by 9,400 = 43.57, so the yearly total is roughly forty-four times the average household leak.

  12. Answer: Fennel Street.
    Its 1,122 gallons per day is about 3.74 times the stated household average and nearly four times the next-highest address on the route, which is Hobbsend Road at 299.2 gallons per day. That gap is far larger than ordinary differences in household size explain.

Differentiation

Support

Give these teams a recording sheet for the fictional Northmill route with the three column headings already labeled as CCF, gallons, and gallons per day, and with Station 1 worked through as an example. Post the chain "CCF x 748 = gallons, then divide by 30 = gallons per day" at each station so the order of operations is visible while they work.

Extension

Ask teams to find the smallest continuous leak rate, in gallons per minute, that would fully account for the difference between the Fennel Street daily use and the 300 gallon per day household average. A second task is to decide what additional information, such as the number of people at each address, would make the ranking more defensible, and to explain why the route data alone cannot settle it.

ELL supports

Provide a photograph or clear drawing of a residential meter face with the CCF register circled, so the unit is anchored to an object rather than an abbreviation. Give a sentence frame for question 12, such as "I would send the crew to ___ because its daily use is ___ gallons per day, which is ___ times the average."

Extensions

Students can find the unit their own utility bills use, which may be CCF, thousands of gallons, or cubic meters, and convert one month of a real household bill into gallons per day for comparison with the fictional route. A follow-up task is to write the short customer notice a utility might mail to the Fennel Street address, stating the reading, the daily rate, and what the household should check first.