Water for Schools
Menu

Worksheet Grade 8 Health & Consumer Science

Nakamura Family Fixture Upgrade: A Grade 8 Water-Savings Worksheet

A grade 8 consumer-science worksheet on home water savings, using scientific notation for yearly gallons and a linear equation to find a fixture's payback time.

Objectives

  1. Students will compute daily and yearly water savings from a lower-flow showerhead.
  2. Students will express yearly gallon amounts in scientific notation and compare them.
  3. Students will solve a linear equation to find a fixture's payback time in months.

Vocabulary

Flow rate
Flow rate measures how much water moves past a point in a certain amount of time, like gallons per minute through a garden hose. Bigger pipes and stronger pushes give bigger flow rates.
WaterSense
An EPA label on toilets, showerheads, faucets, and irrigation controllers that meet water-saving standards. It works like the ENERGY STAR label, but for water.

Also: scientific notation, payback time

Teacher overview

Small changes to home fixtures add up to large yearly water savings, and the math shows how. This worksheet has students compare a standard showerhead to a WaterSense-labeled model, scale the difference up to a full year, express those yearly gallons in scientific notation, and then figure out how long the water savings take to pay back the cost of the new showerhead. A standard showerhead flows at 2.5 gallons per minute, while a WaterSense-labeled model uses 2.0 gallons per minute or less.

Nakamura Family Fixture Upgrade: A Grade 8 Water-Savings Worksheet — Grade 8 Health & Consumer Science
Name: ____________________________ Date: ______________

Student Worksheet

Suppose the Nakamura family, a fictional household in Meadowvale, is deciding whether to replace a standard 2.5 gallon-per-minute showerhead with a WaterSense-labeled 2.0 gallon-per-minute model.

  1. How many gallons does each showerhead use during a 10-minute shower? Find the amount for the 2.5 gpm model and for the 2.0 gpm model.
  2. How many gallons does the family save per 10-minute shower by switching to the WaterSense model?
  3. The family takes 4 showers a day, each 10 minutes long. How many gallons do they save per day by switching?
  4. How many gallons is that per year? Use 365 days, round to the nearest hundred, and write the result in scientific notation.
  5. A faucet in the house drips once per second. EPA WaterSense says a drip like this can waste more than 3,000 gallons per year, so use 3,000 gallons. Write 3,000 in scientific notation.
  6. Household leaks in a typical home waste about 9,400 gallons per year. Using scientific notation for both, about how many times larger is the yearly leak waste (9,400 gallons) than the yearly faucet drip (3,000 gallons)? Round to one decimal place.
  7. In this scenario, water costs 0.01 dollars per gallon. Using your daily savings from item 3, what is the dollar value of the water the family saves per day?
  8. Over a 30-day month, how many dollars does the family save?
  9. The WaterSense showerhead costs 24 dollars. Write and solve the linear equation 24 = 6m to find the number of months m of savings needed to pay back the cost.
  10. Explain why a small difference of 0.5 gallons per minute leads to a large yearly savings, using your scientific-notation answer from item 4.

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: 25 gallons and 20 gallons.
    The 2.5 gpm model uses 2.5 times 10 = 25 gallons; the 2.0 gpm model uses 2.0 times 10 = 20 gallons.
  2. Answer: 5 gallons.
    25 gallons minus 20 gallons equals 5 gallons saved per 10-minute shower.
  3. Answer: 20 gallons per day.
    4 showers times 5 gallons saved each equals 20 gallons saved per day.
  4. Answer: 7.3 times ten to the third gallons.
    20 gallons per day times 365 days equals 7,300 gallons per year, which is 7.3 times ten to the third power.
  5. Answer: 3.0 times ten to the third.
    3,000 written in scientific notation is 3.0 times ten to the third power.
  6. Answer: About 3.1 times larger.
    9,400 is 9.4 times ten to the third and 3,000 is 3.0 times ten to the third; 9.4 divided by 3.0 is about 3.1.
  7. Answer: 0.20 dollars per day.
    20 gallons times 0.01 dollars per gallon equals 0.20 dollars saved per day.
  8. Answer: 6 dollars.
    0.20 dollars per day times 30 days equals 6 dollars saved per month.
  9. Answer: 4 months.
    24 = 6m gives m = 24 divided by 6 = 4 months to pay back the cost.
  10. Answer: Each shower saves a little, but the year multiplies it.
    The 0.5 gpm difference is only 5 gallons per shower, yet repeated across 4 showers a day for 365 days it grows to 7.3 times ten to the third gallons, a large yearly total.

Differentiation

Support

Provide a worked example of scaling a per-shower savings up to a yearly total before item 4, and let students use a calculator with a scientific-notation display. Give the payback equation in item 9 already set up so students only solve for m.

Extension

Ask students to suppose the family also replaces two faucet aerators that together save another 8 gallons per day, and to recompute the yearly savings and the payback time if the aerators cost 12 dollars total. Have them compare the two payback times and say which upgrade pays back faster.

ELL supports

Pre-teach flow rate, per minute, and payback with a simple picture of a showerhead and a calendar. Provide a sentence frame for item 10, such as "A small savings each shower becomes large because ___."