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Worksheet Grade 7 Math

Wrensfield's Chlorine Residual: A Grade 7 Rate Worksheet

A grade 7 worksheet where students find the loss of chlorine per mile along a fictional town's water main and compute percent decrease and predictions.

Objectives

  1. Students will compute a unit rate of chlorine loss per mile from paired sample readings.
  2. Students will predict a chlorine level at a new distance using a constant loss rate.
  3. Students will calculate the percent decrease between two chlorine readings.

Vocabulary

Chlorine residual
Chlorine residual is the small amount of chlorine still left in the water after it leaves the treatment plant. It keeps protecting the water from germs all the way to your faucet.
Water main
A big underground pipe that carries drinking water beneath the streets to a neighborhood. Smaller service lines branch off it to reach each building.

Also: unit rate, percent decrease

Teacher overview

Treated water leaves a plant carrying a small amount of chlorine, called the residual, which keeps the water safe on its way to customers. That residual fades as the water travels, so operators sample it at points along the main and watch the trend. How fast it fades depends on temperature, pipe condition, and how long the water has been in the pipe, and a real main rarely loses the same amount in every mile; the readings in this worksheet were chosen to fall at a steady rate so that one unit rate describes the whole main. Federal rules cap the residual at 4.0 mg/L, and utilities aim to stay well under that while keeping enough at the far end of the system. This worksheet follows a fictional main in the town of Wrensfield, and the error to watch for is students dividing miles by milligrams per liter instead of the other way around, which produces a rate that cannot be used to predict the next reading.

Wrensfield's Chlorine Residual: A Grade 7 Rate Worksheet — Grade 7 Math
Name: ____________________________ Date: ______________

Student Worksheet

Suppose the fictional town of Wrensfield runs one main from its treatment plant to a storage tank 6 miles away. Operators sampled the chlorine residual at five points along that main on the same morning. The table shows what they found.

Sample point Distance from plant (miles) Chlorine residual (mg/L)
Plant tap 0 1.20
Elm Street 1.5 1.05
Bridge Road 3.0 0.90
Quarry Lane 4.5 0.75
Storage tank 6.0 0.60
  1. How much chlorine residual is lost between the plant tap and Elm Street?
  2. Use your answer to item 1. What is the loss per mile between those two points?
  3. What is the loss per mile between Bridge Road and the storage tank?
  4. The loss per mile stays the same along the whole main. What residual would you expect at mile 5.0?
  5. What is the percent decrease in residual from the plant tap to the storage tank?
  6. Wrensfield wants at least 0.20 mg/L at every tap. At the same loss per mile, how far from the plant can water travel before it drops to 0.20 mg/L?
  7. A branch main runs 2 1/4 miles from the treatment plant. How much residual is lost over that branch?
  8. What residual is left at the end of that 2 1/4-mile branch?
  9. In cold weather the loss slows to 0.06 mg/L per mile. What residual would reach the storage tank then?
  10. Explain why Wrensfield samples at five points instead of only at the plant.

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: 0.15 mg/L. Subtract the two readings: 1.20 minus 1.05 equals 0.15 mg/L.
  2. Answer: 0.10 mg/L per mile. Divide the loss by the distance: 0.15 divided by 1.5 equals 0.10 mg/L per mile.
  3. Answer: 0.10 mg/L per mile. The drop is 0.90 minus 0.60, or 0.30 mg/L, over 3.0 miles, and 0.30 divided by 3.0 equals 0.10.
  4. Answer: 0.70 mg/L. Five miles at 0.10 mg/L per mile is a loss of 0.50, and 1.20 minus 0.50 equals 0.70 mg/L.
  5. Answer: 50 percent. The drop is 1.20 minus 0.60, or 0.60 mg/L, and 0.60 divided by 1.20 equals 0.50.
  6. Answer: 10 miles. The allowed drop is 1.20 minus 0.20, or 1.00 mg/L, and 1.00 divided by 0.10 equals 10 miles.
  7. Answer: 0.225 mg/L. The branch is 2.25 miles, and 2.25 times 0.10 equals 0.225 mg/L lost.
  8. Answer: 0.975 mg/L. Start at the plant reading and subtract the loss: 1.20 minus 0.225 equals 0.975 mg/L.
  9. Answer: 0.84 mg/L. Six miles at 0.06 mg/L per mile is a loss of 0.36, and 1.20 minus 0.36 equals 0.84 mg/L.
  10. Answer: To see where the residual falls too low. One reading at the plant shows only the starting amount, so sampling along the main shows how fast the residual fades and warns the utility before the far end drops under its target.

Differentiation

Support

Give these students the first two rows of the table already subtracted, with the difference of 0.15 written in, and a printed reminder that the unit rate is the drop divided by the miles. Allow calculators, and rewrite 2 1/4 as 2.25 for them before they begin items 7 and 8.

Extension

Ask students to write an equation using d for miles from the plant that gives the residual at any point on the fictional main, then use it to check items 4 and 8 and explain what the two numbers in the equation stand for.

ELL supports

Pre-teach "residual," "main," and "loss per mile" with a simple line drawing of a pipe running from a plant to a tank, marked at each sample point. Provide the frame "The residual dropped ___ over ___ miles, so it falls ___ each mile" for items 2 and 3.