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Worksheet Grade 7 Careers & CTE

A Farnwell Operator Trainee's Conversion Log

A grade 7 worksheet of single-step operator conversions from a fictional plant, covering gallons, pounds, flow, pressure head, acre-feet, and basin volume.

Objectives

  1. Students will apply a stated conversion factor to change between units used at a treatment plant.
  2. Students will compute the volume of a rectangular basin and express it in gallons.
  3. Students will explain what a conversion factor is and why it stays the same.

Vocabulary

Acre-foot
The amount of water it takes to cover one acre of land, about the size of a football field, one foot deep. Western states use acre-feet to measure large amounts of water.

Also: conversion factor, head, basin, logbook

Teacher overview

Operators keep a logbook, and much of what goes in it starts as a measurement in one unit and has to be reported in another. A trainee studying for a state exam practices these conversions until they are automatic. This worksheet uses one day of entries from a plant in the fictional town of Farnwell, and every conversion item is a single step with the factor supplied. The common error here is inverting the factor, so a student who multiplies by 7.48 to turn gallons into cubic feet gets a number far too large; the last item asks students to name the factor and say why it never changes.

A Farnwell Operator Trainee's Conversion Log — Grade 7 Careers & CTE
Name: ____________________________ Date: ______________

Student Worksheet

Suppose you are a trainee operator at the plant in the town of Farnwell. Each item gives you the conversion factor you need. Show your work.

  1. One cubic foot holds 7.48 gallons. A section of a storage tank holds 500 cubic feet of water. How many gallons is that?
  2. One gallon of water weighs 8.34 pounds. How much do 250 gallons of water weigh?
  3. One million gallons per day equals 694 gallons per minute. The plant is running at 3 million gallons per day. What is that flow in gallons per minute?
  4. One psi of pressure equals 2.31 feet of head. The water in a standpipe stands 92.4 feet above the gauge. What pressure does the gauge read in psi?
  5. One foot of head equals 0.433 psi. A tank stands 150 feet above a house. What pressure does that height produce in psi?
  6. One acre-foot equals 325,851 gallons. A reservoir released 4 acre-feet overnight. How many gallons is that?
  7. A 1 percent chemical solution equals 10,000 mg/L. What concentration in mg/L is a 0.8 percent solution?
  8. A rectangular settling basin measures 40 feet long, 12 feet wide, and 10 feet deep. What is its volume in cubic feet?
  9. That same basin holds 4,800 cubic feet. Using 7.48 gallons per cubic foot, how many gallons does it hold?
  10. Every item above except item 8 used one fixed number to move between two units. Explain what that fixed number is called and why it does not change from one problem to the next.

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: 3,740 gallons. Multiply 500 cubic feet by 7.48 gallons per cubic foot.
  2. Answer: 2,085 pounds. Multiply 250 gallons by 8.34 pounds per gallon.
  3. Answer: 2,082 gallons per minute. Multiply 3 by 694 gallons per minute.
  4. Answer: 40 psi. Divide 92.4 feet by 2.31 feet per psi. A student who multiplies gets about 213 and should be asked whether a plant gauge could read that high.
  5. Answer: 64.95 psi. Multiply 150 feet by 0.433 psi per foot.
  6. Answer: 1,303,404 gallons. Multiply 325,851 gallons by 4.
  7. Answer: 8,000 mg/L. Multiply 10,000 mg/L by 0.8.
  8. Answer: 4,800 cubic feet. Multiply 40 feet by 12 feet, which gives 480 square feet, then multiply by the depth of 10 feet.
  9. Answer: 35,904 gallons. Multiply 4,800 cubic feet by 7.48 gallons per cubic foot.
  10. Answer: It is called a conversion factor. Accept any explanation noting that the relationship between the two units is fixed, so the same factor works for every measurement, and only the measured value changes.

Differentiation

Support

Give students a printed factor card listing each conversion once, with an arrow showing which direction multiplies and which divides. Reduce the set to items 1, 2, 3, 8, and 10. For item 8, provide the two-step reminder that length times width gives area, and area times depth gives volume.

Extension

Ask students to write two new logbook items for a classmate, one that multiplies and one that divides, using factors from this worksheet and values of their own. They must supply a worked solution for each and state what a wrong answer would look like if the factor were inverted.

ELL supports

Pre-teach "head," "basin," and "logbook" with a labeled sketch of a tank, a rectangular basin, and a notebook page. Provide a two-column word bank matching each unit to its everyday meaning, such as psi with pressure and acre-foot with a large volume. Allow item 10 to be answered in a short phrase with an example.

Extensions

Have students build a one-page conversion card of the kind an operator carries into a certification exam. The card lists each factor once, groups them by what they measure, and includes one worked example per group. Students then swap cards and solve a partner's example without looking at their own card.