Water for Schools
Menu

Worksheet Grade 6 Math

Dursley Water District's Apprentice Log: Hours and Percent

A grade 6 worksheet following a water utility apprentice's training log, with percent complete, an hours-per-week unit rate, and a percent increase in pay.

Objectives

  1. Students will find what percent of a training requirement an apprentice has completed.
  2. Students will find a unit rate of hours worked per week and use it to predict hours.
  3. Students will find the percent increase between two hourly pay rates.

Vocabulary

Key words: apprentice, percent, unit rate, percent increase

Teacher overview

Water utilities count training in logged hours, because a state operator license is earned by examination after a set amount of supervised work and classroom instruction. The Bureau of Labor Statistics projects about 10,000 openings each year, on average, for water and wastewater treatment plant and system operators from 2025 to 2035. Total employment in the occupation is projected to decline 6 percent over that time, so all of those openings come from replacing operators who retire or move to other work. The figure describes operators specifically rather than the whole water workforce, and utilities fill many of those seats through apprentice programs while others are filled by graduates of certificate and degree programs. This worksheet follows one apprentice at the fictional Dursley Water District through her log, so students practice percent of a total and a rate per week on numbers that a training coordinator actually tracks.

Dursley Water District's Apprentice Log: Hours and Percent — Grade 6 Math
Name: ____________________________ Date: ______________

Student Worksheet

At the fictional Dursley Water District, an apprentice must log 1,800 hours of supervised plant work and 60 hours of classroom instruction before she can sit for the state exam. Her log is the source of every item below. Round any percent that does not come out even to the nearest tenth.

  1. She has logged 450 of the 1,800 plant hours. What percent of the plant hours has she finished?
  2. She works 30 hours each week in the plant. At that rate, how many weeks does 1,800 hours take?
  3. She has 1,350 plant hours left. At 30 hours each week, how many weeks does she have left?
  4. She has finished 24 of the 60 classroom hours. What percent of the classroom hours has she finished?
  5. Of her 450 plant hours, 90 were spent with the distribution crew. What percent of her plant hours is that?
  6. Over one 6-week stretch she logged 189 hours. What was her average number of hours each week?
  7. Suppose she keeps that same weekly average. How many hours would she log in 8 weeks?
  8. The district pays apprentices 19 dollars an hour. What does a 30-hour week pay?
  9. After she passes the exam, her pay goes to 26 dollars an hour. How many more dollars an hour is that?
  10. What is the percent increase from 19 dollars an hour to 26 dollars an hour?
  11. Which requirement is further along, her plant hours or her classroom hours? Use the percents from items 1 and 4 to explain.

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 percent.
    Divide the part by the whole: 450 divided by 1,800 is 0.25, which is 25 percent.
  2. Answer: 60 weeks.
    Divide the total hours by the weekly hours: 1,800 divided by 30 is 60 weeks.
  3. Answer: 45 weeks.
    Divide the hours left by the weekly hours: 1,350 divided by 30 is 45 weeks. That agrees with item 2, since she has already used 15 of the 60 weeks.
  4. Answer: 40 percent.
    Divide the part by the whole: 24 divided by 60 is 0.4, which is 40 percent.
  5. Answer: 20 percent.
    Divide the crew hours by her plant hours: 90 divided by 450 is 0.2, which is 20 percent.
  6. Answer: 31.5 hours per week.
    Divide the hours by the weeks: 189 divided by 6 is 31.5 hours each week.
  7. Answer: 252 hours.
    Multiply the weekly rate by the weeks: 31.5 times 8 is 252 hours.
  8. Answer: 570 dollars.
    Multiply the hourly pay by the hours: 19 times 30 is 570 dollars for the week.
  9. Answer: 7 dollars per hour.
    Subtract the two rates: 26 minus 19 is 7 dollars more each hour.
  10. Answer: 36.8 percent.
    Divide the increase by the original rate: 7 divided by 19 is 0.368, which rounds to 36.8 percent.
  11. Answer: The classroom hours.
    Her classroom hours are 40 percent finished and her plant hours are 25 percent finished, so the classroom requirement is further along even though it counts far fewer hours.

Differentiation

Support

Give these students a percent bar for the fictional apprentice marked in quarters, so 450 out of 1,800 can be located before any division. Assign items 1, 2, 4, 5, and 8, and provide item 1 with the division already written as 450 divided by 1,800.

Extension

Ask these students to plan a schedule that would let the fictional apprentice finish her remaining 1,350 plant hours in 30 weeks rather than 45. They should state the hours each week that plan needs, find the percent increase over her current 30 hours a week, and write one sentence on what else would have to change at the plant for that schedule to work.

ELL supports

Pre-teach apprentice, logged hours, and percent increase with a labeled drawing of a time sheet and a two-bar chart of the old and new pay rates. Provide these sentence frames: "She finished ___ of ___ hours, so she is ___ percent done." and "The pay went up by ___ dollars, which is ___ percent of the old rate."

Extensions

Have students find the two or three utilities or public works departments nearest the school and list what each one says about entry requirements for an operator trainee, then compare those requirements with the fictional district's 1,800 hours. A short class chart of what different employers ask for makes the point that the hour totals in this worksheet are one utility's rules rather than a national standard.