Worksheet Grade 6 Math

Ludbury Water District Logbook: Expressions for Hours

A grade 6 worksheet where students write and evaluate expressions such as 8d + 40 to track a trainee operator's hours toward a state license.

Grade: Grade 6
Subject: Math
Material: Worksheet
Time: 35 min
Prep: No prep
Materials: None

Standards

6.EE.A.2 Common Core Math

Write, read, and evaluate expressions in which letters stand for numbers.

How this material aligns: Items 1 and 9 have students write an expression with a letter for shifts worked, items 2, 3, and 10 evaluate that expression for given values, and item 11 explains what each term represents.

All materials for 6.EE.A.2 →

6.RP.A.3 Common Core Math

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations, including finding a percent of a quantity and converting measurement units.

How this material aligns: Item 5 asks what percent of the required hours a trainee has finished, and items 7 and 8 use rate reasoning to turn hours into shifts and shifts into weeks.

All materials for 6.RP.A.3 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will write an algebraic expression for total hours from a rate and a fixed amount.
Students will evaluate an expression for given values of the variable.
Students will describe what each term in an expression represents.

Vocabulary

Key words: expression, variable, term, evaluate, operator license

Teacher overview

Operators who run drinking water plants earn a state license by passing an exam and logging a required number of hours on the job, and utilities keep those hours in a training logbook. This worksheet uses the logbook of a trainee at the fictional Ludbury Regional Water District as a setting for writing and evaluating expressions. People reach water-sector work by several routes, including on-the-job training with a state license, a technical certificate, a two-year or four-year degree, and graduate study, and item 12 asks students to name two of them. The misconception to watch for is reading 8d + 40 as 8 times the quantity d plus 40; students who report 8 times 65 for a 25-shift trainee have grouped the terms incorrectly.

Ludbury Water District Logbook: Expressions for Hours — Grade 6 Math

Name: ____________________________ Date: ______________

Student Worksheet

Suppose a trainee at the Ludbury Regional Water District has already finished 40 hours of classroom training. Every shift the trainee works on the plant floor adds 8 more hours to the logbook. Let d stand for the number of shifts worked.

People prepare for work in the water sector in several ways. Some begin right after high school with on-the-job training and earn a state operator license. Others finish a technical certificate program, a two-year or four-year degree, or graduate study. No single route is required for every job in the sector.

Write an expression for the trainee's total logged hours after d shifts.
Evaluate your expression from item 1 for d equal to 25.
Evaluate your expression from item 1 for d equal to 60.
The state license requires 1,040 logged hours in all. After 60 shifts, how many hours does the trainee still need?
After 60 shifts, what percent of the 1,040 required hours has the trainee finished?
Take the 40 classroom hours away from the 1,040 required hours. How many hours must come from shifts on the plant floor?
Each shift is 8 hours long. How many shifts give the number of hours you found in item 6?
The trainee works 5 shifts each week. How many weeks does it take to work the number of shifts you found in item 7?
A second trainee finished 64 classroom hours and works 6-hour shifts. Write an expression for that trainee's total logged hours after d shifts.
Evaluate the expression from item 9 for d equal to 40.
In the expression 8d + 40, explain what the 8 stands for and what the 40 stands for.
Name two different ways a person can prepare for a job in the water sector.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

Answer: 8d + 40.
Each shift adds 8 hours, so d shifts add 8 times d. The 40 classroom hours are already finished, so they are added once.
Answer: 240 hours.
8 times 25 equals 200, and 200 plus 40 equals 240 hours.
Answer: 520 hours.
8 times 60 equals 480, and 480 plus 40 equals 520 hours.
Answer: 520 hours.
1,040 required hours minus the 520 hours logged equals 520 hours still needed.
Answer: 50 percent.
520 divided by 1,040 equals 0.50, which is 50 percent.
Answer: 1,000 hours.
1,040 required hours minus 40 classroom hours equals 1,000 hours from shifts.
Answer: 125 shifts.
1,000 hours divided by 8 hours per shift equals 125 shifts.
Answer: 25 weeks.
125 shifts divided by 5 shifts per week equals 25 weeks.
Answer: 6d + 64.
Each shift adds 6 hours, so d shifts add 6 times d, and the 64 classroom hours are added once.
Answer: 304 hours.
6 times 40 equals 240, and 240 plus 64 equals 304 hours.
Answer: The 8 is the hours added by one shift, and the 40 is the classroom hours already finished. The 8 is multiplied because it repeats with every shift. The 40 is added once because it does not change as d grows.
Answer: Any two of the paths named in the passage above.
Accept on-the-job training with a state operator license, a technical certificate program, a two-year or four-year degree, or graduate study. All of these are legitimate routes into the sector, and no single one is required for every job.

Differentiation

Support

Give students a filled table with columns for shifts, hours from shifts, and total hours, with the rows for 1, 5, and 10 shifts already complete. Reading the pattern down the columns makes the structure of 8d + 40 visible before students write it. Allow a calculator for items 5 through 8.

Extension

Ask students to write and evaluate an expression for a trainee who logs 8 hours on weekday shifts and 10 hours on weekend shifts, using two letters, and then to find the number of weeks needed if the trainee works four weekday shifts and one weekend shift each week.

ELL supports

Pre-teach "shift," "logbook," "license," and "expression" with a simple picture of a wall clock next to a notebook page. Provide the sentence frame "The ___ tells how many hours each shift adds, and the ___ tells how many hours are already finished" for item 11.

Extensions

Students can look at the expression 8d + 40 as a table and then as a graph on the coordinate plane, plotting shifts on the horizontal axis and total hours on the vertical axis. The steady climb of 8 hours per shift previews the linear functions they will meet in grade 8.