Math problem set Grade 6 Careers & CTE

Calderway's Log Pages: Which Training Hours Count

A grade 6 careers problem set in which students use one month of a water trainee's log pages to decide which supervised hours count toward a Class 2 operator license.

Grade: Grade 6
Subject: Careers & CTE
Material: Math problem set
Time: 45 min
Prep: No prep
Materials: Calculators

Standards

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: Problems 4, 7, and 10 find a percent of a stated total, including the share of September hours the state board will not count.

All materials for 6.RP.A.3 →

6.RP.A.2 Common Core Math

Understand the concept of a unit rate a/b associated with a ratio a:b with b not equal to 0, and use rate language in the context of a ratio relationship.

How this material aligns: Problem 9 uses the rate of 160 counted hours each month to find how many months of supervised work remain.

All materials for 6.RP.A.2 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-09-23.

Objectives

Students will apply a licensing rule about signatures to decide which logged training hours a state board will count.
Students will find what percent of a license hour requirement an operator-in-training has completed.
Students will explain why the license class of a supervising operator decides whether a signed log page is accepted.

Vocabulary

Key words: operator-in-training, log page, supervising operator, license class, counted hours, process control

Teacher overview

This set follows one operator-in-training through a single month of log pages at the fictional Calderway Public Water Works, and every problem draws on that month's record. The Bureau of Labor Statistics describes the usual route into plant operation as a high school diploma, on-the-job training, and a state license earned by examination, with licenses issued in classes tied to the size of plant a person may run. The log page is the document that proves a trainee's supervised hours, so the rule about who signs it decides as much as the hours themselves do. One misconception is worth correcting before students begin. Many students assume that every hour a trainee spends at the plant counts toward the exam application, so they add the four pages together and stop. The hours payroll pays are not always the hours a state board counts, because a page signed by an operator whose license class sits below the class the trainee is applying for is returned uncounted, and problems 3 through 5 depend on holding those two totals apart.

Calderway's Log Pages: Which Training Hours Count — Grade 6 Careers & CTE

Name: ____________________________ Date: ______________

Problems

The Calderway log book. At the fictional Calderway Public Water Works, an operator-in-training works beside licensed operators and keeps a log page for each week. The page records the hours she spent on each kind of duty, and both she and the operator supervising her sign it when the week ends. The training office sends those pages to the state board when she applies to take the Class 2 operator exam. In this fictional state the board applies three rules to the pages.

The applicant must show 2,000 counted hours of supervised work at a plant.
At least 500 of those hours must be process control duty, which covers jar tests, chemical feed settings, and watching the filters.
A page counts only when the operator who signed it holds a license at Class 2 or higher, because the board treats the signature as that operator's own statement that the work was done.

During week 3 of September the shift supervisor was away, and a Class 1 operator signed that week's page. Show every step of your work.

September log pages

Week	Process control	Laboratory	Maintenance	Other duties	License class of the signer
Week 1	12	8	6	14	Class 3
Week 2	10	6	8	16	Class 3
Week 3	14	10	4	12	Class 1
Week 4	8	6	10	16	Class 2

Week 1's page lists 12 hours of process control, 8 hours of laboratory work, 6 hours of maintenance, and 14 hours of other duties. How many hours are on that page in all?
Each of the four September pages lists 40 hours. How many hours did the trainee log during September?
A page counts only when the operator who signed it holds a license at Class 2 or higher. Week 3's page, which lists 40 hours, was signed by a Class 1 operator. Of the 160 hours logged in September, how many count toward the Class 2 application?
The trainee logged 160 hours in September, and 40 of those hours cannot be counted. What percent of the month's logged hours is that? Name the rule that kept them out.
The board requires at least 500 hours of process control duty. The three pages that count list 12, 10, and 8 hours of process control. How many process control hours from September count toward that 500?
Before September the trainee had 560 counted hours, and September added 120 counted hours. How many counted hours does she have now?
The Class 2 exam requires 2,000 counted hours, and the trainee now has 680 of them. What percent of the requirement has she finished?
The requirement is 2,000 counted hours and she has 680. How many counted hours does she still need?
Suppose every month from now on brings four pages of 40 hours, each one signed by an operator holding Class 2 or higher, so 160 hours count every month. She still needs 1,320 counted hours. How many whole months of that work does she need?
Five licensed operators work at the fictional Calderway plant: two hold a Class 1 license, two hold a Class 2 license, and one holds a Class 3 license. What percent of them may sign a log page for her Class 2 application?

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: 40 hours.
Add the four duty columns on week 1's page. 12 plus 8 equals 20, 20 plus 6 equals 26, and 26 plus 14 equals 40 hours.
Answer: 160 hours.
Each page lists 40 hours, and 4 pages times 40 hours equals 160 hours logged during September.
Answer: 120 hours.
Week 3's page was signed by a Class 1 operator, which sits below the Class 2 license she is applying for, so its 40 hours are not counted. 160 minus 40 equals 120 counted hours. Weeks 1, 2, and 4 were signed at Class 3, Class 3, and Class 2, and all three meet the rule.
Answer: 25 percent.
40 divided by 160 equals 0.25, which is 25 percent. The rule that kept those hours out is the signature rule, because the operator who signs a page must hold a license at least equal to the class the trainee is applying for.
Answer: 30 hours.
Only weeks 1, 2, and 4 count, so add the process control hours on those three pages. 12 plus 10 equals 22, and 22 plus 8 equals 30 hours. Week 3's 14 process control hours are lost along with the rest of that page.
Answer: 680 hours.
560 counted hours earned before September plus the 120 hours counted in September equals 680 counted hours.
Answer: 34 percent.
680 divided by 2,000 equals 0.34, and 0.34 written as a percent is 34 percent.
Answer: 1,320 hours.
2,000 minus 680 equals 1,320 counted hours still to be logged and signed.
Answer: 9 months.
1,320 divided by 160 equals 8.25 months. Part of a month does not finish the requirement, so she needs 9 full months, and at the end of the ninth month she stands 120 hours past the 2,000 the board asks for.
Answer: 60 percent.
Operators at Class 2 or higher may sign, which means the two Class 2 operators and the one Class 3 operator, or 3 of the 5. 3 divided by 5 equals 0.6, which is 60 percent. The two Class 1 operators may still supervise her work, yet a page they sign will not count toward this application.

Differentiation

Support

Give these students the fictional Calderway table with a sixth column headed "Does this page count?" so that the signature rule is settled before any arithmetic starts, and print problem 4 with the fraction already written as 40 over 160. Assign problems 1 through 7, and allow a calculator throughout.

Extension

The training office at the fictional Calderway utility returns any page that reaches it more than 30 days after the month ends, and those hours are lost as surely as an unsigned page. Ask these students to find the last date each of the next three months' pages could arrive, then to rework problem 9 for a trainee who loses one page of 40 hours every month, which leaves 120 counted hours a month and brings the answer to 11 months.

ELL supports

Pre-teach "log page," "supervising operator," "license class," and "counted hours" with a labeled drawing of one fictional Calderway page showing the four duty columns and the two signature lines. Provide the sentence frame "This page was signed by a Class ___ operator, so its ___ hours ___ count." Allow students to answer aloud before they write.

Extensions

Have students find how their own state describes operator license classes and the supervised experience each class requires, then set that beside the fictional Calderway board's 2,000 counted hours and its 500 process control hours. Students then write two sentences explaining why a state board asks a licensed operator rather than a payroll supervisor to sign a trainee's page, and one sentence on what a trainee should do in a month when the usual supervisor is away.