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Math problem set Grade 7 Careers & CTE

Certification Hours and Pay: An Operator's Math at Anders District

A grade 7 careers math set following an operator's continuing-education hours and license-class pay, using percent and unit-rate reasoning with real operator pay data.

Objectives

  1. Students will compute what percent one quantity is of another and a percent increase between pay levels.
  2. Students will compute a unit rate of continuing-education hours per month.

Vocabulary

Key words: continuing education, percent increase, unit rate

Teacher overview

Operators keep their license by earning continuing-education hours, and moving up a license class can raise their pay. This set follows Theo, an operator at the fictional Anders Water District, through his renewal hours and a possible raise. A common misconception this set corrects is finding a percent increase by dividing the change by the new amount; the change should be divided by the original amount.

Certification Hours and Pay: An Operator's Math at Anders District — Grade 7 Careers & CTE
Name: ____________________________ Date: ______________

Problems

Theo works at the fictional Anders Water District. Use these facts for every problem. His continuing-education requirement and the higher-class pay figure are made up for this set; the operator pay range is real and describes treatment plant operators specifically.

  • Theo must earn 30 continuing-education (CE) hours to renew his license.
  • He has finished 18 CE hours so far.
  • Each approved course is worth 6 CE hours.
  • Theo currently earns the operator median pay of $60,020 per year.
  • The 90th percentile pay for operators is $91,060 per year.
  • A higher license class at Anders District would pay $72,024 per year.
  1. What percent of his 30 required CE hours has Theo finished? Round to the nearest whole percent.
  2. How many CE hours does Theo still need to reach 30?
  3. What percent of the 30 hours does he still need? Round to the nearest whole percent.
  4. Suppose 18 months remain in Theo's renewal cycle. If he spreads his remaining hours evenly, what is his required rate in CE hours per month? Round to the nearest hundredth.
  5. If Theo moves up to the higher license class, his pay would rise from $60,020 to $72,024. What is the percent increase? Round to the nearest whole percent.
  6. How many more dollars per year is the higher-class pay of $72,024 than Theo's current pay of $60,020?
  7. Theo's current pay of $60,020 is what percent of the 90th-percentile pay of $91,060? Round to the nearest whole percent.
  8. Theo wonders whether the CE hours are worth the effort. Using the pay numbers, explain why finishing his hours and moving up a class could be worth it.

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: 60 percent. Theo finished 18 of 30 hours, so 18 ÷ 30 = 0.6, and 0.6 × 100 = 60 percent.
  2. Answer: 12 hours. He needs 30 hours and has 18, so 30 − 18 = 12 hours remain.
  3. Answer: 40 percent. He still needs 12 of 30 hours, so 12 ÷ 30 = 0.4, and 0.4 × 100 = 40 percent.
  4. Answer: 0.67 hours per month. He has 12 hours left over 18 months, so 12 ÷ 18 = 0.6667, which rounds to 0.67 hours per month.
  5. Answer: 20 percent. The change is $72,024 − $60,020 = 12,004 dollars. Then 12,004 ÷ 60,020 = 0.20, and 0.20 × 100 = 20 percent.
  6. Answer: 12,004 dollars. $72,024 − $60,020 = 12,004 dollars per year.
  7. Answer: 66 percent. $60,020 ÷ $91,060 = 0.659, and 0.659 × 100 ≈ 65.9, which rounds to 66 percent.
  8. Answer: Accept reasoning using the numbers, such as noting that the 30 hours (only two more courses beyond what he has) could support a move to a class paying $72,024, a 20 percent raise over his current $60,020. The one-time effort leads to higher pay every year after.

Differentiation

Support

Provide the subtraction results for problems 2, 5, and 6 already computed, so students focus on setting up each percent. Give a worked percent-increase example with different numbers before problem 5.

Extension

Ask students to find how many total courses Theo needs to reach 30 hours if he starts from zero, then how many he still needs from 18 hours, and to explain the difference in one sentence.

ELL supports

Pre-teach "continuing education," "percent increase," and "unit rate" with a simple labeled example. Provide a sentence frame for problem 8: "The hours are worth it because ___, which raises his pay by ___."