CareerStart lessons: Grade eight

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Essential question: How are formulas containing radicals — such as those for sight distance — useful to the military and in other careers?

Learning outcomes

Students will practice using formulas involving radicals to calculate the answers to problems, and will learn how these calculations can be relevant in some careers.

Teacher planning

Materials needed

  • “Free Falling” worksheet (Includes answer key)
  • Transparency copy of worksheet
  • Overhead projector and pens
  • Calculator for each student
  • Optional: computer with internet access

Time required for lesson

30 minutes


Before beginning this lesson, students should have learned about radicals. This mini-lesson works especially well as a wrap-up activity for a lesson about radicals.


  1. Review radicals with the students. Hand out the “Free Falling” worksheet and have the students work through it.
  2. As a class, brainstorm careers that might use radicals in their line of work. (Examples might include careers in space exploration, tour guides, skydivers, army parachutists, etc.) If students need help brainstorming, you may choose to access the following websites:

    For details about a few specific examples, see “Career Information” below.

Career information

Career information comes from the Bureau of Labor Statistics’ Occupational Outlook Handbook.

Firefighters are on call and expected to respond immediately to an emergency. Other than responding to fires, firefighters are usually the first to arrive at traffic accidents or other types of medical emergencies. Firefighters in rural settings may specialize in fighting forest fires. During these fires, planes or helicopters may be used to drop water to help extinguish areas of the fire. In computing the drop, accuracy is important and using radicals instead of rounding increases the chance of success.

  • Education: High-school diploma
  • Pay: $31,000 - $58,500
  • Growth: Average growth; 12% increase over the next 10 years
Armed forces
Enlisted personnel are assigned in specialized areas based on an aptitude exam. Some areas of specialty include infantry, artillery, Special Forces, construction, transportation, and mechanics. Special Forces are sent at a moment’s notice into volatile areas and may need to parachute in to the location. Using radicals in computations increase accuracy to the location, which could make a big difference in the success of the mission.

  • Education: High-school diploma or GED (Officers require a bachelor’s degree)
  • Pay: Starting pay is $1300 a month plus free room and board or a housing allowance, and free medical and dental care
  • Growth: Faster than average

North Carolina curriculum alignment

Mathematics (2004)

Grade 9–12 — Algebra 1

  • Goal 1: Number and Operations - The learner will perform operations with numbers and expressions to solve problems.
    • Objective 1.02: Use formulas and algebraic expressions, including iterative and recursive forms, to model and solve problems.

  • Common Core State Standards
    • Mathematics (2010)
      • High School: Algebra

        • Reasoning with Equations & Inequalities
          • ALG.REI.2Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.