LEARN NC

K–12 teaching and learning · from the UNC School of Education

Light it up

http://illuminations.nctm.org/LessonDetail.aspx?ID=L606

A lesson plan for Grades 9–12 Algebra 1 and Algebra 2

Provider: National Council of Teachers of Mathematics

About this resource

Appropriate grades
9–12
Subjects
mathematics (algebra, applied mathematics)
Provider
National Council of Teachers of Mathematics

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In this cooperative learning activity, students are presented with a real-world problem: Given a mirror and laser pointer, determine the position where one should stand so that a reflected light image will hit a designated target. This investigation allows students to develop several rational functions that models three specific forms of a rational function. Students explore the relationship between the graph, the equation, and problem context. Illuminations provides an activity sheet, carousel cards, and detailed instructions for completing the lesson.

Students will:

  • State the domain, range and end behavior of rational functions.
  • Write rational functions that model problem situations.
  • Use rational functions to solve problems.

NCTM Standards and Expectations:

  • Generalize patterns using explicitly defined and recursively defined functions.
  • Draw reasonable conclusions about a situation being modeled.
  • Use symbolic algebra to represent and explain mathematical relationships.

North Carolina Curriculum Alignment

Mathematics (2004)

Grades 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.
    • Objective 1.03: Model and solve problems using direct variation

Grades 9–12 — Algebra 2

  • Goal 2: Algebra - The learner will use relations and functions to solve problems.
    • Objective 2.01: Use the composition and inverse of functions to model and solve problems; justify results.
    • Objective 2.05: Use rational equations to model and solve problems; justify results.
      • Solve using tables, graphs, and algebraic properties.
      • Interpret the constants and coefficients in the context of the problem.
      • Identify the asymptotes and intercepts graphically and algebraically.