Lesson 1: Introduction to Recursion

Grade Levels: Appropriate for grades 9-12 in courses such as Discrete Mathematics, Advanced Functions and Modeling (AFM) and Algebra II

This lesson is the first in a series that covers the topic of recursion. It presents the motivation to discuss recursion in high school mathematics and introduces students to how the topic can be applied to real-world problems. Throughout this unit, you will find interactive lessons and example problems that help develop student reasoning skills and encourage students to think independently. Links are included for demonstration videos, student handouts, and full teacher solutions.

Are you wondering why recursion is important and how it can be used in the real world? Take a look at our introductory video (running time: 2:59) to help you get started!

A lesson plan for Introducing the Concept of Recursion

Learning Outcomes

Students will learn the basic ideas of recursion and how to set up recursive systems that represent certain real-world phenomena. They will answer questions using the recursive systems and learn how to use technology to obtain visual representations of these systems.

Teacher planning

This lesson plan contains two videos to help guide you as you proceed through the plan. One is provided to instruct you on how to use the calculator to graph recursive systems, and the other is an enactment of one of the class activities, called “Pass the Candy.”

TIME REQUIRED FOR LESSON

2 - 3 days

MATERIALS/RESOURCES

• Headache Medicine Problem Download Headache Medicine Problem
• Headache Medicine Problem and Exercises Solutions Download Headache Medicine Problem and Exercises Solutions
• Homework Problems Sheet Download Homework Problems Sheet
• Class Exercises Sheet Download Class Exercises Sheet
• Class Exerccises Days 2 and 3 Solutions Download Class Exerccises Days 2 and 3 Solutions
• Fish & Wildlife Group Assessment Download Fish & Wildlife Group Assessment
• Fish and Wildlife Problem Solution Download Fish and Wildlife Problem Solution
• Fish and Wildlife Problem Rubric Download Fish and Wildlife Problem Rubric
• MP3 Player Group Assessment Download MP3 Player Group Assessment
• MP3 Player Problem Solution Download MP3 Player Problem Solution
• MP3 Player Problem Rubric Download MP3 Player Problem Rubric
• Tally sheet for “Pass the Candy” activity Download Tally sheet for “Pass the Candy” activity

TECHNOLOGY RESOURCES

• TI-83 or TI-84 calculator
• Excel spreadsheet program

Pre-activities

Teacher will have briefly introduced the idea of recursion: A recursive system defines a process in which each successive step in the process uses previous step’s (or steps’) outcome(s). (For teachers who are unfamiliar with recursion as a topic, solutions are provided for each activity and handout given in the lesson plan. These solutions display each step involved in solving the problems, and some contained detailed annotation of justification for the steps. It is recommended that teachers review the solutions provided after they have worked the problems on their own.

Activities

DAY 1

1. Teacher begins the lesson by presenting the Headache Medicine Problem. The teacher introduces the notation used in defining recursive systems, and the teacher and students work together to define the system for the Headache Medicine Problem #1. The teacher displays the graph of the system on the calculator, and the class discusses what they see. (30 minutes)
2. Teacher walks the students through the process of entering the recursive system in the calculator. The students follow along using their own calculators. (The following video (running time: 4:28) provides a step-by-step tutorial on how to enter recursive equations in the TI-83 or TI-84 calculator.) (10 minutes )

3. Teacher has the students work in groups on #2, 3 and 4 of the Headache Medicine Problem. (30 minutes)
4. The class reconvenes to discuss their solutions to Headache Medicine Problem #2, 3 and 4. (20 minutes)
5. For homework, the teacher assigns students problems #1 and 2 on the Homework Problems sheet.

DAY 3

1. Teacher begins the session by having students discuss their answers to the homework with each other in small groups. (15 minutes)
2. Teacher leads a discussion of the homework problems with the class. (20 minutes)
3. Teacher has students work on Chlorine Problem on Class Exercises sheet. (20 minutes)
4. Teacher leads discussion of the Chlorine Problem on Class Exercises sheet problem with the class. (10 minutes)

 

"Pass the Candy" Activity

Tally sheet for “Pass the Candy” activity Download Tally sheet for “Pass the Candy” activity

 

Assessment

Group quiz on Fish and Wildlife Problem (25 minutes)

Additional Assessment (if desired)

Graded Homework Assignment on MP3 Player Problem

Common Core Standards alignment

• F-BF.1. Write a function that describes a relationship between two quantities.
  • Determine an explicit expression, a recursive process, or steps for calculation from a context.
• F-BF.2. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
• F-IF.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

 

Contact Taylor Gibson with questions.