MA.912.D.1.1Archived Standard

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Use recursive and iterative thinking to solve problems, including identification of patterns, population growth and decline, and compound interest.

Remarks

Example 1: How many handshakes would occur in this room if everyone shook hands with everyone else? Create a spreadsheet that will find the number of handshakes starting with one person and increasing the number to 15.

Example 2: Mary has $1000 at the beginning of 2008. She is going to invest all that money plus $600 every year from now in a certain account that brings in an annual yield of 6.8%.  Assume that the interest rate is stable. Let B0 represents the initial money, B1 represents the amount of money at the end of 2008 (year1), B2 represents the amount of money at the end of 2009 (year2), and so on. Write a recursive function to find out Mary’s money at the end of any given year (year n).

General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 912
Body of Knowledge: Discrete Mathematics
Idea: Level 2: Basic Application of Skills & Concepts
Standard: Recursion - Understand and apply recursive methods to solve problems, including the use of finite differences.
Date Adopted or Revised: 09/07
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Video/Audio/Animations

MIT BLOSSOMS - Fabulous Fractals and Difference Equations :

This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of difference equations.

Type: Video/Audio/Animation

MIT BLOSSOMS - Guess the Last Ball: An Exercise in Mathematical Modeling:

This video lesson uses the technique of induction to show students how to analyze a seemingly random occurrence in order to understand it through the development of a mathematical model. Using the medium of a simple game, Dr. Lodhi demonstrates how students can first apply the 'rules' to small examples of the game and then, through careful observation, can begin to see the emergence of a possible pattern. Students will learn that they can move from observing a pattern to proving that their observation is correct by the development of a mathematical model. Dr. Lodhi provides a second game for students in the Teacher Guide downloadable on this page. There are no prerequisites for this lesson and needed materials include only a blackboard and objects of two different varieties - such as plain and striped balls, apples and oranges, etc. The lesson can be completed in a 50-minute class period.

Type: Video/Audio/Animation

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Video/Audio/Animation

MIT BLOSSOMS - Fabulous Fractals and Difference Equations :

This learning video introduces students to the world of Fractal Geometry through the use of difference equations. As a prerequisite to this lesson, students would need two years of high school algebra (comfort with single variable equations) and motivation to learn basic complex arithmetic. Ms. Zager has included a complete introductory tutorial on complex arithmetic with homework assignments downloadable here. Also downloadable are some supplemental challenge problems. Time required to complete the core lesson is approximately one hour, and materials needed include a blackboard/whiteboard as well as space for students to work in small groups. During the in-class portions of this interactive lesson, students will brainstorm on the outcome of the chaos game and practice calculating trajectories of difference equations.

Type: Video/Audio/Animation

Parent Resources

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