Recursive Challenge Problem - The Double and Add 5 Game
Lesson Plans and Worksheets for Algebra I
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More Lessons for Algebra I
Common Core For Algebra I
Examples, videos, and solutions to help Algebra I students learn the meaning and notation of recursive sequences.
New York State Common Core Math Module 1, Algebra I, Lesson 26, Lesson 27
New York State Common Core Math Algebra I, Module 1, Lesson 26, Lesson 27
Worksheets for Algebra 1Lesson 26 Student Outcomes
Students learn the meaning and notation of recursive sequences in a modeling setting.
Following the modeling cycle, students investigate the double and add 5 game in a simple case in order to understand the statement of the main problem.
Definitions
A sequence can be thought of as an ordered list of elements. The elements of the list are called the terms of the sequence.
An example of a recursive sequence is a sequence that is defined by
(1) specifying the values of one or more initial terms, and
(2) having the property that the remaining terms satisfy a recurrence relation that describes the value of a term based upon an algebraic expression in numbers, previous terms, or the index of the term.
Exit Ticket
The following sequence was generated by an initial value a0 and recurrence relation ai+1 = 2ai + 5, for i ≥ 0
1. Fill in the blanks in the sequence:
(___, 29, ___, ___, ___, 539, 1083).2. In the sequence above, what is a0? What is a5?
Lesson 27 Student Outcomes
Students learn the meaning and notation of recursive sequences in a modeling setting.
Students use recursive sequences to model and answer problems.
Students create equations and inequalities to solve a modeling problem.
Students represent constraints by equations and inequalities and interpret solutions as viable or non-viable options in a modeling context.
Lesson 27 Summary
The formula, an = 2n(a0 + 5) - 5 describes the nth term of the “double and add 5” game in terms of the starting number a0 and n. Use this formula to find the smallest starting whole number for the “double and add 5 game” that produces a result of 10,000,000 or greater in 15 rounds or less.
Lesson 27 Exit Ticket
Write a brief report about the answers you found to the Double and Add 5 game problems. Include justifications for why your starting numbers are correct.
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