5/10 FA 7.5 Recursive Sequences

Last updated over 2 years ago

14 questions

Note from the author:

OBJECTIVES & STANDARDS
Math Objectives
Write recursive formula for a given sequence
Use a recursive formula to model debt repayment
Common Core Math Standards
Link to all CCSS Math
CCSS.HSF.IF.A.3
CCSS.HSF.BF.A.1
CCSS.HSF.BF.A.1.A
CCSS.HSF.BF.A.1.B
Personal Finance Objectives
Calculate how a debt amount decreases over time, given the interest rate and regular payment amounts
National Standards for Personal Financial Education
Managing Credit
1b: Compare the cost of borrowing $1,000 using consumer credit options that differ in rates and fees

Instructions

OBJECTIVES & STANDARDS
Math Objectives
Write recursive formula for a given sequence
Use a recursive formula to model debt repayment
Common Core Math Standards
Link to all CCSS Math
CCSS.HSF.IF.A.3
CCSS.HSF.BF.A.1
CCSS.HSF.BF.A.1.A
CCSS.HSF.BF.A.1.B
Personal Finance Objectives
Calculate how a debt amount decreases over time, given the interest rate and regular payment amounts
National Standards for Personal Financial Education
Managing Credit
1b: Compare the cost of borrowing $1,000 using consumer credit options that differ in rates and fees

Intro

Learn It

Explore It

Learn It

Practice It

Required

The End!

5/10 FA 7.5 Recursive Sequences

Last updated over 2 years ago

14 questions

Note from the author:

OBJECTIVES & STANDARDS
Math Objectives
Write recursive formula for a given sequence
Use a recursive formula to model debt repayment
Common Core Math Standards
Link to all CCSS Math
CCSS.HSF.IF.A.3
CCSS.HSF.BF.A.1
CCSS.HSF.BF.A.1.A
CCSS.HSF.BF.A.1.B
Personal Finance Objectives
Calculate how a debt amount decreases over time, given the interest rate and regular payment amounts
National Standards for Personal Financial Education
Managing Credit
1b: Compare the cost of borrowing $1,000 using consumer credit options that differ in rates and fees

Instructions

OBJECTIVES & STANDARDS
Math Objectives
Write recursive formula for a given sequence
Use a recursive formula to model debt repayment
Common Core Math Standards
Link to all CCSS Math
CCSS.HSF.IF.A.3
CCSS.HSF.BF.A.1
CCSS.HSF.BF.A.1.A
CCSS.HSF.BF.A.1.B
Personal Finance Objectives
Calculate how a debt amount decreases over time, given the interest rate and regular payment amounts
National Standards for Personal Financial Education
Managing Credit
1b: Compare the cost of borrowing $1,000 using consumer credit options that differ in rates and fees

Intro

INTERACTIVE: Tower of Hanoi
The Tower of Hanoi is a mathematical puzzle that has inspired many myths about its origins. According to one version, priests were tasked with solving this puzzle using 64 disks and when the puzzle was completed, the world would end. Explore this classic puzzle to see what patterns you can discover!

Required

Complete the puzzle using 4 disks, and then 5 disks. Record any observations below, like how many moves you took or what patterns you noticed.

Required

Learn It

Recursive Sequences
As you add more disks to the Tower of Hanoi, you can use the previous solutions that had fewer disks to help you figure out the puzzle. The pattern we discovered for the minimum number of moves is an example of a recursive sequence.
Sequence: a list of numbers
Term: a number in a sequence
Recursive sequence: a sequence in which a term is defined using a previous term.
Example
Here is a sequence: 11, 13, 15, 17, 19, 21…
We could define this sequence recursively by saying it starts with 11 and each term is 2 greater than the previous term.

Required

Write a sequence of numbers where the first term is 5 and each term is 2 times the previous term.
_______, _______, _______, _______ ,_______, _______,....

Explore It

Describing Sequences
Let’s practice describing recursive sequences and finding patterns in them.

Required

Given the sequence: 20, 10, 5, 2.5, 1.25, 0.625…
What is the 4th Term? _______ 

Required

Describe the pattern used to get from one term to the next.

Given the sequence f(n) below.

Required

What is the 3rd term?_______ 

Required

What is the 5th term?_______ 

Required

Describe the pattern used to get from one term to the next.

Learn It

Writing Recursive Formulas
Throughout this lesson, you’ve been noticing patterns and describing how to get from one term to the next.
We can capture that information using a recursive formula.
A recursive formula specifies the first term of the sequence and the steps to get from one term to the next.
The formula includes two parts:
One of the terms in the sequence (usually the first)
The pattern: how you can find a specific term by using the previous term
The notation f(n-1) represents “the previous term”
Example
Here is the recursive formula for the sequence you saw earlier in the Explore It Question 1.
Sequence: 20, 10, 5, 2.5, 1.25, 0.625…

Practice It

The Tower of Hanoi
Let’s write a recursive formula for the Tower of Hanoi problem in the Intro.

Required

Write a recursive formula for the sequence of minimum moves in the Tower of Hanoi. You can use this video walkthrough to guide you through the process.

Required

Check your formula by using f(4) to find f(5). Show your work.

Required

ACTIVITY: DESMOS LINK: MOVE: Matching Recursive Sequences
Let’s practice matching recursive formulas with their sequences. 20 POINTS
This link completes 3 desmos in 1:
1. Card Sort
2. Application Level 1
3. Application Level 2

Write a brief reflection of the desmos activities and I will transfer your Desmos grade here.

The End!

5/10 FA 7.5 Recursive Sequences

5/10 FA 7.5 Recursive Sequences

Complete the puzzle using 4 disks, and then 5 disks. Record any observations below, like how many moves you took or what patterns you noticed.

Describe the pattern used to get from one term to the next.

Describe the pattern used to get from one term to the next.

Write a recursive formula for the sequence of minimum moves in the Tower of Hanoi. You can use this video walkthrough to guide you through the process.

Check your formula by using f(4) to find f(5). Show your work.

Complete the puzzle using 3 disks. Try to complete it in the minimum number of moves possible (7). Did you complete it in less than 7 moves?

Complete the puzzle using 4 disks, and then 5 disks. Record any observations below, like how many moves you took or what patterns you noticed.

Patrice says she used the solution for 3 discs to help her solve the puzzle for 4 discs. How could she do that?

Describe the pattern for the number of moves as required the number of disks increases. If you prefer, you can draw a representation instead.

Describe the pattern used to get from one term to the next.

Describe the pattern used to get from one term to the next.

Write a recursive formula for the sequence of minimum moves in the Tower of Hanoi. You can use this video walkthrough to guide you through the process.

Check your formula by using f(4) to find f(5). Show your work.

Complete the puzzle using 3 disks. Try to complete it in the minimum number of moves possible (7). Did you complete it in less than 7 moves?

Patrice says she used the solution for 3 discs to help her solve the puzzle for 4 discs. How could she do that?

Describe the pattern for the number of moves as required the number of disks increases. If you prefer, you can draw a representation instead.