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Names: Thomas Danias, Matt Taylor, Barry Sanner, Gary Luft,

                  Lorena Mummert

Grade Level: 9th – 12th                 Content Area: Alg/Func/Calc

Pa standard(s) addressed:  2.8 11C

NCTM standard(s) addressed: Communications, Connections, Problem Solving, Reasoning, Algebra, Calculus, and Data Analysis

 

Problem name: “You’re Invited”

 

YOU’RE INVITED

 

Problem:  Frank is having a fund raiser featuring the band “Bernie Rubric and The Waste Products.”  On day 1, Frank mails out 5 invitations to friends.  On day 2, each of the 5 recipients of these invitations will mail out 2 invitations to additional friends.  On day 3, each of the newest recipients will mail 2 invitations to other friends.  This will continue for “n” days.

 

(Note: Other than Frank, who sent 5 invitations, no recipients will mail more than 2 invitations.)

 

Directions:

A.   How many total invitations were mailed out after 5 days?  Show and explain your work.

 

B.    What is the total number of invitations if the time was extended to 7 days?  Show and explain your work.

 

C.   Write a general formula for the number of invitations mailed out for “n” number of days? Show and explain your work.

 

D.   Each invitation included a ticket that cost $5.  How many days of mailing must be done to raise $7,500?  Show and explain your work.

 

 

 

Problem Solutions:

Part A

 

 

 

Part D

Number of Days

Number of Letters Sent

Total Invitations Sent

 

Money Taken In

1

5*2^0 =5

5

 

$25.00

2

5*2^1 =10

15

 

$75.00

3

5*2^2 =20

35

 

$165.00

4

5*2^3 =40

75

 

$375.00

5

5*2^4 =80

155

 

$775.00

 

 

 

 

 

 

 

 

 

Part B

 

 

 

 

6

5*2^5 =160

315

 

$1,575.00

7

5*2^6 =320

635

 

$3,175.00

8

5*2^7 =640

1275

 

$6,375.00

9

5*2^8 =1280

2555

 

$12,775.00

 

 

 

 

 

 

 

 

 

 

Part C

 

 

 

 

n

5*2^(n-1) =2.5 * 2^n

 

 

We utilized a graph to help

determine we had an

 exponential pattern.

 

 

 

 

 

 

 

 

 

 

 

Part D

According to our “Money Taken  In” chart it would take nine days of mailing to reach $7500.

 

 

Alternate Method for part A:

 

 

 

 

 

 

 

 

 


Specific Rubric:

 

Advanced Understanding:

5:   Correct responses with work shown and explained for Parts A,

      B, C, and D.

 

Satisfactory Understanding:

4A   Parts A, B, and D are correct and all work shown and explained.

4B   Parts A, B, and D are correct with some work, and with some parts of

       C attempted.

 

Almost Satisfactory Understanding:

3A    Parts A, B, and D correct, adequate work shown, some steps are

         missing or not explained, but can follow what is done.

3B     Incorrect answer to either A, B, or D.  Correct procedures used.  Part

         of C is adequately shown or explained.

3C     Incorrect answer to either A, B, or D with minimal work shown,

         however all work correct with part C.

 

Partial Understanding:

2A    Correct answer to Part A, B, and D with some work /explanation.

2B    Correct answer to Part A and B with all work.

2C    Correct procedures in Part A, B, and D.   Answers incorrect due to

        calculation errors.

 

Minimal Understanding:

1A     Correct response to 2 parts with minimal work shown.

1B     Correct response to 3 parts with no work shown.

1C     Some work that correctly addresses the problem (such as the

         following: develop a table, charts, patterns or graphs for letters sent out

         and total invitations)

 

No Understanding:

0                  No correct work that addresses the problem.

 

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