Number sequences: About stars and marbles

 

Mike Munroe, Johnna Norbut, Candice Sagliano, Lynnea Swanson

 

Our excel project looked at patterns and number sequences to find their sums. One goal of the activity was to implement the NCTM Standards. Under the category of patterns and functions in the Standards, we identified and used functional relationships; developed and used tables, graphs, and rules to describe situations; and interpreted among different mathematical representations.

This material was appropriate for middle school. It could be implemented as a semester long project individually or in groups for a shorter time period. If the students were in groups, they would be assigned roles to fulfill accomplishment of the assignment. A major finding of the excel project was that there are many equations in finding the sums of sequences that result in the same answer.

Positive effects of using excel: cooperative groups, familiarization of excel, use of technology, creative and visual learning. Negative effects of excel: students may not understand how to do the math, but are still capable of using the spreadsheet; time consuming; and students may worry more about the visual presentation instead of the math problem.

 

***Here is the actual problem that was assigned:

2. Number sequences: About stars and marbles

We look for the following sequences:

a)

*

* *

* * *

* * * *

* * * * *

.

.

.

How many stars are there? How many stars are there if you have 10 rows, n rows? .

b)

*

* * *

* * * * *

* * * * * * *

* * * * * * * * *

.

.

.

 

How many stars are there? How many stars are there if you have 10 rows, n rows?

c) Here you see a pyramid of marbles, one on the top, then 3, then 6. You might go on this way. How many marbles will the pyramid have, if there are ten flights?

 

Click Here to Download the Excel Files

1. Sum of Levels

2. Sum of Rows