Illinois State University Mathematics Department

 MAT 326: Technology Tools for Secondary School Mathematics Dr. Roger Day (day@ilstu.edu)

### Session #7

1 October 2012

Warming Up: Gathering Lottery Simulation Data (from final activity, last class)

Brainstorming Session: Classroom Activities/Lessons Implementing Dynamic Geometry Software or Spreadsheets

Return and Comment on Submitted Materials

Next Time: Mid-Term Small-Group Assessment: GSP, Spreadsheets, and Technology Perspectives

• Fibonacci Explorations
• Now that you have a spreadsheet that generates the Fibonacci Sequence, use it to carry out one or more mathematical explorations of this famous sequence.
• Generate a third column to show the ratio of successive terms in the sequence. That is, what is the ratio of F(2) to F(1)? F(3):F(2)? F(4)/F(3)? and so on. Create and label the column and copy it to at least 25 rows in your table.
• What do you notice? Write a conjecture to describe what you observe.
• Does you conjecture hold for DIFFERENT initial values of the sequence? Change F(1) and F(2). Observe and record.
• Use the Internet to search on "Golden Ratio." Study what you discover and connect that to the results that eem to be occurring in third column of your spreadsheet.
• Now create a fourth column to show the ratio of pairs of terms in the sequence that are two terms from each other. That is, what is the ratio of F(3) to F(1)? F(4):F(2)? F(5)/F(3)? and so on. Create and label the column and copy it to the bottom of your other columns.
• What do you notice? Write a conjecture to describe what you observe.
• Does you conjecture hold for DIFFERENT initial values of the sequence? Change F(1) and F(2). Observe and record.
• Continue by creating:
• a fifth column: F(4):F(1), F(5):F(2), F(6):F(3), and so on
• a sixth column: F(5):F(1), F(6):F(2), F(7):F(3), and so on
• a seventh column: F(6):F(1), F(7):F(2), F(8):F(3), and so on
• an eighth column: F(7):F(1), F(8):F(2), F(9):F(3), and so on
• a ninth column: F(8):F(1), F(9):F(2), F(10):F(3), and so on
• Here's a screen capture of the first few rows after all 9 columns are created and F(1)=1 and F(2)=1 remain in use:
• Explore the limiting values apparent within your columns and describe what you see. Alter F(1) and F(2) and record how the limiting values of the columns change.
• How do these limiting values relate to each other? Investigate such connections and conjecture any relationships you observe. Record your findings and conjectures.
• Organize and record your written comments and be prepared to submit those to me, before you leave tonight, for your small group.
• Compound Interest
• Create a spreadsheet that will allow a user to explore the results of making regular deposits into a savings account earning compound interest.
• Include input/reference cells into which you can enter the following parameters:
• amount of regular deposit
• annual interest rate earned on money in the account
• number of equal deposits per year
• number of years the regular deposits will be made
• Create a table that shows the term-by-term (month-by-month, year-by-year, and so on) results of such deposits. This is an iterative/recursive way to address the requirements for the spreadsheet. Your table should show the following columns and others as you wish. Here is a video to offer suggestions for this.
• the term number (1,2,3,...)
• the deposit made that period
• the interest earned that period
• the new balance in the account
• Optional: Create an output cell that simply shows the end result based on the four input values stipulated above (amt dep, int rate, etc). This is an explicit way to address the requirements for the spreadsheet. Video help for this.
• Use your spreadsheet to suggest at least two alternatives for each of the following scenarios: You determine values for up to all four of the parameters described as input values for the spreadsheet. Be sure to state any assumptions you are making together with the values for the parameters.
• After giving birth to their daughter Bonnie, Ronnie and Lonnie begin making regular monthly deposits into an account for Bonnie's college expenses. Upon age 18, the account should fully or in part provide funds for Bonnie's college costs.
• Bart begins full-time employment t age 24 and wants to retire at age 60 with a million dollars in his savings account!
• Organize and record your written responses and be prepared to submit those to me for your small group.

When your group has completed all three activities, assemble the spreadsheets into one file with three tabs (sheets). Name the file as follows: 326SSactivities03name, where "name" is replaced by the last name of the person in your group who would be listed first in an alphabetized list of last names. Attach that file to an email and send it to me with the subject line, "Spreadsheet Activities #3" (no quote marks). On your spreadsheet and at the top of your email message, show the first name and last name of each person in your group.

Mobile Apps: A Preview

Here's an algebra prep/review app for mobile devices.

Here's an example of an iPad app that a school mathematics teacher might use.

Assignments for Session #8 (8 Oct 2012)

• Complete Spreadsheet Activities #3 as begun in class and described above. Requirement: Spreadsheet file submission by email, due Sunday, October 7, by 9:05 am. Note that one submission is required per group! Each group member, however, should retain a copy of the Excel file.
• Next Week: Mid-Term small-group activities assessment.
• Continue to look for and critique mobile apps that focus on school mathematics, preferably secondary school mathematics. More info on this to follow.
• Search for an online warm-up activity to share with others. Details to follow.

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