Illinois State University Mathematics Department

MAT 326: Technology Tools for Secondary School Mathematics

Dr. Roger Day (

Session #5

17 September 2012

Warming Up: Free Rice, Anyone? or Algebra Problem of the Day

New Groups via SmartBoard shake-up.

A Problem to Explore: College Laundry
My son Avery is about to begin his first year in college. Among all the other things he has to think about is laundry! At Drexel University in Philadelphia, students can use the washing machines and dryers in their dorms free of charge. They even have a SmartPhone ap that will signal them when a batch of clothes is done.

Students do, however, have to provide laundry detergent, and, as he was browsing the web,  my son got some interesting suggestions about doing laundry in college. Among others was this:
"I use a liquid laundry detergent, and every time I fill the cap with the required amount of detergent, I add back to the container a half-cap of water! This helps me extend the detergent and save me some money along the way. Give it a try."
So one of our dinner-time conversations a week or two ago was about this suggested practice. Of course, we wanted to mathematize the whole situation! Here are some of the questions that emerged from our discussion:
  • Could this be a worthwhile practice? What comments and concerns immediately come to mind?
  • What sorts of calculations could you carry out to determine whether this was a worthwhile practice?
  • What are some of the variables inherent in this practice that we need to identify in order to create a mathematical model for it?
Phase I Exploration
In your small group, explore the mathematics of this situation and try to create a model for the add-back process. Take notes and record your attempts, results, questions, and road blocks. Be ready to share your efforts with the rest of the class.

Phase II Exploration
Continuing in your small group, ask me for the College Laundry Phase II Exploration guide. Follow the instructions, again keeping accurate, detailed, and specific notes of your results.

Spreadsheet Warm-Ups: Work through these practice sets in groups of no more than three people.

  • Set I
  • Set II
    • Create one spreadsheet file to contain a separate tab (sheet) for each of the following situations.
      • Create a spreadsheet that will allow a user to enter the coordinates of two points (ordered pairs) and the spreadsheet will then show two equations for the line containing those two points, including the point-slope form for a line and the slope-intercept form. Look at the video here for a guide to the format of your spreadsheet file. Name the tab (sheet) Linear Equation.
      • Create a spreadsheet that will allow a user to enter a value for which a square root approximation is desired and the spreadsheet will then show the steps of Newton's Method in determining that approximation. Look at the video here for a guide to the format for this spreadsheet file. Name the tab (sheet) Newton's Method.
      • Create a spreadsheet that will allow a user to enter the numerical coefficients of any fourth-degree polynomial together with a specific value of x and the spreadsheet will show an approximation for the numerical value of the derivative of the polynomial at the specified point. Look at the video here for a guide to the format for this spreadsheet file. Name the tab (sheet) Polynomial Derivative.
    • When all three tabs (sheets) are complete in one file, name the file as follows: 326SSwarmup01name, 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 Warm-Up #1" (no quote marks). At the top of your email message, show the first name and last name of each person in your group.
Quadratic Explorations: Group Work to Return with Comments

Mobile Apps: A Preview

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

Assignments for Session #6 (24 Sept 2012)

  • Complete the Spreadsheet Warm-Up activities as described above, through the first item in the Set II spreadsheets, Linear Equations. Requirement: Spreadsheet file submission by email, due Saturday, September 22, by 9:54 pm. Note that one submission is required per group! Each group member, however, should retain a copy of the Excel file.
  • 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.

Last Session
Next Session
326 Homepage

Here is the guide for Phase II of the College Laundry Problem.

  1. Load the Excel file named collegelaundry01.xlsx. The spreadsheet provides blanks for you to enter numerical values related to the problem.
  2. Suppose a container with 128 ounces of detergent, selling for $12.59, has a 2-ounce cap, and a capful of liquid is used for a full load of laundry.
  3. Fix the add-back ratio at 50% (0.5). Vary the concentration threshold and observe the results. Write a sentence or two to describe your results.
  4. Fix the concentration threshold at 75% (0.75). Vary the add-back ratio and observe the results. Write a sentence or two to describe your results.
  5. Explore various combinations of add-back ratio (a value between 0 and 1) and concentration threshold (also a value between 0 and 1). Determine three different pairs (add-back ratio, concentration threshold) that seem to result in the most worthwhile application of this ad-back strategy. Be sure to include your definition of "worthwhile" here!
  6. Write a few sentences in response to each question:
(a) How did this spreadsheet help or hinder your exploration of the problem?
(b) What improvements, modifications, or corrections to the spreadsheet would you suggest that would help your exploration?
Include names of all your group members and submit your written work (3,4,5,6 above) to me, into my grubby little paws, tonight!