Making Mathematical Claims about Rates of Change
This project will give you a great opportunity to grow your own creature and gain information about making mathematical claims and finding rates of change. It will require you to collect FOUR days of data about your creature. You will be growing it and then shrinking it back. You will be using a spreadsheet (EXCEL), statistics/graphing software (Fathom) and a word processor (MS WORD) to generate your final report that will include charts and graphs of your data.  

Grow your creature for a minimum of 48 hours. If it fails to grow within the four hours past the minimum 48 hours, you may take it out of the water and begin the shrinking process. If your creature continues to grow without any indication of slowing down, take it out of the water at noon on day 3 (55 hours old). Note on your log when the creature is removed from the water for good. Data must be collected on the log sheets that have been provided and should take place NO CLOSER THAN ONE HOUR apart – preferably every one to two hours.  The more data that you collect, the better your results will be!

Throughout the data collection period, you are to make a minimum of 7 tracings of your creature. You should trace it before you begin, one time while it is growing, when you take out of the water and start shrinking it, once while it is shrinking and once again when you stop taking measurements.  When you take it out of the water to shrink it, dry it off, and trace it and label it with the day and time, the age of the creature, its length, its width, and it’s thickness. Then attach these drawings to your final report.

For 15 points (out of 25) on the data collection part of this project, you must have at least 6 data measurements per day on each of days 1, 2, 3, and 4 - each must be taken no closer than 1 hour apart.

For 20 points on the data collection part of this project, you must have at least 8 data measurements per day on days 1, 2, 3, and 4 – each must be taken no closer than 1 hour apart.  

For 25 points on the data collection part of the project, you must have at least 10 data measurements per day on days 1, 2, 3, and 4 – each must be taken no closer than 1 hour apart.

Make your Hypothesis
Then analyze your data and make your hypothesis.  You will email (or hand in a typed copy of) your hypothesis of what you think the class data will look like, based on what you find out from your data.  To complete your hypothesis, cut and paste these statements into an email but fill in the blanks before you email it to me at:  (powelln@district87.org)

1. If these creatures are submerged in water, they will grow for _________ hours.

2. If these creatures are taken out of the water, they will shrink for _________ hours.

3. If these creatures grow as big as possible, they will grow to be _____ % of their original size.

4. If these creatures shrink as small as possible, they will shrink back to be _____ % of their original size.

You will calculate or interpolate your data (assuming that the growth between measurements is linear) for every hour on your log sheet . You will create 2 excel spreadsheets – a growing log excel spreadsheet and a shrinking log spreadsheet for your creature, each must have a minimum of 48 hours of data

• You will post your data (the 2 excel spreadsheet files attachment) to the
  Algebra Web board.

• You will graph your data and also make additional graphs of data collected by other student in the class - collected by you and your classmates. You should find a partner to do this with you.   Your report should follow the form on your report outline sheet and evaluation sheet .

Make your Mathematical Claim about the growing creatures!
After you test your hypothesis using other data that has been collected, make 1 or more mathematical claims based on your data for the creatures that your class grew. Write a short description (1 - 2 sentences) to use in the company’s catalog which contains a mathematical claim about the way the creatures change when put into the water based on your study. 

Other applications?
When you’ve completed the three introduction applications and a full study collecting real life data, find THREE advertisements that make mathematical claims and either cut them out or write them down. For each, describe how they may have come up with that claim. What data do you think that they collected and analyzed? 

Extra Credit 
After the reflections section in your report, add a section called Applications of Rates of Change.  Describe up to two different real-world situations where rates of change would be crucial to know. Tell what the application is, where or in what industry it would be important, how the rates would be measured – include units used, and who would use this information.  Site your sources – book, magazine, web page, etc. (5 points possible for each application – 10 points maximum.) extra tracings/extra data log entries (5 points maximum) other possibilities if okayed by Mrs. Powell ahead of time!  (Submit a proposal!)