Name _____________________ Investigating the Height of a Stack of Rice Cakes Objective: to use collected data to develop a model and make predictions. Procedure: 1. You have been given 9 cakes. Create a stack of rice cakes using as few or as many as you wish. Use a metric ruler to measure (to the nearest 0.1 cm), the height of the cake stack and record your data below. Repeat this process for a total of five different measurements. You will be using your measurements that you choose to make a prediction of a stack of 10 cakes so choose wisely. Place cookies on a paper towel, not directly on your desk! Number of Rice Height of Stack Cakes (cm) 2. Use the data collected to predict what the height of 10 rice cakes would be. Briefly explain how you arrived at this number. 3. Once you have written your hypothesis, ask your teacher for another rice cake. Measure the height of a stack of 10 cakes and record the measurement. ______ cm 4. Was your predicted height for 10 cakes correct? Explain. 5. We will now enter the collected data into a mathematical model using Excel. Go to the following website: http://academic.pgcc.edu/~ssinex/excelets/. Scroll down to the third table (it is a mustard yellow color). Click on “Investigating the Height of a Stack of Cookies ("Just add data" Excel)” and open the Excel file if it does not open automatically. 6. Click on the “Cookie Stack Height” tab and input your data into the table. Note that you may leave the height of stack column blank for data points you did not collect. 7. The spreadsheet will calculate a line of best fit by performing a linear regression. The blue line is the line of best fit that shows the trend of the experimental data. Describe what the graph looks like: 8. Using this model, we are able to make predictions. Find the predicted height of a stack of 15 cookies by entering “15” in the yellow box labeled “enter number of cookies” and then press the Enter key. Repeat this process for 150 cookies. Record the predictions based on your model below: Number of Cookies = 15, Predicted Height _______________ Number of Cookies= 150, Predicted Height _______________ 9. The computer has generated a model based on your experimental data. Which predicted height do you think is the most accurate on your model, 15 cookies or 150 cookies? Explain. 10. Get with another group and combine your cookies to carefully form a stack of 15 cakes. Measure the height of the cookies and record the value here. ______ cm 11. Compare the predicted cake height to the actual cake height. How accurate is the model? 12. Do you think your predictions would be more accurate with more experimental data? Explain. 13. List at least 2 possible sources of error that might account for any differences between the predicted and experimental values. 14. If you were given enough supplies, how could you verify the calculated prediction for the height of 150 cookies? How practical would it be to do this? 15. How would the graph change if regular sized cakes were used instead of mini rice cakes? 16. Scientists often use mathematical models of data in their research. What are some of the benefits of modeling data?