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Is there a relationship between the height of a stack of sandwich cookiesand the number of cookies in the stack?

Objectives:

1. Develop a mathematical model from experimental data

2. Make predictions with the model

3. Consider variations in the model and their influence

Instructions for use of this spreadsheet:

Using a centimeter rule, measure the height of a variety of stacks of sandwich cookies,

such as Oreos. Record your data, to the nearest 0.1 centimeters,

in the yellow cells on the next tab. The spreadsheet will automatically respond.

Worksheet? Click here for a pdf activity

http://academic.pgcc.edu/~ssinex/cast/cookies_stack.pdfhttp://mathforum.org/mathtools/http://academic.pgcc.edu/~ssinex/cast/cookies_stack.pdf

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Investigating the height of a stack of cookies - Your measurements in centimeters!

Enter your data in the appropriate yellow cells in the table on the left.

number heightof cookies of stack

0 #DIV/0! #DIV/0! The regression line (blue)

1 #DIV/0! #DIV/0! or the line of best-fit, its

2 #DIV/0! #DIV/0! equation, and r2 will appear

3 #DIV/0! #DIV/0! #DIV/0! when data are entered.

4 #DIV/0! #DIV/0!

5 #DIV/0! #DIV/0! If you don't have data

6 #DIV/0! #DIV/0! for a certain number

7 #DIV/0! #DIV/0! of cookies, leave the

8 #DIV/0! #DIV/0! cell blank.

9 #DIV/0! #DIV/0!

10 #DIV/0! #DIV/0!

Simulation

Using the regression equation from the graph, the following can be calculated: change average thicknesse green ne appears

enter number of cookies = predicted height of stack = new slope 1 increasePredictions #DIV/0! 10

measured stack height = predicted number of cookies = decrease

NOTE: The #DIV/0! error will be removed when data is entered!

Sinex 2006

0.00.10.20.30.40.50.60.70.80.91.0

0 2 4 6 8 10

heightofstack,cm

number of cookies

http://academic.pgcc.edu/~ssinexhttp://academic.pgcc.edu/~ssinex

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Investigating the height of a stack of cookies - Adding some variation in cookie thickness!

This graph uses the average thickness or slope from the Cookies Stack Height tab. Errors!

number heightof cookies of stack

0 #DIV/0! The regression line (blue)

1 #DIV/0! or the line of best-fit, its

2 #DIV/0! equation, and r2 will respond

3 #DIV/0! to any variation added below.

4 #DIV/0!

5 #DIV/0! What happens if the cookie

6 #DIV/0! thickness was to have

7 #DIV/0! considerable variation ?

8 #DIV/0!

9 #DIV/0! Increase the variation in thickness

10 #DIV/0! and observe the scatter plot.

These stacks are made Simulation

from all the cookies add variation to thicknessbeing the average From the average thickness, we generate a perfect fit.

thickness in a stack. variation 0 increaseaverage thickness = #DIV/0! R2 = #DIV/0! 0.000 0

When we add variation decrease

watch the height in

the blue cells above!

Analysis ToolPak must be loaded for this worksheet to function. Sinex 2006

Chick herefor instructions

y = 0.000R = #N/A

0.00.10.2

0.30.40.50.60.70.80.91.0

0 2 4 6 8 10

he

ightofstack,cm

number of cookies

http://academic.pgcc.edu/~ssinexhttp://academic.pgcc.edu/~ssinex/excelets/Analysis_ToolPak.pdfhttp://academic.pgcc.edu/~ssinex/excelets/Analysis_ToolPak.pdfhttp://academic.pgcc.edu/~ssinex