www.tootsie.com

Dear Students:

In an attempt to satisfy the recent nationwide demand for patriotic items, our company decided to market the “I Love USA” Tootsie Roll^Ò. In a rush to get the product out to the consumer, several batches were shipped to stores without passing through our random quality control checkpoint. We are considering a recall of this candy. As you can imagine, this would be costly to our corporation and an inconvenience to our customers.

At the advice of our technical department we are sending these samples in hopes that you can aid us by doing some random product testing. In order to maintain quality control we request that you do the following analysis:

1. Data Analysis: Please check the mass to volume ratio for each of the samples we have sent you. Collect your data and enter volume readings in L1 and mass readings in

L2 in your graphing calculator. Calculate, by paper and pencil, the slope between data points for a large and small TR, large and medium TR, and medium and small TR.

2. Graphical Analysis: Determine the line of best fit by doing a linear regression analysis. Store your equation in Y1. Draw up the results on graph paper. How does the slope of the regression equation compare to the slopes between data points calculated in (1) above? Is the point (0,0) on the curve? Should it be?(Why or why not?)

3. Extension questions: What would be the approximate weight of a TR that had a volume of 10.3 mL? Could this information be used for addressing quality control issues? Describe how.

4. Symbolic Analysis: Substitute a linear equation with a linear equation with rational coefficients that could be used as an approximation equation. Solve for Volume as a function of Mass. Substitute your value for mass found for question #3 and calculate how closely your volume is to 10.3 mL.Is your line with rational coefficients a good enough approximation?

We are sending candies to schools across your state in hopes of collecting a great deal of data at low cost. We appreciate your help and although we cannot compensate you monetarily, we hope you will accept these samples of other products we make.

Yours truly,

Matt Matiks

Director Quality Control

Notes to the teacher:

This lab examines the linear relationship between mass and volume for a particular object. This can be used to study proportions, graphing, range of axes, slopes, comparing calculated single values (m/v=d) to average values derived from the slope of the line of many points. Best fit lines, sampling and other ideas that you can think of could be examined.

• You will need 2 or 3 sizes of Tootsie Rolls, at least 1 of each size per group and then use class data. You could have each group test more than the 1 of each size candy if time permits. If you can’t find a third size of TR you could cut large ones into smaller pieces.

You probably won’t be able to find the American Flag TR. You could just take regular tootsie rolls and change the story, or unwrap them. You could also rewrap regular tootsie rolls in colored Saran wrap or Aluminum foil. Again, change the story.

Also needed:

• 100 ml Graduated cylinders and water if you will measure the volume by water displacement. You probably could use Pr²h if you can smash the TR into a more regular shape. Then, you will need rulers.

• 2 or more electronic or triple beam balances (borrow them from the science dept)

When doing this lab, I’d prefer not to tell the kids anything else; let them figure out what to do and what the significance of the ratio is...some of the kids will have learned about density, previously. Of course, you could have a class brainstorming session to determine what should be done and what exact procedures to use. You could talk about density being m/v before beginning the activity, or not. Add questions and analysis based on your level of student and the class you are teaching and the sophistication of data analysis you want them to do.

If you provide “product samples”, Tootsie Roll makes Dots, Sugar Daddies and Sugar Babies, Charms Blow Pops, Junior Mints and other stuff. Check out their website. www.tootsie.com

Variation:

Use marshmallows, mini and normal size or compare different brands of marshmallows.