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. Please start by measuring the masses of 12 pieces of different sized candies and then also measure the volume for each of the candies I have sent you. Compare the same sizes of Tootsie Rolls^Ò to each other, and also check to see how the different sizes compare to each other. You will be doing your work on the TI-83 calculator which will allow you to enter all your data, produce a graph, and analyze the graph for slope and y-intercept.. We will then determine the significance of the slope in regards to our data. Once we have figured out the importance of the slope in terms of the Tootsie Rolls we will decide if the red white and blue tootsie rolls are legitimate tootsie rolls and do not be recalled.

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

Objectives :

1. Take measurements of both mass and volume of various objects of different sizes.
2. Use the TI-83 in order to enter data into a list format.
3. Use linear regression on the TI-83 in order to calculate the slope and y-intercept .
4. Using the slope and y-intercept produce 2 graphs-one manually and the other on the TI-83.
5. Determine the significance of the slope in relation to a certain characteristic of the Tootsie Rolls.

Procedure:

Take 12 pieces of differently sized candies and find the mass using digital balances and the volume using graduated cylinders.

1. Using the TI-83 Calculator go to Stat, and then go to Edit and under List 1 enter your volume measurements. Under List 2 enter your mass measurements.
2. Using the TI-83 Calculator go back to Stat and now go to Calc #4 ( Linear Regression ax+ b) . The a will be the slope and the b will be the y-intercept.
3. If you would like the computer to draw the graph for your data after you type in Calc Lin Reg, hit the Vars button, go to Y-Vars, go to Function, go to Y 1 and hit enter.You will get the slope and y-intercept first and then by hitting graph you will get the graph of Mass vs. Volume for Tootsie Rolls.

Questions :

1. What are the labels for mass and volume?

2. Which way should you graph mass and volume ? Which should go on the x-axis and which on the y-axis?

3. What is the significance of the slope from your graph?

4. What if the significance of the y-intercept from your graph? What should your y-intercept value be if you did your experiment correctly?

5. How can you decide if the red white and blue candy fits the Tootsie Roll standards?

6.Using the value of the slope from your graph , what would be the value of a tootsie roll’s mass if the volume is 5.256 ml?

7. Using the value of the slope again, what would the volume be if the tootsie rolls mass is 15.44 grams?

Conclusion

Write a paragraph about how the slope of your line is an effective tool for determining if an object will meet the Tootsie Roll Company’s standard for excellence in their candies.

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.