Task 651

Hershey’s vs. KitKat

Each of you has been given a Hershey’s chocolate bar and aKitKat bar. They cost the same amount at the store. They alsoweigh very close to the same amount (there is only a 1-gramdifference between them). Hershey’s chocolate bars are longerthan KitKats. KitKats are thicker than Hershey’s bars.

These are my questions to you:

• Is there a big difference between their cubic units?• How do their cubic units compare to their weights?

Conduct a math investigation to reach conclusions about thesequestions.

1 of 9Hershey’s vs. KitKat

Copyright 2008, Exemplars, Inc. All rights reserved.

Hershey’s vs. KitKat

Suggested Grade Span

6–8

Grade(s) in Which Task Was Piloted

6, 7 and 8

Task

Each of you has been given a Hershey’s chocolate bar and a KitKat bar. They cost the sameamount at the store. They also weigh very close to the same amount (there is only a 1-gramdifference between them). Hershey’s chocolate bars are longer than KitKats. KitKats arethicker than Hershey’s bars.

These are my questions to you:

• Is there a big difference between their cubic units?• How do their cubic units compare to their weights?

Conduct a math investigation to reach conclusions about these questions.

Alternative Versions of Task

More Accessible Version:

Each of you has been given a Hershey’s chocolate bar and a KitKat bar. They cost the sameamount at the store. They also weigh very close to the same amount (there is only a 1-gramdifference between them). Hershey’s chocolate bars are longer than KitKats. KitKats are thickerthan Hershey’s bars. Determine which has a greater volume.

Hint: Use metric measurements.

More Challenging Version:

Each of you has been given a Hershey’s chocolate bar and a KitKat bar. They cost the sameamount at the store. How does their density compare?

Note: Both the KitKat bar and the Hershey’s bar are made of frustums. Use this informationalong with information you gather to reach a conclusion.



NCTM Content Standards and Evidence

Measurement Standard for Grades 6–8: Instructional programs from pre-kindergarten throughgrade 12 should enable all students to ...

Apply appropriate techniques, tools and formulas to determine measurements.

• NCTM Evidence: Select and apply techniques and tools to accurately find length, area,volume and angle measures to appropriate levels of precision.

Solve simple problems involving rates and derived measurements for such attributes as velocityand density.

• Exemplars Task-Specific Evidence: This task requires students to measure items todetermine volumes and then to use the information to make comments about density.

Time/Context/Qualifiers/Tip(s) From Piloting Teacher

This is a medium- to long-length task. Some time is taken up by handing out candy bars andrulers.

Links

This task would complement the following children’s books: Chocolate Fever, by Robert KimmelSmith; The Chocolate War, by Robert Cormier, and Charlie and the Chocolate Factory, byRoald Dahl. It would also link well to science units on density. For fun facts about Hershey'schocolate go to http://www.hersheys.com/products/.

Common Strategies Used to Solve This Task

Most students take measurements of the candy bars. Some use metric measurement whileothers use standard. Students then calculate the volume that leads to considerations about thedensity.

Possible Solutions

Measurements obtained when measuring a sample candy bar in metric:

Length Width Height Volume

Hershey's 13.6 cm 5.5 cm .5 cm 37.4 cubic cm

KitKat 9.2 cm 6.4 cm 1.1 cm 64.768cubic cm



Measurements obtained when measuring a sample candy bar in standard:


Hershey's 5 3/8 or 5.375 inches

2 1/8 or 2.125 inches

1/4 or .25 inches

2.86 cubic in.

KitKat 3 11/16 or 3.6875 inches

2 9/16 or 2.5625 inches

7/16 or .4375 inches

4.134 cubic in.

Weight/Volume = Density

Metric:

Hershey's 43 grams / 37.4 cubic cm = 1.15 grams per cubic centimeterKitKat 42 grams / 64.768 cubic cm = .65 grams per cubic centimeter

Standard:

Hershey's 1.5179 oz / 2.86 cubic in. = .53 oz per cubic inchKitKat 1.4826 oz / 4.134 cubic in. = .36 oz per cubic inch

Therefore, KitKat’s may be larger in volume, but they are less dense.

More Accessible Version Solution:


Hershey's 13.6 cm 5.5 cm .5 cm 37.4 cubic cm

KitKat 9.2 cm 6.4 cm 1.1 cm 64.768cubic cm

Therefore, KitKat has the larger volume.

More Challenging Version Solution:

A frustum is a square pyramid with the top cut off. The formula for determining the volume of afrustum is 1/3 h (a + b + square root of ab), where "a" is the area of the bottom base and "b" isthe area of the top base.

One of my students achieved the following volumes using this formula:

KitKat 46.8923 cubic cm, Hershey’s 35.8506 cubic cm.

This student concluded that the KitKat was made of four frustums, and the Hershey’s bar wasmade of 12 frustums.



Task-Specific Assessment Notes

General NotesThe preciseness of student measurements will dictate the accuracy of the solution. Since youare not necessarily assessing the accuracy of student measurements, you may assess thereasoning in the solution based on his/her measurements.

NoviceThe Novice may address some parts of the task correctly, but much of the solution will beincorrect. There may be no mathematical basis to arguments made. No awareness of audiencewill be communicated, and no connections will be made.

ApprenticeThe Apprentice will have many correct parts of the task, but the final solution will be incorrect orbased on incorrect reasoning. There will be some awareness of audience, and some correctreasoning present (but omissions may be made).

PractitionerThe Practitioner will achieve a correct answer with all supporting work shown and labeled.Representations will be created to organize the work and display the solution. The Practitionerwill recognize math connections.

ExpertThe Expert will achieve a correct answer with all work shown, labeled and justified. Evidencewill be used to support decisions, and connections will be used to extend the solution.



Novice



Apprentice



Practitioner



Expert



Task 651

Documents

Transcript of Task 651