Gold Seal Lesson:
Power Punch: A New Soft Drink

Copernicus Education Gateway

 

Subject:

Mathematics

Grade:

 

 

5-8

 

 

ICLE Standards:

 

 

Geometry: Represent and solve problems using geometric models. Understand and apply geometric properties and relationships.

Measurement: Understand and use measurement ideas in problem solving.

Mathematics and Technology: Understand the principles of design.

Problem Solving: Apply mathematical ideas to the solution of real-world problems.

 

 

Performance Task:

 

 

Jordan is a packaging consultant for a soft drink company. The company is planning to market a new soft drink named Power Punch. Jordan’s supervisor has given him the task of designing and creating a prototype package for the new soft drink. She has asked Jordan to target his package for the teenage consumer. The company’s marketing division has already done some survey work and has developed the following constraints for Jordan to consider in his design:

  • The package must hold eight 12-ounce cans of soda.

  • The package must incorporate the colors red, white and yellow.

  • The package must attract the eye of the teen-ager, but should not be offensive to mom and dad.

  • The design must be a shape other than the usual rectangular solid.
    Jordan has developed the following plan to use for the development of his prototype package:

  1. Get the opinions of some teenagers about what they would find attractive, including both the shape of the package and the design on the package.

  2. Make some sketches of designs to put on the package and of various shapes for the package.

  3. Survey a sample of the target market to get their reaction to his designs and shapes.

  4. Organize and make a graphic display of the sample’s reaction.

  5. Create a design based upon the target market “research.”

  6. Draw a flat pattern or net of the proposed package, complete with dimensions. Jordan knows that he must be very neat and that the pattern must properly use scale and proportion.

  7. Using whatever materials are available (poster board, foil, cellophane, marking, pencils, etc.) and the information gathered, construct the prototype package.

Your task is to carry out the seven steps of Jordan’s plan. When you have completed the construction of the prototype package, execute the following tasks involving the costs of your package.

  1. Calculate the total surface area of your package, including any tabs and/or notches necessary for gluing. Express your answer to the nearest square centimeter.

  2. Calculate the volume of the package in cubic centimeters.

  3. Estimate the cost of producing your prototype. Consider materials, labor, complexity of shape and any other relevant items. Using the total cost estimated, also express the cost as a cost per square centimeter and per cubic centimeter.

  4. Predict how the cost per package would change if the packages were mass produced. Discuss points such as purchasing in quantity, the use of automation, assembly and anything else relevant.

 

 

Knowledge / Skills:

 

 

Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and fractions. (m1)

Understand the best procedures for statistical data collection, organization, and display. (m5)

Compute the perimeter and area of two-dimensional figures. (m13)

Compute the volume of three-dimensional figures (solids). (m17)

Use the technique of dimensional analysis to convert units of measure (e.g., convert km/hr to m/min). (m33)

Plan and apply real or hypothetical models and constructions to facilitate investigation and learning and the solution to practical problems. (s115)

 

 

Rubric:

 

 

4 Points = The student creates sketches of both a label design and package shape, incorporating all of the essential market survey information. He/she surveys the target audience and justifies, with visual displays, the label and shape used. The prototype is constructed carefully and is neat and appealing to the consumer. The follow-up analysis of area, surface area and volume is thorough and precise. The student makes reasonable cost estimates for producing the package, both as a prototype and as a mass-produced item. Evidence is provided to support the estimates.

 

 

3 Points = The student creates sketches for the label and package shape, but does not incorporate all of the essential market survey information. While he/she uses some means to survey the target audience, the final selections for the package are not clearly justified. The prototype shows some inaccuracies in measurement and construction. The student’s calculations show a basic understanding of the mathematics used to analyze the final produce. Little evidence is provided for the student’s cost estimates for producing the package.

 

 

2 Points = The student does not create alternative designs for the label and shape of the package. The student makes unjustified assumptions to construct the final product. He/she shows a limited understanding of the mathematics used to analyze the final product and is able to make only limited projections for packaging cost.

 

 

1 Point = The student does not complete the task. The design process is incomplete and the student shows little evidence of data collection or presentation. The student’s calculations demonstrate that he/she does not understand the mathematics needed for design, construction and prediction of the package cost

 

 

Keywords:

 

 

ALGEBRA
RESEARCH GEOMETRY
AREA
GEOMETRY IN DAILY LIFE
SURFACE AREA
THREE-DIMENSIONAL OBJECTS
TWO-DIMENSIONAL OBJECTS
VOLUME
PERIMETER STATISTICS
INFERENCE
MEASUREMENT
SURVEYS
COMPUTATION 
MODELS & CONSTRUCTION 
RATIOS

 

 

Grades:

 

 

Kg [] - 1 [] - 2 [] - 3 [] - 4 [] - 5 [x] - 6 [x] - 7 [x] - 8 [x] - 9 [] - 10 [] - 11 [] - 12 []

 

 

ICLE Application:

 

 

D

 

 

 

 

 

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