Gold Seal Lesson:
If The Cone Fits...

Copernicus Education Gateway

 

Subject:

Mathematics

Grade:

 

 

9-12

 

 

ICLE Standards:

 

 

Mathematics as Reasoning: Make and test conjectures.

Mathematics as Communications: Reflect upon and clarify thinking about mathematical ideas and
relationships.

Geometry From A Synthetic Perspective: Represent problem situations with geometric models and apply
properties of figures.

 

 

Performance Task:

 

 

A food manufacturer company is preparing to market a mini-size ice cream cone/cup. Your task is to design a package for the ice cream cones/cups. They are produced by a uniform standard as shown below:

  • The number of cones per package to produce maximum profit has not yet been determined. Your supervisor gives you the following criteria that you must take into consideration:

  • All measurements must be in metric units to accommodate international trade

  • The package must be designed to fit a standard size grocery shelf

  • The height of your package must be given as a function of the number of cones it will hold.

Since this is a new product, you decide to purchase other cones on the market to analyze the way the height of the package is affected by how the cones nest in the package. Determine and justify the dimensions of your recommended package based upon the design and the height function.

 

 

Knowledge / Skills:

 

 

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

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

 

 

Rubric:

 

 

4 Points  =  The student makes a complete response to all parts of the task. The height function derived is correct. The supporting data and explanation of the derivation of the function are clear and concise. The dimensions of the package are appropriate for the derived function and the physical design of the cone. He/she shows a thorough understanding of the mathematical ideas and processes contained in the problem.

 

 

3 Points  =  The student needs some coaching to make a complete response to all parts of the task. The height function is correct but the supporting data and explanation of its derivation show some lack of understanding of the mathematical principles. The dimensions of the package are not realistic for the derived function and physical design of the cone.

 

 

2 Points  =  The student makes only partial response to all parts of the task. The height function is incorrect. The supporting data and explanation fail to show an understanding of mathematical principles. The dimensions of the package are given, but are not close to being reasonable.

 

 

1 Point  =  The student does not complete the task. The height function is incorrect or is not give at all. Supportive data are missing or inaccurate. There are no dimensions for the package given. The student shows little or no understanding of the problem.

 

 

Keywords:

 

 

ALGEBRA
PROBLEM SOLVING 
GEOMETRY
THREE-DIMENSIONAL OBJECTS 
MEASUREMENT
COMPUTATION 
MATH IN DAILY LIFE

 

 

Grades:

 

 

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

 

 

ICLE Application:

 

 

D

 

 

 

 

 

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