Scoring Criteria - For Scorers

Regional Team Problem Bridge Strength Problem

The following are suggestions of what to look for when scoring student papers. Each part of the scoring rubic given to the students has been expanded to include suggestions of what you might look for in each category. This is to be used as a guide and is not necessarily all inclusive

The student will use mathematics to define and solve the problem

To meet this standard, the student will:

__________ Construct a solution

• use applicable mathematical concepts and procedures
  • all variables need to be defined
  • choose subsets of the data where only weight bearing capability and one other element vary to determine the three variation relationships
    • weight bearing capability vs thickness
    • weight bearing capability vs width
    • weight bearing capability vs distance between supports
  • construct an elegant, efficient, and valid solution, for example

Part a) If w is the width of planks, t is thickness, d is distance between supports, and S is the weight bearing strength, the equation is

S = wt^2/2d

Part b) Weight bearing capability varies directly with the width of the plank or

As the width increases, the weight bearing capability increases or

May be represented graphically, a line with positive slope

Weight bearing capability varies directly with the square of the thickness of the plank or

As the thickness increases, the weight bearing capability increases greatly or

May be represented graphically, a parabola with vertex at zero, opening up, using only non-negative domain values

Weight bearing capability varies indirectly with the distance between the supports or

As distance between supports increases, weight bearing capability decreases or

May be represented graphically, a line with negative slope

The variation constant is 0.5 or 1/2

(More than one set of data should be used to determine the variation constant)

__________ Formulate questions and define the problem as related to conjecture or recommendation for the bridge construction

Part c) Some of the ideas that students might question or use in defining the problem are:

• reasonable width of bridge,
• cost of materials related to width and thickness of lumber,
• reasonable limitation on thickness and width of lumber,
• reasonable weight support expectations for bridge,
• does the substructure (if any) conform to data,
• combination of putting boards parallel to or perpendicular to the span,
• increasing thickness by stacking two boards rather than using thicker boards (cost effectiveness)

The student will use mathematical reasoning

To meet this standard, the student will:

__________ Predict results and make inferences

• make insightful conjectures and inferences

Some conjectures might be

• layering
• layering increase strength
• layering may be more cost effective than larger dimension lumber
• layering maybe either parallel or lperpendicular

support distance

minimizing support distance will minimize width and/or thickness of lumber

minimizing support distance may not always minimize cost

• direction of decking (parallel or perpendicular to stream) will affect support distances
• the bridge will not reasonably be expected to span the creek without addtional supports at points other than the edge of the creek
• because the bridge must be able to support several people at a time it must be supported at points other than the edge of the creek
• the bridge must be supported at points other than (in addition to) the at the edge of the creek
• other conjectures with support...

__________ Draw conclusions and verify results

• give comprehensive support for results

must have mathematical or reasonable arguements to support for any of the conjectures that they make about the optimum construction of the bridge

• systematically and successfully evaluate effectiveness of procedures and results

Should show several (at least three) data sets to verify the equation that they developed

Discovery any extreaneous data sets --- the data of distance between supports = 1, width of plank = 50, thickness of plank = 5 and weight bearing capability = 125 does not fit the equation

The student will communicate knowledge and understanding in both everyday and mathematical language

To meet this standard, the student will:

In this section you are looking for effectively ways that sutdents use to communicate their problem solving and reasoning as outlined above.

__________ Organize and interpret information

• demonstrate interpretations and understanding in a clear, systematic and organized manner

clearly organized and neatly written charts of subsets of the complete data sets

neatly drawn and clearly labeled graphs of each of the relations

describe any conjectures in an organized and clear manner

__________ Represent and share information

• represent mathematical information and ideas in an effective format

the overall organization of how they presented their method of sovling the problems is effective

how they define the variables and write their equation

the best would be to represent all variable relationships in one equation and determine one variation constant

• use correct mathematical vocabulary effectively

uses the words,such as varies directly, varies inversely , varies directly with the square when describing the relationships between the variables

could use graphs to represent the relationships discovered

Total points

÷ 6 =

Score

=>

Rating

Each category will receive a score of 4, 3, 2, 1, or 0 based on the following table:

4 - meets or exceeds all relvant criteria

3 - meets most relevant criteria

2 - meets some relevant criteria

1 - meets few relevant criteria

0 - not scoreable: off topic, no attempt, can't read, etc.