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Open-Ended Template

 

Names: Mary Ann Kase, Ron Kolb-Wyckoff, Kathleen Polley, Mary Streitman

 

Grade Level:  6-8            Content Area: Geometry/Trigonometry

 

PA Standard addressed:   2.10.8 A  NCTM Standard addressed:  12

 

Problem Name:            The Mile Run

 

Problem:

 

 

 

 

 

Standard 2.10.8 A

 

 

5280 feet = 1 mile

 

Point C indicates

center of court

                                        (NOTE: FIGURE IS NOT DRAWN TO SCALE)

 

A basketball coach requires each team member to run a least one mile in practice.  Each player must start and finish at the same point on the path.  Follow the arrows on the diagram above.  What is the fewest number of complete laps that a player must run?

 

 

 

For full credit, you must do the following:

 

1.      Show OR describe each step of your work, even if you did it in your head (“mental math”) or used a calculator,

2.      Write an explanation stating the mathematical reason(s) why you chose each of your steps.

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Problem Name:             The Mile Run

 

Grade Level:          6-8                Content Area: Geometry/Trigonometry

 

The Problem Solution:

 

         Treat basically as two procedures: find the perimeter of the dotted isosceles triangle; find how many times around the dotted isosceles triangle will be at least one mile.  1 mile = 5280 feet.

 

         To find the perimeter, one can use the Pythagorean Theorem (formula on formula page.)

         ½ of the floor width (50/2)=25; ½ of floor length (94/2)=47

252+472=c2

625+2209= »  53.235 feet

53.235+53.235+94 = 200.47 feet for the perimeter

5280 ¸ 200.47 » 26.3381

The player must run 27 complete laps to meet the one mile requirement.

OR

          Floor width 50 feet; floor length 94 feet

502 + 942 = c2

2500 + 8836 =  » 106.47 feet

This hypotenuse is the same as the two congruent legs of the isosceles triangular path.  This results in the same perimeter of the dotted triangular path.

94 + 106.47 = 200.47 feet for the perimeter

 

The “why” might include the need to find the total perimeter of the path by using the Pythagorean Theorem and adding the relevant segments.  The student must then divide to find the number of laps to determine the answer. 

 

 

Problem Name:            The Mile Run

 

Grade Level:          6-8             Content Area: Geometry/Trigonometry

 

 

Specific Rubric:

 

 

5:       Advanced Understanding: Excellent*

Correct answer with correct procedures and calculations shown or described AND an explanation.

 

4:       Satisfactory Understanding*

A.               Correct answer with correct procedures and calculations shown OR described AND an insufficient or no explanation.

B.                Correct answer with most correct procedures/calculations shown OR described AND some explanation.

 

3.       Almost Satisfactory Understanding

A.               Correct answer with most correct procedures/calculations shown or described AND no explanation.

B.                Correct answer with few correct procedures/calculations shown OR described AND some explanation.

C.               Incorrect answer with correct procedure shown OR described AND some explanation BUT with one calculation or copying error carried throughout.

 

2.       Partial Understanding

A.               Correct answer with few correct procedures/calculations shown OR described OR some explanation.

B.                Incorrect answer with half or more correct procedures/calculations shown OR described AND some or no explanation.   Other procedures may be incorrect or missing.  Student either proceeded incorrectly OR did not proceed far enough.  For example, student gets the correct perimeter but does not divide to find the number of laps OR calculated perimeter with a logical estimate (greater than 47) for missing dimensions.

C.               Incorrect answer with correct procedures shown OR described AND no explanation, but no more than two calculation or copying errors carried through. 

 

1.                 Minimal Understanding

 

A.               Correct answer with procedures, calculations, and explanations that are not legible or not understandable or missing or incorrect.

B.                Incorrect answer with only one correct and critical procedure shown or described or explained (such as writing the Pythagorean Theorem or dividing 5280 by an unjustified perimeter.)

C.               Incorrect answer with correct procedures BUT with three calculation or copying errors carried throughout.

 

0.                 Incorrect

 

A.               Incorrect answer with no correct procedures, calculations, or explanations shown or described. 

 

*Labeling error: a “5” score becomes a “4” and a “4” becomes a “3” score.

  Labeling errors do not affect scores of “3” or lower.

 

NOTE:  Student does not have to label the answers but cannot have incorrect labels.

 

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