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Long String Guesses: Maths Problem Solving Activity

March 17, 2013

Problem solving activities for teenagers – Long String Guesses

Main aim: Find the length of each piece of string

Name: Long String Guesses

Type: Problem solving activities for teenagers

Participants: Individuals. This activity may be undertaken by a small group. Suitable for Middle School or Junior High (Years 7 and 8) students

Duration: 15-20 minutes

Preparation: None

Materials: One piece of long string or rope at least 30 cm long (length of a ruler), scissors and stationery (pencil, eraser etc) for calculations

Instructions

  • Give each person (or group) the piece of string.
  • Each person or group must cut a 2 cm piece off the string.
  • Each person or group must then cut the string into another 4 pieces following these rules:
    • each piece of cut string is a whole number of cm;
    • none of the 5 pieces of cut string (including the first 2 cm piece) is of the same length; and
    • none of the lengths is a multiple of any of the other lengths.
  • The person or group must find out the shortest possible total combined length of the 5 pieces of cut string. There should be leftover string from the 30 cm original string.
  • Note that the person or group should be warned that the remaining 4 pieces of cut string should not be cut until they are sure that they have solved the problem.

Solution

The length of each piece of cut string should be the first 5 prime numbers and the total combined length should be 28 cm.

The students or participants would have to work their way up the lengths in a systematic manner.