Glasses, tubes and tennis balls  |  162 views  |  home  | Dutch version |  Classroom materials,
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The activity



Dutch Mathematics Day Contest 2016 (age group 15 years old)		Glasses, tubes and tennis balls

It is not always immediately clear what form can hold the most volume. Sometimes it appears that one glass can hold much more water than another, but then it shows that this is actually not the case! So you cannot completely trust your instinct in estimating what can hold more volume. The first assignment investigates this aspect. The second assignment: A sheet of A4 paper can be rolled along the length and be made into a tube, but this can also be done along the width. Which results in the largest volume? When taking a rectangle with different measurements than A4, does the same apply? Find the correlation between the sides of a rectangle and the most volume, write down the result of your research. Final assignment: Design a paper packaging with as little paper as possible, packaging ten tennis balls as efficiently as possible. The less space used the better!
Background information

Dutch Mathematics Day Contest

During the Dutch Mathematics Day Contest students work in teams of about 3 to 4 members on an open mathematical problem solving task during a couple of hours. The product of this work is a report (and sometimes a presentation).


Dutch Mathematics Day Contest 		Using your skills in a new setting
  • The task gives the students the opportunity to show what they have learned from mathematics and how they can use the knowledge and skills in a new situation.
  • Students can try, analyze, reason, calculate en design;
  • The (context of the) task is authentic, while the mathematics knowledge is easy to (re)use in this new situation;
  • Different teams can work 'on their own level' and this gives opportunities for differentiation;
  • There is a structure in the task from 'easy first steps' to a more complex end task.

Online learning objects from the Freudenthal Institute (Utrecht University)