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  • Early Years Foundation Stage

Weighty Problem

Age 11 to 14
Challenge Level Yellow star
  • Problem
  • Student Solutions

The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. That way the cabinet can be moved in a series of turns about one corner at a time.

Cabinet on Grid

Presently it is placed (on the X) facing in the direction of the arrows.

The task is to move it, without sliding, in a series of turns about the corners so that it is facing the other way round (and still placed with its edge on the X). The corners of the cabinet do not always have to stand on the corners of the square tiles on the floor.

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Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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