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For younger learners

  • Early Years Foundation Stage

Rearrange the Square

Age 5 to 7
Challenge Level Yellow star
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources

Simply cutting a corner off a square can lead to a puzzling activity.
1st sq
So the little triangle is removed:

2ndsq
This little triangle is then put back making sure that a corner of the triangle is always touching a corner of the shape that the triangle came from, and two edges line up.

We can then make new shapes:

2 examples
Which were made as follows:


answers
So here's the challenge: Can you make all the following and tell us about how they are made from the two shapes?

18 shapes

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A City of Towers

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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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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