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For younger learners

  • Early Years Foundation Stage

Triangle Transformation

Age 7 to 14
Challenge Level Yellow star
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources
 

Draw a triangle on a piece of paper, and cut it out.

Can you find a way to cut your triangle into no more than four pieces, and reassemble the pieces to make a rectangle?

Is it always possible, no matter what triangle you start with?






If you don't know where to start, click below to see some prompts that may help you:


First prompt:

Start with an isosceles triangle. How could you make it into a rectangle?
Is there a relationship between the base and height of your triangle, and the base and height of the rectangle?


Second prompt:

Draw any triangle, find the midpoints of two of the sides, and join them together. What do you notice?


Third prompt:

Once you have joined the midpoints, can you rearrange the pieces to make a parallelogram? Does that help you to create a rectangle?

 

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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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