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'Tiling Into Slanted Rectangles' printed from http://nrich.maths.org/

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This activity has been particularly created for the most able. (The pupils that you come across in many classrooms just once every few years.) It is seen as a possible follow on from

"Tiles in the Garden".

This activity takes "Tiles in the Garden", much further. We can keep the main ideas the same - 

  • Square tiles
  • A corner of a tile at each corner of the rectangle
  • The ability to slice a tile into parts so as to use each part

So this one used $26$ and the slope was generated by going along $1$ and up $5$.

 

This time let's put on a limit of using less than $100$ tiles.

What sizes of rectangles could be filled obeying the three rules?

How many tiles for each rectangle you find?

Are there any numbers of tiles between $10$ and $100$ for which there cannot be a rectangle?