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Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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Towers

A tower of squares is built inside a right angled isosceles triangle. What fraction of the area of the triangle is covered by the squares?

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Framed

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of the pictures.

Perimeter Possibilities

Age 11 to 14 Challenge Level:
Watch the video below.



How many other possible perimeters can you find, for a rectangle with an area of $24\text{cm}^2$?

Now watch the video to see what Alison and Charlie did next.



Here are some questions you might like to consider:
  • What other odd number perimeters can you make, if the area is $24\text{cm}^2$?
  • What is the smallest perimeter you can make, if the area is $24\text{cm}^2$?
  • What about the largest perimeter?
  • Which perimeters in between is it possible to make?

More generally...
  • Is it possible to make a rectangle with a fractional perimeter but a whole number area?
  • Is it possible to make a rectangle with a whole number perimeter but a fractional area?

Take a look at Can They Be Equal? to explore rectangles where the area is numerically equal to the perimeter.