Area - squares and rectangles

problem

Overlapping Squares

Age

7 to 11

Challenge level

Have a good look at these images. Can you describe what is happening? There are plenty more images like this on NRICH's Exploring Squares CD.
problem

Triangle Relations

Age

7 to 11

Challenge level

What do these two triangles have in common? How are they related?
problem

Tiling

Age

7 to 11

Challenge level

An investigation that gives you the opportunity to make and justify predictions.
problem

Tiles in the Garden

Age

7 to 11

Challenge level

How many tiles do we need to tile these patios?
problem

Fencing

Age

7 to 11

Challenge level

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.
problem

Geoboards

Age

7 to 11

Challenge level

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
problem

Tiles on a Patio

Age

7 to 11

Challenge level

How many ways can you find of tiling the square patio, using square tiles of different sizes?
problem

Pebbles

Age

7 to 11

Challenge level

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?
problem

My New Patio

Age

7 to 11

Challenge level

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?
problem

Rope Mat

Age

7 to 11

Challenge level

How many centimetres of rope will I need to make another mat just like the one I have here?