Area - squares and rectangles

problem

Great Squares

Age

7 to 11

Challenge level

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.
problem

Two Squared

Age

7 to 11

Challenge level

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?
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

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?