Area - squares and rectangles

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
Transformations on a pegboard

Age

7 to 11

Challenge level

How would you move the bands on the pegboard to alter these shapes?
problem
Torn shapes

Age

7 to 11

Challenge level

These rectangles have been torn. How many squares did each one have inside it before it was ripped?
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
Area and perimeter

Age

7 to 11

Challenge level

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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.
game
Favourite

Dicey perimeter, dicey area

Age

7 to 11

Challenge level

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?