Squares

problem
Square bisection

Age

11 to 14

Challenge level

Weekly Problem 8 - 2008
In how many ways can a square be cut in half using a single straight line cut?
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
Fraction fascination

Age

7 to 11

Challenge level

This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.
problem
LOGO challenge 4 - squares to procedures

Age

11 to 16

Challenge level

This LOGO Challenge emphasises the idea of breaking down a problem into smaller manageable parts. Working on squares and angles.
problem
LOGO challenge 3 - star square

Age

7 to 16

Challenge level

Creating designs with squares - using the REPEAT command in LOGO. This requires some careful thought on angles
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
Squares in rectangles

Age

11 to 14

Challenge level

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
problem
Complete the square

Age

5 to 7

Challenge level

Complete the squares - but be warned some are trickier than they look!
problem
Trig rules OK

Age

16 to 18

Challenge level

Change the squares in this diagram and spot the property that stays the same for the triangles. Explain...
problem
Square coordinates

Age

11 to 14

Challenge level

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?