Squares

problem
First forward into Logo 1: square five

Age

7 to 16

Challenge level

A Short introduction to using Logo. This is the first in a twelve part series.
problem
Coloured edges

Age

11 to 14

Challenge level

The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?
problem
Square corners

Age

7 to 11

Challenge level

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
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?
problem
Squaring the circle and circling the square

Age

14 to 16

Challenge level

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
problem
Take a square

Age

14 to 16

Challenge level

Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.
problem
A tilted square

Age

14 to 16

Challenge level

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
problem
Similarly so

Age

14 to 16

Challenge level

ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.
problem
Tetra square

Age

14 to 18

Challenge level

ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
problem
2001 spatial oddity

Age

11 to 14

Challenge level

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.