Squares

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 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

Square Within a Square Within...

Age

11 to 14

Challenge level

What fraction of this square is shaded?
problem

Logo Challenge 5 - Patch

Age

11 to 16

Challenge level

Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?
problem

Logo Challenge 7 - More Stars and Squares

Age

11 to 16

Challenge level

Can you use LOGO to create a systematic reproduction of a basic design? An introduction to variables in a familiar setting.
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 - The Logic of Logo

Age

11 to 16

Challenge level

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?
problem

Fitting In

Age

14 to 16

Challenge level

The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest equilateral triangle which fits into a circle is LMN and PQR is an equilateral triangle with P and Q on the line LM and R on the circumference of the circle. Show that LM = 3PQ
problem

Just Opposite

Age

14 to 16

Challenge level

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?
problem

Folding Squares

Age

14 to 16

Challenge level

The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?