Squares

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
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
Geoboards

Age

7 to 11

Challenge level

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
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
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
Two triangles in a square

Age

14 to 16

Challenge level

Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.
problem
Circle box

Age

14 to 16

Challenge level

It is obvious that we can fit four circles of diameter 1 unit in a square of side 2 without overlapping. What is the smallest square into which we can fit 3 circles of diameter 1 unit?
problem
Unusual polygon

Age

14 to 16

Challenge level

What is the perimeter of this unusually shaped polygon...
problem
Square areas

Age

11 to 14

Challenge level

Can you work out the area of the inner square and give an explanation of how you did it?
problem
Dissect

Age

11 to 14

Challenge level

What is the minimum number of squares a 13 by 13 square can be dissected into?