Squares

How many ways can you find of tiling the square patio, using square tiles of different sizes?

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.

Look at how the pattern is built up - in that way you will know how to break the final pattern down into more manageable pieces.

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

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

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

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?

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

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

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.