Squares

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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.
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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

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?
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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?
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Folding Fractions

Age

14 to 16

Challenge level

What fractions can you divide the diagonal of a square into by simple folding?
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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

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

A Swiss Sum

Age

16 to 18

Challenge level

Can you use the given image to say something about the sum of an infinite series?
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Zooming in on the Squares

Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
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Peg and Pin Boards

This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.