Fractions

problem

F'arc'tion

Age

14 to 16

Challenge level

At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and paper.
problem

Archimedes and Numerical Roots

Age

14 to 16

Challenge level

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
problem

What a Joke

Age

14 to 16

Challenge level

Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
problem

Pythagoras' Comma

Age

14 to 16

Challenge level

Using an understanding that 1:2 and 2:3 were good ratios, start with a length and keep reducing it to 2/3 of itself. Each time that took the length under 1/2 they doubled it to get back within range.
problem

Investigating the Dilution Series

Age

14 to 16

Challenge level

Which dilutions can you make using only 10ml pipettes?
problem

Not Continued Fractions

Age

14 to 18

Challenge level

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?
problem

All Tangled Up

Age

14 to 18

Challenge level

Can you tangle yourself up and reach any fraction?
problem

Look Before You Leap

Age

16 to 18

Challenge level

Relate these algebraic expressions to geometrical diagrams.
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?
article
History of Fractions

Who first used fractions? Were they always written in the same way? How did fractions reach us here? These are the sorts of questions which this article will answer for you.