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Rationals Between...

What fractions can you find between the square roots of 65 and 67?

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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.

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Canny Fraction

What fraction of the volume of this can is filled with lemonade?

Circuit Training

Age 14 to 16 Challenge Level:

It is worth spending some time discussing the strategies pupils have adopted.

Another question might be:
What is the ratio of the speeds of the two runners if they are to meet at the start after $1$ lap, $2$ laps, $3$ laps... $n$ laps?.

What is the relationship betweent he ratio of the speeds of the runners and where they meet?