Farey Sequences

There are lots of ideas to explore in these sequences of ordered fractions.

At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the assets of the players at the beginning of the evening?

Plutarch's Boxes

According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have their surface areas equal to their volumes?

Racing Odds

Age 11 to 14 Challenge Level:

An elephant, a hippopotamus and a rhinoceros are entered for a race. The odds for the rhinoceros and the hippopotamus are:

2 to 1 against the rhinoceros winning and

3 to 2 against the hippopotamus winning.

What are the odds against the elephant winning if the race?

Editor's note: The hint explains 2 to 1 against in fractional form

2D shapes and their properties. Ratio. Creating and manipulating expressions and formulae. Similarity and congruence. Fractions. Theoretical probability. Calculating with ratio & proportion. Calculating with fractions. Probability. Experimental probability.

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Farey Sequences

Do Unto Caesar

Plutarch's Boxes

Racing Odds

Age 11 to 14 Challenge Level:

Editor's note: The hint explains 2 to 1 against in fractional form