### F'arc'tion

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.

### Do Unto Caesar

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? # Mixing Lemonade ##### Stage: 3 Challenge Level: I mixed up some lemonade in two glasses. The first glass had$200$ml of lemon juice and$300$ml of water. The second glass had$100$ml of lemon juice and$200\$ml of water.

Which mixture has the stronger tasting lemonade?
How do you know?

Use the interactivity below to compare different mixtures of lemonade and develop a strategy for deciding which is stronger each time.

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Once you are confident that you can always work out which mixture is stronger, here are some questions to consider:

How might you use fractions to help you to work out which mixture is stronger?
How might you use ratios?