### Chocolate

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

### 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?

# Rod Fractions

##### Stage: 3 Challenge Level:

What fraction of the orange rod is the yellow rod?

Use this picture to help you. Note that it only uses orange and yellow rods.

Now use the interactivity below to build similar pictures that will help you to answer the following problems:

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Using as many brown and red rods as you like, but no rods of any other colours, work out what fraction the red rod is of the brown one.

Using as many blue and dark green rods as you like, but no rods of any other colours, work out what fraction the dark green rod is of the blue one.

Using as many pink and orange rods as you like, but no rods of any other colours, work out what fraction the pink rod is of the orange one.

Using as many pale green and orange rods as you like, but no rods of any other colours, work out what fraction the pale green rod is of the orange one.

Pick two other rods of different colours. Given an unlimited supply of rods of each colour, work out what fraction the shorter rod is of the longer one.

Given an unlimited supply of any two differently coloured rods, can you find a general rule to work out what fraction the shorter rod is of the longer one?

Why does your rule work?