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?
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.
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?
Once students have had a chance to develop clear strategies for working out which mixtures taste strongest, share with students the questions to consider from the problem and allow them some time to explore and discuss their answers.
You can read about one teacher's experience of using this task in the classroom.
Spend plenty of time sharing alternative strategies for the first few simple examples on the worksheet, ensuring students understand why they work. Encourage students to work together using each other's methods to solve the harder examples.